Fabrice Ardhuin

Bertrand Chapron

Fabrice Collard

Observation of swell dissipation across oceans

Global observations of ocean swell, from satellite Synthetic Aperture Radar data, are used to estimate the dissipation of swell energy for a number of storms. Swells can be very persistent with energy e-folding scales exceeding 20,000 km. For increasing swell steepness this scale shrinks systematically, down to 2800 km for the steepest observed swells, revealing a significant loss of swell energy. This value corresponds to a normalized energy decay in time β = 4.2 × 10 -6 s -1 . Many processes may be responsible for this dissipation. The increase of dissipation rate in dissipation with swell steepness is interpreted as a laminar to turbulent transition of the boundary layer, with a threshold Reynolds number of the order of 100,000. These observations of swell evolution open the way for more accurate wave forecasting models, and provides a constraint on swellinduced air-sea fluxes of momentum and energy.

Introduction

Swells are surface waves that outrun their generating wind, and radiate across ocean basins. At distances of 2000 km and more from their source, these waves closely follow principles of geometrical optics, with a constant wave period along geodesics, when following a wave packet at the group speed [e.g. [START_REF] Snodgrass | Propagation of ocean swell across the Pacific[END_REF][START_REF] Collard | Routine monitoring and analysis of ocean swell fields using a spaceborne SAR[END_REF]. These geodesics are great circles along the Earth surface, with minor deviations due to ocean currents.

Because swells are observed to propagate over long distances, their energy should be conserved or weakly dissipated [START_REF] Snodgrass | Propagation of ocean swell across the Pacific[END_REF], but little quantitative information is available on this topic. As a result, swell heights are relatively poorly predicted [e.g. [START_REF] Rogers | An investigation into sources of error in low frequency energy predictions[END_REF][START_REF] Rascle | A global wave parameter database for geophysical applications. part 1: wave-current-turbulence interaction parameters for the open ocean based on traditional parameterizations[END_REF]. Numerical wave models that neither account specifically for swell dissipation, nor assimilate wave measurements, invariably overestimate significant wave heights (Hs) in the tropics. Typical biases in such models reach 45 cm or 25% of the mean observed wave height in the East Pacific [START_REF] Rascle | A global wave parameter database for geophysical applications. part 1: wave-current-turbulence interaction parameters for the open ocean based on traditional parameterizations[END_REF]. Further, modelled peak periods along the North American west coast exceed those measured by open ocean buoys, on average by 0.8 s [START_REF] Rascle | A global wave parameter database for geophysical applications. part 1: wave-current-turbulence interaction parameters for the open ocean based on traditional parameterizations[END_REF], indicating an excess of long period swell energy. Theories proposed so far for nonlinear wave evolution or air-sea interactions [e.g. [START_REF] Watson | Persistence of a pattern of surface gravity waves[END_REF][START_REF] Tolman | Source terms in a thirdgeneration wind wave model[END_REF], require order-of-magnitude empirical correction in order to produce realistic wave heights [e.g. [START_REF] Tolman | Validation of WAVEWATCH-III version 1[END_REF]. Swell evolution over large scales is thus not understood. Swells are also observed to modify air-sea interactions [START_REF] Grachev | Upward momentum transfer in the marine boundary layer[END_REF], and swell energy has been suggested as a possible source of ocean mixing [START_REF] Babanin | On a wave-induced turbulence and a wavemixed upper ocean layer[END_REF]. A quantitative knowledge of the swell energy budget is thus needed both for marine weather forecasting and Earth system modelling.

The only experiment that followed swell evolution at oceanic scales was carried out in 1963. Using in situ measurements, a very uncertain but moderate dissipation of wave energy was found [START_REF] Snodgrass | Propagation of ocean swell across the Pacific[END_REF]. The difficulties of this type of analysis are twofold. First, very few storms produce swells that line up with any measurement array, and second, large errors are introduced by having to account for island sheltering. Qualitative investigations by [START_REF] Holt | Tracking storm-generated waves in the northeast pacific ocean with ERS-1 synthetic aperture radar imagery and buoys[END_REF] and [START_REF] Heimbach | Development and application of satellite retrievals of ocean wave spectra[END_REF] demonstrated that a space-borne synthetic aperture radar (SAR) could be used to track swells across the ocean, using the coherent persistence of swells along their propagation tracks. Building on these early studies, [START_REF] Collard | Routine monitoring and analysis of ocean swell fields using a spaceborne SAR[END_REF] demonstrated that SAR-derived swell heights can provide estimates of the dissipation rate. Here we make a systematic and quantitative analysis of four years of global SAR measurements, using level 2 wave spectra [START_REF] Chapron | Wave and wind retrieval from SAR images of the ocean[END_REF] from the European Space Agency's (ESA) ENVISAT satellite. The swell analysis method is briefly reviewed in section 2. The resulting estimates of swell dissipation rates are interpreted in section 3, and conclusions follow in section 4.

Swell tracking and dissipation estimates

Our analysis uses a two step method. Firstly, using SARmeasured wave periods and directions at different times and locations, we follow great circle trajectories backwards at the theoretical group velocity. The location and date of a swell source is defined as the spatial and temporal center of the convergence area and time of the trajectories. We define the spherical distance α from this storm center (α = X/R where X is the distance along the surface on a great circle, and R is the Earth radius).

Secondly, we chose a wave period T and, starting from the source at time t = 0 and an angle θ0, we follow imaginary wave packets along the great circle at the group speed Cg = gT /(4π). SAR data are retained if they are acquired within 3 hours and 100 km from the theoretical position of our imaginary wave packet, and if a swell partition is found with peak wavelength and direction within 50 m and 20 • of their expected values. This set of SAR observations constitutes one swell track. We repeat this procedure by first varying θ0. Tracks with neighboring values of θ0 are merged in relatively narrow direction bands (5 to 10 • wide) in order to increase the number of observations along a track. This Error bars show one standard deviation of the expected error on each SAR measurement [START_REF] Collard | Routine monitoring and analysis of ocean swell fields using a spaceborne SAR[END_REF].

ensemble of tracks is the basic dataset used in our analysis. Such track ensembles are produced for different storms and different wave periods. Because the SAR sampling must match the natural swell propagation, ten storms only produced 22 track ensembles with enough SAR data that satisfies our selection criteria in the period 2003 to 2007. These criteria are wind speeds less than 9 m s -1 , swell heights larger than 0.5 m, and the observations should span more than 3000 km along the great circle, in order to produce a stable estimate of the swell spatial decay rate µ.

In the absence of dissipation (i.e. µ = 0), [START_REF] Collard | Routine monitoring and analysis of ocean swell fields using a spaceborne SAR[END_REF] demonstrated that, in any chosen direction θ0 and at the spherical distance α and time t corresponding to a propagation at a chosen group speed Cg, the swell energy Es decreases asymptotically as 1/[α sin(α)]. The sin(α) factor arises from the initial spatial expansion of the energy front, with a narrowing of the directional spectrum. The α factor is due to the dispersive spreading of the energy packet, because Cg is proportional to T , associated to a narrowing of the the frequency spectrum. [START_REF] Collard | Routine monitoring and analysis of ocean swell fields using a spaceborne SAR[END_REF] also showed that for realistic wave conditions Es should be within 20% of the asymptotic values for distances αR larger than 4000 km from the storm center, where R is the Earth radius. Figure 2. Swell dissipation for 22 events (see auxiliary material for details). (a) Estimated linear attenuation coefficient as a function of the initial significant slope, ratio of the swell significant wave height and peak wavelength, s = 4Hs/L, taken 4000 km from the storm centre, for a variety of peak swell periods (colors). (b) Attenuation coefficient normalized by the viscous attenuation µν (eq. 5), as a function of the significant swell Reynolds number Res determined from significant velocity and displacement amplitudes at 4000 km from the storm.

In our estimation of µ, data within 4000 km of the originating storm are ignored to make sure that the remaining data are in the far field of the storm.

This 4000 km value was estimated for a storm of radius r = 1000 km. This applies to any storm provided that all the energy for the wave period T is confined within this radius at t = 0, with no generation of such long swells for t > 0. Fast moving and long-lived storms may lead to larger values of r and, following [START_REF] Collard | Routine monitoring and analysis of ocean swell fields using a spaceborne SAR[END_REF], deviations from the asymptote larger than 20%. An extreme situation would be a steady storm moving along the great circle at the speed Cg, that would generate a constant swell energy Es as a function of α. No such situation was found in the storms analyzed below.

In each track ensemble, all swells have close initial directions θ0, and the wave field is only a function of α. We define the spatial evolution rate For each track ensemble we take a reference distance α0 = π/5 which corresponds to 4000 km. µ is estimated by finding the pair Es(α0), µ , that minimizes the mean square difference between observed swell energies Es(αi) with i ranging from 1 to N , and the theoretical constant linear decay, Es(αi)αi sin αi = Es(α0)α0 sin α0e -Rµ(α i -α 0 ) .

(2)

Because we only have two parameters µ and Es(α0) to adjust, the minimization is performed by a complete search of the parameter space. [START_REF] Collard | Routine monitoring and analysis of ocean swell fields using a spaceborne SAR[END_REF] estimated that the SAR-derived swell heights Hss = 4 √ Es are gamma-distributed about a true value Hss -bH . The bias is well approximated by bH = 0.11 + 0.1Hss -0.1 max{0, U10SAR -7}

(3)

with Hss in meters and the wind speed U10 in m s -1 . A realistic model of the standard deviation of the measurement error is σH = 0.10m + min {0.25Hss, 0.8m} .

Using this error model, we generated 400 synthetic data sets by perturbing independently each measured swell wave height, in order to obtain a confidence interval for µ. For each swell case, the values of µ and Hss(α0) reported below are the medians of the 400 calculated values. For all our swell data, µ ranges from -0.6 to 3.7 × 10 -7 m -1 (Figure 2.a), comparable 2.0×10 -7 m -1 previously reported for large amplitude swells with a 13 s period [START_REF] Snodgrass | Propagation of ocean swell across the Pacific[END_REF]. Clarifying earlier observations by [START_REF] Darbyshire | The generation of waves by wind[END_REF] and [START_REF] Snodgrass | Propagation of ocean swell across the Pacific[END_REF], our analysis unambiguously proves that swell dissipation increases with the wave steepness. We recall that, in the absence of dissipation, a maximum 20% deviation of Es relative to the asymptote is expected due to the storm shape. This deviation is equal to the one produced by a real 5.0×10 -8 m -1 dissipation over 4000 km. Thus a comparable error on the estimation of µ is expected when, as we do here, the storm shape is not taken into account [START_REF] Collard | Routine monitoring and analysis of ocean swell fields using a spaceborne SAR[END_REF].

Interpretation of swell dissipation

At present there is no consensus on the plausible causes of the loss of swell energy [WISE Group, 2007]. Interaction with oceanic turbulence is expected to be relatively small [START_REF] Ardhuin | On the interaction of surface waves and upper ocean turbulence[END_REF]. Observed modifications and reversals of the wind stress over swells [START_REF] Grachev | Upward momentum transfer in the marine boundary layer[END_REF] suggest that some swell momentum is lost to the atmosphere. The wave-induced modulations of air-sea stresses yield a flux of energy from the waves to the wind, due to the correlations of pressure and velocity normal to the sea surface, and the correlations of shear stress and tangential velocity. An upward flux of momentum, readily observed over steep laboratory waves, can thus result in a wave-driven wind [START_REF] Harris | The wave-driven wind[END_REF]. If these modulations are linearized [e.g. [START_REF] Kudryavtsev | Impact of swell on the marine atmospheric boundary layer[END_REF], the swell dissipation rate becomes linear in terms of the wave energy, with a proportionality constant that typically depends on the wind, but which does increase with the swell steepness, as we observe here.

Our observations show no clear trend with wind magnitude U10 and wind-wave angle θw: the swell age C/U10 or C/(U10 cos θw) averaged over the swell track gives little correlation with µ, even when wheigthed with the swell energy. We thus take a novel approach, and interpret our data by neglecting the effect of the wind, considering only the shear stress modulations induced by swell orbital velocities. Little data are available for air flows over swells, but boundary layers over fixed surfaces are well known, and should have similar properties if their significant orbital amplitudes of velocity and displacement are doubled [START_REF] Collard | Routine monitoring and analysis of ocean swell fields using a spaceborne SAR[END_REF]. The dissipation then depends on the surface roughness and a significant Reynolds number, Re(ϕ) = 4u orb (ϕ)a orb (ϕ)/ν, where u orb and a orb are the significant amplitudes of the surface orbital velocities and displacements.

For Re< 10 5 , the flow should be laminar [START_REF] Jensen | Turbulent oscillatory boundary layers at high Reynolds numbers[END_REF]. The strong shear above the surface makes the air viscosity important, with a dissipation coefficient given by [START_REF] Dore | Some effects of the air-water interface on gravity waves[END_REF] and [START_REF] Collard | Routine monitoring and analysis of ocean swell fields using a spaceborne SAR[END_REF] µν = 2 ρa ρwgCg

2π T 5/2 √ 2ν, ( 5
)
where L is the swell wavelength, L = gT 2 /(2π) in deep water with g the acceleration of gravity. At ambient temperature and pressure, the air viscosity is ν = 1.4 × 10 -5 m 2 s -1 , and µν is only a function of T . As T increases from 13 to 19 s, µν decreases from 2.2 × 10 -8 to 5.8 × 10 -9 m -1 . For larger Reynolds numbers the flow becomes turbulent. The energy rate of decay in time can be written as

β = - dEs/dt Es = Cgµ = ρa4π 2 ρwgT 2 feu orb (6)
where fe is a swell dissipation factor. For a smooth surface, fe is of the order of 0.002 to 0.008 [START_REF] Jensen | Turbulent oscillatory boundary layers at high Reynolds numbers[END_REF], when assumed equal to the friction factor fw.

Re is difficult to estimate from the SAR data only, because ENVISAT's ASAR does not resolve the short windsea waves. However, in deep water we can define the smaller 'swell Reynolds number' Res from u orb,s = 2 √ Es2π/T and a orb,s = 2 √ Es. Our estimates of µ exceed µν by a factor that ranges from O(1) to 28 (Figure 2.b), quantitatively similar to oscillatory boundary layer over fixed surfaces with no or little roughness. Namely, dissipation rates µ of the order of the viscous value µν are found for Res < 5 × 10 4 when the the flow may be laminar, and we only find large values of µ/µν when Res > 5 × 10 4 over a significant portion of the swell track. For reference, a 6.3 m s -1 wind can generate a fullydeveloped wind-sea with Re= 2 × 10 5 , making the boundary layer turbulent for any swell amplitude. Using the numerical wave model described in [START_REF] Ardhuin | Observation and estimation of Lagrangian, Stokes and Eulerian currents induced by wind and waves at the sea surface[END_REF], one finds that this value of Res translates to Re≃ 10 5 . That same model also gives values of u orb . Fitting a constant fe for each track ensemble yields -0.001 ≤ fe ≤ 0.019, with a median of 0.007, close to what is expected over a smooth surface. This suggests that the roughness of the waves for this oscillatory motion is very small compared to the orbital amplitude.

A parameterization of swell dissipation, taking fe constant in the range 0.0035 to 0.007, generally yields accurate wave heights (not shown). The quality of the end result also depends on the other parameterizations for wind input, whitecapping and wave-wave interactions, and requires a rather lengthy discussion [e.g. [START_REF] Ardhuin | Spectral wave dissipation based on observations: a global validation[END_REF][START_REF] Ardhuin | Observation and estimation of Lagrangian, Stokes and Eulerian currents induced by wind and waves at the sea surface[END_REF].

Beyond this simple model, we expect that winds should modify the boundary layer over swell, with a significant effect for winds larger than 7 m s -1 [START_REF] Collard | Routine monitoring and analysis of ocean swell fields using a spaceborne SAR[END_REF]. [START_REF] Kudryavtsev | Coupled dynamics of short waves and the airflow over long surface waves[END_REF] considered the wind stress modulations due to short wave roughness modulated by swells, and found that the preferential breaking of short waves near long wave crests could double the wind-wave coupling coefficient µ for the long waves. Yet, their linear model cannot explain the nonlinear dissipation observed here, because they only considered lowest order effects. Further investigations should probably consider both wind and finite amplitude swell effects to explain the observed variability of µ.

If this dissipation is due to the proposed air-sea friction mechanism, the associated momentum flux ρwgEs/2 goes to the atmosphere. If, on the contrary, underwater processes dominate, an energy flux ρwgCgEs may go into ocean turbulence. Accordingly, these fluxes are small. For 3 m high swells, the momentum flux is 8% of the wind stress produced by a 3 m s -1 wind. This momentum flux thus plays a minor role in observed O(50%) modifications of the wind stress at low wind [START_REF] Drennan | Evidence for the effects of swell and unsteady winds on marine wind stress[END_REF][START_REF] Grachev | Upward momentum transfer in the marine boundary layer[END_REF]. Wind stress modifications are more likely associated with a nonlinear influence of swell on turbulence in the atmospheric boundary layer [START_REF] Sullivan | Large-eddy simulations and observations of atmo-spheric marine boundary layers above nonequilibrium surface waves[END_REF]. This effect may arise as a result of the low-level wave-driven wind jet [START_REF] Harris | The wave-driven wind[END_REF] and its effects on the wind profile around the critical level for the short wave generation [START_REF] Hristov | Dynamical coupling of wind and ocean waves through wave-induced air flow[END_REF] . Whatever the actual process, the dissipation coefficient µ is a key parameter for validating theoretical and numerical models [START_REF] Kudryavtsev | Impact of swell on the marine atmospheric boundary layer[END_REF][START_REF] Hanley | Wave-driven wind jets in the marine atmospheric boundary layer[END_REF].

Conclusions

Using high quality data from a space-borne synthetic aperture radar, ocean swells were systematically tracked across ocean basins over the years 2003 to 2007. Ten storms provided enough data to allow a total of 22 estimations of the swell energy budget for peak periods of 13 to 18 s. The dissipation of small-amplitude swells is not distinguishable from viscous dissipation, with decay scales larger than 20000 km. On the contrary, steep swells lose a significant fraction of their energy, up to 65% over a distance as short as 2800 km. This non-linear behavior is consistent with a transition from a laminar to a turbulent air-side boundary layer. Many other processes may contribute to the observed dissipation, and a full model of the air-sea interface will be needed for further progress. The present observations and analysis opens the way for a better understanding of air-sea fluxes in low wind conditions, and more accurate hindcasts and forecasts of sea states [see [START_REF] Ardhuin | Spectral wave dissipation based on observations: a global validation[END_REF][START_REF] Ardhuin | Observation and estimation of Lagrangian, Stokes and Eulerian currents induced by wind and waves at the sea surface[END_REF], and e.g. the SHOM results in [START_REF] Bidlot | Intercomparison of operational wave forecasting systems against buoys: data from ecmwf, metofficem fnmoc,ncep, dwd, bom, shom and jma[END_REF].

Further investigations are necessary to understand the wind stress modulations and their variations with wind speed, direction, and swell amplitude. Such an effort is essential for the improvement of numerical wave models and their application to remote sensing and the estimation of air-sea fluxes.

Figure 1 .

 1 Figure 1. (a) Observed swell wave height as a function of distance, and theoretical decays with fitted constant coefficients using no dissipation, linear (µ constant) or non-linear (fe constant) dissipation, for the 15 s waves generated by a very strong (top) North Pacific storm on 12 February 2007 (auxiliary table 1: swell number 18) and a weaker (bottom) southern ocean storm on 12 August 2007 (auxiliary table 1: swell number 19). Circled dots are the observations used in the fitting procedure.Error bars show one standard deviation of the expected error on each SAR measurement[START_REF] Collard | Routine monitoring and analysis of ocean swell fields using a spaceborne SAR[END_REF].

  µ correspond to losses of wave energy (Figure 1.a). Negative, but not significant, values are occasionally found (figure 1.b).

Acknowledgments. SAR data was provided by the European Space Agency (ESA). The swell decay analysis was funded by the French Navy as part of the EPEL program. This work is a contribution to the ANR-funded project HEXECO and DGAfunded project ECORS.


Maxime Kaczmarek

Rodrigo Osuna-Orozco

Peter Dearborn Huck

Alberto Aliseda

Nathanaël Machicoane
email: nathanael.machicoane@univ-grenoble-alpes.fr

Spatial characterization of the flapping instability of a laminar liquid jet fragmented by a swirled gas co-flow

Keywords: atomization, coaxial two-fluid atomizer, flapping, spray, gas swirl

A liquid jet destabilized by a co-flowing gas jet is subjected to several instabilities that are responsible for its fragmentation into a spray of fine droplets.

At the large scale, the difference in the velocities of the gas and liquid phases lead to a meandering motion of the liquid jet called the flapping instability.

Flapping is suspected to play a role in the spatio-temporal characteristics of the clouds of droplets further downstream, as it periodically brings a portion of the liquid phase away from the centerline and into the gas jet.

While the scaling law determining the frequency associated to flapping has recently been proposed, a study of its spatial characteristics is lacking in the literature. Two-view high-speed back-lit imaging is used to obtain 3D timeresolved measurements of the liquid phase. The trajectories of the bulk of the liquid is computed using barycenter of the liquid presence. Such trajectories are phase averaged over many flapping periods to yield flapping orbits. In the regime of shear break-up atomization, a transition in the shape of the

Introduction

Atomization has a wide range of applications such as fuel mixing in combustion, cooling and coating processes, pharmaceutical sprays, powder production, or fire extinction. In such applications, the efficiency can be closely connected to the ability to control the spray characteristics, such as the droplet size distribution, the spray spatial spreading, or the frequency of droplet production [1; 2]. The fragmentation of a liquid jet by a coaxial gas jet is often described by the combination of two instabilities that disrupt the gas-liquid interface [START_REF] Marmottant | On spray formation[END_REF]. The Kelvin-Helmholtz instability is primarily responsible for the formation of the interfacial perturbations, stretched by the gas flow into ligaments or thin films. These liquid structures are accelerated and disintegrated into drops following the Rayleigh-Taylor instability. In addition, a large-scale instability lead to a meandering of the liquid jet into the high-speed gas jet. This motion and the associated instability, first reported by [START_REF] Eroglu | Coaxial atomizer liquid intact lengths[END_REF], is referred to as flapping. Note that this meandering motion is also sometimes described as a sinusoidal or helicoidal instability [1; 5; 6; 7; 8; 9]. However, flapping remains to be measured in three dimensions (3D) to answer the open question of whether it is associated with planar or circular motions, which is the aim of this manuscript.

Flapping takes an important role in atomization since it is responsible for the sudden release of dense droplet clouds, periodically and with a certain level of spatial heterogeneity that needs to be better characterized and taken into account for modeling purposes. Recent work by Delon et al. [START_REF] Delon | Flapping instability of a liquid jet[END_REF], studied the flapping frequency experimentally and analytically to elucidate its physical origin as well as scaling laws with relevant parameters. Notably, they demonstrated the existence of a regime where the flapping instability is synchronized with a shear instability. In this regime, the flapping frequency is found to be linearly proportional to both the gas and liquid velocities.

The present contribution focuses on the spatial characterization of the flapping instability, in a small sub-range of the parameter space within this regime. Moreover, the addition of angular momentum in the gas co-flow, or swirl, is also considered, as it is relevant in many applications of gas-assisted atomization. Early on, Hopfinger and Lasheras [START_REF] Hopfinger | Explosive breakup of a liquid jet by a swirling coaxial gas jet[END_REF] demonstrated the existence of a critical value in the ratio of the gas jet angular to longitudinal velocity components, i. e. the swirl ratio, beyond which swirl addition drastically modifies the observed spray formation in the near-field. In parallel, researchers showed that the droplet population in the far-field of the spray was also affected when swirl was added to the gas jet beyond a critical value [1; 12; 13]. It is only recently that a quantitative statistical study of the relevant near-field spray metrics was proposed along variations of the swirl ratio [START_REF] Machicoane | Influence of steady and oscillating swirl on the near-field spray characteristics in a two-fluid coaxial atomizer[END_REF]. The changes in near-field and far-field metrics and the existence of critical values in the swirl ratio for which swirl addition is beneficial for atomization can be understood in the light of a vortex breakdown mechanism of the the gas jet. This mechanisms is similar to the one in single phase swirling jets [START_REF] Billant | Experimental study of vortex breakdown in swirling jets[END_REF]. In the case of a two-fluid atomizer, it happens downstream of the liquid jet. The consequence of vortex breakdown, in the form of a gas recirculation, was observed using high-speed synchrotron X-ray imaging [START_REF] Machicoane | Synchrotron radiography charac-terization of the liquid core dynamics in a canonical two-fluid coaxial atomizer[END_REF]. Recently, [START_REF] Kumar | Large scale instabilities in coaxial air-water jets with annular air swirl[END_REF] used Proper orthogonal decomposition (POD) to extract the flapping frequency and found that it can be increased in the presence of swirl. However, the effect of swirl on the flapping instability lacks a spatial characterization.

This manuscript reports on an experimental study of the near-field of coaxial two-fluid atomization using time-resolved 3D measurements based on two-view high-speed back-lit imaging. A new method to quantify the bulk liquid presence in the near-field is introduced. The method is tested in a wide range of gas-to-liquid dynamic pressure (also called momentum ratio in the literature) and swirl ratios, and offers an alternative to the initial spreading angles of the spray that is comparable to previous work [START_REF] Machicoane | Influence of steady and oscillating swirl on the near-field spray characteristics in a two-fluid coaxial atomizer[END_REF]. In parallel, the previously available statistical description is complemented, in particular with a parametric description of the liquid core length distributions pertaining to its first three statistical moments. This method is then used to study flapping in a small range of parameters where measurements are feasible, i. e.

for lower dynamic pressure ratios where longer liquid cores display a strong temporal and spatial flapping signature. This contribution characterizes the spatial characteristics of the flapping instability at the onset of atomization of a laminar liquid jet by a turbulent gas jet that presents variable levels of swirl. Flapping orbits are retrieved using phase-averaging along many flapping periods and show a transition between planar and circular flapping motions, described quantitatively along the gas-to-liquid dynamic pressure and swirl ratios. Section 2 presents the experimental set-up and measurement methods. Sections 3 and 4 pertain to the statistical description of the liquid core length and the method to study how the liquid is redistributed in the near-field of a spray. Section 5 characterizes flapping in 3D, followed by a discussion and concluding remarks in Sec. 6 and 7.

Experimental setup

Coaxial two-fluid atomizer

The spray studied here is produced by an open-source canonical two-fluid coaxial atomizer (described in detail in [16; 18]). The atomizer is composed of an inner nozzle, referred to as liquid nozzle (inner diameter d l = 2 mm and outer diameter D l = 3 mm), used to inject a laminar flow at a rate Q l , and of a coaxial outer nozzle, referred to as gas nozzle (diameter d g = 10 mm), used to inject the gas co-flow responsible for the atomization of the liquid jet (see Fig. 1a). Using the mean exit liquid velocity The gas is introduced in the nozzle through 8 inlets. Four of them are aligned on the atomizer's axis and produce a gas stream without angular momentum at a rate Q N S , while the other four are shifted off the axis and produce a gas stream with angular momentum at a rate Q SW . The liquid presence in the near-field is obtained in two transverse planes, perpendicular with respect to each other, thanks to two-view high-speed back-lit imaging.

U l = Q l A l where A l =
axis of the atomizer (i. e. the longitudinal axis x, aligned with gravity), which produces a gas stream without angular momentum at a rate Q N S , referred to as non-swirl gas flow rate. The second group is composed of 4 inlets that are shifted off the axis of the atomizer, and therefore create a gas stream with angular momentum at a rate Q SW , referred to as swirl gas flow rate (see Fig. 1b). In order to study the impact of swirl addition on the behavior of the spray, the total gas flow rate, defined as

Q T ot = Q N S + Q SW , is kept constant
for any given M , while the swirl ratio, defined as SR = Q SW /Q N S is varied between 0 to 0.75.

Using the mean exit gas velocity where ρ i is the fluids' density and the subscripts l and g stand for the liquid and gas respectively (M is also referred to as gas-to-liquid momentum ratio in the literature).

U g = Q T ot Ag where A g = πd 2 ef f 4 with d ef f = d 2 g -D 2 l ,
A subset of the parameter space is studied in detail for the transition in shape of the flapping orbits (Sec. 5). The total gas flow rates, as well as the swirl ratio values are reported in Table 1. For every conditions, the atomization regimes correspond to shear break-up modes, following the nomenclature of [START_REF] Lasheras | Liquid jet instability and atomization in a coaxial gas stream[END_REF], where the break-up events mostly follow large-scale motions of the liquid jet associated with the flapping instability (see Fig. 3a-b ber is Re g = 4Q g / 4πA g ν g , the gas-to-liquid dynamic pressure ratio is M = ρ g U 2 g /ρ l U 2 l , the liquid mass loading is m = ρ l A l U l /ρ g A g U g and the Weber number is based on the liquid diameter as W e d l = ρ g (U g -U l ) 2 d l /σ. The fluids are air and distilled water, at an ambient temperature of 25 • C, with kinematic viscosities of ν g = 1.56 10 -5 m 2 s -1 and ν l = 8.96 10 -7 m 2 s -1 , densities ρ g = 1.18 kg m -3 and ρ l = 996.9 kg m -3 , surface tension σ = 72 mN m -1 . For M = 5.3, 4 values of the swirl ratios are also considered: SR = 0, 0.25, 0.5 and 0.75. are found roughly transverse to the gas flow. The bags are blown larger and larger until they break, producing very small droplets, while the rim yields larger drops. This atomization regime, a sub-regime of shear breakup, is referred to as bag break-up. For dynamic pressure ratio M ≥ 5 here, bag formation is also found on small-scale interfacial perturbations, that are initially observed to be roughly tangential to the liquid jet and are due to the Kelvin-Helmholtz instability. The perturbations are elongated and then stretched into bags along the liquid jets (in contrast to bags found towards the end portion of the liquid jet at lower values of M that are related to flapping).

Two-view high-speed imaging

Similarly to the two-view approach of [START_REF] Matas | Flapping instability of a liquid jet[END_REF], two high-speed cameras are used to obtain back-lit imaging of the spray along two perpendicular projections. This is done by placing two bright sources of light behind the spray, each pointing toward a camera. The cameras are positioned in a horizontal plane and are orthogonal to each other (see Fig. 1b). Both cameras are synchronized and are trigged by the same input signal. A frame rate of 10 000 Hz with duration of 1 s, an exposure time of 7 µs, a resolution of 52 µm/pixel, and a field of view of 42 × 34 mm 2 are used in the data collection. Both cameras capture orthogonal projections of the spray, leading to the ability to measure the 3D position of imaged objects, via a calibration step.

The imaging technique and image processing steps are identical to the ones described in [START_REF] Machicoane | Influence of steady and oscillating swirl on the near-field spray characteristics in a two-fluid coaxial atomizer[END_REF]. Similarly, the liquid core length can be determined on each image as the longitudinal extent of the portion of the liquid jet that is still attached to the nozzle. Each background-corrected image is nearly binary and assimilated to a phase indicator where black pixels correspond to liquid presence (and not mass). The liquid core corresponds then to the longest object which is still attached to the nozzle.

Skew normal distributions of the liquid core length

This section complements a previous contribution ( [START_REF] Machicoane | Influence of steady and oscillating swirl on the near-field spray characteristics in a two-fluid coaxial atomizer[END_REF]) to fully describe the statistics of the liquid core length of a laminar liquid jet surrounded by a turbulent gas jet, leading to atomization regimes from bag-break-up to fibertype atomization. The probability density functions (PDF) of the liquid core were reported to deviate from Gaussian functions (positively skewed), but their shape were not parameterized. We introduce skew normal distributions, whose probability density functions can be expressed as follows:

P DF (x) = 1 ω √ 2π e -1 2 ( x-ξ ω ) 2 1 + erf α(x -ξ) √ 2ω ( 1
)
where erf is the error function, and ξ, ω, and α are 3 parameters respectively called location, scale, and shape parameter:

• Shape parameter, α = 2 π 1 + 4 -π 2β 2 3 -1 -1 2 (2)
• Scale parameter, • Location parameter,

ω = σ 1 -2δ 2 π (3)
ξ = µ -ωδ 2 π (4) with δ = α √ 1+α 2 .
The parameters can be directly measured from the data using the first 3 standardized moments: mean µ, standard deviation σ and skewness β.

Compared to normal distributions, the use of skew normal distributions results in significantly better modeling of the PDF of the liquid core length.

(see Fig. 2a). It provides a very good prediction of the liquid core behavior over the whole range of conditions studied. Moreover, the skew normal distribution derived from the mean, standard deviation, and skewness of the data set provides results very similar to those obtained by fitting a skew normal distribution on the PDF. The average relative error between the two is less than 4% over the entire data set studied, with 77% of the relative errors being less than 5% and the maximum error being 14%. This means studying the first 3 moments of the liquid core length data is enough to describe the entire statistics. Figure 2c) reports the skewness of the liquid core length, that was not reported previously. Note that a convergence study, taking 4 additional independent measurements, conducted on the condition M = 5 (with and without swirl) lead to an estimation of the convergence error of about 10% on the skewness. It appears that, over the range 5 < M < 80 and irrespectively of the presence of swirl in the gas jet, no general trend is observed for the skewness. Higher values of the dynamic pressure M > 40 seem to yield a skewness that is about 50% larger than lower values, indicating even higher probability to have larger lengths than smaller lengths with respect to the mean value. Note that over this whole range, the ratio of standard deviation to mean liquid core length is fairly constant with a value of approximately 25%, with no clear effect of the swirl ratio.

Liquid distribution angle of the spray in the near field

Sliding average barycenters of the liquid phase

The method proposed here is based on a simplification of the spray structure in the near-field, as only the movements of the bulk of the liquid are studied and not the movements of individual features (e. g. ligament, drop). Therefore, the spray images are divided into 10 equal overlapping horizontal windows on which the barycenters of grey shades are calculated in order to determine the mean position of the liquid presence in each window (Fig. 3). As a shadowgraph only gives information about the presence or absence of liquid, and not about the quantity of liquid present, the barycenters are calculated by giving the same weight to all pixels are assigned to contain liquid (see [START_REF] Machicoane | Influence of steady and oscillating swirl on the near-field spray characteristics in a two-fluid coaxial atomizer[END_REF]) instead of taking into account the grey intensity of each pixel.

Moreover, an overlap between two consecutive windows of 33% is used to act as a sliding average over the variation of the barycenters' positions versus longitudinal distance x, while increasing the effective sampling resolution.

The position of the barycenter of each window is computed on each view (for any window at a downstream distance x, view 1 and 2 respectively yield y and z) and is then used to obtain the 3D position of the liquid barycenters (x, y, z), as described in Fig. 3a-c). This simplified three-dimensional representation of the spray is used to study the spatial and temporal evolution of the liquid jet flapping (including both its liquid core and some detached liquid inclusions without distinction).

Note that the liquid presence barycenter method with two-view back-lit imaging, while representing well the spatiotemporal dynamic of the bulk of the liquid phase in the near-field of a two-fluid coaxial atomizer, would not be adequate to describe the spray mid and far-field or phase objects of complex shape such as large deformed bubbles. In the former, the presence of small liquid droplets far from the centerline could for instance lead to overestimate weights in the barycenter computation compared to much larger drops close to the center. In the latter, projected areas can be drastically overestimated, especially for non-convex shapes (see [START_REF] Masuk | A robust virtual-camera 3d shape reconstruction of deforming bubbles/droplets with additional physical constraints[END_REF] for an in-depth discussion).

Liquid distribution angle of the spray in the near field

From the liquid barycenters method described above, a new metric is proposed to describe the spray expansion in the near field: the liquid distribution angle. By calculating the radii r 95% that contain 95% of the barycenter positions at different downstream distance x, one can note a linear behavior.

On this basis, the liquid distribution angle can then be defined from the linear regression of r 95% as a function of x/d g (see fig. 3d). Note that similar trends can be obtained by fitting the standard deviation of the barycenter positions σ B as function of the downstream distance x/d g . However, since the barycenter position distributions are not Gaussian, circles of radii 2σ B often cover areas that span more than all the barycenter positions (instead of 95.45% of the data set for a Gaussian).

Figure 3e shows the evolution of the liquid distribution angle with the gas-to-liquid dynamic pressure ratio M for different swirl ratios SR. For a constant dynamic pressure ratio M , one can observe that the liquid distribution angle increases with SR. Moreover, one can note that increasing the swirl ratio from 0 to 0.25 does not result in any significant changes in the liquid distribution angle, in qualitative agreement with previous work that shows the existence of a critical value for the swirl ratio above which swirl starts to affect the spray [11; 14]). On the other hand, for a constant swirl ratio SR, the liquid distribution angle decreases monotonically with M . This method complements the previous definition of initial spreading angle based on the liquid presence probability ( [START_REF] Machicoane | Influence of steady and oscillating swirl on the near-field spray characteristics in a two-fluid coaxial atomizer[END_REF]), with a weight put toward the lo-cation of the bulk of the liquid (and less toward smaller liquid inclusions).

Both methods yield trends that are qualitatively similar, and they both can be used to describe the rate at which the liquid redistributes spatially in the near-field of a coaxial atomizer, for comparisons between experiments and numerical simulations.

Transition in flapping orbit shapes

This section studies a sub-range of the operating parameters (see Table 1) were flapping can be identified without ambiguity. It uses the method introduced in Sec. 4 to obtain flapping orbits in 3D.

Definition of flapping orbits

The temporal and three-dimensional spatial evolution of the large-scale flapping instabilities occurring during the atomization is studied using the liquid barycenters method described above. In order to identify the flapping frequency, the power spectral densities (PSD) of the y-axis and z-axis position of each barycenter can be calculated from their time series obtained with this method (see Fig. 4a). Note that for high values of the dynamic pressure ratio (i. e. for high gas velocities here), flapping happens at high frequency [START_REF] Delon | Flapping instability of a liquid jet[END_REF]. Beyond M = 11, the peak in the PSD that corresponds to flapping is found in the high frequency range where a decaying power law is observed (see Fig. 4 beyond 300 Hz for instance), and a faithful determination of the dominant frequency becomes challenging. This was also the case for the determination of the shedding frequency based on the liquid core length time series in [START_REF] Machicoane | Influence of steady and oscillating swirl on the near-field spray characteristics in a two-fluid coaxial atomizer[END_REF], where a typical timescale was retrieved using auto-correlation functions instead. Such determination would be easier using higher spatial and temporal resolutions, which were not obtainable in the present work. In the following, the study hence focuses on the flapping morphology transition in the shear break-up regime of coaxial atomization for M ≤ 11.

Once the main frequency f 0 is determined as the PSD maximal peak, the 3D positions of all the barycenters (for each x position) are phase-averaged over many periods nT = n/f 0 (n ≥ 50 and n ∈ N N N) and studied over an average complete flapping motion of duration T (Fig. 4b). This yields closed orbits, by definition, that correspond to the average motion of the liquid bulk along one flapping period T . As expected, the orbits extent increases with downstream distance as the flapping motion gains amplitude. The shape of the orbits does not appear however to change with downstream location, and is analyzed in Sec. 5.2. Note that orbits correspond here to the mean motion of the bulk of the liquid that is observed to happen at the flapping frequency.

Instantaneous barycenter trajectories display high level of fluctuations, as can be observed in Fig. 3c (fluctuations of the barycenter positions are observed up to about 0.75d g from the centerline, while the mean flapping orbits only extent up to 0.1d g , Fig. 4b, in the example of M = 5 and SR = 0.5 at x = 1.5d g ).

One can verify that the frequencies determined using the PSD indeed correspond to flapping motions by observing the motion of the liquid over a flapping period on both views (see Fig. 5 and the videos in Supplementary Materials in the case of M = 5 and SR = 0.5). This is checked for all conditions explored in this section, but at the lower range of dynamic pressure studied here, the flapping happens at low frequency (of the order of a few dozen to a few hundreds Hz), so the PSD always present a clear peak associated with flapping (unlike at high value of M , as discussed above).

Figure 4b) shows that, for a dynamic pressure ratio M = 5 and a swirl ratio SR = 0.75, the phase-averaged barycenters have a quasi-circular motion around the axis of the atomizer, suggesting that the flapping motion also follows a circular pattern around the axis of the atomizer here. This is not the case for every sets of parameters studied, and especially at lower M and SR values. For instance, the case (M = 2, SR = 0) leads to a seemingly planar flapping, while the case (M = 5, SR = 0) results in a transitional state between planar and circular flapping, referred to as elliptical here (see Fig. 6). This transitional elliptical state is characterized by a circular motion of the barycenters close to the nozzle of the atomizer, which tends toward a planar motion as they move away from it (or at least with a clear preferential direction, along z in this example). Note that for transitional orbits, there is a change in orbit shape as the downstream distance increases, as orbits close to the exit plane are found to be almost circular. Typical studies in the literature generally use only one camera. This work shows that this would lead to a biased measurements of the flapping amplitudes in cases where planar or transitional 2D-3D flapping is occurring. In the case of M = 5

and SR = 0, the mean flapping amplitude along z can be estimated to be about 3 times larger than along y (which is here the largest error in flapping amplitude that could be made if a one-view measurement was performed along y, see Fig. 5b).

Videos in the Supplementary Materials are provided for the conditions shown in Fig. 6, depicting the positions along the orbits animated along a flapping period. The positions along the orbits present different angles in the (y, z) plane at a given time (i. e. with a phase difference between the orbits at different downstream positions x along the period). Beyond the transition, the flapping motion of the liquid jet is showed to be helical (and not circular), with and without swirl. Out-of-phase mean barycenter positions are also found the case for the planar flapping case, illustrating a meandering motion which oscillates in a plane (unlike a pendulum).

Quantifying orbit shapes

The shape of the flapping orbits are characterized quantitatively by using a shape factor defined using the orbit perimeter P and area A as P/2 √ πA, which equals to 1 for a circle. The shape factor for the planar, ellipsoidal and circular orbits from Fig. 6a, b andc) are approximately 5.36, 1.41 and the critical swirl ratio (so for SR ≥ 0.5 here), the orbits are immediately quasi-circular, with a shape factor close to one.

Alternatively, similar conclusions can be reached by simply measuring the maximal extend of the orbits r max (Fig. 7c-d). Normalizing r max by the longitudinal distance x is enough to collapse the plots from the 3 sampled locations, in agreement with the linear spreading of the liquid observed in Fig. 3d). The orbit maximal radius also serves as a proxy for the flap- gas-to-liquid dynamic pressure ratio yield smaller amplitudes, in agreement with the shorter liquid core lengths, and that the presence of swirl increases the flapping amplitude. For the latter, a factor of about 2 is measured, placing the amplitude at M = 5 and SR = 0.75 almost at the level of the large-amplitude planar flapping motion observed at M = 2 without swirl.

As already demonstrated in the literature (see [START_REF] Delon | Flapping instability of a liquid jet[END_REF]), the flapping frequency increases when the dynamic pressure ratio M increases. This work shows that it also increases with the swirl ratio. Once again, one can note that there are no significant changes between SR = 0 and SR = 0.25, for a constant M . The increased flapping frequency in the presence of swirl beyond a critical swirl ratio is compatible with previous findings concerning faster timescales of the interfacial instability dynamics [START_REF] Ricard | Role of convective acceleration in the interfacial instability of liquidgas coaxial jets[END_REF]. Higher flapping frequencies in the presence of swirl were also reported recently in a wider range of dynamic pressure ratios and several liquid Reynolds numbers [START_REF] Kumar | Large scale instabilities in coaxial air-water jets with annular air swirl[END_REF].

Discussion

A first glance at the spray in the near-field, even when using two perpendicular transverse views, leads to an axisymmetric statistical description of the spray. The angle defined using the liquid barycenters indeed smooth out the potential existence of a preferential direction, and similar results would be obtained if only the moments of the barycenters were used. While this still gives a relevant representation on how the liquid is redistributed by the gas jet in the near-field, allowing for a good comparison between different operating conditions, it lacks the accuracy that is necessary to precisely quantify the liquid distribution and to build models and predictions. While other methods could be used, such as geometric fits of the 2D transverse scatter plots or of 2D transverse probability density functions of the barycenter, the use of phase averaging to determine flapping orbits prove itself to be a simple way to yield a quantitative picture of the liquid mean motion over a flapping period. This representation focuses on the location of the bulk of the liquid in space and time. The phase-averaged closed orbits directly evidence that flapping can have a strong preferential direction, with shape factors larger than 5 (i. e. motions along the preferential direction of about 50 times larger than motions along the direction perpendicular to the preferential direction), with strongly anisotropic liquid flux distributions in the far-field. These observations result from an experimental realization per condition, representing measurements over many flapping periods (50 to 200).

Note that the transition in flapping orbit shape does not seem to affect the scaling law of the flapping frequency. The growth of the frequency with dynamic pressure ratio is indeed monotonous and in good agreement with previously reported data (e. g. [START_REF] Delon | Flapping instability of a liquid jet[END_REF]). This indicates that the mechanism governing the flapping characteristic timescale, and the one determining flapping orbits shape are independent from each other. Furthermore, while the shape of the flapping orbit changes drastically, becoming quasi-circular as soon as swirl is added beyond the critical value at which swirl actually affects the spray, SR ≥ 0.5, the flapping frequency gradually increases with swirl addition. Further study on the effect of the swirl ratio and on a larger range of dynamic pressure ratios would be interesting to determine the scaling law as a functions of both M and SR. On the other hand, the transition in flapping shape has an effect on the flapping amplitude, measured here as the point of the orbit found furthest from the spray axis along an average flapping trajectory. As flapping goes from a planar to a transitional quasi-circular shape when M increases, the flapping amplitudes gradually decreases, by a factor of about 3 when M goes from 2 to 11. However, swirl addition, that leads to quasi-circular orbits also increases the flapping amplitude. The increase, similarly to the change of shape factor, is seen abruptly for SR ≥ 0.5 in opposition to the gradual increase in flapping frequency. This means that the flapping amplitude for both SR = 0.5 and 0.75 is roughly the same, approximately 2 to 3 times the one observed without swirl. Lesser amplitude at high dynamic pressure values are compatible with shorter liquid core lengths compared to lower M , which could lead to large-scale interactions with the gas jet. When swirl is added, the liquid core length is further reduced at a given M [START_REF] Machicoane | Influence of steady and oscillating swirl on the near-field spray characteristics in a two-fluid coaxial atomizer[END_REF], but the azimuthal component of the gas jet creates an additional radially outward pressure term that could lead to larger flapping amplitudes. This is compatible with the wicking dynamic of the liquid jet, which can be observed to wet the outer wall of the liquid nozzle (up to about 0.4 mm upstream of the exit plane, i. e approximately d l /5 or (D l -d l )/2) using X-ray radiography [START_REF] Machicoane | Synchrotron radiography charac-terization of the liquid core dynamics in a canonical two-fluid coaxial atomizer[END_REF]. Note that wicking may play a role in the transition in flapping orbit shape at it drastically modifies the initial condition of the gas-liquid interface. In conclusion, swirl addition leads to flapping motions at both higher amplitudes and frequencies compared to non-swirled gas jet.

At moderate dynamic pressure ratio, where primary break-up events can result from both interfacial instabilities and the large-scale flapping instability, such increased flapping energy could indicate a greater role of flapping in the spray formation mechanisms for these operating conditions. onsets earlier here, and that the prescribed transition around W e d l = 40 is more closely related to the relative role between large-scale and smallscale instabilities becoming more or less comparable in bag formation. The difference in the transition value of W e d l between the present work and the proposed transition in [START_REF] Lasheras | Liquid jet instability and atomization in a coaxial gas stream[END_REF] could be due to subtle dependencies in the atomizer geometry. In particular, while the inlet liquid diameter d l is expressed linearly in W e d l , the ability of the gas to stretched the elongated liquid jet could depend non-linearly on this quantity. This hypothesis would however need to be further investigated in a liquid Reynolds number -gas Weber number parameter space that also includes variable atomizer geometry.

For both low and intermediate values of dynamic pressure ratio, the flapping orbits shape is either planar or elliptical, displaying a strong preferential direction. This is a strong deviation from the axisymmetric inlet conditions related to the coaxial two-fluid atomizer, and the shape is only found to be invariant through rotation of π around the atomizer axis. At higher momentum ratios, or in the presence of swirl, axisymmetry is regained. The profile shape and flapping direction can roughly be described as belonging to the symmetry group SO [START_REF] Dumouchel | On the experimental investigation on primary atomization of liquid streams[END_REF]. Note that for M = 11, the shape factor is equal to 1.13, corresponding to a ratio of the major to minor axes of 1.2, while the smallest shape factor found is at M = 5 and SR = 0.75 with a value of 1.02 (ratio of the major to minor axes of 1.08). These slight deviations from axisymmetry, probably close to the uncertainty of the shape factor of a finite-sample orbit, can be considered negligible, even when compared to the shape factor value of 1.4 for M = 5 without swirl. For M ≤ 5, the strong departure from axisymmetry is expected to have consequences on the liquid- gas interactions and primary break-up in the near-field, as well as transport and secondary break-up further downstream. This needs to be accounted for when taking measurements in the far-field or establishing predictions of spray characteristics, and also possibly in modeling approaches (e. g. spatiotemporal linear stability analysis).

-1 0 1 -1 0 1 0 1 2 -1 0 1 0 1 2 -1 0 1 0 1 2 -1 0 1 -1 0 1 0 1 2 -1 0 1 0 1 2 -1 0 1 0 1 2 a) view 1 M = 2 b) view 2 M = 2 0 1 2 z/d g y/d g c) view 1 M = 5 d) view 2 M = 5 0 1 2 0 1 -1 0 1 -1 x/d g x/d g
The transitional elliptical shape (Fig. 6b) indicates a strong preferential direction, here along z, with deviations along y only when the liquid bulk is located closer to the centerline (at small radial distances). In the absence of bag formation along the liquid jet (i. e. bags only originating from flapping and located approximately in the last third of the liquid core), at M = 2, the liquid bulk flaps back and forth in a plane. The liquid core mostly corresponds to a twisted liquid column which experiences regular fragmentation associated with bag break-up. The rupture at the most stretched portion of the bag propagates up to the rim and break the liquid jet tip altogether.

In contrast, at M = 5, bag formation can also originate from small-scale interfacial instabilities, and partial break-up of the liquid jet happens before the end of the liquid jet. While a bag is inflated, despite representing a very small portion of the liquid mass as the membrane is very thin, it offers a large increase in the aerodynamic drag experienced by the liquid jet (acting like a spoiler). The formation of bags from small-scale interfacial instabilities tend to be associated with a liquid core and detached liquid bulk mostly aligned with the centerline. On the other hand, the bags happening at the extrema of the flapping period are associated with twisted liquid jets, that remain thin up to their tip where the bag is formed. The presence of bags close to the nozzle (at a few liquid diameters), offers a thick liquid column that is sus-pected to yield additional drag, which could oppose large-amplitude flapping in a preferential direction. It is likely that the emergence of this added drag around M = 5 is what leads to the transition in flapping dynamics. This phenomenon results in the region of r < 0.02d g in Fig. 6b) which bounds all of the flapping orbits at the downstream distances sampled. At low dynamic pressure ratio (planar flapping) or with swirl (circular flapping), such region does not exist as the liquid core's main direction strongly deviates from the centerline.

Conclusions

Using high-speed two-view back-lit imaging, the spatio-temporal evolution of the spray in the near-field of a two-fluid coaxial atomizer with tunable gas swirl has been characterized. First, a parametric description of the liquid core length probability density functions has been introduced. It consists in a skew normal distribution, whose 3 parameters are directly computed from the mean, standard deviation and skewness of the liquid core length time series. This parametrization has been shown to represent the data very well over a wide range of gas-to-liquid dynamic pressure and gas swirl ratios (5 < M < 80 and 0 < SR < 0.75).

The skewness and ratio of standard deviation to mean liquid core length were also reported for completeness, showing a not insignificant degree of spread but no clear trends with these parameters. Second, a method was introduced to measure the 3D barycenter time series of the bulk of the liquid. This yielded a simple and robust definition of the liquid distribution angle of the spray in the near-field, which as ex-pected decreases with gas-to-liquid dynamic pressure ratio M and increases with swirl ratio SR, beyond a critical value in agreement with the literature. The method, which does not require any significant image processing, gives access to the transverse motions of the liquid and hence to flapping frequency measurements. Phase-averaging of the liquid motion along the measured flapping periods led to the determination of mean flapping orbits along various transverse planes at growing downstream distance. The shapes of the orbits were found to be invariant with distance (except for transition orbit shapes), but showed changes throughout the parameter space: planar motions were exhibited at low dynamic pressure ratio, while quasi-circular motions were found for either higher ratios and/or in the presence of swirl. This was quantified using a shape factor, defined from the orbits perimeter and area. The flapping amplitudes, measured along the flapping preferred direction when it existed, follow a similar trend than the flapping shape with M , but the opposite trend with SR. This means that at high M values, the flapping amplitude is lower than at low values, but it increases when swirl is added (SR ≥ 0.5). The flapping frequency did not seem to be dependent on the flapping shape, increasing with dynamic pressure ratio, but was found to also increase in the presence of swirl.

The transitions in flapping orbit shapes seems to be related to the occurrence of bag formation along the liquid jet, on interfacial perturbations that originates from small-scale interfacial instabilities. In the absence of bags along the liquid jet, it seems that any deviation from the centerline from the liquid jet (probably triggered by a large-scale gas fluctuation) is countered by an opposing aerodynamic force as the liquid enters the high-speed gas.

The liquid jet may then experience back-and forth motions in a plane whose orientation may originate from a given initial perturbation, as the liquid jet does not present any significant interfacial perturbation at low dynamic pressure ratio. Further investigations, at higher temporal and spatial resolution, for larger gas-to-liquid dynamic pressure ratios, should be conducted to determine what is the evolution of the flapping shape from bag break-up to fiber-type atomization, and how swirl affects the flapping instability at high M . Measurements of the droplet population in the far-field throughout the cross-section of the spray should be considered to assess the spatial heterogeneities in the presence of non-axisymmetric flapping. An additional open-question is the origin and potential reproductibility of the preferential flapping direction. Note that the exhibited preferential direction is observed to be different at different operating conditions (see Fig. 6). Besides consequences on the far-field spray statistics, this could be important to evaluate real-time spray features, such as is done when implementing atomization feedback control [22; 23].

Acknowledgements

πd 2 l 4 ,Figure 1 :

 41 Figure 1: (color online) a) Longitudinal cut of the atomizer. Water is introduced in the center of the nozzle while gas is injected in an orthogonal horizontal plan. The indicated lengths are d l = 2 mm, D l = 3 mm, and d g = 10 mm. b) Transverse cut of the atomizer.

Figure 2 :

 2 Figure 2: (color online) a-b) Comparison between normal and skew normal distributions (for the latter, both a fit and the parametric equation using moments calculated on the data are considered) of the liquid core length L B for different values of M and SR. Evolution of the liquid core length skewness β (c) and ratio of standard deviation to mean σ µ (d) as a function of the gas-to-liquid dynamic pressure ratio M , for different swirl ratios SR.

Figure 3 :

 3 Figure 3: (color online) a-b) Typical synchronized snapshots from both views at M = 5 and SR = 0.5, with associated detected liquid barycenters. c) 3D reconstruction of the barycenter overlayed over 200 subsequent detections (0.02 s, in dashed lines). d) Determination of the angle of the liquid distribution in the near-field of the spray based of the radii r 95% (plotted in blue) that contain 95% of the barycenters in each transverse plane (SR = 0.5 and M = 5). The angle is then determined from the linear regression of r 95% as a function of x/d g (solid black line). e) Evolution of the liquid distribution angle θ as a function of the gas-to-liquid dynamic pressure ratio M , for different swirl ratios SR.

Figure 4 :

 4 Figure 4: (color online) a) Power spectral densities (PSD) of the y and z positions (top and bottom) of the liquid barycenter for x/d g = 0.5. The ♦ symbols show the location of the maxima of the PSD, corresponding to the liquid jet flapping frequency. b) Flapping orbits obtained from the phase average at the measured flapping frequency of the liquid barycenters in each downstream plane. The condition displayed here is M = 5 and SR = 0.5.

Figure 5 :

 5 Figure 5: (color online) Instantaneous snapshots for both views spaced in time along a flapping period T determined from Fig. 4 (M = 5, SR = 0.5). The dashed lines' purpose is to guide the eyes through the flapping motion. The horizontal axes correspond to y for view 1 and z for view 2, normalized by d g .

Figure 6 :

 6 Figure 6: (color online) Flapping orbits displaying different shapes obtained for M = 2 (a, planar), M = 5 (b, ellipsoidal) without swirl, and for M = 5 and SR = 0.75 (c, circular).

Figure 7 :

 7 Figure 7: (color online) Shape factor obtained from the orbit measured perimeters P and area A without swirl as a function of M (a), and for M = 5 as a function of SR. The shape factor is averaged over three downstream locations x/d g = 0.09, 0.3 and 0.5, and the errorbars correspond to the convergence error. Similarly, c-d) and e-f) display the flapping amplitude measured through the orbit maximal radii r max (at three downstream distances) and the flapping frequencies f .

Figure 8 :

 8 Figure 8: Snapshot displaying bag formation originating from the large-scale flapping instability at M = 2 (a-b) and from a small-scale interfacial instability at M = 5 (c-d).

  This work was sponsored by the Office of Naval Research (ONR) as part of the Multidisciplinary University Research Initiatives (MURI) Program, under grant number N00014-16-1-2617. The views and conclusions contained herein are those of the authors only and should not be interpreted as representing those of ONR, the U.S. Navy or the U.S. Government.

  and the kinematic viscosity of air ν g , the gas Reynolds number Re g =

	d ef f Ug νg	ranges from 1.4×10 4 to 8.4×10 4 , depending on the total gas flow
	rate Q T ot . Alternatively, variations of total gas flow rate are characterized
	by the gas-to-liquid dynamic pressure ratio M =	ρgU 2 g l ρ l U 2	varying from 2 to 82,

Table 1 :

 1 Flow parameters for fixed laminar liquid injection (Re l ≃ 1200), varying the gas flow rate, in the vicinity of the transition in flapping orbit shapes. The gas Reynolds num-

	and movies in

The transition in flapping shape is reached for M = 5 here, with the shape parameter falling below 1.5. This operating condition corresponds to a Weber number, based on the inlet velocity differences between each phase U g -U l and on the liquid inner diameter d l , of W e d l = 39.1. This value is very close to the one reported for transition between shear break-up and bag-break-up: the phase diagram of qualitative atomization regimes from [START_REF] Lasheras | Liquid jet instability and atomization in a coaxial gas stream[END_REF] points toward a transition around W e d l = 40 for the laminar liquid Reynolds number Re l = 1200. However, in the current range of operating conditions for this atomizer, bags are observed even at the lower Weber number value explored of W e d l = 15.4 (see Fig. 8a-b, corresponding alternatively to M = 2). In this case, as the liquid core meanders due to the flapping instability, bags are blown in the last portion of the jet, where the liquid resembles a hook shape. The bottom of this hook presents a region that is transverse to the gas jet which stretches it into a thin membrane that is referred to as a bag. On the other hand, for W e d l ≥ 39.1, another mechanism leads to the formation of bags. Small-scale interfacial instabilities, namely shear-driven Kelvin-Helmholtz, produce interfacial perturbations that once elongated by the gas stresses, can be blown into bags that are attached to the side of the liquid core (see Fig. 8c-d). These bags coexist with the ones originating from the large-scale flapping instability (Fig. 8c-d is for instance taken right after the rupture of such a bag, and the larger drops resulting from the rim are visible on the snapshots. Movies in Supplementary Materials illustrate the difference in bag formation and liquid core morphologies for both of these conditions (M = 2 and M = 5). It appears that the described transition between (bag-less) shear break-up and (shear) bag break-up described in [START_REF] Lasheras | Liquid jet instability and atomization in a coaxial gas stream[END_REF]


Samuel Auclair
email: s.auclair@brgm.fr

Christian Iasio
email: c.iasio@brgm.fr

Andreï Balgiu
email: andrei.balgiu@qualiconsult.fr

Antoni Blasquez
email: antoni@bg-arquitectes.com

Jean-Christophe Castagnos
email: jean-christophe.castagnos@hautes-pyrenees.gouv.fr

Emilie Crochet
email: emilie.crochet@interieur.gouv.fr

Olivier Dalverny
email: olivier.dalverny@enit.fr

Xavier Goula
email: afpsxaviergoula@gmail.com

Paco Martinez

Philippe Méresse

Hedi Karray

Antonio De Nicola

Nada Matta

Hemant Purohit

Philippe Soulé-Péré
email: philippe.soule-pere@sdis65.fr

Ghislaine Verrhiest-Leblanc

Post-earthquake damage assessment: feedback from a cross-border crisis exercise

Keywords: Crisis exercise, Earthquake, Post-earthquake damage assessment, Cross-border disaster management, Crisis management digital platform Post-earthquake damage assessment

INTRODUCTION

The Pyrenean massif, which is the natural border between France and Spain, and which is also home to the Principality of Andorra, is one of the regions most exposed to earthquakes in mainland France and Spain, with hundreds of earthquakes recorded each year, of which about ten are felt locally. Despite their relatively moderate seismic activity compared to other European countries, the Pyrenees have historically experienced many destructive earthquakes, including the events of 1428, 1660, 1750and 1967(SisFrance database, Jomard et al., 2021).

Despite the relative rarity of destructive earthquakes occurring in the Pyrenees, the occurrence of such a disaster cannot be excluded. It is therefore essential to be prepared to face such an event. This preparedness is even more important in contexts of moderate seismicity such as that of the Pyrenees, where the low frequency of destructive earthquakes limit the experience of the services concerned [START_REF] Borodzicz | Individual and group learning in crisis simulations[END_REF]. Furthermore, an effective decision-making process of crisis management requires that the operator is trained both in the devices, tools and interfaces he will have to implement during the crisis, and in the mobilization of his knowledge and thinking skills [START_REF] Fredholm | Emergency management as co-ordinated cognitive modelling on different time-scales[END_REF]. Thus, crisis management exercises become essential for improving the skills of involved actors, as they ensure an adequate appropriation of practices and technical tools.

In this context, an exercise mobilizing French, Spanish and Andorran stakeholders was held in the French Pyrenees in November 2021, focused on the management of early post-earthquake damage assessment.

PROBLEMATIC

The recent Le Teil earthquake in France on November 11, 2019, and before it the Lorca earthquake in Spain on May 11, 2011, have confronted the French and Spanish civil protection authorities with the issue of conducting mass damage assessments, which triggered the need of improving existing practices, from a methodological, technical and organizational point of view. Feedback from these two earthquakes [START_REF] Martínez | Lorca Resiliente "Lecciones aprendidas del terremoto de Lorca[END_REF]Taillefer et al., 2020;[START_REF] Peverelli | Séisme du 11 novembre 2019 -Retour d'expérience de la gestion de crise communale -Rapport technique AFPS et Mairie du Teil[END_REF], corroborated by the experience of the 2016 Central Italy seismic crisis [START_REF] Auclair | Rapport de mission postsismique -Italie centrale[END_REF], highlights two main areas for progress:

1. The coordination of the parties involved in damage assessments tasks, with in particular the need for greater collaboration between the associative experts mandated by the authorities, and the structural specialists among the firefighters of Urban Search and Rescue (USAR) teams.

2. The workflow of the damage assessment, from the request made by the citizens to the Certificate of Occupancy inspection, passing through the field survey, the feedback to the DAC (Damage Assessment Coordination) and the synthesis of the information for the coordination of the crisis management.

Experience shows that the timing required by this process needs optimization of supporting digital tools, such as the ERIKUS system, used by the Italian Civil Protection [START_REF] Mayneri | ERIKUS: An open source geographical tool for earthquake risk management[END_REF].

PRESENTATION OF THE EXERCISE

Objectives and scenario

Co-organized by the partners of the European POCRISC project (https://pocrisc.eu), the prefecture and the departmental emergency service of the Hautes-Pyrénées (SDIS-65), and the municipality of Séméac, in the practice this exercise aggregated several independent initiatives, to take advantage of the presence of cross-border teams and to test the capacity for cooperation of local and foreign resources.

Following the occurrence of a magnitude 6 earthquake south of the city of Tarbes and the damage to the prefecture, the scenario planned to move the departmental crisis center (COD) to the site of the Tarbes engineering school (ENIT). It is in this degraded environment, with limited equipment and without knowing the workplace, that the prefecture's crisis director had to organize the management of the event. The exercise included both a tabletop part, with a COD coordinated by the prefecture in ENIT, and a field part. The exercise mobilized 75 participants for the part described in this article (Figure 1), and more than 250 (players, observers and facilitators) in total, from France, Spain and Andorra.

Among the issues that the players were confronted with, particular attention was paid to the emergency assessment of building damage. It aimed to provide the crisis manager with tangible elements for the identification of premises useful to the crisis response and recovery (strategic buildings or buildings intended to accommodate populations), and the sheltering needs assessment, based on the damage rate of residential buildings located in the impacted perimeter.

Practitioner 2. To encourage the French local authorities to engage firefighters together with the experts from the French earthquake engineering association (AFPS), mandated by the French civil protection for post-earthquake building damage assessment.

3. To coordinate effectively response and recovery resources available from regional (from neighbor French departments) and cross-border (from Spain and Andorra) entities. Within the scope of the exercise, outside the framework of the European civil protection mechanism (UCPM), this assistance were considered to be mainly operational. In particular, building inspectors from Cataluña integrated SDIS-65 and AFPS (activation of the Catalan earthquake engineering association integrated in the Association of Structural Consultants -ACE) field survey teams.

FEEDBACK ON DAMAGE ASSESSMENT

The purpose of the feedback is to evaluate the decisions and actions taken during the exercise, by comparing the points of view of all the stakeholders, and to start an improvement process that may involve updating plans and procedures. After the organization of a "hot" feedback immediately after the end of the exercise, a "cold" feedback is being carried out. To facilitate the collection of the participants' feedback, an on-line questionnaire was proposed to all the participants. We will present hereafter a first analysis of 41 responses we got, with a specific focus on the coordination and conduct of damage assessment function.

Articulation within COD between the coordination and the DAC

The management of a seismic crisis requires the activation of numerous coordination functions attached to the COD. Among them, a task force dedicated to the damage assessment was created: the DAC, aimed to coordinate the damage assessment, and to report to the chief coordination unit only the information necessary for the overall management of the crisis (Figure 2). The answers to the questionnaire show contrasting opinions upon the interactions between these two units (Figure 3).

The areas for improvement identified relate in particular to the requirement:

-For the authorities, to identify the experts available for intervention (associations, institutions, etc.), to assign them prioritized tasks and to provide them with the means for effective coordination;

-For the experts, to identify the expectations of the authorities and to advise them on the prioritization and results of the expert assessments carried out.

Practitioner

Functioning of the DAC

Exercise participants involved in the DAC were asked about its composition, its working mode, and the strategy adopted by this coordination and relaying task force (Figure 4). Concerning the strategy adopted by the DAC, the principle retained for the constitution of the field survey teams was to prioritize mixed pairs, associating an inspector from the voluntary associations with an expert firefighter. This principle, which was suggested following the Le Teil earthquake (Auclair et al., 2020) and successfully tested during the damage assessment mission carried out in the southeast of France in the aftermath of storm Alex in October 2020 (Auclair et al., 2020). It is supposed to allow the enrichment of professional cultures and facilitate the homogeneity of the survey outcome. This configuration was strongly appreciated. The identification of criteria for prioritizing inspections tasks was difficult due to the time actual duration of the exercise.

Contribution of the POCRISC digital platform

The POCRISC digital platform was generally appreciated by the participants, both for the functions provided and its general usability. Nevertheless, the two components of the platform should be considered separately: at the DAC level, the coordination function was used via a web-GIS platform, while the field inspectors used a smartphone mobile application (Figure 2 and Figure 5).

Use of the coordination digital platform by the DAC

Concerning the coordination platform, it first allowed the allocation of building assessment tasks by pairs, either by identifying sectors to be investigated on the map, or by identifying buildings individually. After a training phase, the tool proved to make this activity relatively easy, despite problems related to the tasking of certain target areas very large: the identification of large sectors can indeed correspond to hundreds of buildings, each one representing an assessment task. It is interesting to note here that the DAC had to manage, at the request of the coordination unit, the sectorization of an area not covered by the cadastral data pre-loaded into the tool for the exercise. Nevertheless, the use of the GIS back-end and the technical assistance of DeveryWare made it possible to quickly integrate the missing data and plan the survey. This unforeseen event highlighted the agility of the tool, and its ability to be deployed quickly.

However, the most valuable feature for the DAC remains the ability to receive real-time results from teams deployed in the field. It provides a constantly updated view of the situation and allows to save a considerable amount of time for data consolidation, compared to workflows based on paper forms. This process of dynamic data transfer from the field proved to be very efficient, and the DAC had access to an updated map showing the progress of the building assessment campaign, as well as the individual building findings. Even if a dashboard with summary indicators is also available on the platform, it turned out that these indicators and their restitution modes did not meet the COD's needs. The objective of defining the indicators useful to the decision-makers was partially attained: work should be done to identify them clearly in peacetime, so that they can be automatically produced on the dashboard. In addition, users and observers pointed out the lack of functions to use field data more easily to report effectively damage to municipal authorities, so that they can take decisions and safeguard measures about the occupancy.

Use of the mobile application by field inspectors

Apart from a few difficulties in downloading and configuring it, the mobile application worked correctly on Android devices (application not available for iOS). The assignment of tasks worked without any problems other than the one already reported, when hundreds of tasks were scheduled at a time. This situation caused slowing data transmission. Once the tasks were assigned, the inspectors could go to the field to inspect the assigned buildings one by one. While the mapping provided in the application made it relatively easy for inspectors to find the survey area, the exact positioning of the buildings was more difficult. The users suggest improving the use of the on-board GPS (refresh rate and accuracy of the GPS questioned by the respondents), and adding an aerial view map background, as well as the use of on-board navigation services such as GoogleMap.

This question of localization raises the more fundamental question of the choice of the referential used to identify buildings and postal addresses useful for navigation (cadastral parcels, building footprints, address database, etc.). Although apparently simple, this issue is not trivial as the precise positioning of buildings is essential for building damage assessment in dense urban areas for inspectors not familiar with the survey area. In the case of the exercise, the referential in use did not allow to have a postal address.

Practitioner Paper -Track Name Proceedings of the 19th ISCRAM Conference -Tarbes, France May 2022 Hedi Karray, Antonio De Nicola, Nada Matta, Hemant Purohit

Once the building was located, the in-situ entry of the survey form via the application proved to be functional, even if many inspectors pointed out the need to improve the navigation within the form, in particular by reproducing the logical path of its paper version, as well as by offering a synthetic view of the information before validation. A valuable benefit of digital entry via the application was the ability to attach photos taken in the field. Another strong point of the application is the ability to embed different technical reference forms: French inspectors were able to work on the AFPS system, while Spanish and Andorran inspectors used the ACE system. When the reference forms result compatible each other (as in this case), the digital management of the form allows different inspectors to collaborate effectively even if they do not know each other and are used to different assessment plan.

Some inspectors complained that it was difficult to get feedback from the DAC. The application, at its current stage, does not include any protocol for inspectors to communicate with DAC. Furthermore, once an assessment task is validated by an inspector, the result is automatically transmitted to DAC and the task disappears from the app. This is very frustrating for the inspector and possibly harmful when the inspector needs to review tasks, by request of the DAC, which is a fairly common issue at the beginning of early damage assessment investigations. Thus, many inspectors ask for an overview of their work and neighbors', as well as getting possibility to reopen and correcting tasks already completed. Many inspectors also advocate the use of both paper and digital devices, and entering only information on the application that is strictly useful to DAC.

CONCLUSION

Unlike other very seismic European countries, carrying out exercises such as the one described in this article is critical for regions with moderate seismicity such as the Pyrenees. The exercise thus made participants aware of the criticality of the function of damage assessment. Beyond the organizational issues that must be dealt with on a case-by-case basis depending on the civil protection organization specific to each country, we were able to discuss the question of the tools to be deployed to support the coordination and the realization of postseismic damage assessment.

In this regard, the POCRISC digital tool tested as part of the exercise was favorably appreciated. Although improvements needs to make it more effective, the majority of participants to the questionnaire would like to use it in the future (Figure 7). While many tools already exist for digital input of diagnostic results in the field and raising them to a level of coordination, the originality and added value of the POCRISC tool lies in its bidirectional mode, allowing in particular the allocation duties to inspectors. However, the feedback also shows that the use of highly automated tasking systems, such as the Pocrisc platform, should not distract stakeholders from the need for frequent feedback between inspectors in the field and their points of contact in DAC. Furthermore, the conduct of such damage assessments, which can involve many different entities, sometimes from several countries, raises the question of the interoperability of procedures and tools. This question deserves to be addressed at the international level, and with regard to Europe, within the framework of the European Civil Protection Mechanism (UCPM).

  Paper -Track Name Proceedings of the 19th ISCRAM Conference -Tarbes, France May 2022 Hedi Karray, Antonio De Nicola, Nada Matta, Hemant Purohit of the function of the participants in the exercise by country This main purpose led three specific objectives:1. To test the digital platform developed by the DeveryWare company within the POCRISC project. It is composed of a mobile application for field inspectors and a web GIS tool for coordinators, and allows planning building assessment tasking, data entry in the field, and results monitoring from the DAC (Martinez and Goula, 2019).

  Paper -Track Name Proceedings of the 19th ISCRAM Conference -Tarbes, France May 2022 Hedi Karray, Antonio De Nicola, Nada Matta, Hemant Purohit

Figure 2 .Figure 3 .

 23 Figure 2. Functional representation of the technical and organizational "damage assessment" system used in the exercise

Figure 4 .

 4 Figure 4. Participant satisfaction with DAC operations (number of responses received)First, the action of the DAC is generally judged positively. A particular level of satisfaction was expressed concerning the composition of the workgroup and its management. It was appreciated that the coordination of the associative and firefighters' systems was brought together within the same unit. Another positive highlight was about the delegates appointed to represent the various international teams supporting the building damage assessment. Although the official language was French, the experts were able to understand each other. To improve the efficiency of the work of the DAC, and in particular for the right interpretation of the results of the assessments and the rapid exploitation of information got from the inhabitants, some participants suggested

Figure 5 .

 5 Figure 5. Screenshots of the POCRISC platform: mapping from the mobile application (left) and the coordination tool (center), and coordination dashboard (right)

Figure 7 .

 7 Figure 7. Participants' desire to use the POCRISC application in the future (number of responses received)

ACKNOWLEDGMENTS

The work presented in this article was conducted within the framework of the POCRISC project co-financed by the European regional development fund (FEDER) through the Spain France Andorra Interreg V-A program (POCTEFA 2014(POCTEFA -2020)). The authors would like to warmly thank all the organizers and participants to the exercise whose feedback is treated here.