Patrice Meunier

Peter J Diamessis

Geoffrey R Spedding

Self-preservation in Stratified Momentum Wakes

A general model is described for drag wakes in a linearly stratified fluid, based on the selfpreservation of the flow. It is assumed that the buoyancy-controlled self-similar wake expands in the horizontal direction due to turbulent diffusion and in the vertical direction due to viscous diffusion. The mean characteristics of the wake (height, width and velocity defect) are analytically derived and show good agreement with existing data from experimental and numerical results.

Moreover, the three regimes previously found in the literature that characterise different dynamical phases of the wake evolution are recovered, and two new regimes are found. The model allows for prediction of characteristic length and velocity scales at the high Reynolds numbers of large-scale applications of geophysical and naval origin.

I. INTRODUCTION

Research on stratified wakes has both meteorological (flow over islands, mountains or sea-mounts) and naval applications (submerged bodies). In each case, the Reynolds number (Re = U B D/ν, for an object of diameter D in a uniform freestream U B ) is several orders of magnitude higher than obtained in both laboratory experiments and numerical simulations.

By contrast, the appropriate internal Froude number (F = 2U B /N D, for a fluid of buoyancy frequency N = -(g/ρ)(∂ρ/∂z), which ranges from 10 -1 to 10 3 , can be readily obtained experimentally and numerically. At sufficiently large values of Reynolds number and Froude number, the initial (near) wake is fully-turbulent in all three directions. Chomaz et al. [START_REF] Chomaz | The Structure of the Near Wake of a Sphere Moving Horizontally in a Stratified Fluid[END_REF] found the necessary criterion on F to be F ≥ 4.5, and a minimum value of F 4 was

shown in scaling arguments [START_REF] Spedding | The long-time evolution of the initially-turbulent wake of a sphere in a stable stratification[END_REF] and later in experiments [START_REF] Spedding | Turbulence, Similarity Scaling and Vortex Geometry in the Wake of a Towed Sphere in a Stably Stratified Fluid[END_REF] where F and Re were varied independently. In [START_REF] Spedding | The Evolution of Initially Turbulent Bluff-Body Wakes at High Internal Froude Number[END_REF] it was demonstrated that all wakes for 4 ≤ F ≤ 240 have similar scaling behaviour, provided Re is also sufficiently large (an approximate minimum value of 5 × 10 3 was suggested). Physically, the reason for the similar scaling is that since local wake velocities decrease, while local length scales increase, then a local Froude number based on these scales will decrease so that it becomes of order one, and thus the late stages of even a weakly stratified wake are eventually dominated by buoyancy effects.

The observations were consistent with previous experiments, simulations and analysis of decaying stratified turbulence, where buoyancy forces start to act at N t ≈ 1 when the local dynamics experience the onset of buoyancy control (see Riley and Lelong [START_REF] Riley | Fluid Motions in the Presence of Strong Stable Stratification[END_REF] for a review). In experiments on self-propelled slender bodies, Lin and Pao [START_REF] Lin | Wakes in Stratified Fluids: a Review[END_REF] showed that buoyancy begins to affect the flow at N t = 2, suspending the expansion of the wake in the vertical direction.

This was followed by the emergence of large coherent structures as shown by dye pictures, which also showed that their aspect ratio (horizontal length scale compared with vertical extent) was large. The origin of these structures was later traced [START_REF] Spedding | The Streamwise Spacing of Adjacent Coherent Structures in Stratified Wakes[END_REF] to Kelvin-Helmholtz free shear-layer instabilities generated at the edge of the near wake and the gradual supression of vertical motions by the density gradient ensures that only these so-called pancake vortices persist into the late wake.

Ref. [START_REF] Spedding | The Evolution of Initially Turbulent Bluff-Body Wakes at High Internal Froude Number[END_REF] found that two different regimes could be distinguished in the velocity field of the intermediate and late wakes. Initially, decay rates of horizontal mean velocity were found to be surprisingly low, with U ∼ N t -0.25 (instances where the defect velocity even increases have been reported [START_REF] Bonnier | Experimental investigation of the collapse of a turbulent wake in a stably stratified fluid[END_REF]). There is then a transition to a steeper decay rate with exponents of approximately -0.76, with the transition time apparently constant in buoyancy timescales of N t ≈ 50. (While this transition time appeared to be independent of F for the towed sphere experiments, a survey of the literature suggested large variation from N t = 10 to N t = 180 in the transition time between different laboratory or numerical experiments.) The subsequent steeper decay rate was maintained for all measurable times up to N t ≈ 2000. The preceding intermediate regime is one where vertical velocities gradually become small, associated with radiation of internal waves from the wake to the ambient, and, it was conjectured, with conversion of potential to kinetic energy close to the wake centre. This adjustment period was termed the non-equilibrium regime (NEQ). The subsequent, late wake is characterised by the relative insignificance of vertical velocities and largely-horizontal motions account for almost all the remaining kinetic energy in the flow. The flow field however, is not two-dimensional (and its decay rate is not the same as for a two-dimensional wake, which would have a -0.5 exponent) because there is significant variability in the vertical, and the horizontal vorticity marking the shearing between neighbouring layers is stronger than the vertical vorticity [START_REF] Spedding | Vertical structure in stratified wakes with high initial Froude number[END_REF]. This late wake regime was named the quasi-2D, or Q2D regime.

During both NEQ and Q2D, the wake width grows as N t 1/3 (or x/D 1/3 ), which is the same as would occur in a fully three-dimensional, unstratified turbulent wake. Since growth rates of vertical scales are very slow during NEQ, and since the stratified wake does not grow laterally faster than its 3D counterpart, momentum conservation requires that NEQ is associated with the observed low decay rates. Finally, it was argued by [START_REF] Spedding | The Evolution of Initially Turbulent Bluff-Body Wakes at High Internal Froude Number[END_REF] that the very early wake at moderate to high F would most likely evolve with buoyancy forces playing little part and so a sequence of 3D-NEQ-Q2D was identified as characterising stratified wakes.

The basic phenomenology of the NEQ and Q2D regimes has been replicated also in numerical simulations [START_REF] Gourlay | Numerical modeling of initially turbulent wakes with net momentum[END_REF][START_REF] Dommermuth | Numerical Simulation of the Wake of a Towed Sphere in a Weakly Stratified Fluid[END_REF], but agreement on vertical length scales has been more elusive.

Chomaz et al. [START_REF] Chomaz | Vertical Diffusion in the Far Wake of a Sphere Moving in a Stratified Fluid[END_REF] found that the wake height increases very rapidly in the late wake, and a transition from almost zero growth to rapid growth (but different growth rates than [START_REF] Chomaz | Vertical Diffusion in the Far Wake of a Sphere Moving in a Stratified Fluid[END_REF]) of vertical length scales was reported in further experiments by Spedding [START_REF] Spedding | Vertical structure in stratified wakes with high initial Froude number[END_REF]. Numerical simulations appeared to share similar features [START_REF] Gourlay | Numerical modeling of initially turbulent wakes with net momentum[END_REF][START_REF] Dommermuth | Numerical Simulation of the Wake of a Towed Sphere in a Weakly Stratified Fluid[END_REF], but the setting of the initial vertical length scales according to F was never resolved as the simulations would typically be run for only one finite value of F . This vertical growth of the wake is not yet well understood and precise measurements have been difficult to obtain, both experimentally and numerically.

The experimental results were obtained for the particular case of the wake of a sphere, but were successfully extended to the general case of other bluff bodies [START_REF] Meunier | A Loss of Memory in Stratified Momentum Wakes[END_REF], by considering the momentum thickness as the proper lengthscale rather than the body diameter. For an axisymmetric bluff body, the momentum thickness is defined as

D m = D c D /2
, where c D is the drag coefficient for the bluff body in an unstratified fluid. In fact, the very same wake scalings could be extended to almost all wakes generated by propelled bluff bodies [START_REF] Meunier | Stratified Propelled Wakes[END_REF] (including all those of practical interest), if the momentum thickness is defined

as D m = D c D /2 1 -U 2 C /U 2 B
, where U C is the particular velocity of the self-propelled bluff body for which the wake becomes momentumless. The relevant non-dimensional parameters become a momentum Reynolds number Re m = U B D m /ν and a momentum Froude number

F m = 2U B /N D m .
The empirical scaling laws describing the velocity defect and wake width as developed in [START_REF] Spedding | Turbulence, Similarity Scaling and Vortex Geometry in the Wake of a Towed Sphere in a Stably Stratified Fluid[END_REF][START_REF] Spedding | The Evolution of Initially Turbulent Bluff-Body Wakes at High Internal Froude Number[END_REF][START_REF] Meunier | A Loss of Memory in Stratified Momentum Wakes[END_REF][START_REF] Meunier | Stratified Propelled Wakes[END_REF] apply to any bluff body wake or jet in a uniform, stable density gradient. However, they remain empirical findings, linked by incomplete arguments and a coherent theoretical framework has not been proposed. Moreover, compared with practical applications where Reynolds numbers are usually in the range of 10 6 -10 8 , the limited range of Re of the experiments upon which they are based makes the extrapolation of these scaling arguments to higher Re somewhat speculative. The laboratory experiments show no significant Re dependence over Re ∈ [5 × 10 3 , 2.8 × 10 4 ] and the largest Re in numerical experiment was 10 5 , indicating that the results might at least be only weakly Re-dependent. On the other hand, high Re, high resolution, numerical simulations of a simple stratified flow geometry [START_REF] Riley | Dynamics of turbulence strongly influenced by buoyancy[END_REF] have indicated that as Re increases, more small-scale instabilities of the vertical shear layers develop, becoming a continuous source of small-scale turbulence, and raising the idea that at sufficiently high Re, the large-scale coherent structures seen in laboratory experiment may never develop, or survive. However in the range of Re l ∈ [800, 6400], where l is a numerically-imposed initial length scale of the Taylor-Green vortices, the large-scales were only weakly dependent on Re l , a finding that is consistent with the increased fine structure of the higher Re wake simulations of Dommermuth et al. [START_REF] Dommermuth | Numerical Simulation of the Wake of a Towed Sphere in a Weakly Stratified Fluid[END_REF], but which still produced large-scale structures in the late wake.

In this paper, some scaling relations are derived, based on the evolution of self-similar solutions of reduced equations of motion for stratified momentum wakes with high Reynolds number and high Froude number. Analytical results will be derived for the horizontal and vertical length scales, and for the mean and turbulence profiles. The agreement with existing data from laboratory and numerical experiment will be shown to be good, and the scaling behaviour for high Reynolds number can be clearly shown.

II. A SELF-PRESERVING THEORY A General equations

We will suppose that the fluid is linearly stratified with a constant buoyancy frequency N and a density ρ 0 at the bluff body's height, and write the Navier-Stokes equations in the Boussinesq approximation:

∂u ∂t + (u • ∇) u = -∇p ρ 0 + ν u + ρ ρ 0 g (1)
together with the incompressibility condition:

∇u = 0 (2)
and the equation for the evolution of the density

∂ρ ∂t + u • ∇ ρ = κ ρ. (3)
Since the flow is stationary in the frame of reference moving with the bluff body, U = U (y, z), the velocity can be decomposed as a temporal mean and a fluctuating part u = U + u . The mean velocity is equal to the bluff body velocity U B in the far field, and the wake has a defect velocity of the order of U 0 , as indicated schematically on figure 1. We then follow the standard analysis for the turbulent wake in a non-stratified flow, found for example in Tennekes and Lumley [START_REF] Tennekes | A First Course in Turbulence[END_REF]. By averaging the streamwise component of the momentum equation [START_REF] Chomaz | The Structure of the Near Wake of a Sphere Moving Horizontally in a Stratified Fluid[END_REF], one arrives at:

U ∂U ∂x + V ∂U ∂y + W ∂U ∂z + ∂ u 2 ∂x + ∂ u v ∂y + ∂ u w ∂z = - 1 ρ 0 ∂P ∂x + ν U (4)
Note that on this component of velocity, stratification effects are in fact absent, except insofar as they would lead to non-zero mean values of u w . This is a consequence of assuming w to be small at late times, and thus retaining only the streamwise momentum components. Now, following [START_REF] Tennekes | A First Course in Turbulence[END_REF], we assume that the flow is nearly parallel, so the lengthscale l in the y and z direction is smaller than the lengthscale L in the x direction. Since the focus is on late wake evolution, we may also assume that the velocity amplitude U 0 is much smaller than the tow speed U B , which is valid at least far from the bluff body. The second, third and fourth terms in eq.( 4) can therefore be neglected since they are of order U 2 0 /L, which is U 0 /U B smaller than the first term. The pressure term can be shown to be of the order of ∂ v 2 /∂x by inspection of the leading order terms in the cross-stream momentum equation, which are again negligible with respect to the first term. At high Reynolds numbers, the viscous terms could be entirely neglected at early stages, but will be retained because they will reappear later, as the local Reynolds number decreases in time. Here though, the term ∂ 2 U/∂x 2 is small compared with ∂ 2 U/∂y 2 and may be omitted. Finally, the mean velocity U can be replaced by U B in the first term, which leads to a simple form for the streamwise momentum equation:

U B ∂U ∂x = - ∂ u v ∂y - ∂ u w ∂z + ν ∂ 2 U ∂y 2 + ∂ 2 U ∂z 2 . (5)
It has been shown experimentally that mean profiles are close to Gaussian in both nonstratified wakes [START_REF] Tennekes | A First Course in Turbulence[END_REF] and also in stratified wakes [START_REF] Spedding | Turbulence, Similarity Scaling and Vortex Geometry in the Wake of a Towed Sphere in a Stably Stratified Fluid[END_REF][START_REF] Spedding | The Evolution of Initially Turbulent Bluff-Body Wakes at High Internal Froude Number[END_REF], and an example of the latter is shown in Fig. 2(a) from [START_REF] Spedding | Anisotropy in Turbulence Profiles of Stratified Wakes[END_REF]. Thus we may search for Gaussian solutions to eq.( 5), of the form

U = U B -U 0 exp - y 2 2L 2 y - z 2 2L 2 z , (6)
where the velocity defect U 0 , the wake width L y and height L z are functions of x only. Other solutions might be found [START_REF] Afanasyev | Wakes behind towed and self-propelled bodies: Asymptotic theory[END_REF], but this Gaussian solution is convenient since it is the simplest self-similar solution for a momentum wake.

Under the Boussinesq approximation, the momentum flux

J = ρU B (U -U B )dy dz is equal to ρ 0 U B (U -U B )dy dz.
By integrating (5) on a transverse section, the mean momentum flux can be shown to be independent of the position x and equal to the drag force

F D = c D ρ 0 U 2 B πD 2 /8
, where c D is the body drag coefficient. Thus by defining the momentum thickness as D m = D c D /2, the integration of ( 6) leads to a relation between U 0 , L y and L z :

U 0 L y L z = U B D 2 m /8. (7)
B Initial three-dimensional regime

At high Froude numbers, the stratification is negligible in the early stages and the flow may be expected to be three-dimensional and the mean velocity to be axisymmetric. It is common practice to suppose that the Reynolds stress is proportional to the mean shear ( u v = -ν 3 ∂U/∂y), with an eddy viscosity ν 3 independent of y and z in the 3D regime.

Partial experimental support for this notion has been found in [START_REF] Meunier | A Loss of Memory in Stratified Momentum Wakes[END_REF][START_REF] Meunier | Stratified Propelled Wakes[END_REF] for stratified wakes.

Based on the mixing length model, or based on dimensional grounds, the eddy viscosity should be proportional to U 0 L y , which defines a turbulent Reynolds number R 3 = U 0 L y /ν 3 for the 3D regime. Bevilaqua & Lykoudis [START_REF] Bevilaqua | Turbulence Memory in Self-Preserving Wakes[END_REF] found

R 3 = 4
in the case of the sphere, for the same definitions of the mean profile, and this value will be used in the following.

We will also assume that the Reynolds number is sufficiently high to neglect the viscous terms in the 3D stage (it will be shown to be true when F << Re 3 ). The momentum equation thus becomes a standard diffusion equation,

U B ∂U ∂x = U 0 L y R 3 ∂ 2 U ∂y 2 + U 0 L z R 3 ∂ 2 U ∂z 2 , (8)
except that the diffusion coefficient U 0 L y /R 3 is now x-dependent. Imposing a Gaussian form of the mean profile ( 6) into ( 8), leads to U0

U 0 + y 2 L 2 y Ly L y + z 2 L 2 z Lz L z = U 0 R 3 L y U B y 2 L 2 y -1 + U 0 R 3 L z U B z 2 L 2 z -1 , (9)
where the dot denotes the derivative with respect to the downstream distance ( U0 = dU 0 /dx).

The Gaussian form introduced in ( 6) is a solution of the Navier-Stokes equations if and only if eq. ( 9) is valid for any y and z. Since this equation only contains 3 types of terms (terms in y 2 , terms in z 2 and terms independent of y and z), (6) is a solution if and only if their three coefficients vanish, which leads to three independent equations:

Ly = U 0 R 3 U B ( 10
) Lz = U 0 R 3 U B ( 11
) U0 U 0 = - U 0 R 3 L y U B - U 0 R 3 L z U B ( 12
)
Since there are three variables U 0 , L y and L z , a Gaussian solution can exist. By summing (10)/L y +(11)/L z +(12), we recover that U 0 L y L z is constant, as was found using the momentum flux [START_REF] Spedding | The Streamwise Spacing of Adjacent Coherent Structures in Stratified Wakes[END_REF]. Then, introducing this condition (7) into [START_REF] Gourlay | Numerical modeling of initially turbulent wakes with net momentum[END_REF] and [START_REF] Dommermuth | Numerical Simulation of the Wake of a Towed Sphere in a Weakly Stratified Fluid[END_REF], we also recover the solution given by Tennekes and Lumley [START_REF] Tennekes | A First Course in Turbulence[END_REF]:

L y = L z = D m 3x 8R 3 D m 1/3 (13) U 0 = U B 8 3x 8R 3 D m -2/3 (14)
This solution is valid when the local Froude number (defined as U 0 /N L y ) is larger than one, which is met only close to the bluff body. Indeed, this local Froude number decreases as 1/x and reaches unity for x I /D m = R 3 F m /6 ≈ 0.66F m . This transition distance is in good agreement with previous experimental results [START_REF] Lin | Wakes in Stratified Fluids: a Review[END_REF][START_REF] Spedding | The Evolution of Initially Turbulent Bluff-Body Wakes at High Internal Froude Number[END_REF], where it was shown, or inferred, that the wake is 3D until N t ≈ 2, i.e. until x I /D m = F m in our units. W e may also note that since the form of the reduced equations ( 5) and the presumed existence of self-similar solutions (6) requires that x/D is large, then the simultaneous requirement of large x/D and large local F limits this model system to flows with large initial F . Only then can a self-similar flow be imagined before the transition distance, x I . In fact, the exact value of this transition distance very weakly influences the late stages and we will assume that the transition occurs for x I /D m = F m . The vertical width of the wake at this point is thus:

L v = D m 3F m 8R 3 1/3 (15)
This classical solution, with no stratification effects, will now be extended into the stratified regime, which occurs for x larger than x I .

C Stratified regime

In the late wake, vertical velocity fluctuations eventually subside as one component of the wake disturbance propagates away in the form of internal waves [START_REF] Spedding | Anisotropy in Turbulence Profiles of Stratified Wakes[END_REF], leaving residual motions whose time evolution is much slower [START_REF] Riley | Nonlinear Properties of Internal Waves[END_REF][START_REF] Lighthill | Internal Waves and Related Initial-Value Problems[END_REF]. Consequently the vertical Reynolds stress u w becomes much smaller than the horizontal Reynolds stress u v in the far-wake, strongly-stratified regime. The experimental results of Fig. 2(b) compare these two terms at N t = 44 and show that the first term is about an order of magnitude smaller than the second.

As a convenient simplifying assumption, valid at least for the far wake, we will therefore neglect the vertical Reynolds stress in the averaged momentum equation [START_REF] Riley | Fluid Motions in the Presence of Strong Stable Stratification[END_REF]. However, we should note how neglecting u w removes much physics from this intermediate regime. All contributions from internal wave motions which lead to significant peaks in experimental measurements of u w as late as N t = 15 [START_REF] Spedding | Anisotropy in Turbulence Profiles of Stratified Wakes[END_REF] are omitted, as are any production terms where energy is drawn to the mean flow from the turbulent motions. Anisotropy of the dissipation rate tensor and of the velocity and vorticity energy balance has been noted and discussed in simulations of stratified turbulence [START_REF] Itsweire | Turbulence in Stratified Shear Flows: Implications for Interpreting Shear-Induced Mixing in the Ocean[END_REF][START_REF] Smyth | Anisotropy of turbulence in stably stratified mixing layers[END_REF] and specifically for DNS of stratified wakes [START_REF] Gourlay | Numerical modeling of initially turbulent wakes with net momentum[END_REF][START_REF] Dommermuth | Numerical Simulation of the Wake of a Towed Sphere in a Weakly Stratified Fluid[END_REF]. The analysis that follows must be considered one where such intermediate dynamics are ignored, valid at the latter stages of the wake evolution only when w ≈ 0 and u w << u v . It will prove instructive to see how much (or how little) of the mean flow dynamics can be found with this strong simplification.

We may recall that one of the purposes of this model is to find simplified expressions that both respect current results from laboratory and computational work, and at the same time give explicit predictions on how decaying turbulence scales at the much higher Reynolds numbers characteristic of ocean conditions. Higher Reynolds number simulations are just now becoming available, and some [see 15] raise the question as to whether the pancake vortices may be unstable with respect to the mean shear. (See also Fig. 5(c) of Waite & Bartello [START_REF] Waite | Stratified turbulence dominated by vortical motion[END_REF] for small scale instabilities at moderate stratifications.) These instabilities (Kelvin-Helmholtz) could lead to non-zero vertical Reynolds stresses, and if this is shown to be the case then the strong assumption of u w << u v will need to be modified.

The turbulent motion in the horizontal direction will continue to be modelled as a turbulent diffusion and so we will continue to assume that the horizontal Reynolds stress is proportional to the mean shear ( u v = ν 2 ∂U/∂y), consistent with available experimental evidence (see Fig. 2b). The eddy viscosity is therefore now characterized by a two-dimensional

Reynolds number (R 2 = U 0 L y /ν 2 ). It is two-dimensional because the supression of vertical velocities by the stratification at late times (N t ≥ 40, for example) has allowed us to assume that u w << u v . This flow regime is denoted BC for buoyancy-controlled, where the effect of the stratification is supposed to be sufficiently strong that the averaged equations of motion in a horizontal plane have no explicit buoyancy terms in them. Note that by neglecting the buoyancy terms entirely, this approach differs from the usual scaling expansion where F << 1 (e.g. [START_REF] Riley | Nonlinear Properties of Internal Waves[END_REF][START_REF] Lilly | Stratified Turbulence and the mesoscale variability of the atmosphere[END_REF][START_REF] Billant | Self-similarity of strongly stratified inviscid flows[END_REF]).

In late wakes of towed bluff bodies in stratified fluids R 2 was found to be close to 15, regardless of initial conditions (within 30%) [START_REF] Meunier | A Loss of Memory in Stratified Momentum Wakes[END_REF], so this numerical value is retained in the following. By neglecting the vertical Reynolds stress while retaining the horizontal Reynolds stress in (5), we reach again a standard diffusion equation for the buoyancy-controlled flow,

U B ∂U ∂x = ( U 0 L y R 2 + ν) ∂ 2 U ∂y 2 + ν ∂ 2 U ∂z 2 . ( 16
)
As in the 3D regime, a Gaussian solution is introduced ( 6) into [START_REF] Tennekes | A First Course in Turbulence[END_REF], which leads to an equation with only terms in y 2 , terms in z 2 and terms independent of y and z. The Gaussian form ( 6) is thus a solution if and only if the three coefficients of these terms vanish, corresponding to the three following equations:

Ly = U 0 R 2 U B + ν U B L y (17) Lz = ν U B L z (18)
U0

U 0 = - U 0 R 2 L y U B - ν U B L 2 y - ν U B L 2 z (19)
As before, the conservation of the momentum flux is recovered (7) by summing (10)/L y +(11)/L z + [START_REF] Chomaz | Vertical Diffusion in the Far Wake of a Sphere Moving in a Stratified Fluid[END_REF]. The equation for the vertical wake width ( 18) is characteristic of a laminar diffusion and can be integrated by setting initial conditions

L z = L v at x/D m = F m to arrive at L z = L 2 v + 2D 2 m Re m (x/D m -F m ). ( 20
)
This solution is plotted in Fig. 3(a) as a dotted line for x/D m > F m , together with the non-stratified solution (13) for x/D m < F m . For small x/D, L z ≈ L v in eq.( 20) and vertical growth is at first negligible. The second term eventually becomes larger than L 2 v (i.e. at sufficiently large x/D), and when these two terms in the square root of eq.( 20) are of equal magnitude, a second transition point can be identified at a downstream distance of the order of the Reynolds number:

x II /D m = Re m 2 3F m 8R 3 2/3 . ( 21
)
The wake height then increases as √

x due to viscous diffusion as the wake enters the quasi-2D regime (Q2D). It can be noted that for higher Reynolds numbers, the NEQ and buoyancycontrolled (BC) regimes will last longer. Since the NEQ regime in particular is associated with quite rich dynamics and complex interactions between internal waves and turbulence, the implication is that at full scale, these complex fields will assume even more importance in turbulence evolution in a stratified ambient. The possible consequences in geophysical and naval applications will be discussed in the conclusion.

To calculate the horizontal wake width, we introduce ( 7) into [START_REF] Spedding | Anisotropy in Turbulence Profiles of Stratified Wakes[END_REF], which leads to:

L y Ly = D 2 m 8L z R 2 + ν U B
This can be integrated by introducing the expression of the vertical wake width [START_REF] Riley | Nonlinear Properties of Internal Waves[END_REF], with

initial conditions L y = L v at x/D m = F m : L y = L 2 v + D m Re m 4R 2 L 2 v + 2D 2 m Re m ( x D m -F m ) -L v + 2D 2 m Re m ( x D m -F m ) 1/2 (22)
The solution is plotted in Fig. 3(a) as a dash-dotted line. In the BC regime (x I < x <

x II ), the horizontal wake width increases asymptotically (when

F m << x/D m << Re m ) as x/L v R 2 D m /2
, with the same power law that was found theoretically for a two-dimensional non-stratified wake [START_REF] Tennekes | A First Course in Turbulence[END_REF]. This regime is entered only after passing through the NEQ phase, which has been discovered experimentally [START_REF] Spedding | The Evolution of Initially Turbulent Bluff-Body Wakes at High Internal Froude Number[END_REF][START_REF] Bonnier | Experimental investigation of the collapse of a turbulent wake in a stably stratified fluid[END_REF]. It appears here not as a regime defined explicitly, but as a transient between 3D and BC stages (note however, that this is simply a consequence of modelling decisions made initially). This transient stage lasts until x/D m = 50F m , independent of the Reynolds number. The BC regime ends at x II defined previously, giving rise to the quasi-2D regime (Q2D), for which the wake width increases more slowly

as x 1/4 : L y ∼ (Re m x/2D m ) 1/4 D m / √ 2R 2 .
This approximation can be obtained by a Taylor expansion of ( 22) assuming x I << x II << x. Finally, at very late stages, a new regime appears, which we denote the viscous 3D regime (V3D), since now the wake width also increases by viscous diffusion as 2νx/U B . This regime starts for downstream distances larger than x III , defined as

x III /D m = Re 3 m 32R 2 2 , (23)
which is obtained when the second and third terms inside the square root of eq.( 22) are equal, i.e. when turbulent diffusion in the horizontal is accompanied by equal or greater molecular diffusion. The flow is expected to be laminar and axisymmetric, since the horizontal and vertical wake width become equal again. It was assumed in the model that the stratified effects would occur before the viscous effects, which is valid if x I << x III , i.e. when F << Re 3 , which is easily met even for moderate Reynolds numbers.

Finally, the theory gives a prediction for the velocity defect U 0 , by introducing ( 20) and ( 22) into [START_REF] Spedding | The Streamwise Spacing of Adjacent Coherent Structures in Stratified Wakes[END_REF]:

U 0 = U B 8 L 2 v D 2 m + 2 Re m ( x D m -F m ) -1/2 * L 2 v D 2 m + Re m 4R 2 L 2 v D 2 m + 2 Re m ( x D m -F m ) -L v + 2 Re m ( x D m -F m ) -1/2 ( 24
)
This solution is plotted in Fig. 3(b). In the BC stage, the velocity defect decreases

as U B D m R 2 /xL v /4.
This state is reached after a transient (at least in this framework) stage (the NEQ regime) in which the velocity decreases very slowly. The BC regime is followed by the Q2D regime, in which the velocity defect scales as x -3/4 :

U 0 ∼ √ R 2 (2Re m ) 1/4 (x/D m ) -3/4 U B /8
. This regime ends at x III /D m , and the wake then enters the viscous 3D regime (V3D), in which the velocity defect decreases even faster:

U 0 ∼ (U B D m )/(16Re m x)
. This regime has never been observed experimentally as it occurs for very far downstream distances.

The theory outlined above gives a universal prediction for wake width, height and velocity defect in a stratified wake given by ( 22), ( 20) and [START_REF] Waite | Stratified turbulence dominated by vortical motion[END_REF]. The model recovers the approximate scaling behaviour of the experimentally-determined 3D-NEQ-Q2D progression from fully three-dimensional to quasi two-dimensional (strongly stratified) flow. It also predicts a

Reynolds number dependence in transition lengths between these regimes, and in particular, the NEQ regime extends into a strongly buoyancy-controlled (BC) regime, where the dominating influence of the stratification is to constrain the flow to evolve in two-dimensional layers, when the stratification then, paradoxically, has no direct influence. At the end of the Q2D regime there appears a viscous 3D regime (V3D), in which the wake becomes laminar and grows in all directions by diffusion only. Neither the BC, nor the V3D regimes have been observed yet, because experiment Reynolds numbers and observation times have not been large enough. The model predictions can now be compared with laboratory and numerical experiment for specific values of the Reynolds and Froude number.

III. COMPARISON WITH EXPERIMENT A Variations with the downstream distance

The mean characteristics of the wake predicted by the model were plotted in Fig. 3 at a high Reynolds number, and for a large range of downstream distances. This was designed to define clearly the different regimes and to show their asymptotic behaviours. We will now focus on a common Froude number and Reynolds number pair encountered in the literature, to compare the model to data from both laboratory and numerical experiment.

A momentum Froude number of 8.89, and a momentum Reynolds number of 2250 correspond to F = 4 and Re = 5000 for the canonical towed-sphere example, allowing comparisons with experimental results from three different facilities [START_REF] Chomaz | Vertical Diffusion in the Far Wake of a Sphere Moving in a Stratified Fluid[END_REF][START_REF] Spedding | The Evolution of Initially Turbulent Bluff-Body Wakes at High Internal Froude Number[END_REF][START_REF] Bonnier | Experimental investigation of the collapse of a turbulent wake in a stably stratified fluid[END_REF] and with numerical simulations that used three different methods [START_REF] Gourlay | Numerical modeling of initially turbulent wakes with net momentum[END_REF][START_REF] Dommermuth | Numerical Simulation of the Wake of a Towed Sphere in a Weakly Stratified Fluid[END_REF][START_REF] Diamessis | Scaling laws of high Reynolds number turbulent stratified wakes in LES[END_REF].

First, we compare the horizontal wake width L y in Fig. 4. All experimental and numerical data fall on the model within 30%. The model is thus seemingly in good agreement with the data, even though it does not contain any fitting parameter. Note however, that the experimental growth rates (over 4 ≤ F ≤ 240 and 4.7 ≤ Re ≤ 10.6 × 10 4 ) have a constant power law exponent of 0.35 ± 0.03, which is different from both the early (NEQ/BC:

x 1/2 )
and later (Q2D: x 1/4 ) time exponents of the model. The reason for the apparent agreement in Fig. 3 is Re is low enough for the NEQ and BC regimes to be barely distinguishable. The mixed result of exponents between the two (0.5 and 0.25 respectively), combined with the initial phase of Q2D in the theory gives a result that looks like the data. The prediction is that if Re is high enough (for example, in a field measurement), then the separate regimes will be observed.

The vertical wake height L z is compared in Fig. 5. This measurement is hard to achieve experimentally, and there is an observed dependence of initial wake height on F , which is not taken into account in this figure. The results included here of Chomaz et al. [START_REF] Chomaz | Vertical Diffusion in the Far Wake of a Sphere Moving in a Stratified Fluid[END_REF] were re-analysed and plotted by assuming that the mean profiles were Gaussian so as to calculate an equivalent quantitative value of the wake height. Although these particular results do not all fall within the agreement of the other experimental data (at least at moderate x/D), the slope is in fact quite consistent with a purely viscous diffusion growth process, and not significantly accelerated, as seemed to be the case when shown in their original form( [START_REF] Chomaz | Vertical Diffusion in the Far Wake of a Sphere Moving in a Stratified Fluid[END_REF], Fig. 9). In general, both numerical and experimental results show a large plateau, followed by a steep increase at later stages. This corresponds to the NEQ and BC regimes in which the wake height is constant, followed by the Q2D regime in which the wake height increases by viscous diffusion as √ x. This basic phenomenon therefore requires no more complex an explanation than initial suppression of vertical growth by stratification, followed by viscous diffusion in the vertical at later times, as specified in the model problem. However, it is also important to note that considerable differences persist at late times (Q2D), and that any F -dependence in NEQ/BC remains unaccounted for in this plot.

The mean velocity defect U 0 is compared in Fig. 6. In experiment (dotted line in Fig. 6), the initial decay rate is imagined to be x -2/3 as for an unstratified wake, followed by the non-equilibrium period when measured decay rates are significantly lower x -0.25±0.04 [START_REF] Spedding | The Evolution of Initially Turbulent Bluff-Body Wakes at High Internal Froude Number[END_REF].

(Measurements by Bonnier and Eiff [START_REF] Bonnier | Experimental investigation of the collapse of a turbulent wake in a stably stratified fluid[END_REF] in fact show a possible increase in U 0 at early-NEQ, as shown by the crosses for one of their experiments.) In the model, NEQ is supposed to last from x/D m = F m to x/D m ≈ 50F m . In experiment, NEQ was found to begin at N t ≈ 2 and end at N t ≈ 50 and the equivalent x/D varies with F (as x/D = N t.F/2). U 0 then decreases more rapidly, as x -0.75 , which is characteristic of the Q2D regime: in experiments, the decay exponent was found to be -0.76 ± 0.12. The agreement between model predictions (solid line) and laboratory (dotted line, crosses) and numerical (open symbols) experiment is good given that all numerical and experimental measurements fall within 50% of the model prediction. Again, the NEQ and BC regimes of the model are very close at this Re, and the net effect is to mimic the experimental results reasonably well. The collapse of points in the Q2D regime is also good. Fig. 6 can be viewed as a consequence of momentum conservation, given Figs 4 and 5, and just as any F -dependence is omitted from Fig. 5, so it is also absent in Fig. 6.

The following section considers the F and Re dependence in the model and experimental data in more detail.

B Dependence on the Froude and the Reynolds number

By varying the Froude number over almost two decades, Spedding [START_REF] Spedding | The Evolution of Initially Turbulent Bluff-Body Wakes at High Internal Froude Number[END_REF] showed that the velocity defect scales as (N t) -0.76 F -2/3 at the beginning of the Q2D regime. This dependence on the Froude number can be recovered theoretically by looking at the velocity defect in the BC regime, where

U 0 ∼ 1/ √ xL v ∼ (N t) -1/2 F -2/3
. The dependence differs slightly in the Q2D regime (U 0 ∼ (N t) -3/4 F -3/4 ), but such variations might be difficult to distinguish in practice.

The primary feature of stratified wakes is that the wake height saturates at a specific vertical lengthscale L v , which can be readily deduced from experimental and numerical results by looking at the value of the initial plateau of the wake height. These values are compared in Fig. 7 with the theoretical prediction given by Eq. ( 15). The model predicts that L v scales as F 1/3 , while it was found to vary as F 0.6 experimentally [START_REF] Spedding | Vertical structure in stratified wakes with high initial Froude number[END_REF]. The discrepancy is perhaps unsurprising, given the complete neglect of physical mechanisms involving any correlation of vertical velocities, density field structure and internal wave dynamics. Further improvements in the model will be especially important at high Froude number, for example, where L v is underestimated by a factor 2. Although the numerical simulations show good agreement, they do not predict the variation of L v with the Froude number, since they were always performed at low F . Moreover, it is far from a trivial matter knowing how a numerical simulation should be initialised with correct initial length scales where any L v could be truly claimed to be an independent outcome of the model, rather than an input.

Finally, we can determine the downstream distance x II at which the transition between the BC and the Q2D regime occurs. It is plotted in Fig. 8 shows that the model might be improved. This might include improved modeling and/or higher order correction of terms leading to vertical transport, or some way of accounting for initial conditions whose effect could be felt out to x II . Further experiments and numerical simulations over a broad range of Re and run for long times might help to point out ways in which this can be done.

IV. CONCLUSIONS

The general theory developed here predicts the mean profile evolution of a drag wake in a linearly stratified fluid. The model is based on an assumption of eddy viscosity in the horizontal direction, which allows the mean momentum equations to be closed by assuming that the horizontal Reynolds stress is proportional to the mean shear. The (constant) value of the eddy viscosity is chosen from relevant experiments in stratified wakes, and not as an a posteriori fitting parameter. The evolution of the wake in the vertical is modelled by viscous diffusion alone for N t > 1, which is reasonable for the moderate Re in laboratory experiments and numerical simulations. In this respect, the approach is analagous to stratified dipole and turbulence evolution experiments where experimental data were quite closely matched by numerical models with turbulent and viscous diffusion in the horizontal and vertical, respectively. [START_REF] Praud | Decaying grid turbulence in a strongly stratified fluid[END_REF][START_REF] Praud | The structure and dynamics of dipolar vortices in a stratified fluid[END_REF] The averaged equations of motion show that a Gaussian solution can be found and allow an analytical determination of the wake height, the wake width and the velocity defect.

Existing results from the literature for wake height, wake width and velocity defect, from both laboratory and numerical experiment, agree with the theoretical predictions within 50%. The three different regimes found in the literature that characterise decaying stratified flows (3D, NEQ and Q2D regimes) are recovered, and two new regimes are proposed: a buoyancy-controlled (BC) regime which should be observed (as distinct from the NEQ regime) at very high Reynolds numbers, and a viscous 3D regime, which should be observed at very late stages. Note that since the formulation involves self-similar solutions of simplified equations of motion, transients at relatively small x/D, such as the acceleration phase noted by [START_REF] Bonnier | Experimental investigation of the collapse of a turbulent wake in a stably stratified fluid[END_REF], are not accounted for.

These results apply to any self-similar shear flow in a stratified fluid, where a momentum thickness is defined by D m = D c D /2. Such a model can even be extended to the majority of cases of self-propelled bodies [START_REF] Meunier | Stratified Propelled Wakes[END_REF], whenever the wake momentum balance departs from zero by more than 2%; that will be the case for even small accelerations, whenever there is significant wave drag, and whenever the ambient is non-uniform.

The extension to high Reynolds numbers is of interest to many practical geophysical and naval applications. Examples include large-scale submerged bodies and atmospheric wakes of mountains or oceanic wakes of islands and sea-mounts. The mean characteristics of the wake are given analytically by the model in equations ( 20), ( 22) and ( 24) and the previous experimental and numerical results can be extrapolated to high Reynolds numbers using the similarity laws of the model.

One of the principal consequences is that the Q2D regime appears later for higher

Reynolds numbers (at x/D = ReF 2/3 , or N t = ReF -1/3 ). Since the mean velocity decay rates in the intervening NEQ and BC regime are lower than in either the surrounding 3D or Q2D regimes, this scaling behaviour predicts that the high magnitude defect wakes that have been observed in laboratory experiment should be even more evident with higher

Re. In this regard, the model described in this paper bears a certain similarity with another, spectrally based, theoretical model of localized stratified turbulence, [START_REF] Gibson | Marine Turbulence[END_REF] and despite fundamental differences in their formulation, both models identify a signature of the initial Re on the intermediate-to-late-time flow dynamics, which persists for longer times with increasing

Re.

The model could be extended to more specialised cases, such as bluff body wakes with an angle of attack [START_REF] Gallet | Empirical scaling of antisymmetric stratified wakes, to appear[END_REF], and to the particular case of exactly momentumless wakes. In both cases, the mean profiles are not simple Gaussians and it would be interesting to test other scaling functions.

The support of ONR Grant no. N00014-04-1-0034 administered by Dr. R. Joslin is most gratefully acknowledged. x -3/4

x -1/2 x -2/3

x / D m U 0 / U B FIG. 3: Evolution of (a) the wake height L z (dotted line) and wake width L y (dash-dotted line), and of (b) the velocity defect U 0 , given by the model: Eqs.( 20),( 22) and ( 7) respectively.

The thin solid lines correspond to the asymptotic predictions for each stage. The thin dashed line corresponds to the standard theory for a homogeneous fluid ( 13), [START_REF] Meunier | Stratified Propelled Wakes[END_REF]. Same caption as in Fig. 4. Experimental results from [START_REF] Bonnier | Experimental investigation of the collapse of a turbulent wake in a stably stratified fluid[END_REF] for F m = 13.3 and Re m ≈ 3 × 10 3 are also shown as × symbols. The uncertainties in the experimental results [START_REF] Spedding | The Evolution of Initially Turbulent Bluff-Body Wakes at High Internal Froude Number[END_REF] is of the order of 40%.

  as a function of the Froude and the Reynolds number. While the general dependence of x II as Re m F , for any given Re m or F m , the model always overestimates x II , which again

FIG. 1 :FIGURES 2 FIG. 2 :

 122 FIG. 1: Schematic of the wake created by a bluff body of diameter D translated horizontally at U B in a linearly stratified fluid.

F m = 20 and

 20 Re m = 50 × 10 3

FIG. 4 : 9 ,

 49 FIG.4: Time evolution of the wake width L y for a sphere at F m = 8.9 and Re m = 2.25×10 3 .The model predictions (solid line) are compared with the experimental results from[START_REF] Spedding | The Evolution of Initially Turbulent Bluff-Body Wakes at High Internal Froude Number[END_REF] (dotted line). Numerical simulations (open symbols) from[START_REF] Dommermuth | Numerical Simulation of the Wake of a Towed Sphere in a Weakly Stratified Fluid[END_REF] ( ) for F m = 8.9, Re m = 4.5 × 10 3 , from[START_REF] Gourlay | Numerical modeling of initially turbulent wakes with net momentum[END_REF] ( ) for F m = 22.2, Re m = 4.5 × 10 3 and from[START_REF] Diamessis | A spectral multidomain penalty method model for the simulation of high Reynolds number localized incompressible stratified turbulence[END_REF] (•) for F m = 8.9, Re m = 2.25 × 10 3 are also shown. The uncertainties in the experimental results[START_REF] Spedding | The Evolution of Initially Turbulent Bluff-Body Wakes at High Internal Froude Number[END_REF] is of the order of 25%.

FIG. 5 :

 5 FIG.5: Temporal evolution of the wake height L z for F m = 8.9 and Re m = 2.25 × 10 3 . Same caption as in Fig.4. Experimental results from[START_REF] Chomaz | Vertical Diffusion in the Far Wake of a Sphere Moving in a Stratified Fluid[END_REF] for F m ≈ 8.9 and Re m ≈ 2.25 × 10 3 are also shown by + symbols. The uncertainties in the experimental results[START_REF] Spedding | The Evolution of Initially Turbulent Bluff-Body Wakes at High Internal Froude Number[END_REF] is of the order of 25%.

FIG. 6 :

 6 FIG.6: Time evolution of the mean velocity defect U 0 for F m = 8.9 and Re m = 2.25 × 10 3 .

7 :FIG. 8 :

 78 FIG. 8: Downstream distance x II of the second transition, between a buoyancy-controlled (BC) regime and a quasi-2D regime (Q2D), as a function of (a) the Froude number and (b) the Reynolds number. Caption as in Fig. 7. solid line corresponds to Eq. (21).


Bernard Bel
email: bernard.bel@lpl-aix.fr

Technology at the Meeting Point of Hardware, Software and 'Mindware'

The aim of this paper is to reflect upon the impact of technology on data collection, analysis and interpretation in a work environment for the sharing of research material, tools and methods by experimental and field linguists. An analogy is drawn between expectations of this approach and successful contributions of experimental/computational techniques to ethnomusicology in the past decades. The author is in charge of the development and maintenance of the Speech & Language Data Repository (SLDR), a submission site on the OAIS model for the long-term preservation of linguistic resources. Items in the repository are generic, which makes it possible to extend the notion of corpus to all kinds of primary data collected during experimental or field sessions. This flexibility has an incidence on the life cycle of research projects, as exemplified by an 'event-driven' project on the documentation and revitalisation of rare local languages conducted in narrow collaboration with the development of the archival system.

Background

A research engineer in a multidisciplinary speech research laboratory (Laboratoire Parole et Langage), 1 the author is in charge of the development of the Speech & Language Data Repository (SLDR), 2 a free-of-charge service for sharing oral/linguistic data and archiving it with the help of procedures compliant with the OAIS model for longterm preservation. 3 This service has been implemented in the context of a pilot project coordinated by TGE-Adonis in 2008-2010. 4 An innovative aspect of SLDR is its ability to cope with the life cycle of research projects from the initial description of resources in the making to their long-term preservation in an institutional archive. 5 This implies a trade-off between the versatility of data/metadataupgrading versions and setting up their access rightsand legal constraints associated with the use of a public archive. Access rights must stay compliant with the French heritage code (Code du patrimoine) which has provision for retention periods with respect to personal data (Bel, 2011). In order to assess the relevance of implemented features, priority was given to checking in great detail the OAIS model on material produced by a small number of projects in very different domains. In addition, new projects have been undertaken along parallel lines with the development of SLDR, thereby raising issues on methodology in terms of technical performance as well as interactions between archive curators, research scholars and project 1 http://lpl-aix.fr 2 http://sldr.org 3 Open Archival Information System, http://public.ccsds.org/publications/archive/650x0b1.pdf 4 TGE-Adonis, http://tge-adonis.fr. The set of working papers and reports produced during the pilot project is available from a public archive: http://sldr.org/ark:/87895/1.4-187408 5 Centre Informatique National de l'Enseignement Supérieur (CINES), http://cines.fr participants/informants. In this context, a project dealing with the documentation and revitalisation of a 'forgotten' local language in the North Occitan area (patois de Valjouffrey)6 was launched in 2009 under the direction of sociolinguist Médéric Gasquet-Cyrus. The author is involved as a collaborator and sound engineer. The project team is now in charge of a cross-disciplinary work group dealing with cross-fertilisation (and contradictions) between experimental and field approaches in linguistics.7

Early investigations in ethnomusicology

To some extent, the Valjouffrey project and, more generally, linguistic resource collection and analysis projects taking advantage of new technology, are reminiscent of issues raised by ethnomusicology in the early 1980s. In those days, new tools and methods were being developed for the study of productions and interactions in musical performance and training. The main targets of this investigation were the tonal and rhythmic systems of North Indian classical music, the former of which had been a subject of speculative debate for more than two centuries (Bel, 1988; 1992). The challenge of a 'hard-science' study was to reconcile the approach of systematic musicology -looking at music as material lending itself to structural analysis -with that of musicology centred on musicians and processes of creation/reception/institutionalisation (Bel & Bor, 1984; Bel & Vecchione, 1992). Significant results had been achieved owing to the combination of two methodologies: (a) collecting the largest possible amount of data from musical performances in a format suitable for statistical analysis, and (b) constructing a computational model of music production/perception reflecting human processes and evaluated by its own informants, i.e. inductive learning techniques associated with an expert system 8 (Bel & Kippen, 1989).

Figure 1: A flowchart of interactions in an expert-system setup for the identification of drum improvisation 'languages' in North India (Kippen & Bel, 1989).

Analysis of oral poetry

In 1995 the author became aware of a monumental documentation work conducted for several decades in rural Maharashtra by a group of social activists and scholars under the banner of Centre for Cooperative Research in Social Science (CCRSS) 9 and Village Community Development Association (VCDA). 10 In the context of action-research projects aiming at the emancipation of down-trodden communities, the team was addressing forms of expression and communication displaying a characteristic continuity between 'traditional' and 'modern' thought processes. Among these, social animators had been involved in the collection of songs composed and performed by peasant women at dawn during their work at the grindmill. At this stage of the project, more than 100,000 song texts have been transcribed (in Marathi devan!gar" script) and their contents analyzed in the framework of a detailed semantic classification scheme. This corpus has been stored in a relational database (see figure 2) linking texts with information on performers, villages, pictures and an index of more than 100 hours of sound recordings highlighting their specific modes of performance (Bel, Caelen-Haumont & Rairkar, 2000). The entire corpus is in the process of being shared in open access along with English translations of texts and all sound fragments listed in the index. 11 This knowledge base became fully operational after the implementation of a LEXICON table containing lexemes and words from which a script can be activated to compile occurrences of their written variants in the SONGS database and a profile of these occurrences with respect to spatial location (districts and talukas), periods of time and the social status of performers. This query tool was used extensively by Guy Poitevin and Hema Rairkar to capture semantic and contextual information about concepts specific to the oral poetic language shared by peasant women of all classes. This process facilitated the work of extracting thematic corpora12 and using them for publications (Poitevin & Rairkar, 2008; Bel, ed., 2009).

Figure 2: The relational database of grindmill songs at CCRSS in 1996.

New trends

The notion of 'corpus'

Designing SLDR as a generic submission site for an OAIS archive led us to redefine a 'corpus' as a nonrestrictive set of primary data collected during experimental or field sessions. In experimental linguistics, corpora may include audio/video recordings as well as physiological activity measurements: endoscopy, evoked potentials, palatography, etc. In field sessions video recording is becoming systematic for a better tracking of interactions and growing interest in the analysis of gestures and facial expressions. Sound recordings are of higher quality thanks to head-worn microphones recorded on multiple separate tracks.

In order to preserve and share 'historical' corpora (such as EUROM13 ) it was necessary to accept that the information package of an information package in category 'primary data' may include secondary data (annotations etc.).

In our field research, all participants have been incited to hand over informative documents from various sources which in the long term might become indispensable for a proper recollection of contextual information associated with interactions and interviews: photographs, drawings, written notes, maps, computer documents etc.

Our broad interest in primary data is consistent with the idea of collecting "the largest possible amount of data" which had been successful in ethnomusicology. Indeed, it may look extravagant to store more than 150 Gbytes of sound/video recordings, photographs and written documents in a single Valjouffrey 2010-2011 corpus.14 Critical minds are asking what we plan to do with all this data… There are at least two answers:

1) The data we collect is meant to be shared with the research community at large. Different teams from a wide range of disciplines might get involved: descriptive linguistics, sociolinguistics, linguistic anthropology, social psychology and history, to name a few.

2) The agenda of future research will focus on pieces of information which the original team had judged merely contextual. For instance, the scans of hand-written municipal archives may be appended to the corpus as they are required for drawing genealogic trees. This suggestion is supported by the fact that factual information on lineage is a sensitive topic of discussion in the community under study.

Our claim to collect, preserve and share exhaustive research material beyond the range of linguistics deserves criticism for its lack of methodological insights. An anthropologist or an historian may feel worried that nondirective interactions eluded 'the right questions'; an experimental linguist may claim that a careful planning of lab experiments would highlight language features which an uncontrolled approach is likely to miss (Xu, 2010). All this criticism is relevant though it should be balanced against the patrimonial value of a corpus dealing with rare or endangered languages (Grenoble & Whaley, 2006; Austin & Sallabank, 2011).

Versatile knowledge

We had a debate in the TGE-Adonis pilot project as to whether items in a repository should only contain atomic entities in a fixed format (e.g. a single sound file) or an unrestricted collection of digital documents in multiple formats. Following the extended notion of 'corpus' we (at SLDR) decided to implement a model handling generic information packages. These are automatically segmented (in a manner invisible to users) when the limits of 30,000 files and/or 40 Gbytes imposed by the archive and dissemination sites is reached. File names and hierarchical tree structures are re-encoded in such a way that any complex structure with 'exotic' names (in Unicode format) is acceptable, and downloaded items are reconstructed identical to the source. 15 Maintaining 'heavy' packages in a long-term preservation scheme is problematic since all versions must be preserved by the archive. This led us to divide each item into two forks: a DATA fork containing stable documents (e.g. source recordings and photographs) and a DESC fork containing a set of descriptive documents that may need to be upgraded from time to time. In practice, the DESC fork does not contain primary data, which amounts to calling it 'metadata' in a broad sense. Further, we implemented a management of access rights that makes it possible to modify access attributes via a simple update of descriptive files. 16 This flexible versioning technique has tremendous implications on the phasing of projects associated with the production of linguistic resources: 1) Scholars create records describing the data and resources they plan to elaborate during the project. These records may remain invisible if they wish so. They provide persistent URIs that may be cited in project proposals.

2) Data collected during field or experimental sessions is uploaded to the corpus and stored in medium-term preservation. This type of storage produces versions that may be deleted once the item has been submitted for longterm preservation.

3) Storage in medium-term preservation is identical to storage in long-term preservation with respect to the dissemination of data and metadata (the OAI-PMH repository). Thus it is possible for project teams to immediately start sharing selected parts of their corpus and its annotations. Sharing may be open-access or restricted based on user/institution groups or more restrictive targets authenticated by identifiers and passwords. Thus, medium-term preservation is a period of intensive activity during which data producers may take advantage of sharing partial results with fellow members of the work group as well as other teams and individuals. 4) Once the data contained in a package has become stable, it may be submitted for long-term preservation. Former versions are deleted and a new thread of versioning is started. Since all versions must there from be preserved, submitting a new version should be motivated. Nonetheless, submitting new versions of descriptive files is a routine procedure. This makes it possible to modify access rights once intellectual property issues have been sorted out and informed consent documents signed by participants (with their scans uploaded to the archive as 'descriptive files'). Further, restricting access (to the current and previous versions) of a document is technically easy in case participants withdraw their consent, which must be possible at any time according to the Law. In short, SLDR management makes it possible to modify access rights to documents despite their immutable content in the archive. This flexibility is a significant advance given that failure to collect the full set of informed consent documents before the completion of a project is often dissuasive of handing over its corpus to an institutional archive.

Event-driven field research

Our fieldwork on Valjouffrey and neighbouring dialects may be called 'event-driven' rather than 'protocol-driven'. Language description was not the focus of our work because a priority had been given to creating conditions in which the very small number of speakers (aged from 65 to 82) would feel at ease to communicate and revive a language they had not practiced for two decades. The initial impulse was therefore antagonist with linguistic purism, codification and the dream of reviving 'authentic' or 'traditional' language usage. Despite this, as we shared documents on SLDR wiki pages 17 cited by a local non-profit society interested in the valley's cultural heritage, we received calls and mails from two retired experts, Clément Girard and Marcelle Péry, who had produced unpublished dissertations on the Valjouffrey 18 and Valbonnais 19 patois respectively. They quickly became members of our team.

In 2010-2011, Marcelle Péry organised regional encounters on patois at her home in Valbonnais. These events have been entirely covered in video for public access. 20 In Summer 2010, Julien Gaillard, our senior informant in Valjouffrey, decided on his own to document the names of places and details relevant to mountain climbing in the valley. To this effect he sought assistance from Robert Jamos, an artist and mountain-climber, for the drawing of accurate views of the documented sites. This event oriented our research to the documentation of verbal interactions associated with the elaboration of this toponymy. 21 Event-driven research produces information packages of very diverse contents. Hand-written dissertations have been scanned, archived and disseminated in open access. More than ten hours of old recordings supplied by Clément Girard have been digitized and are available in open access as a complement of his scanned dissertation. Drawings and maps, lexica will be preserved as 'linguistic resources' attached to the corpus, etc. This is further evidence that an archive submission site should be able to manage generic items.

Figure 4: A recording session in Valjouffrey, using headworn microphones and a multitrack recorder.

'Empowering' linguistic research

In the research community at large, i.e. beyond institutional and geographical borders, there is a growing urgency to build distributed research infrastructures of integrated and interoperable language resources and tools that serve researchers and the students in the humanities and social sciences (Wittenburg, 2010). In Summer 2011 partners of the ORTOLANG project22 decided to draw from the experience of SLDR and CNRTL (Centre National de Ressources Textuelles et Lexicales) 23 to build a network infrastructure offering a repository of language data (corpora, lexicons, dictionaries, etc) and tools and their treatment, set up according to the guidelines of CLARIN centres.24 Among arguments of this proposal is the contention that "[…] in our society of information, only the strongly equipped and modelled languages that can be used for automatic language processing, are likely to remain as common languages for work and exchange in scientific, economic, industrial and cultural disciplines.

The remaining ones are likely to be reduced to their simple vernacular dimension."

To meet this challenge, simple descriptive linguistics is being superseded by formal linguistics covering lexical, syntactical or semantic aspects, working with models based on a double validation, explanatory from a linguistics point of view and operational from a dataprocessing point of view. This has given way to the emergence of corpus linguistics (Habert, Nazarenko & Salem, 1997) making it possible for linguists to go beyond the accumulation of language facts and to confront their theories with the effective use of language. This change of paradigm has strong implications both on the production of vast linguistic resources of high quality (corpora, dictionaries and lexicons) and the structuring and standardisation of linguistic knowledge -phonetics, morphology, lexical, syntactics, semantics, etc.imbedded in annotations and metadata.

Annotation

The issue of annotation is an important focus of debate and experimentation in large-scale projects (such as OTIM25 ) notably because of a growing interest in interaction processes, the formal study of which requires taking into account the whole set of modalities and the way they interact. This will render experimental linguistics increasingly attractive (and challengeable) to field linguists who have long been associated with interactional analysis (Gumperz, 1982; Mondada & Markaki eds., 2006).

When dealing with small groups of speakers, work is made easier owing to multitrack recordings of head-worn microphones. We are now working on the automatic preprocessing of separate tracks that will identify the borders of phrase units, perform basic prosodic analysis (MOMEL/INTSINT) 26 and create a stereo mix using panoramic/volume setups completed with a PRAAT TextGrid combining annotations tiers for all speakers. Multimodal information may be captured with the aid of standard video recording, a technique that is increasingly affordable, including 3D which produces material for future automatic gesture/expression analysis. In addition, the technologies of articulatory phonology are bound to become accessible for field research, e.g. the evaluation of speech production (including airflow and pressure),27 ultrasound tongue imaging28 and (to some extent) electromagnetic articulography (Kaburagi & Honda, 2002).

Standardisation

Standardisation is a technical obligation for data repositories playing the game of interoperability. This should not be achieved at the cost of becoming unable to cope with linguistic diversity. As shown by variationist sociolinguists the complexity of real-life communication processes may in term become a subject of systematic research in which regularities are traced at a different level and scale (Tagliamonte, 2011; Labov, 1994, 2001, 2010). We must also keep in mind that standardizing the symbols that make sense to speakers/writers of a local language may be problematic because of the associated loss of cultural identity at the benefit of scholars perceived as 'outsiders'. "Distinct scripts support notions of independence" (Spolsky 2004: 29). Nonetheless, the same local actors feel the need to resort to normalisation as it reinforces their roles as experts in the context of language revitalisation (Thomas-Aguillon, Gasquet-Cyrus & Bel, 2011).

The interest of a formal/computational approach is that background knowledge is made explicit by the training of inductive-inference devices (Bel & Kippen, 1989). This makes it possible to displace the focus of research from the standard description of a linguistic/musical process to questioning the validity of 'background' information mobilised for this description. Individual and group variations are taken into consideration after having been neglected in the process of standardisation. Keeping in mind this care for variation and diversity, research scholars need to elaborate data categories and associated value domains to be shared by humans and machines, for which a sophisticated representation framework is required. Such is the challenge of ISOcat. 29

Informants turn researchers

When trying to identify drum improvisation 'languages' in an expert-system setup in the early 1980s, the author was inspired by a methodology promoted by anthropologist/musicologist John Blacking at the Queen's University of Belfast: let informants participate in both the elaboration and the validation of models describing their expertise. 30 Applied to the grammars of finite languages, this approach lent itself to computational interactions that rendered language identification feasible in an acceptable number of steps (Kippen & Bel, 1992). Dealing with infinite (natural) languages is not so straightforward. It remains that if a certain amount of expertise can be embedded in a computational model, expert speakers/writers will take interest and may eventually feel proud of its consistency. This is one further step in an empowerment starting with assertions of a normative symbolic system (script and spelling).

Conclusion

Our interdisciplinary approach aims at reconciling (a) the quality requirements of experimental linguistics, (b) needs for the preservation and pooling of resources and (c) ethics and quality requirements of field linguistics.

The material versus human and data versus process controversies are always reactivated when technology makes it possible to deal with accurate statistical measurements on a population of presumably similar human subjects (as it is the case in neurosciences) while field research remains cautious of ethnocentrism and individual variation. Thus, musicologists using computational methods are still on a knife edge, and unsurprisingly similar questions are raised by linguists addressing the study of speech and communication processes at large. The ambitious agenda of event-driven field research is to capture and theorize "the motivations and perceptions of speech communities" beyond the initial objective of describing their languages "address[ing] a narrow audience of 'external' linguists with similar concerns…" 33 To achieve this, equipment (hardware) and methods (software) confined in laboratories need to be adapted to their usage in field sessions trying to capture parameters which so far had been studied qualitatively or ignored by linguists.

Success in this direction will depend on the capacity of research scholars to share data, acquisition and analysis techniques, combinations of qualitative and quantitative approaches, interpretation of results, and insights into innovative methodologies -all of which may be termed as 'mindware'. This porosity of research domains is among the major challenges of our Laboratoire Parole et Langage and its unique CEP experimental platform. 34

Figure 3 :

 3 Figure 3: The making of a submission information package on SLDR

Figure 5 :

 5 Figure 5: Electromagnetic articulography in a laboratory setup (Centre d'Expérimentation sur la Parole at LPL).

Figure 6 :

 6 Figure 6: Audrey Thomas-Aguillon, Robert Bois and Hubert Balmet during a work session for the elaboration of a script of patois de Valjouffrey The quest for consistency is an incentive for experts to participate in experiments based on sophisticated protocols, for instance the AMPER study of intonation patterns of Roman languages, 31 designing a script for their

  ,32 or undertaking a detailed inventory of place names that delineate their living space.

	29 ISOcat Data Category Registry, ISO 12620:2009,

http://www.isocat.org/files/12620.html 30 Though Blacking suggested the term 'dialectical anthropology' to designate this approach, this term is now used with a different denotation, see http://en.wikipedia.org/wiki/Dialectical_Anthropology 31 AMPER : Atlas Multimédia Prosodique de l'Espace Roman, http://w3.u-grenoble3.fr/dialecto/AMPER/amper.htm revitalized language

http://sldr.org/wiki/Valjouffrey

Groupe de recherche transversal « Méthodologies linguistiques » in Laboratoire Parole et Langage http://ling-metho.hypotheses.org

Gangubai, oai:sldr.org:sldr000759.

oai:sldr.org:sldr000741

oai:sldr.org:sldr000764

http://sldr.org/wiki/accessRightsSettings_en

http://sldr.org/wiki/ORTOLANG

http://www.cnrtl.fr

http://www.clarin.eu

OTIM -Tools for Multimodal Information Processing, http://lpl-aix.fr/~otim

MOMEL, oai:sldr.org:sldr000031. INTSINT, oai:sldr.org:sldr000032.

EVA2, http://www.sqlab.fr/evaRootUK.htm

SSRC Ultrasound Tongue Imaging, http://www.qmu.ac.uk/ssrc/ultra/

Acknowledgements

This paper is the outcome of passionate discussions with colleagues at LPL and more particularly during our fieldwork on the Valjouffrey project. Médéric Gasquet-Cyrus suggested most recent bibliographical sources.


Bernard Bel
email: bernard.bel@lpl-aix.fr

A Trusted Digital Repository based on the OAIS model with integrated management of access rights

is in charge of an archive submission site called Speech & Language Data Repository (SLDR, www.sldr.org). The aim of SLDR is to preserve data eligible for (field or laboratory) speech/linguistic research or cultural heritage and facilitate its dissemination via non-commercial or shared licences. It is open to research and documentation projects worldwide. Currently (2012), SLDR is storing 262,000 documents dealing with 340 registered users from 46 countries. SLDR is a generic service able to handle any type of item (information package). Resource pooling is constructed on an interoperable system involving two major computing centres (CINES and CC-IN2P3) in a joint project coordinated by the Adonis VLRI, currently the French branch of DARIAH (www.dariah.eu). SLDR for speech, and CNRTL (www.cnrtl.fr) for text, are the resources centres from which a French sub-network of CLARIN (www.clarin.eu) centres is being built: the ORTOLANG project (www.ortolang.fr/english) associated with the CORPUS VLRI (www.corpus-ir.fr). This project is focusing on interoperability following CLARIN guidelines with respect to metadata (DC OLAC, CMDI…), persistent identifiers and controlled vocabulary (ISOcat).

Background of the project

In 2006 the office of the Social Science and Humanities department at the French Centre national de la recherche scientifique (CNRS) issued a call for projects aiming at the creation of digital data repositories for speech research. Two projects were selected under the label Centre de Ressources pour la Description de l'Oral (CRDO): CRDO-Aix and CRDO-Paris supported by Laboratoire parole & langage (LPL) and Langues et civilisations à tradition orale (LACITO) respectively. While CRDO-Paris mostly replicated the design of the existing LACITO archive [START_REF] Michailovsky | A simple architecture for the fine-grained documentation of endangered languages: the LACITO multimedia archive[END_REF], CRDO-Aix was built from scratch after a comparative study of existing data repositories [START_REF] Bel | Le Centre de Ressources pour la Description de l'Oral (CRDO)[END_REF].

In 2008, TGE Adonis (www.tge-adonis.fr) was commissioned to promote the longterm preservation and sharing of oral resources in social sciences and the humanities. Its pilot project involved the two branches of CRDO as submission sites connected with major computing centres: Centre informatique national de l'enseignement supérieur (CINES, www.cines.fr) for long-term preservation and Centre de calcul de l'Institut national de physique nucléaire et de physique des particules (CC-IN2P3, cc.in2p3.fr) for data dissemination [START_REF] Bärring | Hosting of IT services and data for Human and Social Sciences in France[END_REF]. Following the example of spatial agencies, managers opted for the Open Archival Information System (OAIS) promoted by the Consultative Committee for Space Data Systems.

CRDO-Paris and CRDO-Aix became fully operational in Summer 2010 as their longterm preservation modules switched to the 'production' mode. At the term of this experimental phase in 2011, partners were instructed by INSHS (the social science and humanities institute of CNRS) to give up the 'CRDO' acronym. Thereafter, CRDO-Aix was renamed Speech & Language Data Repository (SLDR, www.sldr.org) without modifying its operational process.

A comprehensive implementation of the OAIS model

The Open Archival Information System (OAIS) is ISO 14721 standard. It was imposed by institutions heading the pilot project to comply with formal agreements between the French National Archive, CINES and CNRS. The actual implementation is addressing specific features of oral/linguistic resources, notably:  The diversity of file formats: sound/video, all signals associated with speech/singing, pictures, texts, tables etc.  Secondary data (annotations etc.) and metadata are mutable and extensible.  Multilingual support for descriptive metadata, extra-European scripts, transliteration/annotation standards (IPA etc.)

Preserving data is the primary requirement of long-term preservation. Further, data should be eligible for reuse after an unspecified period of time (typically more than 30 years). To this effect, the project is relying on an institutional archive (CINES) rather than a consortium of computing centres. CINES is beneficiary of the Data Seal of Approval (sldr.org/wiki/DSA) as a first step towards certification. Its commitment is threefold: (1) preserving data and its associated metadata; (2) preserving access right information;

(3) preserving the usability of data which is achieved by migrating file formats (without loss of data) when these are becoming obsolete.

Procedures for submitting and retrieving information packages to/from SLDR are illustrated figure 1. Data is first sent to CINES in Montpellier (left part) and assessed for correctness with respect to long-term preservation: compliance with structural specifications for the Submission Information Package (SIP), acceptance of file formats and consistency of file contents. This automated check-up is purely technical as the informational content (scientific correctness and relevance) remains under the responsability of the submission site. If the SIP is accepted it is completed with archival metadata and assigned an an ARK (Archival Resource Key) identifier to be stored as an Archival Information Package (AIP). This AIP is forwarded along with dissemination information to the dissemination site (CC-IN2P3) in Lyon which is running a Fedora Commons (www.fedora-commons.org) repository.

Access to data is illustrated on the right part of figure 1. Users may get direct access to datastreams on the dissemination site when these are in open access. Otherwise they must proceed to a (non-commercial) transaction with SLDR: identify themselves as a registered user belonging to a group authorized for the particular resource or file, check SLDR licence (and optional ones) for approval, following which SLDR will set up a 'channel' for downloading the datastream(s) from CC-IN2P3. In neither case CINES is involved in the dissemination of data.

SLDR is able to reconstruct the source data and metadata of an item from datastreams stored at the dissemination site. This makes it possible to delete items on the submission site after their successful submission for long-term (or medium-term) preservation.

Dealing with mutable/extendible data

In a given item there are bits of information that remain persistent (e.g. primary data of sound/video resources) whereas others (such as descriptive metadata and access rights settings) may need to be updated more frequently. An institutional archive preserves all versions of successfully submitted information packages. It would be detrimental to upoload a new version of the entire package every time a small amount of its descriptive data or access rights have been modified.

This problem has been solved in the OAIS framework thanks to a sophisticated structure of Submission Information Packages. Each SIP contains two folders: one which is dedicated to persistent data and the other one to "documentary files". It is possible to submit a new version either for the entire package or only its documentary files and/or access rights settings. The latter is called "metadata updating".

Item segmentation, ARK identifiers and PIDs

Technical constraints on the archive and dissemination sites imply limitations of the size of Archival Information Packages. Currently, packages may not exceed 40 Gbytes / 30,000 files. Therefore, large items need to be segmented to several AIPs, a segmentation that remains invisible to users. For example, The Open ANC (sldr000770) containing more than 60,000 files is segmented to seven AIPs. Each AIP is assigned an ARK (Archival Resource Key) identifier. There is no global resolution mechanism for ARK identifiers. We implemented a local name mapping authority, e.g: http://sldr.org/ark:/87895/1.4-183706 points to segment 2 of The Open ANC.

A finer grain of identification is required that does not rely on AIPs. To this effect, a persistent identifier (PID) is assigned to each itemyet not every AIP. We use the Handle system (www.handle.net) and construct PIDs with comprehensive syntax, e.g.: hdl:11041/BeQuali-000532 (case insensitive) points to item BeQuali-000532 whose canonic URL is http://sldr.org/BeQuali-000532 (case insensitive). Some PIDs need to point directly to a document whereas others may point to a descriptor of (a set of) document(s) which may be machine-readable (e.g. metadata in a XML format) or human-readable (e.g. a web page). Currently, in SLDR, a PID pointing to an item displays its descriptive page but suffixes will be used to retrieve metadata in OAI_DC, OLAC, CMDI etc. formats.

PIDs are also assigned to each file contained in each version of an item, e.g.: hdl:11041/swedia-000788_v1_f388 points to file index 388 of version 1 of item swedia-000788. If the version number is not specified then the latest version is fetched. We are planning to implement optional alternate PIDs in which file indexes may be replaced with identifiers derived from original file names so that the same document remains traceable should its index be modified accross versions.

Systematic use of PIDs is an important topic under debate in Virtual Competency

Centres VCC1-VCC3 of the DARIAH network (www.dariah.eu) and the APARSEN Network of Excellence (www.aparsen.eu). Therefore, we avoid implementing early options that might turn out obsolete once a broad consensus has been reached on guidelines conducive to better interoperability.

Integrated management of access rights

France takes advantage from a significant advance on archive law, owing to its Code du patrimoine (the Heritage Code) clarifying the status of "public archive" with a set of formal rules regulating the access to archived documents (Act of 15 July 2008, articles L213 1-5). This framework implies a radical change of practice with respect to the long-term preservation and sharing of digital data, as any public archive shall be immediately in open access with the exception of 24 derogations applicable to certain categories of documents.

According to Art. L213-5, "Any administration […] is compelled to give reasons for denying access to a public archive." This implies that when attempting to download a document under restricted access, users should be given the reason for denial and the date of its future public release. This process is illustrated on figure 3. A sound corpus is publicly available in 'low' resolution (AAC format) whereas the same files in 'high' resolution (WAV format) are shared with identified scholars exclusively. This procedure is compliant with research participants' agreement that anyone may listen to their speech production while remaining cautious about possible alterations and misuse of source files by unidentified persons. In this example, moving the mouse over a restricted link displays the AR048 derogation to public access: "protection of private data", a frequent property of ethnographic and oral/linguistic data. This warning is displayed in the navigation language chosen by the user and it contains the date at which the document is expected to become open-accessible. In its daily set-up, SLDR brodcasts messages to administrators notifying them that the status of an item or document needs to be changed from restricted to public (or the other way around).

Clicking the link prompts the user to sign in on the site, check her/his status, verify whether access is granted to this document and request the user to approve licence(s) attached to this item. This whole process is stored in memory so that it will be bypassed when accessing similar documents during the same session. In this way, complex queries may be performed on multiple documents, multiple items and later multiple sites once Single Sign-On has been implemented among partner repositories.

Access right conditions must be made  The institution is referenced on SLDR site;  The user is registred on SLDR site and affiliated with this institution;  A copy of the resource is disseminated by SLDR;  SLDR owns documents proving that the licence is valid for the institution.

Conclusion

We hope that policy makers will go on supporting the construction of very large research infrastructures for social sciences and humanities in association with networks such as CLARIN and DARIAH in Europe. Their commitment is crucial in response to a strong demand for cooperative resource development and sharing.

Fig . 1 :

 1 Fig . 1: Submitting and retrieving data to/from SLDR.

Fig. 2 :

 2 Fig. 2: File sharing in 'high' and 'low' resolutions

Fig. 3 :

 3 Fig. 3: Access right information in the OLAC DC for item hdl:11041/sldr000027