Jc Nicholls

Eric Schoen

D Van Vliet

S Mookhoek

N Meinen

J De Visscher

A Vanelstraete

T Blumenfeld

S Bohm

Mmj Jacobs

G G Van Bochove

F Hammoum

S Böhm

C Schulze

Development of a Ravelling Test for Asphalt

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Ravelling is a common mode of early failure for many types of asphalt pavement. Recently several simulative laboratory tests have been developed to give an indication of the ravelling potential of an asphalt mixture. These tests use scuffing machines that repeatedly apply a scuffing action to specimen samples to replicate in service loading. The test methods for four such scuffing devices had been written up as a draft technical specification by Comité Européen de Normalisation (CEN) as CEN/TS 12697-50, Resistance to scuffing, subsequently published with minor revisions as a technical specification (CEN, 2016A).

The four machines were the Aachener Ravelling Tester (ARTe, Figure 1), the Darmstadt Scuffing Device (DSD, Figure 2), the Rotating Surface Abrasion Test (RSAT, Figure 3) and the TriboRoute Device (TRD, Figure 4). Each device and most of the method using them were written up in separate Annexes. Ideally, these methods need to be culled or combined so that there is only one (harmonised) test method for this one property before the technical specification can be converted into a test standard.

The Conference of European Directors of Roads (CEDR) has an interest in developing the test into a truly harmonised standard. Therefore, in its transnational research programme "Call 2014: Asset Management and Maintenance" included one to investigate which should be the preferred option(s) for The DRaT project looked at the methods of testing and the results produced for the four scuffing devices in order to identify: • The extent to which sample preparation needs to be standardised, such as compaction level, evenness, storage conditions and age when tested. • The most effective method of measurement in terms of extent of differentiation, validity as a measure of ravelling and practicality. • Whether the results from one or more scuffing devices can be validated from experience on site. • Whether the results from different scuffing devices can be converted to a common measure. • Estimates of the precision of the results with each scuffing device or, if the results can be converted to a common measure, of the common measure. • Whether the results from either pair of similar devices are comparable and their results are reproducible. • A procedure to identify if other scuffing devices can be used for the standard test. It was not known at the start of the project whether these findings would be the same for all asphalt mixture types or different for different types.

REVIEWS

A review was carried out into the parameters influencing the propensity of asphalt to ravel [START_REF] Nicholls | Review of parameters influencing the propensity of asphalt to ravel[END_REF]. The review found a dearth of literature on ravelling rather than just giving references to it. However, many factors were identified that had affected the potential for ravelling, including: Materials: • Hydrophobic aggregates are preferred with better potential affinity to bitumen. • Aggregates should be clean when mixed into asphalt. Mix design:

• The binder content should be as high as practicable without causing other problems such as bleeding in order to minimise the potential for ravelling. • The use of more viscous binders will reduce the tendency for ravelling whilst the advantage of using polymer-modified bitumen is uncertain. • Both larger maximum aggregate size and coarser grading tend to increase the potential for ravelling. Construction:

• Poor compaction results in high air voids contents, which reduces the adhesion of particles to the mat. • Segregation will also result in areas with high air voids contents. • The layer thickness should not be less than twice the maximum aggregate size. • Asphalt that is not sufficient hot when compacted is liable to ravel. • Asphalt should not be laid in the wet. In situ:

• Bitumen ageing from overheating during mixing leads to premature ravelling while that from weathering affects the potential for ravelling in the longer term. • Ravelling damage tends to be more severe during cold weather. • Heavy rainfall can also exacerbate ravelling.

• Direct load does not cause, but lateral, shear of torsion forces can cause it so ravelling will predominate where braking, acceleration and cornering are present. • Joints and slot cuts are potential areas where ravelling will start. It was concluded that the basic strategy to minimise ravelling is to produce and lay a material that will overcome these various causes for ravelling. Also, that the best indicators for a propensity to ravel are the phase angle from the flexural fatigue test the fracture toughness from the semi-circular bending test. Finally, repair technics include pothole repairs, removal followed by an overlay and surface treatments depending on the area affected and the precise cause.

A review was also carried out into the sites with reported ravelling and any quantitative assessment of the extent [START_REF] Nicholls | Compendium of sites and the extent of ravelling[END_REF]. The review found data on the performance of different sites with different mixtures in the Netherlands, Belgian and the United Kingdom with respect to ravelling. The findings from these studies are as follows:

The Dutch studies showed that: • There can be a significant scatter in the extent of ravelling with the same asphalt mixture. • Higher binder contents do reduce the tendency to ravel. • The use of polymer-modified bitumen does not reduce the tendency to ravel. • Slag aggregate makes asphalt more susceptible to ravelling.

The Belgian trial showed that twin-layer porous asphalt is more susceptible to ravelling than more dense asphalts.

The British survey showed that: • Ravelling increases with age, as would be expected. • The ranking of three mixture types for resistance to ravelling is stone mastic asphalt (SMA) as best, then asphalt concrete for very thin layers (BBTM) and finally asphalt for ultra-thin layer (AUTL). • Higher binder contents tend to reduce scuffing.

• Larger aggregate sizes tend to reduce scuffing. However, the last three correlations are very weak and the findings are indicators rather than conclusive.

ROUND-ROBIN TEST PROGRAMME

Based on the review into the sites with reported ravelling, the following three asphalt surface course mixtures were select for the trial [START_REF] Jacobs | Sample preparation[END_REF]):

• a Dutch porous asphalt (PA) in accordance with EN 13108-7 (CEN, 2016b); • a French BBTM in accordance with EN 13108-2 (CEN, 2016c); and • a German SMA in accordance with EN 131085 (CEN, 2016d). However, no quantitative estimate of their propensity to ravel could be identified.

For each generic type of mixture, the design for a typical mixture was identified and then two variations, which were expected to have inferior scuffing resistance, were developed. The variations were a reduced binder content and compaction at a lower temperature. The main parameters are given in Table 1.

The aggregates for each mixture were Listeral Grauwacke coarse crushed rock, natural sand from Putman river, Moraine crushed sand and factoryproduced filler. Cellulose fibres were included as an anti-stripping agent. The asphalt was mixed in a laboratory plug mill mixer and then compacted in 600 mm x 600 mm x 43 mm moulds with a wooden underlayer and metal top frame (Figure 5). The compaction was achieved with a new roller that, therefore, had a perfect round drum (Figure 6). The samples were rotated midway through the compaction procedure in order to ensure uniform compaction.

The slabs were extensively tested in order to minimise any difference between slabs of the same mixture variant:

• The flatness of each specimen was measured at several points to ensure that there were no variations greater than ± 1 mm. • Nuclear density measurements were taken at four locations but were found to have questionable repeatability and reproducibility. Therefore, the calculated density was determined from the volume and mass and checked to be ± 15 kg/m³ of the target value, although it gives no information about the density distribution over the slab. • Sand-patch texture measurements were made at four locations on each BBTM and SMA sample with a variation coefficient ≤ 8,8 %. • Visual inspections for binder-rich spots with a diameter greater than 20 mm and lean areas of more than 5000 mm² per slab. These checks resulted in nine of the 177 slabs produced being rejected.

The slabs were cut into suitable sized slabs for the different devices, with four samples being able to be cut for the DSD and TRD equipment but only one for the ARTe and RSAT. Four samples were required for each variant of each mixture for each laboratory, making a total requirement of 17 slabs per mixture variant.

TEST RESULTS

The DRaT test programme deviated from the draft standard (De Visscher, 2017) by increasing the number of replicates tested from two to four in order to have be able to undertake a more accurate statistical analysis. Also, the age of the samples between compaction and testing was extended from below 42 days to (10 ± 1) weeks because of the number of samples to be manufactured, transported and tested.

Further harmonization was made in those requirements not common to all devices in the draft standard. The changes were: • The conditioning was set at the test temperature ± 2 °C for at least 4 h. • The initial measurements were to include at least dimensions and mass together with top view and 45 ° angle view photographs. • Removal of all loose material by vacuum cleaner initially and during the test. • Test temperature was set at (20 ± 2) °C for all devices except the DSD, which was left as (40 ± 2) ° C (although BRRC repeated the tests with the DSD at 20 °C). • The final measurements were to include at least the dimensions and mass, top view and 45 ° angle view photographs and the mass of aggregate lost during test. • Measurements were also required at a quarter, half and three quarters of the number of cycles. After the testing had been completed, the test conditions achieved were compared with those required. The observed deviations were as follows:

• At ISAC, the enclosure temperature was 23 °C (> 22 °C) for the tests on SMA and the sample surface temperature at start of the measurements were not always within range (18 -22) °C with a maximum temperature of 35 °C for tests on M3. • At BAM, all test conditions were as specified • At BRRC, the test load was increased from 1000 N to 2000 N and the number of load cycles to 50 load cycles at the tests at 20 °C because of limited loss of material at the original load. Also, the enclosure temperature was between 20 and 24 °C (> 22 °C) during the period of testing and the sample surface temperature at start of the measurement not always within range (18 -22) °C with, for a few specimens, the maximum temperature at start being 23 °C. Finally, there was a delay of 12 months for PA, 11 months for BBTM and 9 months for SMA samples.

• At TU Darmstadt, the sample surface temperature at the start of the measurement for a few measurements was above 42 °C. • At Heijmans, the conditioning temperature were different for different mixtures with 20 °C for PA and 5 °C for SMA and BBTM and there was a delay before testing of 1 month for PA and 2 months for BBTM and SMA. • At IFSTTAR, the enclosure temperature was 24 °C (> 22 °C) for all SMA and one BBTM sample and the sample surface temperature at start of the measurement were not measured. Also, there was a delay of approximately 1 month for the BBTM and 2 months for SMA samples. The detailed results are given elsewhere (De Visscher, 2017). The rate of material loss (slope of the curves) behaved differently depending on the test device. The DSD showed an increasing rate, especially for the PA and BBTM mixtures, while RSAT showed a decreasing rate. The rate is roughly constant for the other two devices.

Plots of mass loss against either density or texture show no correlations. This finding is not surprising because the variations in density and MTD within each series of samples of the same mixture were very small. The conclusion is that the repeatability of the sample manufacturing for this test programme was very good and that the mass loss measurements were not biased by differences in density and texture variations.

Pictures were taken from the test specimens before and after testing. It is very difficult to evaluate the damage from pictures, since the resolution, lighting and angle vary.

Inspection of the pictures did not reveal anything special. However, a few general points were noted. The PA test specimens from the DSD showed the most heavily damaged surface while those from the TRD showed no damage, both consistent with the relative stone loss measure. The BBTM test specimens were similar except that the aggregate size was smaller and those from the TRD show some ravelling/abrasion in the middle of the specimen. It was more difficult to see stone loss on the SMA test specimens because the texture of the surface is more closed.

STATISTICAL ANALYSIS

Separate statistical analyses are conducted for each type of asphalt and each laboratory [START_REF] Schoen | Report on analysis of results[END_REF] in order to establish whether the weight loss in the low temperature (lt) and low bitumen (lb) sets of slabs were higher than in the standard (s) set. Onesided t-tests were made on the differences between the low temperature and low bitumen sets with the standard set using log-transformed data. The t-test results in the correct probability values when:

• individual weight losses in each set of slabs are normally distributed; and • the standard deviation of the data is the same for each set of slabs. Data were collected for both the primary results (determined as the difference between the mass of the slab before and after testing for all and the secondary results, which varied with laboratory. For TUD, BRRC and Heijmans, the secondary result was the weight of the material recovered during the test (aggregate and mortar for TUD and BRRC or aggregates > 2 mm for Heijmans) while for IFSTTAR it was the weight loss of PA and SMA slabs after 6,000 cycles and for BAM it was weighings including the wooden frame. There was no secondary result for ISAC.

The reports from the six laboratories showed deviations from the measurement in three cases. The results of these measurements were disregarded in the data analysis. Three further possible outlying weight losses in the data were also identified.

With regards to precision, the devices show large coefficients of variation (often more than 30 %), limiting the discrimination potential strongly without increasing the number of slabs tested. The four replicates tested in this project permitted discrimination between poor quality and standard materials in 14 of the 36 combinations of laboratory and mixture variant.

The primary purpose of the round robin was to make out whether the scuffing devices can be used interchangeably and, if not, which of them gives the most informative results. The presence or absence of a statistically significant increase in weight loss between the different qualities of an asphalt type based on four replicates is tabulated in Table 2.

ARTe ISAC 0 1 0* 0* 0 0 BAM 1 1 0 1 1 0 DSD TUD 0 1 0 0 0 0 BRRC 0 1 0 0 0 0 RSAT Heijmans 1 2 1 0 0 1 1 1 TRD IFSTTAR 0 0 0 1* 1 1 2 1
Only for primary weight loss 2 Only for secondary weight loss * After removal of statistical outliers All devices except the TRD showed an increased weight loss for the PA/lb slabs while only two laboratories showed an increased weight loss for the PA/lt slabs. The implication is that there was a quality difference which was not picked up by four of the laboratories.

No increased weight loss for the BBTM/lt slabs was established, possibly due to the good quality of these slabs. Two laboratories showed an increased weight loss for BBTM/lb slabs which again suggests a quality difference which was not picked up by four of the laboratories.

There were quality differences with respect to the standard in both SMA/lt and SMA/lb slabs although they were not picked up by all the laboratories. It appears that the current test procedures for each device are insufficient to cause ravelling to a properly designed SMA material.

When looking at the results by device rather than mixture type, the DSD appeared insensitive for detecting differences in PA/lt, BBTM and SMA mixtures. The RSAT was sensitive for detecting differences in PA and SMA but not BBTM samples, but there were inconsistencies in the primary and secondary weight loss results. The TRD seems sensitive for BBTM and SMA to detect designed quality differences, but the detection is not consistent for lb and lt differences. Also, the number of cycles for the TRD test needs to be unified from the different materials different loading times for different asphalt types.

There were substantial differences between the results from the two laboratories using the ARTe. The BAM device seemed particularly capable of discriminating between the PA qualities whereas the ISAC device only showed statistically significant differences for PA/lb slabs from the standard. The differences between the laboratories can only be explained only by a different experimental conduct or by (unknown) differences between the individual devices.

The anticipated ranking of the asphalt types for ravelling propensity under the same loading conditions was PA, then BBTM and finally SMA. This ranking was generally found from the results except with the TRD, which ranked PA last. However, there was a problem with permanent deformation during the PA testing with the TRD causing the limited mass loss.

The potential of different devices to discriminate between standard and poor-quality materials of the same asphalt type were not comparable, so it would appear that the scuffing devices cannot be used interchangeably. In addition, no single device appeared to be capable of detecting all the designed differences between the standard and poor-quality materials according to the current test methods. The comparison between the devices for the three materials demonstrates that there are clear differences in the design and effects of the testing devices. No uniform correlation between the devices could be found nor could their results be culled or unified for a performance or loading time that would convert to a common measure. or scaling factor to turn the results of one device to another. Furthermore, some of the devices showed a different damage development in time. Therefore, the results of the individual devices could not be converted to a common measure.

RECOMMENDATIONS TO UPDATE STANDARD

The research provided no definitive answer (for all or for specific asphalt mixture types) as to whether there are:

• a 'best' device to be used universally;

• any 'bad' devices to be removed from the list; or • robust correlation factors to equate results from the different devices. Nevertheless, it was considered that there was sufficient useful information gained to produce a revised draft of PR CEN/TS 12697-50:2016 [START_REF] Nicholls | Proposals for revision of standard prCEN/TS 12697-50[END_REF].

The main issue with the revision was to put the separate test methods into a single test method with only certain parameters and options defined for the separate devices that cannot be harmonized (such as sample size) still in separate annexes. However, there is a need to normalise the results for each device into a common measure. Although the correlations were not consistent, these values were averaged to give an estimated normalisation factors as shown in Table 3. Separate normalisation factors were not calculated for different asphalt mixtures because that would imply greater precision than is the case.

Given the variability in the values used to produce these values, it was proposed to round them off to 2.8 for the ARTe, 2.6 for the DSD, 1.0 for the RSAT and 10 for the TRD. However, on further reflection the consortium decided that these factors were not sufficiently robust to be included in a standard and they were relinquished to a separate appendix in case the CEN committee felt differently.

It was recommended to increase the minimum number of replicates per test from two to three: four would be better but there was concern that four replicates would make the test too expensive and inhibit its use.

In addition, a normative annex was proposed for alternative devices that may be developed in the future. The annex would cover checking the equivalence of the new device together with the calculation of the normalising factor. However, without normalising factors to calibrate against, the consortium also decided not to include this annex in their proposed draft of the standard.

Most of the harmonisation applied to the round robin programme (Section 3) was recommended for the revision of the standard. Several other aspects included in proposed revision are described below.

The first recommendation to the new draft was to extend the definitions because it was appreciated that terms such as 'scuffing' and 'ravelling' are not understood to mean the same thing universally. The proposed definitions added included:

• scuffing: the action of tyres, particularly when the wheels are rotating about an axis not perpendicular to the direction of travel of the vehicle (or relative motion of the tyres and asphalt surface simulating the vehicle movement) which causes material loss from the surface of the asphalt • material loss; amount of material that has been lost from the surface of the asphalt due to scuffing divided by the area being scuffed • ravelling: loss of coarse particles from the surface of the asphalt due to scuffing divided by the area being scuffed • fretting: loss of fine material from the surface of the asphalt due to scuffing divided by the area being scuffed The definitions were deliberately worded in order to apply to the scuffing of a road surface by passing vehicle tyres or to the simulated scuffing of a test sample by the tyres on scuffing apparatus during a test.

It was proposed that the sample preparation requirements should include: • Checking the bulk density of the slab or core by the dimensions procedure (as already included by the test method) with a maximum allowable difference of 0.050 Mg/m³. • Checking the thickness of the samples at nine positions with a calliper to ensure a maximum allowable difference of 2.5 mm. • Checking the overall dimensions and flatness (±1.0 mm) of each sample. • Checking the visual condition is acceptable.

It was proposed that the samples should be required to have all loose material removed with a vacuum cleaner initially and before each set of measurements. The material vacuumed off will need to be retained for determining the material lost.

It was proposed that measurement should be made at the end of the test and not less than three equally spaced intervals during the test. At each set of measurements, the following initial measurements should be made: • Dimensions of the sample.

• Mass of the sample.

• Mass of lost coarse particles (not initially, optional otherwise). • Photographs of the top surface of the sample from above and at a 45 ° angle. The location relative to the sample from which the pictures are taken together with the lighting and camera settings also needed to be recorded so that they can be replicated for subsequent photographs It was proposed to have two test durations, the standard number of cycles and an extended number of about double the standard. However, no investigations have been made as to whether the same nor-malisation factors should be applied for the extended loading cycle because of the different development in damage over time and loading.

It was found that that the test methods have relatively large geometric standard deviations, often more than 30 % [START_REF] Schoen | Report on analysis of results[END_REF], as summarised in Table 4.

These values are for single measurements, so can be reduced by dividing by the square root of three for test results which are the mean of tests on three samples. However, it is proposed that these values will only be given as guidance for repeatability rather than to make estimates of repeatability and reproducibility because of the limited number of devices involved.

A revised draft of PR CEN/TS 12697-50 with recommendations incorporated was produced with the changes highlighted. The highlights were red for major additions, mauve for minor changes in terminology, blue for moved sections, green for a compilation of ideas from the Annexes into the main text and grey across gaps from which text has been removed. However, because these changes were so extensive, the highlighting could only be indicative.

GUIDANCE ON SCUFFING

A separate informative annex was also proposed giving advice on scuffing and the choice of scuffing device [START_REF] Nicholls | Proposals for revision of standard prCEN/TS 12697-50[END_REF]. The annex starts by discussing the difference between early stage ravelling and ravelling at the end of the service life.

Early stage ravelling results from the shear stresses imposed by vehicles which can be high, particularly at bends, crossings and roundabouts. Depending on the type of mixture, these stresses will be applied primarily to either the mortar fraction or the stone particles in the road surface. For continuousgraded mixtures, this load can generate the loss of fine material from the surface, called fretting. This phenomenon can retard or even stop when the coarser fractions of the mixture are exposed at the surface and help to withstand the traffic load. A different process takes place with stone-skeleton mixtures like SMA or PA where the traffic forces are applied directly to the stone particles at the road surface, both initially and thereafter, to cause 'ravelling' (loss of coarse aggregate from the surface).

Ravelling at the end of the service life develops at the end of the life-span particularly of stone-skeleton mixtures like PA and SMA. It occurs in and near the 'wheel tracks' of a road surface, those being the places that mostly bear the loads from the vehicle tyres, not only at crossings or curves but also in straight sections of roads.

These mechanisms, together with other mechanisms such as those for fretting (loss of cohesion of the mortar), are essentially different. They take place in different stages of the life of a pavement, a different combination of mixture parameters and load parameters are relevant to each and different circumstances can be critical (e.g. temperature).

Before using the scuffing test, it would be useful to consider which mechanism(s) is/ are being investigated or their potential monitored and which of the devices is most targeted at the area. To assist in such a review, some aspects to be considered are listed in Table 5 and the aspects for different devices in Table 6.

CONCLUSIONS

The main limitations of the research were that:

• No quantitative measure of scuffing on site was identified to produce data for validation of the various options. • The round robin did not produce precise correlations, whether between devices for all mixtures or between devices for specific mixtures. • Neither the 'best' device to be selected as the sole one for the test nor any 'bad' devices for exclusion were identified, whether for specific mixtures or for all mixtures Nevertheless, the research forms the basis of an 'improved' proposal for PD CEN/TS 12697-50 with the majority of details in the main text rather than in separate annexes for each device. As such, more details are common between the methods for the different devices while retaining separate annexes for details that remain different. Normalisation coefficients have been calculated to compare results from different devices, although these are not fully validated and are not proposed for the revised standard. Further development is needed when extra data become available with possibly different coefficients for different mixture types.

An additional annex was considered for possible additional devices defining a check for compatibility with existing devices and the calculation of the normalisation coefficient but also discounted.

An additional informative annex for guidance on the choice of scuffing test has been proposed.

The implementation of the 'improved' proposal for PD CEN/TS 12697-50 will be with CEN and for the implementation of the test by road authorities, including CEDR members and local authorities.

Therefore, the open questions left by the research programme are:

• Will CEN agree to the proposal? • Will PD CEN/TS 12697-50 be used extensively?

• Can the Normalisation factors be refined to make them practical? • Will CEN select a preferred test device, possibly different devices for different situations, or adopt a calibration procedure for alternative devices?

Figure 1 .

 1 Figure 1. Aachener Ravelling Tester (ARTe)

Figure 5 .

 5 Figure 5. Moulds used to prepare slabs

Table 1

 1

	. Mixture parameter and variations for the round robin
	Mixture Type	Mixture Code	Binder	Parameters	Variant 1	Variant 2
	PA	PA 16 70/100	70/100	Compaction at 150 ⁰C 5.2 % bitumen ±20 % air voids content	Compaction at 105 ⁰C	4.2 % bitumen
	BBTM	BBTM 6 50/70	50/70	Compaction at 160 ⁰C 5.6 % bitumen (12 -19) % air voids content	Compaction at 110 ⁰C	4.6 % bitumen
	SMA	SMA 11 PmB	PmB 25/55-55 with 3 % SBS polymer	Compaction at 155 ⁰C 6.8 % bitumen ±3 % air voids content	Compaction at 105 ⁰C	5.5 % bitumen

Table 2 .

 2 Statistically significant differences in the round robin tests

				Asphalt type
	Device	Laboratory	PA	BBTM	SMA
		lt	Lb	lt	lb	lt	lb

Table 3

 3

	. Rejected proposal for Normalising factors between devices
	Device		ARTe			DSD		RSAT	TRD
	Laboratory	ISAC	BAM	Mean	TUD	BRRC	Mean	Heijmans	IFSTTAR
	PA	5.0	2.4	3.0	0.2	0.2	0.2	1.6	(91.7) †
	BBTM	15.2	5.3	10.3	0.7	0.7	0.7	1.9	10.1
	SMA	6.9	4.6	5.8	13.3	21.1	17.2	3.5	37.9
	Mean		6.6			6.0		2.3	24.0
	Normalised		2.81			2.59		1.00	10.3
	† Excluding the PA results with the TRD (permanent deformation being observed)

Table 5 .

 5 Aspects to be considered in choice of device

	Reason for investigation or monitoring	Avoid wear and rough texture	Avoid early stage ravelling	Extension service life	Investigation on the residual life of an existing pavement
	Relevant period of service life	Whole pavement life	Beginning of pave-ment life	End of lifetime	End of lifetime
	Damage principle	Fretting	Ravelling	Ravelling	Ravelling
	Revelation form of damage	Loss of fine materi-al from the road surface	Loss of coarse ag-gregate	Loss of coarse ag-gregate	Loss of coarse ag-gregate
		Type of mixture	Continuous graded mixtures	PA, SMA or thin fine graded SMA	PA, SMA or thin fine graded SMA	PA, SMA or thin fine graded SMA
		Type of test pieces	Slab produced in laboratory	Slab produced in laboratory	Slab produced in laboratory	Cores from the road
	Require-	Direction of movement	No requirement	No requirement	All directions	All directions
	ments on		Measuring wear:	Measuring strength:	Generating fatigue	Generating fatigue
	the test de-	Length of test run	moderate/large	limited number of	damage: large num-	damage: large num-
	vice		number of passes	passes	ber of passes	ber of passes
		Final measurements	Loss of weight of test sample	Loss of fines and coarse aggregate	Loss of coarse ag-gregate	Loss of coarse ag-gregate

Table 6 .

 6 Aspects for different apparatus

	Device	Slabs	Test samples	Cores	Direction of move-ment	Length of test run	Principal measurement methods
	ARTe	Laboratory pro-duced slab	3 x 150 mm ᴓ cores per sample	All directions	600 cycles in 2 h	Weight-loss of sample Loss of coarse aggregate Change of texture depth
	DSD	Laboratory pro-duced slab	3 x 150 mm ᴓ cores Single cores per sample	Forward and back	10 cycles	Weight-loss of sample
	RSAT	Laboratory pro-duced slab	3 x 150 mm ᴓ cores per sample	All directions	86.600 cycles in 24 h	Weight-loss of sample Loss of coarse aggregate
	TRD	Laboratory pro-duced slab		n/a	Forward and back	6.000 cycles	Weight-loss of sample


A Orozco Estrada

Raúl C Cruz Gómez

A Cros

P Le Gal
email: legal@irphe.univ-mrs.fr

Orozco Estrada

Cruz Gómez

Le Gal

Coalescence of lenticular anticyclones in a linearly stratified rotating fluid

This study is devoted to laboratory experiments on the coalescence of two lenticular anticyclones in a linearly stratified rotating fluid. These anticyclones are generated by injecting small volumes of fluid at the center of a rotating tank where a linearly stratified layer was previously prepared with salt. The characteristics of the interaction between the vortices are studied by visualization and Particle Image Velocimetry (PIV) as a function of the initial separation distance between the vortices, the Coriolis parameter of the rotating table and the Brünt-Väisälä frequency of the density stratification. Our results show that the merging critical distance depends drastically on the Rossby radius of deformation of the vortices and are in complete agreement with previous numerical modeling of vortex coalescence. We have also observed that mergers involve three-dimensional processes as the vortices intertwine together possibly because of the presence of an elliptic instability that tilts the vortex cores. They are also accompanied by the emission of vorticity filaments and internal gravity waves radiation although we cannot prove that in our experiments these waves are solely due to the merging process.

Introduction

Oceanic meso-scale lenticular vortices play an important role in the redistribution of momentum, heat, salt, nutrients and plankton in oceans and thus contribute to the climate equilibrium and ecological diversity on Earth. These vortices are governed by geostrophic and hydrostatic balances between pressure gradients, Coriolis and buoyancy forces from where they get their shape and aspect ratio as shown by [START_REF] Hassanzadeh | The universal aspect ratio of vortices in rotating stratified flows: theory and simulation[END_REF], [START_REF] Aubert | The universal aspect ratio of vortices in rotating stratified flows: experiments and observations[END_REF] and by [START_REF] De La | A laboratory study of floating lenticular anticyclones[END_REF] for surface vortices. Their chaotic motions in oceans give rise to a quasi-geostrophic turbulence characterized by a reverse energy cascade and a forward enstrophy cascade [START_REF] Kraichnan | Inertial ranges in two dimensional turbulence[END_REF][START_REF] Charney | Geostrophic Turbulence[END_REF]. Understanding the way energy escapes from this mesoscopic turbulence to feed the smallest oceanic scales where dissipation occurs, is the subject of an intense research. In this context, vortex coalescence as observed in oceans [START_REF] Schultz Tokos | Merging and migration of two meddies[END_REF]) can be seen as a building block of these reverse and forward cascades: vortex mergers participate to the reverse cascade towards the large scales of the oceanic turbulence while they generate at the same time fine filaments of vorticity [START_REF] Cushman-Roisin | On the role of filamentation in the merging of anticyclonic lenses[END_REF] as well as internal waves (Viudez 2006, Reinaud and[START_REF] Reinaud | The merger of geophysical vortices at finite Rossby and Froude number[END_REF]) that could feed small dissipative scales. The aim of the present study is to describe and parametrize the merging of two lenticular anticyclones by means of stratified flow experiments performed on a rotating table. For this purpose, we generate pairs of anticyclonic vortices by the gentle injection of two small volumes of water inside a continuously stably stratified rotating layer in a similar way that [START_REF] Griffiths | Coalescing of geostrophic vortices[END_REF] did thirty years ago but for a two layer system. To our knowledge, this problem has never been revisited experimentally for the case of lenticular vortices imbedded in a continuously stratified layer.

Symmetric vortex pairing has been widely studied in two-dimensional, inviscid, incompressible flows [START_REF] Zabusky | Contour dynamics for the Euler equations in two dimensions[END_REF][START_REF] Melander | Symmetric vortex merger in two dimensions: causes and conditions[END_REF][START_REF] Waugh | The efficiency of symmetric vortex merger[END_REF][START_REF] Nielsen | Vortex merging and spectral cascade in two-dimensional flows[END_REF]. It was shown that, in this case, the vortices merge when the ratio of the initial distance d 0 between their centers and their radius R is small enough (typically d 0 /R ≤ 3.3, [START_REF] Waugh | The efficiency of symmetric vortex merger[END_REF], [START_REF] Meunier | Physics of vortex merging[END_REF], [START_REF] Leweke | Dynamics and instabilities of vortex pairs[END_REF]). Nevertheless, when the vortices are baroclinic, the Rossby radius of deformation may drastically modify the critical distance d c for which merging occurs. The Rossby radius of deformation λ gives an order of magnitude of the scale for which the Coriolis effect becomes as important as the buoyancy. It gives the effective length of the horizontal distance between the region of generation of a disturbance and its outermost extent. This Rossby radius of deformation is equal to:

λ = N f H , ( 1
)
where H is the vortex height, f the Coriolis parameter and N the Brünt-Väisälä frequency. For a continuously stratified fluid, N = -g ρ 0 ∂ρ ∂z represents the oscillation frequency of a parcel of fluid with density ρ 0 vertically displaced in a fluid layer of density ρ(z) and where g is the gravity.

As far as we know, the first and unique experimental study on baroclinic vortex pairing in a two-layer stratification was carried out by [START_REF] Griffiths | Coalescing of geostrophic vortices[END_REF] for various values of λ/R and d 0 /R. The vortex height is fixed by the top layer depth and it was found that a strong enough stratification λ/R > 2.0 enhances the merging, and in consequence increases the critical distance d c that separates pairing to non pairing cases. Following this experimental work, two numerical studies evidenced the importance of the initial conditions on the influence of stratification in a two-layer model. First, [START_REF] Polvani | Two-layer geostrophic vortex dynamics. Part 1. Upper-layer V-states and merger[END_REF] found that stratification does not modify the critical initial distance d c ; but this contradictory result was explained a year later by [START_REF] Verron | Sensitivity to initial conditions in the merging of two-layer baroclinic vortices[END_REF] who proved that density stratification has indeed a drastic effect on d c /R if the relative vorticity is zero in the lower layer. This condition was not fulfilled in the work of [START_REF] Polvani | Two-layer geostrophic vortex dynamics. Part 1. Upper-layer V-states and merger[END_REF] who enforced a zero potential vorticity in the lower layer. [START_REF] Verron | Sensitivity to initial conditions in the merging of two-layer baroclinic vortices[END_REF] found that the barotropic limit is reached when λ/R → 0 as well as for large values of λ/R (λ/R > 4). In the case of zero relative vorticity initialization, the merging is more efficient when λ/R 2.1 as the critical distance reaches a maximum value d c 6.8 R. Nevertheless, it was noted later by [START_REF] Verron | Scale-dependent merging of baroclinic vortices[END_REF] that this maximum can be modified if mixed conditions between zero potential and zero relative vorticity initialization are taken into account. Indeed the peak in the initial distance critical values can shift towards lower values of λ/R and d c /R.

Merger observations in the Atlantic Ocean of strongly interacting meddies were reported by [START_REF] Carton | Meddy dynamics and interaction with neighboring eddies southwest of Portugal: observations and modeling[END_REF][START_REF] L'hégaret | Evidence of Mediterranean water dipole collision in the Gulf of Cadiz[END_REF]. Some mergers were also described by Schultz [START_REF] Schultz Tokos | Merging and migration of two meddies[END_REF], [START_REF] Carton | Meddy coupling with a deep cyclone in the Gulf of Cadiz[END_REF], [START_REF] Rodríguez-Marroyo | Vortex merger in oceanic tripoles[END_REF] and [START_REF] Barbosa | A census of meddies in a long-term high-resolution simulation[END_REF]. Besides these oceanographic observations, merging of two giant anticyclones in the atmosphere of Jupiter is also described by [START_REF] Sanchez-Lavega | The merger of two giant anticyclones in the atmosphere of Jupiter[END_REF]. We can moreover easily imagine other astrophysical applications such as the coalescence of baroclinic vortices in accretion disks for instance. Whereas the two-layer model is a good first order approximation for these natural cases, oceans or atmospheres are continuously stratified. To our knowledge, only one laboratory study has been reported up to now in a linearly stratified rotating fluid but only for pairs of barotropic vortices [START_REF] Cariteau | Etude de la stabilité et de l'interaction de cyclones intenses en fluide stratifié[END_REF]. This laboratory experiment showed that the critical distance for the merging of long columnar vortices increases when stratification increases in agreement with the numerical prediction of [START_REF] Dritschel | Vortex merger in rotating stratified flows[END_REF], who extended the results of Von [START_REF] Hardenberg | Vortex merging in quasi-geostrophic flows[END_REF] to vortices with large aspect ratio H/R = 20f /N . In these last studies, three-dimensional quasi-geostrophic vortices are modeled and the barotropic critical distance is recovered for flat vortices (H/R → 0), whereas unexpectedly d c /R continues to increase with H/R. This enhancement of coalescence for large separating distances is due to the existence of a bending instability (most probably the zig-zag instability of [START_REF] Billant | Zigzag instability of vortex pairs in stratified and rotating fluids. Part 1. General stability equations[END_REF], [START_REF] Otheguy | Pairing of two vertical columnar vortices in a stratified fluid[END_REF]) that brings the vortex cores closer together. Another ingredient that was pointed by [START_REF] Valcke | Interactions of baroclinic isolated vortices: the dominant effect of shielding[END_REF] comes from the possible presence of shielding rings around the vortices. Indeed, as observed numerically in the pairing of realistic oceanic meddies by [START_REF] Ciani | On the merger of subsurface isolated vortices[END_REF], the cyclonic ring around each anticyclone can prevent the merger by a redistribution of the shield cyclonic potential vorticity that generates a repulsive effect on the cores. As we will see later, our laboratory vortices are indeed shielded and our experiments reveal some interesting features already detected in numerical simulations although the shields seem not to prevent coalescence in our present observations.

Our study explores the (λ/R and d 0 /R) space in order to determine the critical merging distance d c as a function of the Rossby radius of deformation λ. Both the global rotation rate and the density stratification will be changed. Around ninety experimental runs (including Particle Image Velocimetry (PIV) measurements and dye visualizations) have been realized. Each experiment is labeled with a number which will be used to identify them. Pairing and non pairing situations are discriminated by measuring the evolution in time of the distance separating the vortex cores. When this separation distance becomes less than a vortex diameter, the merging process will be declared effective. In most of the runs, there are no ambiguities to decide if the pairs have merged or not after a duration of about 20 minutes per run. Besides determining the critical initial distance d c , we have also observed that the injection flux that controls the Rossby number of the vortices, plays a role on the merging time and on the rotation rate of the pair. These results are consistent with the recent numerical simulations of [START_REF] Reinaud | The merger of geophysical vortices at finite Rossby and Froude number[END_REF]. Finally, we will show that a Fourier analysis permits the detection of Internal Gravity Waves (IGWs) that radiate energy away during the vortex generation by injection and during the first instants of coalescence.

Experimental set-up and measurement techniques

2.1.

Rotating table installation and methodology

All the experiments were performed in the Geophysical Fluid Dynamics Laboratory of Guadalajara University. The experimental set-up is shown in figure 1. The rotating transparent Plexiglass tank dimensions are 40 × 40 × 40 cm 3 which are at least ten times larger than the vortex diameters and twenty times deeper that the vortex heights. Two constant density 5 cm deep layers are generated at the bottom and at the top of the total fluid layer, while the stratified region has a vertical extension of 20 cm. The upper layer water is fresh while the bottom layer water is salty and has a density whose value depends upon the desired stratification. The linear stratification is made by the two-bucket method [START_REF] Oster | Density gradients[END_REF] which is a classical method that consists in mixing progressively the water from a bucket of pure water with the brine of a second bucket. Then the Brünt-Väisälä frequency N is determined from the measurement of the density gradient after the fluid was left at rest for more than 12 hours before performing the experiments. The diffusion of salt in water being slow (Schmidt number equal to 700), the stratified layer can be kept for days if not perturbed. The whole device shown in figure 1 is then slowly set into rotation for more than 2 hours until the fluid layer reaches a solid body rotation at a rotation rate Ω. The Coriolis parameter is given by f = 2Ω. A side-view camera allows to determine the depth H of the vortices as shown in figure 1, while the top-view camera records the two vortices evolution after they have been created. The two anticyclones are generated by injecting a small volume of fluid, between 5 ml and 20 ml, at the center of the vertical stratified layer (see for instance [START_REF] Hopfinger | Vortices in rotating fluids[END_REF]) as it is sketched in figure 1. In order to generate controlled vortices, two micro-pumps suck dyed salty water from two distinct tanks whose density is equal to the density in the middle-plane of the stratified layer. Two flow meters allow to measure the flow rate. The dyed water is injected through two rigid 4 mm inner diameter pipes which are fixed on the rotating tank. The separation distance d 0 between the pipes sets the initial distance between the two vortices. Note that some of our experiments were realized by hand injection, using syringes (instead of the pumps), of a 5 ml volume of water in approximately 12 s. As already explained in the introduction, each run is labelled by a number and is characterized by its rotation Coriolis parameter f , its Brünt-Väisälä frequency N , the initial separating distance d 0 and also the flow rate Q of the injection that has, as we will show later, a great influence on the Rossby number of the vortices. Most of the time, both vortices in the pairs were of equal strength and size. However, in about one third of the total number of experiments, the symmetry between both vortices is not perfectly respected (because of uncontrolled experimental uncertainties like tiny bubbles in the injection pipes for instance) and asymmetric fusion takes place [START_REF] Dritschel | Vortex merger in rotating stratified flows[END_REF]. In this case, one of the vortices wraps around the other one as seen in figure 2. Therefore in the following we have removed all the data corresponding to these asymmetric experimental configurations and we are able to produce a state diagram using more than forty data points.

t = 330 s t = 960 s

Visualization and PIV measurements

Most of our experiments have been realized with vortices colored with dye in order to measure their core diameters and heights. One vortex is colored in red and the other one in green (or blue) in order to facilitate the use of simple algorithms to differentiate and track the vortices by video image analysis. Their radius and separating distance are recorded by the top-view camera. Their height is measured by the side-view camera. Radii and heights will be then used to compute the Rossby radius of deformation λ of the anticyclones. In order to calculate the Rossby number of the vortices, but also to describe precisely their shape, Particle Image Velocimetry (PIV) measurements were performed in both horizontal and vertical planes for some experiments. To do so, small polyamide particles (diameter of 50 µm) were added in the water prior to the stratification process. These particles are also added in the salt water that is injected to generate the vortices. A green light laser beam is then used to illuminate the particles in planes crossing the vortices. The top view camera is used to record the movement of the particles with a frame rate of 1 Hz. Two frames of the video sequences are used to estimate the particle displacement using PIVlab [START_REF] Thielicke | PIVlab-towards user-friendly, affordable and accurate digital particle image velocimetry in MATLAB[END_REF] or Flow Manager (Dantec Dynamics c ) softwares. Each image is subdivided in 32 pixels interrogation windows to calculate the instantaneous velocity fields as a function of time at the rate of 1 field per second.

Description of a single anticyclone

The geostrophic balance of the anticyclonic lenses

In order to describe a single vortex before proceeding to the merging experiments, we have studied its velocity field by performing PIV measurements in its equatorial plane. Figure 3a) presents an example of the vorticity field recorded in and around an anticyclone. As can be clearly seen, a cyclonic ring is present around the vortex core. The Rossby number of the vortex, i.e. its magnitude, can be measured by the minimum of the vorticity field ω 0 in its center: Ro = ω 0 /f . This kind of shielded vorticity field is quite classic for oceanic vortices and can be modeled by a modified Gaussian shape:

ω(r) = ω 0 1 - α 2 r L α exp - r L α (2)
where where α and L are free parameters. When α = 2, the vortex is said to be Gaussian. In this experimental run, α lies between 2 and 1.5 as time varies and this will always be the case whatever the parameter values. L is the vortex typical horizontal scale corresponding to the radial location where the vorticity goes through zero. This value also varies in time as the vortex expands when slowing down. Figure 4 presents the temporal variation of the Rossby number Ro, of L and of α respectively. This slow damping of the vortex has been analysed in great details by [START_REF] Facchini | On the lifetime of a pancake anticyclone in a rotating stratified flow[END_REF] and is due to a subtle interplay between viscous dissipation and secondary circulations which advect the density anomaly. As it was shown in previous studies, vortices are governed by geostrophic and hydrostatic balances from where they get their shape that obeys scaling laws (see De la Rosa Zambrano et al. (2017) for instance). Moreover, we have also observed that the Rossby number depends upon the injection rate as the vorticity is a direct consequence of the horizontal radial flow, which by action of the Coriolis effect generates an azimuthal velocity field. Figure 5 shows this dependence for four values of Q, where a linear behaviour is observed. Finally, to complete our description of a single vortex, we have also realized PIV measurements in vertical planes going through the vortex at mid-radius. As this plane is off centered, because of its thickness (1 mm), the projection onto the plane of the particle trajectories can be recorded and analyzed. As presented in figure 6, the evolution of the azimuthal velocity along the vertical direction can be quite nicely fitted by a modified Gaussian function with a typical vertical scale Z and an exponent β. Therefore our laboratory vortices created by injection of fluid in a rotating and stratified layer have a similar three-dimensional shielded structure as the real oceanic vortices [START_REF] Ciani | On the merger of subsurface isolated vortices[END_REF]:

ω(r) = ω 0 1 - α 2 r L α exp - r L α exp - z Z β (3) a) b)

Measurements of the radius and height of the vortices

Most of our experiments were realized using visualizations of the pair of vortices. After injection, we waited several table rotation periods to get a quasi-geostrophic adjustment of the injected patches during which these get their circular shape. Their radii R were then obtained at this initial time by a measurement of the horizontal size of the circular patches visualized by dye (see section 4.3 for details of image processing). To compare R with L, we performed a complementary experiment where both techniques are applied together: visualization of the injected water and PIV measurement. Figure 7 shows that the two values agree by 10%, R being larger than L. Thus a dividing factor of 1.1 has been applied in the following to all our radius R measurements of the dye patches in order to transform these radii R into the proper typical horizontal scales L. In particular, to build the state diagram of figure 16, the initial values of R will be transformed in initial values of L in order to compare our experimental data to former published results. The height H of the vortices are directly measured by image analysis of the videos recorded by the side-view camera to calculate the Rossby deformation radius λ. We will keep the initial values of these heights i.e. after the transients due to the time needed for the anticyclones to reach their geostrophic balance (neglecting the presence of the other vortex in the pair) to perform this calculation.

Coalescence of identical anticyclones

Visualization of the merging process

As explained previously, the vortices are created by injection of 5 to 20 ml of salt water in a layer that was stratified in density with salt and set into rotation for two hours before performing each experiment. The density of the injected water was chosen to be the value of the density at the injection location so that the anticyclones stay at the desired altitude. The top-view camera records the complete process from the injection to the final time when all the fluid motions are damped out, while the side-view camera records only the first minutes of the runs. A complete sequence lasts from 3 to 30 minutes depending upon the initial conditions. Figure 8 presents for f = 1.57 rad/s, N = 2.8 rad/s, d 0 = 8 cm and Q = 45 ml/min, four images from a typical sequence where two anticyclones merge. The first effect of the mutual influence of one vortex onto the other is a global rotation of the pair. Then, when getting closer to each other, the vortices are deformed and a cusp is formed on the inner sides of both of them. The streaklines around these cusps are then elongated, captured and then wrapped around the opposite core to form a Yin and Yang Chinese symbol. As observed on the pictures, the process is threedimensional as the vortices intertwine with overlapping of both cores seen as a superimposition of red and green colors. We also note the presence of dye filaments repulsed away from the final merged vortex core. Figure 9 presents another illustration of the merging process in the case where the cyclonic shields are repulsed in the form of two side cyclonic vortices. For this sequence, f = 1 rad/s, N = 3.12 rad/s, d 0 = 7.5 cm and Q = 25 ml/min. These visualizations are perfect illustrations of the numerical simulations of [START_REF] Valcke | Interactions of baroclinic isolated vortices: the dominant effect of shielding[END_REF] for two layers quasi-geostrophic models and of [START_REF] Ciani | On the merger of subsurface isolated vortices[END_REF] for computations of realistic oceanographic eddy coalescence.

The three-dimensional features of the merging of baroclinic vortices can also be observed by the side-view camera. Figure 10 presents two images where the pair of anticyclones is viewed from the side for two different instants. It is very clear on these images that the vortices are tilted (versus the vertical axis) during coalescence. Although it is difficult to prove, we speculate that an elliptic instability may take place here in the same way it appears in the case of barotropic columnar vortices merging [START_REF] Meunier | Physics of vortex merging[END_REF]. Unlike the elliptic instability of these columnar vortices, the most unstable mode of the elliptic instability of fluids inside rotating ellipsoids [START_REF] Lacaze | Elliptical instability in a rotating spheroid[END_REF]) is a rotation around a tilted axis (the spin-over mode). From the top-view images, it is clear that the mutual interaction between the anticyclonic lenses t = 0 s t = 22 s t = 60 s can deform sufficiently each vortex such that their ellipticity is large and of the order of their diameter, enhancing the possible appearance of the instability in this free of boundary layers flow.

t = 1380 s t = 1680 s

Figure 10. Two observations of the merging process from the side view camera for f = 1 rad/s, N = 3.16 rad/s, Q = 30 ml/min and d 0 = 14 cm. The anticyclonic lenses are clearly tilted when merging, enhancing the three-dimensional process as they intertwine each other. We suspect the elliptic instability to be at the origin of this tilting.

PIV measurements of coalescence

Besides visualization, we have also performed PIV measurements of velocity fields during coalescence. Figure 11 presents an example of the temporal evolution of a vorticity field. At initial times, soon after the vortex generation, we can see the separated cores and their shielding cyclonic rings which, in the present case, have merged in a figure eight shape. Rapidly this shield disappears and as the vortices rotate one around the other, two vorticity arms are formed at the external tips of the pair. These arms wrap around the vortices and become thinner as they are elongated by the core rotation. Finally, these filaments are dissipated while the cores are completely merged.

Image analysis and measurements of the global induced rotation rate and the merging time of the pair

As mentioned before we have tracked the vortices visualized with dye by image analysis. We first determine the center position of each vortex and measure their radius by extracting one frame per second from the video. A red and then a green (or blue, according to the dye color we used) filter is applied to each frame. An intensity filter for each color is then used in order to highlight each vortex. These highlighted images are then binarized such that only the vortices are visible. From these images we can now extract different parameters like the radius and the center position of each vortex. These radii are calculated such that the corresponding disks have the same areas as the binarized patches. The vortex common rotation center is then determined and we can compute the global orbital rotation rate ω orb of the pair and the separation distance between both vortices. Figure 12 shows an example of the merging process for f = 0.5 rad/s, N = 1.75 rad/s, Q = 60 ml/min and d 0 = 8 cm on which we have applied our image analysis. As can be observed, in this case, both vortices have ejected their cyclonic rings in the form Orozco Estrada, Cruz Gómez, Le Gal and Cros Figure 13-a) shows the spiraling trajectories of each vortex in the rotating frame of the table; the numbers beside the plotted points indicate the elapsed time in seconds. From these, we can easily calculate the azimuthal positions θ 1 and θ 2 of each vortex core versus time, and deduce by a simple linear fit the orbital rotation rates ω 1 and ω 2 of each vortex as shown in figure 13-b). As ω 1 and ω 2 have nearly constant and very close values in all the runs, we will, in the following, average them to obtain a measurement of the global orbital rotation rate ω orb . We note a systematic slight increase of ω orb at the end of the merging processes. In the same way, we can measure the distance between the cores as a function of time. Figure 13-c) presents these results from the former example.

As can be observed, we can systematically identify three different stages in the merging process in accordance to what has been previously described in the literature for barotropic vortex coalescence (Melander et al. 1987, Meunier et of the interaction we see that the distance between centers stays constant or varies slightly; this first period of time could be identified as a first diffusive stage. In the second or convective stage a rapid decrease of the separation distance is observed until it reaches a minimum. In the third stage, the vortices have merged and we no longer detect any variation of the distance between their centers. To characterize the merging time, we choose to fit the intermediate (or convective stage,where each vortex feels the velocity field from the other vortex that induces the merging) by a decreasing exponential function of time exp (-t/τ ) where τ represents the characteristic time of coalescence. This method permits to deduce easily and automatically τ in order to describe the duration of the process as function of the experimental parameters.

We have found that both the global rotation rate ω orb of the vortex pair and the merging time τ are influenced by the injection flux Q that creates the vortices. A crude two-dimensional model can be built by applying Stoke's theorem on a circle passing through the centers of both vortices: it is straightforward to show that the global orbital rotation rate ω orb is proportional to the vorticity contained essentially in the vortex cores of radius R and inversely proportional to the square of the initial separating distance d 0 . As the Rossby number of each vortex is itself a linear function of the injection rate Q (see figure 5), we can plot ω orb as a function of QR 2 /d 0 2 to test this prediction. Figure 14 shows that this trend is verified by our experimental data: the larger the radii and the smaller the initial distances are, the higher the orbital angular velocity of the vortices around their barycenter is. We can also observe on figure 14 that high injection fluxes Q correspond to fast angular velocities. This can be understood using the already mentioned link between the Rossby number of each vortex and the injection rate through the Coriolis force action. We can thus conclude that the individual angular velocity measured by the Rossby number of each vortex has a direct effect on the global rotation rate of the pair of vortices.

In the same spirit, we have also found that the injection flux Q directly influences the merging time τ . This is shown in figure 15. As expected, the larger the initial distance and the smaller the radii are, the longer it takes for the vortices to merge. Interestingly, we can also observe Orozco Estrada, Cruz Gómez, Le Gal and Cros that mergers are faster (τ small) for high injection flux Q, i. e. is for large individual Rossby numbers. The role of the Rossby number in the coalescence process has also been discovered by the recent numerical observations of [START_REF] Reinaud | The merger of geophysical vortices at finite Rossby and Froude number[END_REF].

The state diagram

Having varied the initial distance d 0 separating the vortices at their creation, the rotating rate Ω of the rotating table, the density gradient that implies different Brünt-Väisälä frequencies and also the injection rate Q that permits to change the Rossby number and thus the initial dimensions H and L of each vortical pairs, we can build the state diagram in the (λ/L and d 0 /L) plane. When pairing is observed, we represent the result at its corresponding location with a blue star next to its label. When the vortices do not merge, we plot the result as a red circle. Each experiment is labeled with a number which is smaller than 100 for hand injection runs and above 100 for pump injection runs. Figure 16 presents this synthesis. As expected, the blue stars are concentrated at the bottom of the figure, i.e. when the initial separating distance d 0 is small. We have shaded this area in blue. On the contrary, when the initial distance is large, the vortices have more difficulty to merge and the red stars are mostly located in the upper part of the figure. However, it is also clear from our results that the Rossby radius of deformation has a tremendous influence on coalescence. Although we cannot perform experiments at too small values of λ/L (our lowest λ /L is around 0.6) because of the presence of centrifugal or baroclinic instabilities that destroy individual vortices, we observe that our experimental results are compatible with the two-dimensional limit. Together with our experimental data points, we represent also the different results from diverse authors. First, the Griffiths and Hopfinger's curve (1987) is plotted (dashed blue curve). It presents a clear increase of the critical distance when λ/L is between 2 and 4. As can be observed on figure 16, our experimental data points show a similar trend when λ/L is between 1 and 3. Around a value close to 2.5, the vortices are prone to merge even if they are separated by a distance more than twice the two-dimensional critical distance (7.5 × L compared to 3.3 × L). However, contrary to Griffiths and Hopfinger's results but in excellent agreement with the numerical simulations of [START_REF] Verron | Sensitivity to initial conditions in the merging of two-layer baroclinic vortices[END_REF] (dashdotted red curve), our experimental critical curve obviously decreases back when λ/L is larger than 3. Then for λ/L larger than 4, i.e. with strong stratification effects compared to rotation, the vortices and their motions are confined in very shallow layers and the frontier d c between pairing and non pairing dynamics decreases back to its expected two-dimensional value close to 3.3. Note that our results do not support (as expected) the results from the three-dimensional quasi-geostrophic model of [START_REF] Dritschel | Vortex merger in rotating stratified flows[END_REF] (solid black curve) where a secondary instability on tall vortices, not seen in our experiments, was suspected to help coalescence. Amazingly, our results appear to match better with the RVI (see the definition of RVI and PVI in our introduction) two-layer model of [START_REF] Verron | Sensitivity to initial conditions in the merging of two-layer baroclinic vortices[END_REF] than with the two-layer Griffiths and Hopfinger's experiments. Verron et al. discuss that the initial conditions of the Griffiths and Hopfinger's experiments are more consistent with PVI conditions because the injection of fluid in the upper layer would deflect the interface and according to potential vorticity conservation, some relative vorticity should be created in the lower layer. With this argument, they reach some kind of contradiction in the sense that the results from the Griffiths and Hopfinger's experiments are more consistent with RVI type conditions contrarily to their initial conditions which are more consistent with PVI type conditions. They try to explain this contradiction by stating that the vorticity induced in the lower layer is weaker than in the upper layer thus the vortices do not present a barotropic vertical structure. They think that the vorticity field in the lower layer is weak enough to prevent the initial conditions to be entirely of PVI type and that would be the reason why the Griffiths and Hopfinger's experimental results differ from the PVI results. In our case, the linear stratification might act as a shield, isolating the vortices from the fluid above and under the vortices. Therefore the relative vorticity stays zero outside the vortices as it can be observed on figure 6. As a consequence, our initial conditions are very close to RVI conditions, and this explains why our experimental results are so similar to the RVI numerical simulations of [START_REF] Verron | Sensitivity to initial conditions in the merging of two-layer baroclinic vortices[END_REF].

To our point of view, the final picture of baroclinic vortex coalescence could be interpreted as follows. For λ/L lower than unity (in this case the Rossby radius of deformation stands inside the vortex core), the influence of density stratification is weak and the critical distance d c stays close to the two-dimensional limit 3.3 × L. Note that in the experiment by [START_REF] Griffiths | Coalescing of geostrophic vortices[END_REF] as well as in the numerical simulations of [START_REF] Verron | Sensitivity to initial conditions in the merging of two-layer baroclinic vortices[END_REF] and also of [START_REF] Dritschel | Vortex merger in rotating stratified flows[END_REF], there is a small decrease of this limit down to 2.5 × L. Then, for λ > L, as we saw previously, stratification helps coalescence. If we consider that the radius of influence of a vortex is equal to the Rossby radius of deformation (a scale lager than the vortex core radius L in this case) we propose to replace the barotropic criterion d c = 3.3 × L by d c = 3.3 × λ which gives a rather good estimation of the frontier separating pairing to non pairing vortices. Finally, as already noted, coalescence being a three dimensional process, a further increase of the density gradients (and thus of N ) makes vortex pairing more and more difficult. The limit is reached in our experiment for λ/L 3 where the critical distance starts to decrease back towards its two-dimensional value, reached as expected for very flat pairs of anticyclones in highly stratified fluid layers. This return to the barotropic value at large λ/L was not observed in the experiment of [START_REF] Griffiths | Coalescing of geostrophic vortices[END_REF] possibly because of the two layer configuration that confines [START_REF] Verron | Sensitivity to initial conditions in the merging of two-layer baroclinic vortices[END_REF] and explained in [START_REF] Hopfinger | Vortices in rotating fluids[END_REF], the red dash-dotted curve has been shifted by a multiplicative factor √ 2. The yellow area represents the "partial pairing" region detected by [START_REF] Dritschel | Vortex merger in rotating stratified flows[END_REF]. The experimental two layer experiment results of [START_REF] Griffiths | Coalescing of geostrophic vortices[END_REF] are represented by the blue dash curve (---) and our estimation of the extension of the barotropic criterion by the grey dotted curve (• • • ).

the vortices in the top layer.

Fourier modes of the merger and Internal Gravity Waves radiation

Internal Gravity Waves (IGWs) play a major role in the atmosphere and in the ocean where they can be seen as a conveyer of energy from large scale flows to small scales so that they participate to mixing and energy dissipation. Therefore, many studies focus on the spontaneous generation of IGWs from nearly balanced flows (see the review by [START_REF] Vanneste | Balance and spontaneous wave generation in geophysical flows[END_REF]). Among these, several numerical simulations based on primitive equation simulations [START_REF] Sugimoto | Generation and backreaction of spontaneously emitted inertia-gravity waves[END_REF] or based on shallow water models [START_REF] Sugimoto | Cyclone-anticyclone asymmetry in gravity wave radiation from a co-rotating vortex pair in rotating shallow water[END_REF][START_REF] Sugimoto | Inertia-gravity wave radiation from the merging of two co-rotating vortices in the f-plane shallow water system[END_REF] show that vortex dipoles or vortex pairs are prompt to generate IGWs. The ultimate goal of these researches is to quantify the amount of ageostrophic energy loss when the vortices are propagating in the case of a dipole, or merging in the case where they are of the same sign. Therefore, in addition to describing the different regimes that lead or not to coalescence, we will address now the problem of the generation of IGWs during the transient time of the fusion of our lenticular anticyclonic pairs. These were already observed in the numerical simulations of [START_REF] Viudez | Spiral patterns of inertia-gravity waves in geophysical flows[END_REF][START_REF] Sugimoto | Inertia-gravity wave radiation from the merging of two co-rotating vortices in the f-plane shallow water system[END_REF] and of [START_REF] Reinaud | The merger of geophysical vortices at finite Rossby and Froude number[END_REF]. A classical procedure to detect Internal Gravity Waves (IGWs) is to calculate the horizontal divergence of the PIV velocity fields [START_REF] Sugimoto | Inertia-gravity wave radiation from the merging of two co-rotating vortices in the f-plane shallow water system[END_REF][START_REF] Rodda | Kelvin and inertia-gravity waves in the barostrat instability experiment[END_REF]). Then a space-time diagram can be computed by recording the fluctuations of the horizontal divergence along a line going through the pair of vortices (see figure 17-a for an example with f = 0.5 rad/s and N = 0.95 rad/s). As can be observed on figure 17-b), waves clearly propagate away from the merging pair, as expected for f < N . The calculation of the average period of these waves (about 10 seconds) show that their frequency is equal to 0.62 rad/s, a value between f and N as requested by the dispersion relation of IGWs. Note that their wavelength is comparable with the diameter of the initial vortices. As the sign of the phase velocity is a function of f -N , we also present in figure 17-c Figure 18 shows the temporal Fourier spectrum of a time series recorded at a point in one of our PIV horizontal divergence fields for f = 1 rad/s, N = 0.7 rad/s, Q = 25 ml/min and d 0 = 5 cm. The low frequency peaks correspond to the different Fourier modes with different azimuthal wave numbers m associated with the double structure of the field during the vortex pairing. In addition a well defined wave packet is clearly visible in the IGWs authorized band between the buoyancy frequency N and the Coriolis frequency f . Snapshots of these modes and of the propagating IGWs fields are calculated by band-pass filtering the global vorticity field. The low frequency modes are associated with the deformation of the vorticity field due to the mutual induction of the vortices in the pair. All these modes rotate with an identical rotation rate which is that of the vortices orbiting one around the other at the rate ω orb while the IGWs propagate radially with their own phase velocity. Let us note however that if our observations of IGWs wave packets are in agreement with recent numerical computations of [START_REF] Viudez | Spiral patterns of inertia-gravity waves in geophysical flows[END_REF] and of [START_REF] Reinaud | The merger of geophysical vortices at finite Rossby and Froude number[END_REF], we are not able at the stage of our study to separate the IGWs wave trains created by the injection process when generating the vortices to those which can be naturally emitted during merging by the rotating non axi-symmetric vortical patterns.

Conclusion

In this experimental work, we have for the first time studied the coalescence of baroclinic anticyclones that were generated in a rotating and continuously stratified layer. Our results clearly show that the merging process is highly dependent on the Rossby radius of deformation λ. First, when λ is smaller than the vortex core, stratification seems not to play an important role. Then, in a range of λ between 1 and 3, coalescence is greatly enhanced. Our interpretation of this enhancement suggests a modification of the two-dimensional criterion by the replacement of the anticyclones radius by their Rossby radius of deformation as this horizontal length is the effective scale associated to baroclinic vortices. But this positive effect due to stratification is only efficient in a restricted region of λ/L. As coalescence of baroclinic vortices involves three dimensional flows during which the vortices intertwine possibly because of the elliptic instability, it is expected that very flat vortices in highly stratified fluid resist against merging and the twodimensional limit is recovered. As a consequence, the barotropic criterion is recovered at large λ. We have also shown that the merging time and the global rotation rate of the pair depend on the Rossby number of each vortex. Besides the description of the state diagram that confirms the numerical simulation of [START_REF] Verron | Sensitivity to initial conditions in the merging of two-layer baroclinic vortices[END_REF], we have also discovered that internal gravity waves are emitted during mergers. Unfortunately, we cannot discriminate at this point the waves generated by the injections used to create the vortices, to those that are emitted by the non balanced vortex pair during coalescence. As a final point, let us mention the visual analogy of our hydrodynamical system with the merger of two black holes associated with the radiation of gravitational waves [START_REF] Abbott | Observation of gravitational waves from a binary black hole merger[END_REF] .

Figure 1 .

 1 Figure 1. Experimental system scheme with the pipes, tubes and injection pumps that permit the creation of the pair of anticyclones.

Figure 2 .

 2 Figure 2. Example of an asymmetric merging for f = 1 rad/s, N = 1.71 rad/s, Q = 60 ml/min and d 0 = 14 cm.

  Figure 3. The vorticity field of a single shielded anticyclone in the laboratory for f = 1 rad/s, N = 1.02 rad/s and Q = 80 ml/min. b) Vorticity profile showing 1888 data points together with their modified Gaussian fit with α = 1.9 and L = 3.5 cm as described in equation (2).

Figure 4 .

 4 Figure 4. Temporal evolution of the Rossby number Ro (a), of the horizontal typical scale L (b) and of α (c) for the experimental run of figure 3.

Figure 5 .

 5 Figure 5. Variation of the Rossby number Ro for a single vortex as a function of the injection flow rate Q. Data points for five experiments are plotted. Circles show the mean Rossby number for each experiment.

Figure 6

 6 Figure 6. a) The velocity field in a vertical section going through the anticyclone at mid-radius. b) Velocity profile showing the data points together with their modified Gaussian fit with β = 1.87 as described in equation (3).

Figure 7 .

 7 Figure 7. Temporal evolution of the ratio R/L for a single vortex.

Figure 8 .

 8 Figure 8. Temporal sequence showing the coalescence of two anticyclones for f = 1.57 rad/s, N = 2.8 rad/s, Q = 45 ml/min and d 0 = 8 cm.

Figure 9 .

 9 Figure 9. Temporal sequence showing the coalescence of two anticyclones for f = 1 rad/s, N = 3.12 rad/s, d 0 = 7.5 cm and Q = 25 ml/min. Two side cyclones coming from the cyclonic rings are ejected from the merging anticyclonic pairs.

Figure 11 .Figure 12 .

 1112 Figure 11. Temporal sequence showing the vorticity fields during the coalescence of two anticyclones for f = 0.5 rad/s, N = 0.95 rad/s, Q = 60 ml/min and d 0 = 8 cm for: a) t = 1 s, b) t = 30 s, c) t = 90 s and d) t = 200 s. Filaments are formed at the external tips of the vortices and will eventually be dissipated whereas the cores are merged in a unique vortex.

Figure 13

 13 Figure13-a) shows the spiraling trajectories of each vortex in the rotating frame of the table; the numbers beside the plotted points indicate the elapsed time in seconds. From these, we can easily calculate the azimuthal positions θ 1 and θ 2 of each vortex core versus time, and deduce by a simple linear fit the orbital rotation rates ω 1 and ω 2 of each vortex as shown in figure13-b). As ω 1 and ω 2 have nearly constant and very close values in all the runs, we will, in the following, average them to obtain a measurement of the global orbital rotation rate ω orb . We note a systematic slight increase of ω orb at the end of the merging processes. In the same way, we can measure the distance between the cores as a function of time. Figure13-c) presents these results from the former example.As can be observed, we can systematically identify three different stages in the merging process in accordance to what has been previously described in the literature for barotropic vortex coalescence[START_REF] Melander | Axisymmetrization and vorticity-gradient intensification of an isolated two-dimensional vortex through filamentation[END_REF][START_REF] Meunier | Physics of vortex merging[END_REF][START_REF] Leweke | Dynamics and instabilities of vortex pairs[END_REF]. At the beginning

Figure 14 .

 14 Figure 14. The evolution of the orbital rotation rate -ω orb as function of Q R 2 / d 0 2 where R is the radius of the vortex cores, d 0 the initial separating distance, and Q the injection flux which is proportional to the Rossby number. The linear trend as expected by a crude two-dimensional model is recovered.

Figure 15 .

 15 Figure 15. The evolution of the merging time as function of Qd 0 /R where R is the radius of the vortex cores, d 0 the initial separating distance, and Q the injection flux which is proportional to the Rossby number. This shows in particular that the merging time depends on the vortex individual Rossby number.

Figure 16 .

 16 Figure 16. State diagram showing a synthesis of our experiments with the pairing ( ) and the non pairing (•) events together with the different numerical predictions of Verron et al. (1990) (-• -) and of Dritschel (2002) (-). Note that in accordance with the definition of the Rossby radius of deformation used by[START_REF] Verron | Sensitivity to initial conditions in the merging of two-layer baroclinic vortices[END_REF] and explained in[START_REF] Hopfinger | Vortices in rotating fluids[END_REF], the red dash-dotted curve has been shifted by a multiplicative factor √ 2. The yellow area represents the "partial pairing" region detected by[START_REF] Dritschel | Vortex merger in rotating stratified flows[END_REF]. The experimental two layer experiment results of[START_REF] Griffiths | Coalescing of geostrophic vortices[END_REF] are represented by the blue dash curve (---) and our estimation of the extension of the barotropic criterion by the grey dotted curve (• • • ).

Figure 17

 17 Figure 17. a) Horizontal divergence of a PIV velocity field for f = 0.5 rad/s, N = 0.95 rad/s, Q = 60 ml/min and d 0 = 8 cm, with the intersecting line along which the space-time diagram is computed. b) Space-time diagram computed along the preceding line passing through the vortex pair. Wave trains are clearly observed with a period of 10 seconds, compatible with the outwards propagation of IGWs. c) Space-time diagram showing inwards propagation of waves for f = 1.2 rad/s, N = 0.95 rad/s, Q = 60 ml/min and d 0 = 8 cm.

Figure 18 .

 18 Figure 18. Fourier spectrum of a temporal series recorded at a point in the PIV horizontal divergence field together with the spatial structures of the corresponding modes labeled by their azimuthal wave numbers m involved in the vortex merging. The internal gravity waves (IGWs) packet emitted during the merging is visible in the authorized spectral band confined between N and f .

OrozcoCruz-v9Vortex interactions in a linearly stratified rotating fluid

Acknowledgments

This work has been carried out in the framework of the Labex MEC Project 410 (No. ANR-10-LABX-0092) and of the A*MIDEX Project (No. ANR-11-IDEX-0001-02), funded by the "Investissements d'Avenir" French Government program managed by the French National Research Agency (ANR). The authors also acknowledge support from the American Physical Society's International Research Travel Award Program (IRTAP). We also thank for their financial support, the University of Guadalajara and Aix Marseille Université for the fundings "Appel à Projets Actions Internationales" 2016. A. O. E. acknowledges CONACyT for his scholarship.