Ageostrophic contribution by the wind and waves induced flow to the lateral 1 stirring in the Mediterranean Sea

We study the impact of the Ekman currents and Stokes drift on the horizontal mixing and transport properties of theMediterranean Sea. FSLE at the ocean surface are computed over the whole basin using 25 years of satellite altimetry derived geostrophic currents, 10-m wind velocity and wave fields. We find that the transport pathways unveiled by the geostrophic Lagrangian Coherent Structures (LCS) are significantly modified by the ageostrophic currents (i.e. Ekman and Stokes induced velocities), often leading to a decrease of the retention capacity of the eddies. An exhaustive assessment of the regional dependence and temporal variability of the FSLE shows an increase of the horizontal mixing activity, due to the ageostrophic component, up to 37% in regions such as the Gulf of Lion or the Aegean Sea, during the seasons where wind and waves are intense and persistent. Positive trends in the total FSLE (up to 1.2% of the value of FSLE per year in some regions) suggest that Mediterranean Sea has experienced a significant increase in mixing activity over the last decades. Ageostrophic features are considered to play a role in determining the properties of the relative dispersion. Through the analysis of the Lagrangian Anisotropy Index (LAI) using virtual and real pair of drifters, we observe that the particle dispersion is mainly dominated by the zonal flow, and that the ageostrophic currents induce meridional dispersion, particularly in regions where wind and wave are intensified. 14

where is the water density, U s is the wave-induced Stokes drift, U s the Coriolis-Stokes 2016, e.g.), or alternatively as part of a "wavy Ekman balance" involving Stokes Coriolis, vertical 116 mixing, the surface wind stress as a boundary condition, and momentum transfer due to waves In this work, the momentum transfer from waves to the mean flow due to dissipation of wave where is the wind stress, the radiation stress due to the waves at the sea surface, the where SSH is the Sea Surface Height, the acceleration of gravity and the Coriolis parameter.

154
In this work we use the absolute geostrophic velocity fields provided by Copernicus Marine Here, we only consider two-dimensional fields, i.e. r=( , ) with and the longitudinal and in the vertical dimension, z, over the first meter. The position of the particle between two consecutive 200 times and + Δ is obtained integrating Eq. 6: Owing to the temporal and spatial discretization of the data sets an interpolation scheme has to be are integrated using a fourth-order Runge-Kutta scheme with a bilinear spatial interpolation of the 205 velocity field and an integration time step of 1 hour, thus minimizing the numerical diffusion.

206
In order to analyze the influence of wind and waves on the total transport at the sea surface, the 207 motion of the particles is computed using both the total and the geostrophic velocitiy fields: where is the initial separation between a pair of particles, the amplification factor of separation  The analysis is also applied to the OGS drifters dataset described in section 2 with a drogue of and being and the initial distances between pair of particles separated in the longitudinal or in the 265 latitudinal direction. It should be noted that the final distance, in both definitions and , is 266 measured specifically along one direction: longitudinal and latitudinal, respectively.

267
The anisotropy in the dispersion process can be measured computing the difference between the that two fluid particles initially separated a distance 0 need to be finally separated a distance .

278
At the position r and time , the FSLE, is given by: We remark that averages are not performed in this definition of the FSLE in order to have an  Similarly to LAI, we compute the Lagrangian Coherent Structure Anisotropy (LCSA), as:   The average of FSLE is also calculated seasonally from 1994 to 2018 in order to characterize 384 the regional impact of the intra-annual variability of the wind and waves conditions on the LCS. 385 We only focus on the winter-summer differences (not shown all the seasons). The averaged FSLE 386 over winter months (December-January-February-March) is shown in Fig. 6, c) and over summer  Similarly, we compute the normalized contribution of ageostrophic currents to horizontal mixing 391 for winter (Fig. 6, d) and summer (Fig. 6, f). In winter, the ageostrophic component mainly  with a value around 1.8 · 10 −1 days −1 , followed by R1 and R6 (regions experiencing a significant 491 impact of wind stress) with ∼ 1.35 · 10 −1 days −1 , and the lowest corresponding to R4 and Table 1. Values of (· 10 −1 days −1 ), (in km) and the slopes ( ) resulting from the best fitting of the  in the values is observed using real drifters (see Fig. 9, b).

495
Comparing the FSLE curves obtained from geostrophic currents with the obtained for total 509 currents, we observe that both are rather similar over R5 and R6 and slightly higher as The spatial scale identifying the transition between the exponential and the power law separation 514 rate, denoted as , is different in each region. This scale could give some insight about the 515 minimum size of the mesoscale structures governing the relative dispersion. In R1, is around 516 36km, followed by R4 ∼ 41km, R6 ∼ 54km, R5 ∼ 60km and R2 ∼ 62km, and finally in R3 ∼ 517 69km.

518
The best-fitting of the regional FSLE and FSLE curves ( -U and -U , respectively) at larger 519 scales return values of the slopes spanning from −0.97 to −0.66 (see Table 1). In all the regions 520 the relative dispersion obtained from both U and U is associated with a Richardson's turbulent 521 diffusion (scaling rate of −2/3), except for R3, R5 and R6 obtained from U and for R5 obtained 522 from U , where the scaling law is rather related to a ballistic or shear dispersion (scaling rate of 523 −1). It means that in R1, R2 and R4 the main contributors to the separation rate at these large scales 524 are structures with size comparable with the separation itself. Note that, in general, the obtained 525 slope is slightly steeper for -U than for -U , particularly larger over R3, where the regime 526 dispersion at large scales moves from being associated with a Richardson turbulent dispersion in 527 the total field to a shear dispersion in the geostrophic velocity field.

528
The relative dispersion for the real drifters is calculated selecting all the simultaneously available 529 drifters in each SOM-region at least during 2 consecutive days. In Fig. A2  R2, R3 and R6 suggest a plateau between 5 and 20 km (Fig. 9, b), associated with a mesoscale 534 exponential separation, and a ballistic/shear dispersion at scales larger than 20 km, although this 535 has been taken with caution due to the small number of pairs used in the average, particularly in curves and between (0.74-1.56) · 10 −1 days −1 for the meridional FSLE (see Table 1 and Fig. 10).

560
Note that values are larger when considering the total separation distance than only considering 561 the separation along one of the orthogonal directions. This shows that while the leading expansion 562 direction of the separation vector is not only aligned along one exclusive orthogonal direction but 563 a combination of both. In general, the zonal component of the flow has a higher impact on the 564 relative dispersion than the meridional, being more significant at larger scales. As a consequence, 565 the spreading of tracers is more oriented along the zonal direction than along the meridional.  In order to further study the anisotropy of the flow associated with ageostrophic component, we at the south of Crete in summer (Fig. 12, f). This seasonal variability is in agreement with

648
With this work, we have analyzed the horizontal mixing and transport properties at the upper 649 layer of the Mediterranean Sea associated with the wind and waves generated fluid particle motions. 650 We have combined data from real drifters trajectories and the output of a Ekman modified model