Simulations de l'écoulement turbulent marin avec un modèle de déconvolution

International audienceWe display a continous equation for the deconvolution process that generalizes the Van Cittert algorithm in the case of oceanic boundary conditions for a given fixed wind. We deduce a LES model for which we have existence and uniqueness of a strong solution. Finally, we display several numerical simulations showing the practical interest of the model

On the coupling of wave and three-dimensional circulation models : Choice of theoretical framework, practical implementation and adiabatic tests

Many theoretical approaches and implementations have been proposed for the coupling of the three-dimensional ocean circulation with waves. The theoretical models are reviewed and it is shown that the formulation in terms of the quasi-Eulerian velocity circumvents the essential difficulty of alternative formulations for the Lagrangian mean velocity. Namely, models based on this Lagrangian velocity require an estimation of wave-induced motions to first order in the horizontal gradients of the wave field in order to estimate the vertical flux of wave pseudo-momentum. So far, only three-dimensional wave models have been able to provide these estimates, and all published theories based on the simpler Airy theory are not consistent at the leading order, because they ignore or incorrectly estimate the vertical momentum flux. With an adiabatic example on a sloping bottom it is shown that this inconsistency produces very large spurious velocities. These errors are independent of the slope for the inviscid case, and are still significant when a realistic vertical mixing is applied. A quick diagnostic of the potential accuracy of a theoretical model is the vertical profile of the wave-induced forcing terms: if it is not uniform over depth in adiabatic conditions then it will produce spurious artificial flow patterns in conditions with shoaling waves. Although conceptually more challenging, the quasi-Eulerian velocity theories only introduce minor modifications of the solution procedure for the standard primitive equations: a modification of the surface boundary condition for the mass conservation, the addition of the Stokes drift in the tracer advection equations, and sources of momentum and turbulent kinetic energy with associated surface and bottom fluxes. All the necessary modifications of primitive equation models are given in detail. This implementation is illustrated with the MARS3D model, which passes the test of the adiabatic shoaling waves

A comparison of three turbulence models with an application to the West Pacific Warm Pool

In this work, we compare three turbulence models used to parameterize the oceanic boundary layer. These three models depend on the bulk Richardson number, which is coherent with the studied region, the West Pacific Warm Pool, because of the large mean shear associated with the equatorial undercurrent. One of these models, called R224, is new and the others are Pacanowski and Philander's model (R213 model) and Gent's model (R23 model). The numerical implementation is based on a non-conservative numerical scheme. The following (three criteria) are used to compare the models: the surface current intensity, the pycnocline's form and the mixed layer depth. We initialize the code with realistic velocity and density profiles thanks the TOGA-TAO array (McPhaden, 1995). In case of static instability zone on the initial density profile, only the R224 model gives realistic results. Afterwards, we study a mixed layer induced by the wind stress. In this case, the R224 results and the Pacanowski and Philander's results are similar. Furthermore, we simulate a long time case. We obtain a linear solution for all models that is in agreement with Bennis and al

Numerical modelling of algebraic closure models of oceanic turbulent mixing layers

International audienceWe introduce in this paper some elements for the mathematical and numerical analysis of algebraic turbulence models for oceanic surface mixing layers. In these models the turbulent diffusions are parameterized by means of the gradient Richardson number, that measures the balance between stabilizing buoyancy forces and destabilizing shearing forces. We analyze the existence and linear exponential asymptotic stability of continuous and discrete equilibria states. We also analyze the well-posedness of a simplified model, by application of the linearization principle for non-linear parabolic equations. We finally present some numerical tests for realistic flows in tropical seas that reproduce the formation of mixing layers in time scales of the order of days, in agreement with the physics of the problem. We conclude that the typical mixing layers are transient effects due to the variability of equatorial winds. Also, that these states evolve to steady states in time scales of the order of years, under negative surface energy flux conditions

Numerical modeling of buoyant turbulent mixing layers

We introduce in this paper some elements for the mathematical and numerical analysis of turbulence models for oceanic surface mixing layers. In these models the turbulent diffusions are parameterized by means of the Richardson’s number, that measures the balance between stabilizing buoyancy forces and un-stabilizing shearing forces. The wellpossedness of these models is a difficult mathematical problem, due to the partial monotonic nature of the space operators involved. We analyze the existence and stability of equilibria state, and devise a conservative numerical scheme satisfying the maximum principle. We present some numerical tests for realistic flows in tropical seas that reproduce the formation of mixing layers, in agreement with the physics of the problem.Ministerio de Educación y Cienci

Stability of some turbulent vertical models for the ocean mixing boundary layer

We consider four turbulent models to simulate the boundary mixing layer of the ocean. We show the existence of solutions to these models in the steady-state case then we study the mathematical stability of these solutions

Model and method to predict the turbulent kinetic energy induced by tidal currents, application to the wave-induced turbulence

A prediction model for the turbulent kinetic energy (TKE) induced by tidal-currents is proposed as a function of the barotropic velocity only, along with a robust method evaluating the different parameters involved using Acoustic Doppler Current Profiler (ADCP) measurements from Alderney Race. We find that the model is able to reproduce correctly the TKE profiles with coefficients of correlation on average higher than 0.90 and normalised root-mean-square errors (NRMSE) less than 14%. Different profiles are also tested for the mean velocity, no satisfactory prediction model is found but we are able to have decent estimates of the velocity shear and friction velocity. Two applications are then carried out. First the turbulent budget terms are estimated and discussed. We identify the turbulent production and dissipation of TKE as the most important mechanisms, then we discuss the validity of several theoretical results derived for isotropic turbulence for this application. A strong departure for the estimation of the turbulent dissipation is notably found and explained by the turbulent anisotropy. At last the prediction model for the TKE is used to infer the wave-induced TKE. We show the importance of removing the tidal component, waves can have a strong influence down to mid-depth

Eulerian Pressure-Velocity/ Lagrangian Vorticity-Velocity Coupling Applied to Wake and Forces Calculation of Biofouled Tidal Turbines

Marine tidal turbines are subject to the environment in which they are deployed. In the natural environment, they are gradually colonized by sessile species. These fouling organisms modify the flow around the blades and in the wake of the tidal turbine. Unfortunately, they also complicate the numerical study of such tidal turbines by preventing the use of usual methods such as the Blade Element Method or the Lifting Line Theory. In this context, we propose to use an alternative solution, which combines an Eulerian code to study the near field with a Lagrangian code for the wake. After a short presentation of each code, the coupling method is detailed, and applied to the case of a tidal turbine with its own vertical axis. First results are shown and compared to a full Eulerian simulation. Although the data transmission between both codes works well, discrepancies were found due to abnormal increase of energy in the Lagrangian area. A solution is proposed and explained