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Papers by Anne-Claire Bennis

Research paper thumbnail of Simulations de l'écoulement turbulent marin avec un modèle de déconvolution

Comptes Rendus Mathematique, 2009

... I 347 (2009) 445 450 Probl mes math matiques de la m canique Simulations de l coulement turbu... more ... I 347 (2009) 445 450 Probl mes math matiques de la m canique Simulations de l coulement turbulent marin avec un mod le de d convolution Anne-Claire Bennis a , Roger Lewandowski a , Edriss S. Titi b,ca IRMAR, campus Beaulieu, Universit de Rennes I, 35042 Rennes ...

Research paper thumbnail of Numerical modelling of algebraic closure models of oceanic turbulent mixing layers

Mathematical Modelling and Numerical Analysis, 2010

We introduce in this paper some elements for the mathematical and numerical analysis of algebraic... more We 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 wellposedness 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. Mathematics Subject Classification. 76D05, 35Q30, 76F65, 76D03.

Research paper thumbnail of Mixing parameterization: Impacts on rip currents and wave set-up

Research paper thumbnail of Comments on “The Depth-Dependent Current and Wave Interaction Equations: A Revision”

Journal of Physical Oceanography, 2011

Equations for the wave-averaged three-dimensional momentum equations have been published in this ... more Equations for the wave-averaged three-dimensional momentum equations have been published in this journal. It appears that these equations are not consistent with the known depth-integrated momentum balance, especially over a sloping bottom. These equations should thus be considered with caution, because they can produce erroneous flows, particularly outside of the surf zone. It is suggested that the inconsistency in the equations may arise from the different averaging operators applied to the different terms of the momentum equation. It is concluded that other forms of the momentum equations, expressed in terms of the quasi-Eulerian velocity, are better suited for three-dimensional modeling of wave-current interactions.

Research paper thumbnail of Numerical wave modeling in conditions with strong currents: dissipation, refraction and relative wind

Journal of Physical Oceanography, Jul 20, 2012

Currents effects on waves have led to many developments in numerical wave modeling over the past ... more Currents effects on waves have led to many developments in numerical wave modeling over the past two decades, from numerical choices to parameterizations. The performance of numerical models in conditions with strong currents is reviewed here, and observed strong effects of opposed currents and modulations of wave heights by tidal currents in several typical situations are interpreted. For current variations on small scales, the rapid steepening of the waves enhances wave breaking. Using different parameterizations with a dissipation rate proportional to some measure of the wave steepness to the fourth power, the results are very different, none being fully satisfactory, which points to the need for more measurements and further refinements of parameterizations. For larger-scale current variations, the observed modifications of the sea state are mostly explained by refraction of waves over currents and relative wind effects, that is, the wind speed relevant for wave generation is the speed in the frame of reference moving with the near-surface current. It is shown that introducing currents in wave models can reduce the errors on significant wave heights by more than 30% in some macrotidal environments, such as the coast of Brittany, in France. This large impact of currents is not confined to the locations where the currents are strongest, but also downwave from strong current gradients.

Research paper thumbnail of User manual and system documentation of WAVEWATCH-IIITM version 3.14

Technical note, MMAB Contribution, 2003

Research paper thumbnail of 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 threed... more Many theoretical approaches and implementations have been proposed for the coupling of the threedimensional 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.

Research paper thumbnail of Simulations de l'écoulement turbulent marin avec un modèle de déconvolution

Comptes Rendus Mathematique, 2009

... I 347 (2009) 445 450 Probl mes math matiques de la m canique Simulations de l coulement turbu... more ... I 347 (2009) 445 450 Probl mes math matiques de la m canique Simulations de l coulement turbulent marin avec un mod le de d convolution Anne-Claire Bennis a , Roger Lewandowski a , Edriss S. Titi b,ca IRMAR, campus Beaulieu, Universit de Rennes I, 35042 Rennes ...

Research paper thumbnail of Numerical modelling of algebraic closure models of oceanic turbulent mixing layers

Mathematical Modelling and Numerical Analysis, 2010

We introduce in this paper some elements for the mathematical and numerical analysis of algebraic... more We 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 wellposedness 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. Mathematics Subject Classification. 76D05, 35Q30, 76F65, 76D03.

Research paper thumbnail of Mixing parameterization: Impacts on rip currents and wave set-up

Research paper thumbnail of Comments on “The Depth-Dependent Current and Wave Interaction Equations: A Revision”

Journal of Physical Oceanography, 2011

Equations for the wave-averaged three-dimensional momentum equations have been published in this ... more Equations for the wave-averaged three-dimensional momentum equations have been published in this journal. It appears that these equations are not consistent with the known depth-integrated momentum balance, especially over a sloping bottom. These equations should thus be considered with caution, because they can produce erroneous flows, particularly outside of the surf zone. It is suggested that the inconsistency in the equations may arise from the different averaging operators applied to the different terms of the momentum equation. It is concluded that other forms of the momentum equations, expressed in terms of the quasi-Eulerian velocity, are better suited for three-dimensional modeling of wave-current interactions.

Research paper thumbnail of Numerical wave modeling in conditions with strong currents: dissipation, refraction and relative wind

Journal of Physical Oceanography, Jul 20, 2012

Currents effects on waves have led to many developments in numerical wave modeling over the past ... more Currents effects on waves have led to many developments in numerical wave modeling over the past two decades, from numerical choices to parameterizations. The performance of numerical models in conditions with strong currents is reviewed here, and observed strong effects of opposed currents and modulations of wave heights by tidal currents in several typical situations are interpreted. For current variations on small scales, the rapid steepening of the waves enhances wave breaking. Using different parameterizations with a dissipation rate proportional to some measure of the wave steepness to the fourth power, the results are very different, none being fully satisfactory, which points to the need for more measurements and further refinements of parameterizations. For larger-scale current variations, the observed modifications of the sea state are mostly explained by refraction of waves over currents and relative wind effects, that is, the wind speed relevant for wave generation is the speed in the frame of reference moving with the near-surface current. It is shown that introducing currents in wave models can reduce the errors on significant wave heights by more than 30% in some macrotidal environments, such as the coast of Brittany, in France. This large impact of currents is not confined to the locations where the currents are strongest, but also downwave from strong current gradients.

Research paper thumbnail of User manual and system documentation of WAVEWATCH-IIITM version 3.14

Technical note, MMAB Contribution, 2003

Research paper thumbnail of 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 threed... more Many theoretical approaches and implementations have been proposed for the coupling of the threedimensional 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.