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| Gravity Waves | Modelling | Model Outputs Analysis | Coastal Altimetry | 3D Circulations | Sediment transport, Ecology | Data Assimilation |
An original implementation of a non-hydrostatic, free-surface algorithm based on a pressure correction method is proposed for ocean modelling. The free surface is implemented through an explicit scheme combined with a mode-spitting method but the depth-averaged velocity and the position of the free surface are updated at each non-hydrostatic iteration. The vertical momentum equation is also integrated up to the surface enabling a natural and accurate treatment of the surface layer. The consistent specification of the numerical schemes provides balanced transfers of potential and kinetic energy. This algorithm is well-suited for implementation as a non-hydrostatic kernel on originally hydrostatic free-surface ocean models such as Symphonie for which it has originally been developed. Energy balances associated with the propagation of short surface waves and solitary waves are presented for two dedicated well-documented configurations over closed domains. The buoyancy flux, the work rate of the pressure force together with the power of the advective terms are evaluated and discussed for the generation and the propagation of these two types of waves. The dissipation rate is in particular shown to be several orders of magnitude smaller than the work rates of the hydrostatic and non-hydrostatic pressure forces confirming the necessity for the exchanges of energy to be numerically balanced. The algorithm is subsequently applied to the complex generation of non-linear solitary internal waves by surface tides over Georges Bank, in the Gulf of Maine. The generation and the propagation of the observed non-linear and non-hydrostatic features in this region are correctly reproduced. http://dx.doi.org/10.1016/j.ocemod.2010.09.006
Variational Initialization: VIFOP On coastal ocean embedded modeling: Auclair F., Estournel C., Marsaleix P., Pairaud I. (GRL 2006) The initialization and forcing of embedded coastal ocean models is shown to raise several serious difficulties, however, surprisingly enough, very little attention is paid by coastal modelers to resulting dynamical discrepancies introduced over both short and long time scales. A modular and "Knowledge accumulating" approach for coastal ocean embedded modeling is proposed based on a variational approach. The extrapolation situations mostly associated to bathymetry constraints are discussed and are shown to be of great importance for any embedded coastal model. A well adapted extrapolation scheme is proposed. Two variational constraints are more particularly shown to lead to important improvements of the downscaling: the mass balance is satisfied in a dynamically coherent way based on Green's theorem and an optimal scheme is presented to extrapolate both the temperature and the salinity in the deepest regions where no data is available. http://dx.doi.org/10.1029/2006GL026099 Application of an Inverse Method to Coastal Modeling Auclair F., Casitas S., Marsaleix P. (JAOT 2000) Free surface coastal models currently suffer from the difficulty of having to specify the global circulation during the initialization process and along the open boundaries. As an alternative to the long spinup periods, an original explicit approach based on inverse techniques has been developed. Data originating from in situ observations and/or ocean general circulation models are optimally interpolated over the small-scale grid in such a way that the tendency terms are reduced to physically consistent values. The errors on the "true" tendencies and the truncated nonlinear term are evaluated to compute the model covariance. The observation covariance matrix is divided into two parts: the homogeneous, isotropic matrix calculated with a global energy spectrum; and a parameterized nonhomogeneous, nonisotropic matrix. The inverse method is applied to the study of the interaction of a barotropic alongshore current over a narrow canyon. The transient processes following the initialization are drastically reduced and the analysis field can efficiently be used in a flow relaxation scheme along the open boundaries..... doi: 10.1175/1520-0426(2000)017<1368:AOAIMT>2.0.CO;2 |
Resolution issues in numerical models of oceanic and coastal circulation Greenberg D. A., Dupont F., Lyard F. H., Lynch D. R., Werner F. E (CSR 2007) The baroclinic and barotropic properties of ocean processes vary on many scales. These scales are determined by various factors such as the variations in coastline and bottom topography, the forcing meteorology, the latitudinal dependence of the Coriolis force, and the Rossby radius of deformation among others. In this paper we attempt to qualify and quantify scales of these processes, with particular attention to the horizontal resolution necessary to accurately reproduce physical processes in numerical ocean models. We also discuss approaches taken in nesting or down-scaling from global/basin-scale models to regional-scale or shelf-scale models. Finally we offer comments on how vertical resolution affects the representation of stratification in these numerical models. http://dx.doi.org/10.1016/j.csr.2007.01.023 - Toulouse Unstructured Grid Ocean model T-UGO
Energy conservation issues in sigma-coordinate free-surface ocean models Marsaleix P., Auclair F., Floor J. W., Herrmann M. J., Estournel C., Pairaud I., Ulses C. (O.M. 2008) This paper focuses on the energy conservation properties of a hydrostatic, Boussinesq, coastal ocean model using a classic finite difference method. It is shown that the leapfrog time-stepping scheme, combined with the sigma-coordinate formalism and the motions of the free surface, prevents the momentum advection from exactly conserving energy. Because of the leapfrog scheme, the discrete form of the kinetic energy depends on the product of velocities at odd and even time steps and thus appears to be possibly negative when high-frequency modes develop. Besides, the study of the energy balance clarifies the numerical choices made for the computation of mixing processes. The time-splitting technique used to reduce the computation costs associated to the resolution of surface waves leads to the well-known external and internal mode equations. We show that these equations do not conserve energy if the coupling of these two modes is forward in time. Even if non-linear terms are negligible, this shortcoming can be significant regarding the pressure gradient term ‘frozen’ over a baroclinic time step. An alternative energy-conserving time-splitting technique is proposed in this paper. Discussion and conclusions are conducted in the light of a set of numerical experiments dedicated to surface and internal gravity waves. doi: 10.1016/j.ocemod.2007.07.005 |
Open boundary conditions for internal gravity wave modelling using polarization relations Marsaleix P., Ulses C., Pairaud I., Herrmann M.J., Floor J.W., Estournel C., Auclair F., (Ocean Modelling, 2009) This paper proposes an original approach of the open boundary condition problem, within the framework of internal hydrostatic wave theory. These boundary conditions are based on the relations of polarization of internal waves. The method is presented progressively, beginning with a simple case (non-rotating regime, propagation direction normal to the open boundary), ending with a more general situation (rotating regime, multimodal & multi-dimensional propagations and variable background field). In the non-rotating case and as far as we assume that the direction of propagation is locally normal to the open boundary, the so-called PRM (polarization relation method) scheme can be seen as a three-dimensional version of the barotropic Flather boundary conditions. The discrete form of the scheme is detailed. Numerical stability issues proper to leap-frog time stepping are in particular discussed. It is shown that errors on phase speed prescribed in the boundary conditions can notably deteriorate radiation properties. The normal mode approach is introduced to identify coherent structures of propagation and their corresponding phase speed. A simple and robust multi-dimensional propagation scheme can easily be derived from polarization relations. The rotating case is more difficult but it is possible, to some extent, to get around the dependency of phase speed on wave frequency and to keep the non-rotating formulation of the PRM conditions almost unchanged. The PRM scheme being applied to field anomalies, the question of the background reference state is addressed. The latter can be used to introduce incoming waves across the open boundaries or, alternatively, to represent the low-frequency variability of the model itself. The consistency of the pressure and tracer boundary conditions is finally discussed. http://dx.doi.org/10.1016/j.ocemod.2009.02.010 Considerations on Open Boundary Conditions for Regional and Coastal Ocean Models Marsaleix P., Auclair F., Estournel C., (JAOT 2006) This paper reviews the usual open boundary conditions (OBCs) for coastal ocean models and proposes a complete set of open boundaries based on stability criteria, on mass and energy conservation arguments, and on the ability to enforce external information. This set includes a radiation condition for barotropic variables, an equation of wave propagation for baroclinic velocities, and an advection equation for tracers. Considerations on mass and energy conservation properties suggest a suitable numerical treatment of the barotropic scheme, which is different from what is commonly used. Restoring terms, when classically added in the Sommerfeld OBCs, are not consistent with external fields. It is shown that this can be avoided if proper numerical schemes are used or if OBCs are applied on differences between the model and forcing rather than on absolute variables. Finally, this paper shows that simplistic advection-type methods for temperature and salinity should not be used in sigma coordinate models because this introduces errors in the computation of the horizontal pressure gradient. http://dx.doi.org/10.1175/JTECH1930.1 |
