Low Mach number limit of the full Navier-Stokes equations. Archive for Rational Mechanics and Analysis, vol.180, pp.1-73, 2006. ,
Numerical approximation of the 3d hydrostatic Navier-Stokes system with free surface, Ocean Modelling, vol.53, issue.6, pp.1981-2024, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01393147
A multilayer Saint-Venant model : Derivation and numerical validation, Discrete Contin. Dyn. Syst. Ser. B, vol.5, issue.2, pp.189-214, 2005. ,
Finite-volume solvers for a multilayer Saint-Venant system, Int. J. Appl. Math. Comput. Sci, vol.17, issue.3, pp.311-319, 2007. ,
Numerical simulations of 3d free surface flows by a multilayer Saint-Venant model, Internat. J. Numer. Methods Fluids, vol.56, issue.3, pp.331-350, 2008. ,
Approximation of the hydrostatic Navier-Stokes system for density stratified flows by a multilayer model. Kinetic interpretation and numerical validation, J. Comp. Phys, vol.230, pp.3453-3478, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00654642
A multilayer Saint-Venant system with mass exchanges for Shallow Water flows. Derivation and numerical validation, ESAIM: M2AN, vol.45, pp.169-200, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00355730
Kinetic entropy for layer-averaged hydrostatic Navier-Stokes equations. submitted, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01583511
The incompressible Navier-Stokes-Fourier system with free surface, Part II: Numercial scheme & validation, 2018. ,
A robust well-balanced scheme for multi-layer shallow water equations, Discrete Contin. Dyn. Syst. Ser. B, vol.13, pp.739-758, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00538338
An entropy satisfying two-speed relaxation system for the barotropic Euler equations. Application to the numerical approximation of low Mach number flows. working paper or preprint, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01661275
Théorie analytique de la chaleur mise en harmonie avec la thermodynamique et avec la théorie mécanique de la lumière, vol.2, 1903. ,
Homogeneous hydrostatic flows with convex velocity profiles, Nonlinearity, vol.12, issue.3, pp.495-512, 1999. ,
Layer-averaged Euler and Navier-Stokes equations, Commun. Math. Sci, vol.15, issue.5, pp.1221-1246, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01202042
Numerical simulation of two-layer shallow water flows through channels with irregular geometry, J. Comput. Phys, vol.195, issue.1, pp.202-235, 2004. ,
A Q-scheme for a class of systems of coupled conservation laws with source term, M2AN Math. Model. Numer. Anal, vol.35, issue.1, pp.107-127, 2001. ,
Sigma transformation and ALE formulation for threedimensional free surface flows, Internat. J. Numer. Methods Fluids, vol.59, issue.4, pp.357-386, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00275463
Bulk viscosity and compressibility measurement using acoustic spectroscopy, Feireisl and A. Novotný. The Low Mach Number Limit for the Full Navier-Stokes-Fourier System. Archive for Rational Mechanics and Analysis, vol.130, pp.77-107, 2007. ,
A multilayer method for the hydrostatic Navier-Stokes equations: a particular weak solution, Journal of Scientific Computing, vol.60, issue.2, pp.408-437, 2014. ,
A hierarchy of dispersive layer-averaged approximations of Euler equations for free surface flows, Communications in Mathematical Sciences, vol.16, issue.5, pp.1169-1202, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01324012
A new two-dimensional Shallow Water model including pressure effects and slow varying bottom topography, Turbulent Diffusion in Environmental Pollution, vol.38, pp.353-370, 1975. ,
Relaxing the boussinesq approximation in ocean circulation models, Journal of Atmospheric and Oceanic Technology, vol.18, issue.11, pp.1911-1923, 2001. ,
, On the derivation of homogeneous hydrostatic equations. ESAIM: M2AN, vol.33, pp.965-970, 1999.
An Oceanic General Circulation Model in Pressure Coordinates, Advances in Atmospheric Sciences, vol.2, issue.3, pp.14-21, 1971. ,
Generation of an acoustic-gravity wave by two gravity waves, and their subsequent mutual interaction, Journal of Fluid Mechanics, vol.735, p.6, 2013. ,
Including Non-Boussinesq Effects in Boussinesq Ocean Circulation Models, Journal Of Physical Oceanography, p.31, 2000. ,
Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects, European Journal of Mechanic /B, vol.26, pp.49-63, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-02067998
On the Hs theory of hydrostatic Euler equations. Archive for Rational Mechanics and Analysis, vol.204, pp.231-271, 2012. ,
On conservation equations in oceanography: How accurate are boussinesq ocean models?, Journal of Physical Oceanography, vol.32, issue.5, pp.1574-1584, 2002. ,
Sea level variations induced by heating and cooling: An evaluation of the Boussinesq approximation in ocean models, J. Geophys. Res, vol.100, issue.C10, pp.20565-20577, 1995. ,
, On the filtering of sound from the Navier-Stokes equations, 1982.
Thermodynamic properties of standard seawater: extensions to high temperatures and pressures, Ocean Science, vol.5, issue.699, pp.235-246, 2003. ,
Vertically averaged models for the free surface Euler system. Derivation and kinetic interpretation, Math. Models Methods Appl. Sci. (M3AS), vol.46, issue.3, pp.459-490, 2011. ,
URL : https://hal.archives-ouvertes.fr/inria-00551484
Parametric vertical coordinate formulation for multiscale, Boussinesq, and non-Boussinesq ocean modeling, vol.11, pp.298-332, 2006. ,
Trapped internal waves over topography: Non-Boussinesq effects, symmetry breaking and downstream recovery jumps, Physics of Fluids, vol.25, p.66602, 2013. ,
On the boussinesq approximation for a compressible fluid, Tenth report of the joint panel on oceanographic tables and standards, vol.131, pp.442-447, 1960. ,
, Thermodynamic equation of seawater: Calculation and use of thermodynamic properties, 2010.