Energy conservation issues in sigma-coordinate free-surface ocean models

Abstract

International audienceThis 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

Functioning of the planktonic ecosystem on the Gulf of Lions shelf (NW Mediterranean) during spring and its impact on the carbon deposition: a field data and 3-D modelling combined approach

“…The three-dimensional (3-D) primitive equations, sigmacoordinate, free surface SYMPHONIE hydrodynamic model used in this work was described in detail by Marsaleix et al (2008). This model has been primarily used to describe the dynamics of the Rhone River plume and its response to wind forcing (Estournel et al, 1997(Estournel et al, , 2001Marsaleix et al, 1998), and also succeeded in reproducing the coastal circulation in the Gulf of Lions (Estournel et al, 2003;Petrenko et al, 2008).…”

Three-dimensional modelling of wave-induced current from the surf zone to the inner shelf

“…We develop and implement a new method to take into account the impact of waves into the 3-D circulation model SYMPHONIE (Marsaleix et al, 2008(Marsaleix et al, , 2009a following the simplified equations of , which use glm2z-RANS theory (Ardhuin et al, 2008c). These adiabatic equations are completed by additional parameterizations of wave breaking, bottom friction and wave-enhanced vertical mixing, making the forcing valid from the surf zone through to the open ocean.…”

“…Few studies and measurements have been dedicated to the mid-shelf zone (with water depths of order 100 m), or at least to the inner shelf (between the surf zone and mid shelf): Lentz et al (1999Lentz et al ( , 2008 were one of the first to study the influence of waves on the inner shelf. The purpose of this article is to extend the study of wave-current interaction to both the inner shelf and the open ocean by implementing the new set of equations of in the primitive equation model SYMPHONIE (Marsaleix et al, 2008). By using a nested strategy, which allows studies at all scales and by completing the model with additional parameterizations of wave breaking, bottom friction and waveenhanced vertical mixing, we ensure that the forcing is valid from the surf zone through to the open ocean.…”

Estimating geostrophic and total velocities from CTD and ADCP data: Intercomparison of different methods

“…For that purpose, we use the 3D free-surface primitive equation 222 model SYMPHONIE (Marsaleix et al, 1998;Marsaleix et al, 2008), which produces realistic 223 scenarios including a wide variety of structures and processes. In particular, ageostrophic 224 motion caused by current-topography interactions or wind forcing is included; conversely, tides 225…”