@article{fdi:010077066,
  title = {{S}tability analysis of split-explicit free surface ocean models : implication of the depth-independent barotropic mode approximation},
  author = {{D}emange, {J}. and {D}ebreu, {L}. and {M}archesiello, {P}atrick and {L}emarie, {F}. and {B}layo, {E}. and {E}ldred, {C}.},
  editor = {},
  language = {{ENG}},
  abstract = {{T}he evolution of the oceanic free-surface is responsible for the propagation of fast surface gravity waves, which approximatively propagate at speed root g{H} (with g the gravity and {H} the local water depth). {I}n the deep ocean, this phase speed is roughly two orders of magnitude faster than the fastest internal gravity waves. {T}he very strong stability constraint imposed by those fast surface waves on the time-step of numerical models is handled using a mode splitting between slow (internal/baroclinic) and fast (external/barotropic) motions to allow the possibility to adopt specific numerical treatments in each component. {T}he barotropic mode is traditionally approximated by the vertically integrated flow because it has only slight vertical variations. {H}owever the implications of this assumption on the stability of the splitting are not well documented. {I}n this paper, we describe a stability analysis of the mode splitting technique based on an eigenvector decomposition using the true (depth-dependent) barotropic mode. {T}his allows us to quantify the amount of dissipation required to stabilize the approximative splitting. {W}e show that, to achieve stable integrations, the dissipation usually applied through averaging filters can be drastically reduced when incorporated at the level of the barotropic time stepping. {T}he benefits are illustrated by numerical experiments. {I}n addition, the formulation of a new mode splitting algorithm using the depth-dependent barotropic mode is introduced.},
  keywords = {{O}cean models ; {B}arotropic mode ; {M}ode splitting ; {S}tability analysis},
  booktitle = {},
  journal = {{J}ournal of {C}omputational {P}hysics},
  volume = {398},
  numero = {},
  pages = {art. 108875 [26 ]},
  ISSN = {0021-9991},
  year = {2019},
  DOI = {10.1016/j.jcp.2019.108875},
  URL = {https://www.documentation.ird.fr/hor/fdi:010077066},
}