@book{fdi:010062863,
  title = {{O}n the use of a depth-dependent barotropic mode in ocean models : impact on the stability of the coupled barotropic/baroclinic system},
  author = {{D}emange, {J}. and {D}ebreu, {L}. and {M}archesiello, {P}atrick and {L}emari{\'e}, {F}. and {B}layo, {E}.},
  editor = {},
  language = {{ENG}},
  abstract = {{E}volution of the oceanic free-surfaceﰒis responsible for the propagation of fast surface gravity waves which roughly propagates at speed 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 steep stability constraint imposed by those fast surface waves on the time-step of numerical models is handled using a splitting between slow (internal / baro- clinic) 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. {W}e show that the use of such a depth-dependent barotropic mode allows a much stable integration of the mode-split equations. {A}s a consequence, the amount of dissipation required to achieve stable integrations, usually applied through averaging filters, can be drastically reduced. {I}t results in a much improved effective resolution even for complex flows. {I}n addition, the formulation of a new mode splitting algorithm using the depth-dependent barotropic mode is introduced. {T}he benefits of this new formulation are illustrated by idealized numerical experiments.},
  keywords = {{CIRCULATION} {OCEANIQUE} ; {PROFONDEUR} ; {METHODE} {D}'{ANALYSE} ; {MODELE} {MATHEMATIQUE} ; {ALGORITHME} ; {GRAVITE}},
  address = {{G}renoble},
  publisher = {{INRIA}},
  series = {{R}apport de {R}echerche - {INRIA}},
  pages = {27},
  year = {2014},
  ISSN = {0249-6399},
  URL = {https://www.documentation.ird.fr/hor/fdi:010062863},
}