On the use of a depth-dependent barotropic mode in ocean models: impact on the stability of the coupled barotropic/baroclinic system

Abstract : Evolution of the oceanic free-surfaceﰒis responsible for the propagation of fast surface gravity waves which roughly propagates at speed gH (with g the gravity and H the local water depth). In the deep ocean, this phase speed is roughly two orders of magnitude faster than the fastest internal gravity waves. The steep stability constraint imposed by those fast surface waves on the time-step of numerical models is handled using a splitting between slow (internal / baroclinic) and fast (external / barotropic) motions to allow the possibility to adopt specific numerical treatments in each component. The barotropic mode is traditionally approximated by the vertically integrated flow because it has only slight vertical variations. However, the implications of this assumption on the stability of the splitting are not well documented. In this paper, we describe a stability analysis of the mode-splitting technique based on an eigenvector decomposition using the true (depth-dependent) barotropic mode. We show that the use of such a depth-dependent barotropic mode allows a much stable integration of the mode-split equations. As a consequence, the amount of dissipation required to achieve stable integrations, usually applied through averaging filters, can be drastically reduced. It results in a much improved effective resolution even for complex flows. In addition, the formulation of a new mode splitting algorithm using the depth-dependent barotropic mode is introduced. The benefits of this new formulation are illustrated by idealized numerical experiments.
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Jérémie Demange, Laurent Debreu, Patrick Marchesiello, Florian Lemarié, Eric Blayo. On the use of a depth-dependent barotropic mode in ocean models: impact on the stability of the coupled barotropic/baroclinic system. [Research Report] RR-8589, INRIA. 2014. ⟨hal-01063414⟩

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