Some properties of a non-hydrostatic stochastic oceanic primitive equations model
Résumé
In this paper, we study how relaxing the classical hydrostatic balance hypothesis
affects theoretical aspects of the LU primitive equations well-posedness. We focus on
models that sit between incompressible 3D LU Navier-Stokes equations and standard
LU primitive equations, aiming for numerical manageability while capturing non-
hydrostatic phenomena. Our main result concerns the well-posedness of a specific
stochastic interpretation of the LU primitive equations. This holds with rigid-lid type
boundary conditions, and when the horizontal component of noise is independent of
z. In fact these conditions can be related to the dynamical regime in which
the primitive equations remain valid. Moreover, under these conditions, we show
that the LU primitive equations solution tends toward the one of the deterministic
primitive equations for a vanishing noise, thus providing a physical coherence to the
LU stochastic mode
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