In this paper we are mainly concerned with stochastic perturbations of transport type. The introduction of additive and multiplicative noise into models for geophysical flows can be used on the one hand to account for numerical and empirical uncertainties and errors and on the other hand as subgrid-scale parameterizations for data assimilation, and ensemble prediction as described in the review articles. Detailed information on the geophysical background for the various versions of the deterministic primitive equations are given e.g. They are derived from the Navier-Stokes equations in domains where the vertical scale is much smaller than the horizontal scale by the small aspect ratio limit. The primitive equations are one of the fundamental models for geophysical flows used to describe oceanic and atmospheric dynamics. In this paper we study the stochastic primitive equation with transport noise and turbulent pressure.
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