  The aim of this paper is to provide a stochastic version under location
uncertainty of the compressible Navier-Stokes equations. The modelling under
location uncertainty setting is used here to derive a physically consistent
stochastic dynamical system for compressible flows. It relies on an extended
stochastic version of the Reynolds transport theorem involving stochastic
source terms. In a similar way as in the deterministic case, this conservation
theorem is applied to density, momentum and total energy in order to obtain a
transport equation of the primitive variables, i.e. density, velocity and
temperature. For the modelling of ocean dynamics, the transport of mass
fraction of species, such as salinity, is also considered. We show that
performing low Mach and Boussinesq approximations to this more general set of
equations allows us to recover previous versions of incompressible stochastic
Navier-Stokes equations and the stochastic Boussinesq equations, respectively.
Finally, we provide some research directions on the use of this general set of
equations in the perspective of relaxing the Boussinesq and hydrostatic
approximation for ocean modelling.
