arXiv subjects

Étienne Mémin

Publications and source records attributed to Étienne Mémin.

5 recordsLinked to original sources

arXiv2026

Stochastic compressible Navier-Stokes equations under location uncertainty and their approximations for ocean modelling

This paper presents a joint theoretical and numerical study of a stochastic version of the compressible Navier-Stokes equations within the location uncertainty (LU) framework, applied to problems related to upper ocean vertical mixing. This approach builds on an extended stochastic form of the Reynolds transport theorem, incorporating stochastic source terms. As in the deterministic case, this conservation theorem is applied to mass, mass of species (such as salinity), momentum, and total energy, leading to transport equations for the primitive variables: density, mass fraction of species, velocity, and temperature. We subsequently apply the Boussinesq approximations to this general system, and recover existing formulations of the incompressible stochastic Navier-Stokes and stochastic Boussinesq equations. We employ this new framework in a Boussinesq large-eddy simulation of temperature-driven free convection event, and highlight the potential of stochastic transport to reproduce penetrative convection effects at the base of the mixed layer under the Boussinesq approximation. Compression effects identified in our stochastic Boussinesq hydrostatic model are found to be negligible in the temperature equation when expressed in terms of internal energy, in agreement with Boussinesq approximation. However, when expressed in terms of potential energy, compression effects become significant, and reveal interesting properties of the stochastic pressure terms within the mixed layer. We believe this later results open new physical modelling perspective enabling to represent oceanic dynamics within a stochastic framework that more fully accounts for physical uncertainties and approximations, while also providing a basis for improving the energetic consistency of subgrid-scale vertical models used in ocean general circulation models.

physics.flu-dyn↗

arXiv2026

Interpretation of stochastic primitive equations with relaxed hydrostatic assumption as a higher order approximation of 3D stochastic Navier-Stokes

In this paper, we investigate the convergence of solutions of a stochastic representation of the three-dimensional Navier-Stokes equations to those of their primitive equations counterpart. Our analysis covers both weak and strong convergence regimes, corresponding respectively to rigid-lid and "fully periodic" boundary conditions. Furthermore, we explore the impact of relaxing the hydrostatic assumption in the stochastic primitive equations by retaining martingale terms as deviations from hydrostatic equilibrium. This modified model, obtained through a specific asymptotic scaling accessible only within the stochastic framework, captures non-hydrostatic effects while remaining within the primitive equations formalism. The resulting generalized hydrostatic model has been shown to be well-posed when the additional terms are regularized using a suitable filter for divergence-free noises under suitable assumptions. Within this setting, we demonstrate that the model provides a higher-order approximation of the 3D Navier-Stokes equations for appropriately scaled noises.

math.AP↗

arXiv2026

Stochastic interpretations of the oceanic primitive equations with relaxed hydrostatic assumptions

In this paper, we investigate how weakening the classical hydrostatic balance hypothesis impacts the well-posedness of the stochastic LU primitive equations. The models we consider are intermediate between the incompressible 3D LU Navier-Stokes equations and the LU primitive equations with standard hydrostatic balance. As such, they are expected to be numerically tractable, while accounting well for phenomena within the grey zone between hydrostatic balance and non-hydrostatic processes. Our main result is the well-posedness of a low-pass filtering-based stochastic interpretation of the LU primitive equations, with rigid-lid type boundary conditions, in the limit of ``quasi-barotropic'' flow. This assumption is linked to the structure assumption proposed in the work of Agresti et al., which can be related to the dynamical regime where the primitive equations remain valid. Furthermore, we present and study two eddy-(hyper)viscosity-based models.

math.AP↗

arXiv2025

Some properties of a non-hydrostatic stochastic oceanic primitive equations model

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 model.

math.PR↗

arXiv2024

Derivation of stochastic models for coastal waves

In this paper, we consider a stochastic nonlinear formulation of classical coastal waves models under location uncertainty (LU). In the formal setting investigated here, stochastic versions of the Serre-Green- Nagdi, Boussinesq and classical shallow water wave models are obtained through an asymptotic expansion, which is similar to the one operated in the deterministic setting. However, modified advection terms emerge, together with advection noise terms. These terms are well-known features arising from the LU formalism, based on momentum conservation principle.

math.PR↗