arXiv subjects

Gilles Tissot

Publications and source records attributed to Gilles Tissot.

4 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↗

arXiv2023

Ensemble forecasts in reproducing kernel Hilbert space family

A methodological framework for ensemble-based estimation and simulation of high dimensional dynamical systems such as the oceanic or atmospheric flows is proposed. To that end, the dynamical system is embedded in a family of reproducing kernel Hilbert spaces (RKHS) with kernel functions driven by the dynamics. In the RKHS family, the Koopman and Perron-Frobenius operators are unitary and uniformly continuous. This property warrants they can be expressed in exponential series of diagonalizable bounded evolution operators defined from their infinitesimal generators. Access to Lyapunov exponents and to exact ensemble based expressions of the tangent linear dynamics are directly available as well. The RKHS family enables us the devise of strikingly simple ensemble data assimilation methods for trajectory reconstructions in terms of constant-in-time linear combinations of trajectory samples. Such an embarrassingly simple strategy is made possible through a fully justified superposition principle ensuing from several fundamental theorems.

math-ph↗

arXiv2023

Linear wave solutions of a stochastic shallow water model

In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind or coming as the feedback of the ocean on the atmosphere and leading in a very fast way to the selection of some wavelength. This interwoven, yet simple, mechanism explains the emergence of typical wavelength associated to near inertial waves. Ensemble-mean waves that are not in phase with the random forcing are damped at an exponential rate, whose magnitude depends on the random forcing variance. Geostrophic adjustment is also interpreted as a statistical homogenization process in which, in order to conserve potential vorticity, the small-scale component tends to align to the velocity fields to form a statistically homogeneous random field.

physics.flu-dyn↗

arXiv2022

Input-output analysis of the stochastic Navier-Stokes equations: application to turbulent channel flow

Stochastic linear modelling proposed in Tissot, Mémin & Cavalieri (J. Fluid Mech., vol. 912, 2021, A51) is based on classical conservation laws subject to a stochastic transport. Once linearised around the mean flow and expressed in the Fourier domain, the model has proven its efficiency to predict the structure of the streaks of streamwise velocity in turbulent channel flows. It has been in particular demonstrated that the stochastic transport by unresolved incoherent turbulence allows to better reproduce the streaks through lift-up mechanism. In the present paper, we focus on the study of streamwise-elongated structures, energetic in the buffer and logarithmic layers. In the buffer layer, elongated streamwise vortices, named rolls, are seen to result from coherent wave-wave non-linear interactions, which have been neglected in the stochastic linear framework. We propose a way to account for the effect of these interactions in the stochastic model by introducing a stochastic forcing, which replace the missing non-linear terms. In addition, we propose an iterative strategy in order to ensure that the stochastic noise is decorrelated from the solution, as prescribed by the modelling hypotheses. We explore the prediction abilities of this more complete model in the buffer and logarithmic layers of channel flows at $Re_τ=180$, $Re_τ=550$ and $Re_τ=1000$. We show an improvement of predictions compared to resolvent analysis with eddy viscosity, especially in the logarithmic layer.

physics.flu-dyn↗