Variational principles for fully coupled stochastic fluid dynamics across scales - Centre Henri Lebesgue
Pré-Publication, Document De Travail Année : 2024

Variational principles for fully coupled stochastic fluid dynamics across scales

Résumé

This work investigates variational frameworks for modeling stochastic dynamics in incompressible fluids, focusing on large-scale fluid behavior alongside small-scale stochastic processes. The authors aim to develop a coupled system of equations that captures both scales, using a variational principle formulated with Lagrangians defined on the full flow, and incorporating stochastic transport constraints. The approach smooths the noise term along time, leading to stochastic dynamics as a regularization parameter approaches zero. Initially, fixed noise terms are considered, resulting in a generalized stochastic Euler equation, which becomes problematic as the regularization parameter diminishes. The study then examines connections with existing stochastic frameworks and proposes a new variational principle that couples noise dynamics with large-scale fluid motion. This comprehensive framework provides a stochastic representation of large-scale dynamics while accounting for fine-scale components. The evolution of the small-scale velocity component is governed by a linear Euler equation with random coefficients, influenced by large-scale transport, stretching, and pressure forcing.
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Dates et versions

hal-04865618 , version 1 (06-01-2025)

Identifiants

  • HAL Id : hal-04865618 , version 1

Citer

Arnaud Debussche, Etienne Mémin. Variational principles for fully coupled stochastic fluid dynamics across scales. 2025. ⟨hal-04865618⟩
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