Deterministic and Stochastic Euler-Boussinesq Convection

TL;DR

This paper develops and compares three stochastic parameterisations of the Euler-Boussinesq equations, incorporating stochastic transport and forcing, to better model uncertainty in fluid convection systems.

Contribution

It introduces three novel stochastic models for Euler-Boussinesq convection derived from Hamilton's principle, each with distinct Hamiltonian structures and physical interpretations.

Findings

Models incorporate stochastic transport and forcing effects.

Different variants exhibit unique Hamiltonian structures.

Framework enhances understanding of uncertainty in fluid convection.

Abstract

Stochastic parametrisations of the interactions among disparate scales of motion in fluid convection are often used for estimating prediction uncertainty, which can arise due to inadequate model resolution, or incomplete observations, especially in dealing with atmosphere and ocean dynamics, where viscous and diffusive dissipation effects are negligible. This paper derives a family of three different types of stochastic parameterisations for the classical Euler-Boussinesq (EBC) equations for a buoyant incompressible fluid flowing under gravity in a vertical plane. These three stochastic models are inspired by earlier work on the effects of stochastic fluctuations on transport, see, e.g., Kraichnan [1968, 1994] and Doering et al. [1994]. They are derived here from variants of Hamilton's principle for the deterministic case when Stratonovich noise is introduced. The three models possess different variants of their corresponding Hamiltonian structures. One variant (SALT) introduces stochastic transport. Another variant (SFLT) introduces stochastic \emph{forcing}, rather than stochastic \emph{transport}. The third variant (LA SALT) introduces nonlocality in its stochastic transport, in the probabilistic sense of McKean [1966].