Dissipation properties of transport noise in the two-layer quasi-geostrophic model

TL;DR

This paper investigates how transport noise affects the dissipation properties of the two-layer quasi-geostrophic model, showing that under certain conditions, solutions tend to deterministic models with enhanced dissipation and stationary states.

Contribution

It introduces a stochastic version of the 2LQG model with multiplicative transport noise and proves convergence to deterministic models with increased dissipation and stationary solutions.

Findings

Solutions converge to deterministic models with enhanced dissipation.

Transport noise acts on both layers, modeling unresolved small scales.

Long-term solutions approach deterministic stationary states.

Abstract

A stochastic version of the two-layer quasi-geostrophic model (2LQG) with multiplicative transport noise is analysed. This popular intermediate complexity model describes large scale atmosphere and ocean dynamics at the mid-latitudes. The transport noise, which acts on both layers, accounts for the unresolved small scales. After establishing the well-posedness of the perturbed equations, we show that, under a suitable scaling of the noise, the solutions converge to the deterministic 2LQG model with enhanced dissipation. Moreover, these solutions converge to the deterministic stationary ones on the long time horizon.