Two-layer baroclinic turbulence with arbitrary layer depths

TL;DR

This paper extends vortex-gas scaling theory to two-layer baroclinic turbulence with arbitrary layer depths, providing quantitative predictions for turbulent transport validated by numerical simulations.

Contribution

It introduces a mapping from arbitrary to equal-depth systems in turbulence modeling, enabling parameter-free predictions for various layer depths.

Findings

Quantitative predictions for turbulent transport across layer depths

Validation of theory with numerical simulations

Mapping approach applicable in low-drag regimes

Abstract

While heat transport by baroclinic turbulence in oceans and planetary atmospheres is well described by a two-layer model, the relative depth of the two layers varies greatly depending on the situation of interest, making it an important parameter governing the transport properties of the system. Focusing on the low-drag turbulent regime, we extend the vortex-gas scaling theory to address the case of arbitrary layer depths. To wit, we map the arbitrary-layer-depth system onto an equivalent equal-depth system with rescaled parameters, establishing the asymptotic validity of the mapping for weak bottom drag. This approach leads to quantitative predictions for the turbulent transport by two-layer baroclinic turbulence with arbitrary layer depths, without additional free parameters. We validate these predictions using an extended suite of numerical simulations with either linear or quadratic bottom drag.