Statistical State Dynamics based study of turbulence in Eady fronts. Part 1. Instability

TL;DR

This paper demonstrates that the turbulence-sustaining mechanism identified in unstratified shear flows also operates in the stratified Eady front, advancing understanding of turbulence formation in geophysical fronts.

Contribution

It adapts the SSD stability analysis to the Eady front, revealing the same turbulence mechanism as in unstratified shear flows, bridging geophysical and engineering turbulence dynamics.

Findings

The SSD mechanism underlies RSS formation in the Eady front.

Turbulence and symmetric instability interact to sustain RSS.

Mechanistic parallels are established between geophysical and engineering shear flows.

Abstract

The streamwise roll and streak structure (RSS) is prominent in observations of the planetary boundary layer in the atmosphere and ocean and in unstratified wall-bounded shear flows. Although the RSS in these systems is structurally similar, the mechanism forming and maintaining the RSS in both remains controversial. This study demonstrates that the same turbulence-sustaining mechanism identified to underlie the RSS in the Statistical State Dynamics (SSD) formulation of unstratified wall-bounded shear flow dynamics (Farrell & Ioannou 2012; Farrell et al. 2016) also operates in the Eady front. We analyze the mechanism by which turbulence and symmetric instability interact to form the RSS in the baroclinic stratified Eady front model by adapting to the Eady front problem the stability analysis of the second order closure of the SSD used previously to study roll formation in unstratified wall-bounded shear flows. Our findings advance mechanistic understanding of RSS formation in the turbulent geostrophic front regime and establish foundational parallels between geophysical turbulent front dynamics and turbulence dynamics in engineering-scale shear flows.