Statistical State Dynamics Based Study of the Turbulent Ekman Layer

TL;DR

This paper applies Statistical State Dynamics to analyze the formation and maintenance of streamwise roll and streak structures in the turbulent Ekman layer, revealing mechanisms similar to those in wall-bounded shear flows.

Contribution

It extends SSD-based stability analysis to the Ekman layer, demonstrating the same turbulence sustaining mechanisms as in wall-bounded shear flows.

Findings

Reynolds stress driven instability contributes to RSS formation.

Inflectional instability also plays a role in RSS maintenance.

Mechanistic link established between geophysical and engineering shear flows.

Abstract

Streamwise roll and streak structures (RSS) are prominent features observed in both atmospheric and oceanic planetary boundary layers (PBL) as well as in laboratory scale Wall bounded shear flows. Despite their structural similarity across these systems, the mechanisms responsible for forming and sustaining the RSS remain debated. This study demonstrates that the same turbulence sustaining mechanism previously identified in Wall bounded shear flows using the Statistical State Dynamics (SSD) formulation of the Navier Stokes equations (Farrell & Ioannou 2012; Farrell et al. 2017) also operates in the Ekman layer. By extending the SSD based stability analysis methods previously used for studying roll formation in wall bounded shear flows to the Ekman layer, we show that the well known Reynolds stress driven instability mechanism in wall-bounded turbulence acts together with inflectional instability to produce and sustain RSS in the Ekman layer. These results enhance the mechanistic understanding of RSS formation and evolution in the turbulent Ekman layer and provide a fundamental link between geophysical Ekman-layer turbulence and turbulence in engineering-scale shear flows.