The glue effect of turbulence in the evolution of an insulated two-layer quasi-geostrophic flow

TL;DR

This paper analytically investigates how turbulence causes two-layer quasi-geostrophic flows to initially behave independently and eventually merge into a single-layer system, with circulation converging to a weighted average of initial circulations.

Contribution

It provides an analytic solution demonstrating turbulence's glue-like effect in the evolution of two-layer quasi-geostrophic flows, showing the transition to a single-layer system over time.

Findings

Initially, layers evolve independently due to turbulence.

Over time, layers' circulations align and converge.

Final circulation is a weighted average of initial circulations.

Abstract

A two-layer quasi-geostrophic flow is quite insulated from the surrounding fluid, while the layers interact each other by means of the modulation of the interface between them and of the turbulence affecting the layers in the proximity of the interface. In this framework, the time evolution of the circulation of the flow along the lateral boundaries (upper and lower) is investigated under the assumption of arbitrary initial conditions. The analytic solution shows the glue-like behaviour of turbulence, which is parameterized in the standard way (Pedosky, 1996): initially the glue is wet and each layer evolves almost independently of the other while, for times far enough from that initial, the glue hardens and the system converges to a singlelayer one. Indeed, the circulation of the thinner layer tends to adjust itself in a parallel way with respect to the thicker layer and the final circulation of the consequent single-layer system is given by the average of the initial circulations, each being weighted by the thickness of the related layer.