Large-scale instability in hydrodynamics with stable temperature stratification driven by small-scale helical force

TL;DR

This paper demonstrates that small-scale helical forcing can induce large-scale vortex instability in stably stratified fluids, leading to stationary vortex structures, despite initial assumptions of stability.

Contribution

It introduces a novel mechanism of large-scale instability driven by small-scale helical forces in stably stratified fluids, supported by rigorous multi-scale asymptotic analysis.

Findings

Large-scale vortex instability occurs despite stable stratification.

Non-linear saturation results in stationary spiral vortex structures.

Discovery of stationary helical solitons and kinks as new structures.

Abstract

In this work we consider the effect of a small-scale helical driving force on fluid with a stable temperature gradient with Reynolds number Re<<1. At first glance, this system does not appear to have any instability. However, we show that large-scale vortex instability appears in fluid despite its stable stratification. In the non-linear mode, this instability gets saturated and gives a large number of stationary spiral vortex structures. Among these structures there is a stationary helical soliton and a kink of a new type. The theory is built on the rigorous asymptotical method of multi-scale development.