Stabilizing two-dimensional turbulent Kolmogorov flow via selective modification of inviscid invariants

TL;DR

This paper introduces a method to stabilize two-dimensional turbulent Kolmogorov flow by selectively modifying inviscid invariants, transforming unsteady flow into steady states and effectively controlling energy cascades.

Contribution

The study presents a novel selective modification technique that autonomously alters forcing inputs to achieve steady states in turbulent flows, especially managing inverse energy cascading.

Findings

Successfully stabilizes Kolmogorov flow into steady states

Effectively controls inverse energy cascade dynamics

Steady states resemble invariant solutions of original flow

Abstract

We stabilize two-dimensional turbulent Kolmogorov flow by selectively altering the time rate of change of inviscid invariants (energy and enstrophy) of the flow. This method has earlier been demonstrated to modify the two-dimensional unforced decaying turbulent flow to reach steady states. However, Kolmogorov flow exhibits flow unsteadiness over a range of spatial and temporal scales which are driven by constant external forcing at wave number $k_f$. The energy injected at scale ($k \approx k_f$) is distributed to large ($k > k_f$) and small ($k < k_f$) wave numbers through interactions of different scales called direct and inverse energy cascading, respectively. The selective modification strategy autonomously identifies additional forcing inputs into the governing equations which results in the transformation of Kolmogorov flow into a non-trivial steady state. We demonstrate that this method is highly effective in altering the inverse energy cascading, a particularly intricate challenge in fluid dynamics. Intriguingly, we have also found that the steady states achieved through this approach resemble an invariant solution of the original Kolmogorov flow, highlighting the potential significance of our method.