How vortices and shocks provide for a flux loop in two-dimensional compressible turbulence

TL;DR

This paper investigates how vortices and shock waves interact in two-dimensional compressible turbulence, revealing a flux loop where energy cascades inversely via vortices and directly via shocks, especially at finite Mach numbers.

Contribution

It demonstrates the formation of a flux loop in 2D compressible turbulence, highlighting the roles of vortices and shocks in energy transfer mechanisms at finite Mach numbers.

Findings

Inverse cascade of kinetic energy up to the sound scale

Shock waves facilitate a direct energy cascade

Long-living vortex condensates form in small systems

Abstract

Large-scale turbulence in fluid layers and other quasi-two-dimensional compressible systems consists of planar vortices and waves. Separately, wave turbulence usually produces a direct energy cascade, while solenoidal planar turbulence transports energy to large scales by an inverse cascade. Here, we consider turbulence at finite Mach numbers when the interaction between acoustic waves and vortices is substantial. We employ solenoidal pumping at intermediate scales and show how both direct and inverse energy cascades are formed starting from the pumping scale. We show that there is an inverse cascade of kinetic energy up to a scale $\ell$, where a typical velocity reaches the speed of sound; this creates shock waves, which provide for a compensating direct cascade. When the system size is less than $\ell$, the steady state contains a system-size pair of long-living condensate vortices connected by a system of shocks. Thus turbulence in fluid layers processes energy via a loop: Most energy first goes to large scales via vortices and is then transported by waves to small-scale dissipation.