Structure formation in turbulence as instability of effective quantum plasma

TL;DR

This paper extends a quantum plasma formalism to turbulence in compressible Navier-Stokes flows, revealing modulational instabilities including a supersonic-specific one and a Kelvin-Helmholtz-type instability, aiding MHD turbulence understanding.

Contribution

It introduces a novel extension of the quantum-like plasma formalism to compressible turbulence, analyzing modulational instabilities in shear flows.

Findings

Identified two modulational instabilities in shear flows.

Discovered a new instability specific to supersonic flows.

Generalized Kelvin-Helmholtz instability in this framework.

Abstract

Structure formation in turbulence is effectively an instability of "plasma" formed by fluctuations serving as particles. These "particles" are quantumlike; namely, their wavelengths are non-negligible compared to the sizes of background coherent structures. The corresponding "kinetic equation" describes the Wigner matrix of the turbulent field, and the coherent structures serve as collective fields. This formalism is usually applied to manifestly quantumlike or scalar waves. Here, we extend it to compressible Navier--Stokes turbulence, where the fluctuation Hamiltonian is a five-dimensional matrix operator and diverse modulational modes are present. As an example, we calculate these modes for a sinusoidal shear flow and find two modulational instabilities. One of them is specific to supersonic flows, and the other one is a Kelvin--Helmholtz-type instability that is a generalization of the known zonostrophic instability. This work serves as a stepping stone toward improving the understanding of magnetohydrodynamic turbulence, which can be approached similarly.