Structure formation in turbulence as an instability of effective quantum plasma

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.

Wave-kinetic approach to zonal-flow dynamics: recent advances

“…In this paper, we overview the recent advances in the wave-kinetic theory of inhomogeneous DW-ZF interactions [22][23][24][25][26][27][28][29][30][31][32][33] and present a consolidated high-level physics picture of ZF physics, mostly based on the mHME model. A special focus is made on understanding drifton phase-space dynamics, associated solitary structures, merging and splitting of ZFs, as well as the KHI and the tertiary instability.…”

“…Recently, the wave-kinetic description of inhomogeneous DW turbulence has been re-examined from first principles and applied to make quantitative predictions in a number of problems. [22][23][24][25][26][27][28][29][30][31][32][33] Although still limited to simplified DW models, those results indicate that important qualitative physics has been overlooked in the past but can be described transparently if the wave-kinetic formalism is properly amended. In particular, the "improved" WKE reveals an important effect of the ZF "curvature" (second radial derivative of the zonal velocity) on dynamics and stability of DWs and ZFs.…”