Density operator approach to turbulent flows in plasma and atmospheric fluids

TL;DR

This paper introduces a wave-mechanical statistical framework for modeling dissipation and instabilities in 2D turbulent flows of plasmas and atmospheric fluids, revealing new energy and enstrophy exchange mechanisms.

Contribution

It develops a novel density operator approach using a non-Hermitian Hamiltonian to describe turbulence as a macroscopic wave phenomenon, extending beyond traditional wave kinetic models.

Findings

Predicts mechanisms of energy transfer between drift waves and zonal flows.

Shows the system's evolution depends on environmental effects on stability.

Provides a phase-space formulation including conservation laws.

Abstract

We formulate a statistical wave-mechanical approach to describe dissipation and instabilities in two-dimensional turbulent flows of magnetized plasmas and atmospheric fluids, such as drift and Rossby waves. This is made possible by the existence of Hilbert space, associated with the electric potential of plasma or stream function of atmospheric fluid. We therefore regard such turbulent flows as macroscopic wave-mechanical phenomena, driven by the non-Hermitian Hamiltonian operator we derive, whose anti-Hermitian component is attributed to an effect of the environment. Introducing a wave-mechanical density operator for the statistical ensembles of waves, we formulate master equations and define observables: such as the enstrophy and energy of both the waves and zonal flow as statistical averages. We establish that our open system can generally follow two types of time evolution, depending on whether the environment hinders or assists the system's stability and integrity. We also consider a phase-space formulation of the theory, including the geometrical-optic limit and beyond, and study the conservation laws of physical observables. It is thus shown that the approach predicts various mechanisms of energy and enstrophy exchange between drift waves and zonal flow, which were hitherto overlooked in models based on wave kinetic equations.