Potential landscape and flux field theory for turbulence and nonequilibrium fluid systems

TL;DR

This paper develops a potential landscape and flux field theory to describe turbulence as a nonequilibrium system, revealing how detailed balance breaking leads to a non-Gaussian landscape and irreversible flux, which underpin turbulence phenomena.

Contribution

It introduces a novel theoretical framework linking nonequilibrium steady states, potential landscapes, and fluxes to turbulence dynamics, highlighting the role of detailed balance breaking.

Findings

Identification of a 'nonequilibrium trinity' comprising potential landscape, flux, and detailed balance breaking.

Connection of energy flux and turbulence scaling laws to the nonequilibrium trinity.

Explanation of the four-fifths law as a consequence of nonequilibrium dynamics.

Abstract

Turbulence is a paradigm for far-from-equilibrium systems without time reversal symmetry. To capture the nonequilibrium irreversible nature of turbulence and investigate its implications, we develop a potential landscape and flux field theory for turbulent flow and more general nonequilibrium fluid systems governed by stochastic Navier-Stokes equations. We find that equilibrium fluid systems with time reversibility are characterized by a detailed balance constraint that quantifies the detailed balance condition. In nonequilibrium fluid systems with nonequilibrium steady states, detailed balance breaking leads directly to a pair of interconnected consequences, namely, the non-Gaussian potential landscape and the irreversible probability flux, forming a 'nonequilibrium trinity'. The nonequilibrium trinity characterizes the nonequilibrium irreversible essence of fluid systems with intrinsic time irreversibility and is manifested in various aspects of these systems. The nonequilibrium stochastic dynamics of fluid systems including turbulence with detailed balance breaking is shown to be driven by both the non-Gaussian potential landscape gradient and the irreversible probability flux, together with the reversible convective force and the stochastic stirring force. We reveal an underlying connection of the energy flux essential for turbulence energy cascade to the irreversible probability flux and the non-Gaussian potential landscape generated by detailed balance breaking. Using the energy flux as a center of connection, we demonstrate that the four-fifths law in fully developed turbulence is a consequence and reflection of the nonequilibrium trinity. We also show how the nonequilibrium trinity can affect the scaling laws in turbulence.