Turbulent Drag Reduction in Magnetohydrodynamic Turbulence and Dynamo from Energy Flux Perspectives

TL;DR

This review explains how energy flux suppression in magnetohydrodynamic turbulence and related flows leads to turbulent drag reduction, highlighting universal mechanisms across different turbulent systems and flow conditions.

Contribution

It introduces a universal energy flux framework to understand turbulent drag reduction in MHD and related turbulence, connecting various flow types under a common perspective.

Findings

Suppression of kinetic energy flux correlates with drag reduction.

Turbulent drag reduction is observed across multiple flow types including MHD and stratified turbulence.

Large-scale flow acceleration is a common feature associated with drag reduction.

Abstract

In this review, we describe turbulent drag reduction in a variety of flows using a universal framework of energy flux. In a turbulent flow with dilute polymers and magnetic field, the kinetic energy injected at large scales cascades to the velocity field at intermediate scales, as well as to the polymers and magnetic field at all scales. Consequently, the kinetic energy flux, $ \Pi_u(k) $, is suppressed in comparison to the pure hydrodynamic turbulence. We argue that the suppression of $\Pi_u(k)$ is an important factor in the reduction of the inertial force $\langle {\bf u \cdot \nabla u} \rangle$ and \textit{turbulent drag}. This feature of turbulent drag reduction is observed in polymeric, magnetohydrodynamic, quasi-static magnetohydrodynamic, and stably-stratified turbulence, and in dynamos. In addition, it is shown that turbulent drag reduction in thermal convection is due to the smooth thermal plates, similar to the turbulent drag reduction over bluff bodies. In all these flows, turbulent drag reduction often leads to a strong large-scale velocity in the flow.