Inverse Energy Cascade in Turbulent Taylor-Couette Flows

TL;DR

This study uses large eddy simulations to analyze the inverse energy cascade in turbulent Taylor-Couette flow, revealing its occurrence in the core region at high Reynolds numbers due to zero shear stress and flow singularities.

Contribution

It uncovers the mechanism of inverse energy cascade in Taylor-Couette flow linked to zero shear stress and flow singularities, expanding understanding of turbulence dynamics.

Findings

Inverse energy cascade occurs in the core region at high Reynolds numbers.

Zero shear stress and flow singularities induce high turbulent energy and small-scale vortices.

Energy spectrum peaks at middle frequency due to small-scale vortex concentration.

Abstract

The inverse energy cascade in turbulent Taylor-Couette flow is studied in line with the results of the large eddy simulation. The simulation results show that the inverse energy cascade first occurs within the core region of the flow channel of the Taylor-Couette flow at higher Reynolds number. It is uncovered that this phenomenon is induced by the pulsed zero shear stress resulting from the singularities of the Navier-Stokes equation. In the core area between the two cylinders, the shear stress is nearly zero at higher Reynolds number. The turbulence generated there has high turbulent energy due to discontinuity of the tangential velocity. Since the energy transfer between the fluid layers is inhibited due to the low shear stress, the turbulent energy cannot be transferred along the radial direction, and small-scale vortices with high turbulent energy are produced. These small-scale vortices are located with the large-scale vortices and cannot be dissipated owing to low shear stress. A peak in the energy spectrum at middle frequency (or wave number) is formed due to the concentration of the small-scale vortices. As the number of the singular points of the Navier-Stokes equation increases with the increasing Reynolds number, the region with zero shear stress expands along the radial direction, intensifying nonlinear instability and energy accumulation. This, in turn, leads to more prominent peaks in the energy spectrum, resulting in a more pronounced inverse energy cascade.