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

In this study we report numerical results of turbulent transport of heat $Nu$ and angular momentum $\nu_{t}/\nu$ in Taylor-Couette (TC) flows subjected to a radial temperature gradient. Direct numerical simulations are performed in a TC cell with a radius ratio $\eta=0.5$ and an aspect ratio $\Gamma=8$ for two Rayleigh numbers ($Ra=10^5$, $10^6$) and two Prandtl numbers ($Pr=0.7$, $4.38$), while the Reynolds number $Re$ varies in the range of $0 \le Re \le 15000$. With increasing $Re$, the flows undergo two distinct transitions: the first transition being from the convection-dominated regime to the transitional regime, with the large-scale meridional circulation evolving into spiral vortices; the second transition occurring in the rotation-dominated regime when Taylor vortices turn from a weakly non-linear 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: $Nu\sim Re^{0.619\pm0.015}$ for $Pr=4.38$, $Nu\sim Re^{0.590\pm0.025}$ for $Pr=0.7$ and $\nu_{t}/\nu\sim Re^{0.588\pm0.036}$ 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 turbulent 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.