How small-scale flow structures affect the heat transport in sheared thermal convection

Abstract

We investigate the counter-intuitive initial decrease and subsequent increase in the Nusselt number $Nu$ with increasing wall Reynolds number $Re_w$ in the sheared Rayleigh–Bénard (RB) system by studying the energy spectra of convective flux and turbulent kinetic energy for Rayleigh number $Ra = 10^{7}$ , Prandtl number $Pr=1.0$ and inverse Richardson numbers $0 \leq 1/Ri \leq 10$ . These energy spectra show two distinct high-energy regions corresponding to the large-scale superstructures in the bulk and small-scale structures in the boundary layer (BL) regions. A greater separation between these scales at the thermal BL height correlates to a higher $Nu$ and indicates that the BLs are more turbulent. The minimum $Nu$ , which occurs at $1/Ri=1.0$ , is accompanied by the smallest separation between the large- and small-scale structures at the thermal BL height. At $1/Ri=1.0$ , we also observe the lowest value of turbulent kinetic energy normalized with the square of friction velocity within the thermal BL. Additionally, we find that the domain size has a limited effect on the heat and momentum transfer in the sheared RB system as long as the domain can accommodate the small-scale convective structures at the thermal BL height, signifying that capturing the large-scale superstructures is not essential to obtain converged values of $Nu$ and shear Reynolds number $Re_{\tau }$ . When the domain is smaller than these small-scale convective structures, the overall heat and momentum transfer reduces drastically.

From sheared annular centrifugal Rayleigh–Bénard convection to radially heated Taylor–Couette flow: exploring the impact of buoyancy and shear on heat transfer and flow structure

“…2020, 2021; Yerragolam et al. 2022 a , b ). As shear increases from , the flow regime moves from the buoyancy-dominated regime, through the transitional regime, and finally into the shear-dominated regime.…”