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

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-Benard (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 <= 1/Ri <= 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.