The eddy heat-flux in rotating turbulent convection

Abstract

The three components of the heat-flux vector $F =\rho C_p <u^\prime T^\prime> are numerically computed for a stratified rotating turbulent convection using the NIRVANA code in a flat box. The latitudinal component $F_\theta$ proves to be negative (positive) in the northern (southern) hemisphere so that the heat always flows towards the poles. As a surprise, the radial heat-flux $F_r$ peaks at the equator rather than at the poles (Taylor numbers O(10^6)). The same behavior is observed for the radial turbulence intensity $<u_r^{\prime 2}>$ which for \emph{free} turbulence is also believed to peak at the poles (see Eq. (19) below). As we can show, however, the consequences of this unexpected result (also obtained by Kaepylae, Korpi and Tuominen 2004) for the theory of differential rotation are small as mainly the $F_\theta$ is responsible to solve the `Taylor number puzzle'. In all our simulations the azimuthal component $F_\phi$ proves to be negative so that the rotating turbulence produces an westwards directed azimuthal heat-flux which should be observable. Fluctuations with higher temperature are expected to be anticorrelated with their own angular velocity fluctuations. We find this rotation-induced result as understandable as the $F_\phi$ is closely related to the radial \Lambda-effect which is known to be also negative in stratified and rapidly rotating convection zones.