Relationships Among Eddy Fluxes of Heat, Eddy Temperature Variances and Basic-State Temperature Parameters in Thermally Driven Rotating Fluids

Abstract

Relationships are examined among radial eddy fluxes of heat, eddy temperature variances and basic-state temperature parameters (e.g., radial gradients and variances of the azimuthally averaged temperature) over a broad range of dimensionless parameters in thermally driven rotating annuli of fluid. We consider, first, changes of the time-averaged eddy heat flux and of the time and azimuthally averaged radial temperature gradient which take place when we conduct experiments at different imposed temperature differences With the rotation rate held fixed, or at different rotation rates with the imposed temperature difference held fixed. It is found that the observed changes of these variables cannot be described by a positive proportionality between the eddy heat flux and some positive power of the radial temperature gradient, except perhaps over limited ranges of dimensionless-parameter space. Within the regular wave regime, not too far from marginal stability, the eddy heat flux increases and the azimuthally averaged radial temperature gradient decreases with increasing rotation rate, when the imposed temperature contrast is held constant, suggesting that the effect of the eddies is to reduce substantially the magnitude of the temperature gradient. Evaluations are made also of the time variations of the eddy heat flux and of the azimuthally averaged radial temperature gradient at fixed points in dimensionless parameter space. The lag correlation function between these two variables is found to exhibit a unique characteristic which is common to all experiments. A lag correlation function calculated by Peter Stone using atmospheric data reveals a similar characteristic. The results suggest a new time-dependent parameterization of heat flux variations in terms of the basic-state temperature gradient.