FORCED AND FREE AXIALLY-SYMMETRIC CONVECTION PRODUCED BY DIFFERENTIAL HEATING IN A ROTATING FLUID

Abstract

When heat is applied to the outer portion and removed from the inner portion of a rotating fluid, a forced direct symmetric convection is set up. The intensity of this motion is directly proportional to the rate of heating and inversly proportional to the square of the rate of rotation. It therefore must be very weak when the rate of rotation is large. However, when the temperature gradient becomes higher than a certain upper limit, a more violent symmetric convection will occur. This violent convection may be considered as an amplifying free convection, or a forced convection under near-resonance conditions. The criterion for this upper transition is obtained in this article by a simple method and expressed in terms of a Richardson number which combines the effects of rotation, static stability, viscosity, conductivity, radial temperature contrast, and the relative vorticity of the mean zonal flow into a single parameter. A comparison between this criterion and Fultz' experimental results suggests that the relative vorticity of the mean zonal current has a larger effect on this transition at lower rotation rates.