Rotating deep annulus convection: The steady high amplitude wave regime—Internal thermal fields

Abstract

In the high-amplitude wave regime, at each point in the axial plane, the temperature has a maximum, a minimum, and a time (or longitudinally) averaged value due to the propagation of the regular waves. The axial-plane profile of each of these three temperature fields was measured for 53 different combinations of ω, Δr _w T and n. A few sample profiles are displayed.

Correlations of several internal thermal parameters (especially Ro _g,t ) with the externally imposed parameters, are given along with the spatial variation of the thermal fields. Ro _g,t is always less than the value which would occur if the symmetrical regime existed, while the variation of Sz _g,t with the imposed parameters is about the same as for the symmetrical regime. The parametric variation of the wave amplitude is the only quantity dependent on n. Based on the parametric variation of the fields, the wave regime diagram can be subdivided into several different regions : a quasi-conductive, a conductive-convective zone, and a region at large rotation rates and temperature differences characterized by Ro _g,t = Ro _g,w ², Sz _o,l = Ro _g,w , and ΔT′ = (z′)^0.6.

The Ro _g, l fields are compared to existing theory and some of the experimental stability diagrams of Fultz et al. (1964) are reconstructed using the internal instead of the externally imposed Rossby number. The transition from three to four waves via a “minor wave” is illustrated.