Experiments on Wave-Transition Spectra and Vacillation in an Open Rotating Cylinder

Abstract

Rotating thermal convection experiments, of the same type as those carried out in the early 1950's, were conducted using an open cylinder with rim heating and center cooling. Many improvements, especially provision of a rim-thermostatted bath, allowed far more stable and reproducible results to be obtained. Moderate internal heating distributions due to ordinary incandescent lights were found to produce profound alterations in the fluid responses over rotation ranges that in the earlier works led only to irregular Rossby regime flows. All the qualitative types of flow observed in the extensive work on annulus convection-completely symmetric Hadley flows, steady waves and periodic vacillation states-were found with transition curves on at least one spectrum diagram as sharp or sharper than those previously observed only in annuli. Thus comparatively small changes of the vertical distribution of diabatic heating are capable of switching the system response completely to a sharply defined spectrum. Moreover, the shift in statistically averaged static stability between the two types of responses is also small. The vacillation states, mostly with zonal wavenumber 2, had dimensionless cycle periods up to 200 revolutions, much longer than the usual range for annulus cases, and of the order of the thermal diffusion times. One case of vacillation between wavenumber 2 and symmetry at about 80 revolution cycle period, in spite of great sensitivity to measurement probes, allowed a sufficient number of top-surface velocity and internal temperature measurements to make feasible at least rough estimates of all the elements of a Lorenz-type zonal energy budget, an eddy energy budget and the associated conversion rates. In the course of analyzing this energy budget, we discovered that what now appears to be the most appropriate method of representing it in nondimensional form consists of normalizing energy quantities by the solid rotation kinetic energy of the fluid body at the basic rotation Ω and normalizing transfer rates by this energy times Ω. Energy budget diagrams for this experiment and atmospheric statistics of various kinds then show dimensionless correspondences for most energies and rates within O(1) factors.