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D. Fultz

Abstract

Results elucidating the mechanism by which overstable (oscillating) cellular convection occurs in rotating layers are given. There is a close connection with the elastoid-inertia oscillations in a rotating cylinder discussed by Kelvin, Solberg, and Bjerknes, and it is found that diffusion of heat by conduction acts in a deslabilizing way in the motion. Simple experiments in a rotating cylinder on the elastoid-inertia oscillations show a remarkably close agreement with the free periods calculated theoretically. This, in the field of meteorological experiments, is important in establishing close agreement with meteorological theory in a situation where the flow can be strongly ageostrophic.

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D. Fultz
and
P. Frenzen

Abstract

Certain aspects of Long's experiments (and some later extensions) with fluid motions around obstacles in a rotating hemispherical shell are discussed. For westerly currents, Long demonstrated that Rossby-Haurwitz waves could be produced at proper values of an angular kinematic Rossby number, R ≡ ω r /Ω. These and a wide variety of other experiments give strong evidence of quasi-geostrophic properties when-ever suitable kinematic Rossby numbers are of the order of 0.1. On the other hand, easterly currents of about the same intensity as give Rossby-Haurwitz waves for westerly currents, give with a long meridional barrier a cusped wave pattern of a much more ageostrophic character than Rossby-Haurwitz waves. Some general questions suggested by this phenomenon, especially concerning the possibility of a genera1 stability difference between east- and west-wind currents, are posed.

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D. Fultz
and
T. S. Murty

Abstract

Systematic changes in the finite-amplitude vortex instability of axisymmetric elastoid-inertia oscillations in circular bodies of fluid with a quadratic law of depth are shown to occur depending on whether the depth increases or decreases radially. The instability is a new type that may have an essentially invicid mechanism and suggestions are made as to possible connections with atmospheric general circulation instability mechanisms. Phase speed measurements of certain observed propagating waves compared with several theoretical estimates suggest very strongly that they are Rossby waves excited by some conversion mechanism from the original inertia modes.

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T. W. Spence
and
D. Fultz

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.

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