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Y. K. Sasaki and L. P. Chang

Abstract

In a diagnostic study by expanding global data in normal mode functions, Kasahara and Puri found that for zonal wavenumber one, even the seventh vertical mode (the highest mode they presented) contains about 50% of the energy of the external mode. The vertical normal modes are eigensolutions of the vertical structure equation, and each mode is associated with well‐defined physical significance. Consequently, it is of interest to look into the accuracy of representation of, say, the first ten vertical modes in a discretized model because seriously misrepresented normal mode functions may not be able to honestly express the physics embedded in the data to be expanded. Along this line, a systematic method of obtaining matching eigensolutions of the vertical structure equation of a multilayered stratified atmosphere was developed. The resultant eigensolutions were used to investigate the influence of the upper boundary condition, the judicious method of the vertical grid levels and the relative accuracy of a finite‐difference and a finite‐element method in obtaining the discretized vertical normal mode functions. An important conclusion of this study is that in a discretized model, an inadequate grid resolution in the upper domain may result in considerable misrepresentation of the vertical structure functions even in the lower part of the domain for vertical modes higher than mode 5.

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E. M. Wilkins, Y. Sasaki, and H. L. Johnson

Abstract

Adiabatic thermals rising through an environment which has formed a friction layer by rotating in contact with a roughness plate are studied in the laboratory. The effects of frictionally induced motions on the growth of thermals and vortexes are assessed by comparing the friction situations with identical ones in which the roughness plate has been removed.

The analysis shows that convergence created by the friction layer gives rise to additional upward motion at the center of the cloud tank, and this tends to offset the rotational suppression of the thermal's growth. Entrainment of the environmental fluid by the thermal appears to be increased, and the enhancement of volumetric growth may be due in part to entrainment of turbulent fluid from the friction layer. An attempt is made numerically to evaluate this effect. Vortexes formed in the friction layer are found to be fatter and less intense than in the low-friction environment, and they also break contact with the ground.

The results of the laboratory experiments are found to agree very well with those of a numerical simulation in which the initial conditions were similar.

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