I. On the Dust Devils. II. Linearized Theory of Conical Turbomachines

Citation

Michelson, Irving (1951) I. On the Dust Devils. II. Linearized Theory of Conical Turbomachines. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/PZKM-9280. https://resolver.caltech.edu/CaltechETD:etd-03042009-142746

Abstract

Dust devils are small-scale atmospheric motions of instability arising from the development of large thermal stratifications in the lowest layers above the surface of the earth. A theory is proposed in Part I to describe the conditions of formation of these motions and depends on the new result that shear provides a powerful stabilizing influence even in non-viscous fluid motions in which denser fluid is situated above less dense. Those features of the flow which can be predicted by the theory and compared with observations are found to be in reasonably good agreement, and it is therefore indicated that the theory, which is based on a highly simplified model of flow, furnishes at least a qualitatively correct correlation of the basic ideas involved in the stable flow of very slightly viscous fluids containing density inversions. Applications to technically interesting flows of this type, in large-scale atmospheric motions as well as in high speed aerodynamic boundary layers, are indicated but not analyzed in detail. In Part II the perfect fluid flow is determined for a turbomachine of conical shape and prescribed blade loading. On the basis of the assumption that the stream surfaces are conical in shape, a linear, elliptic partial differential equation of the second order is obtained. The associated boundary value problem is of the Sturm-Liouville type and is solved completely. An asymptotic representation of the solution is determined which is convenient for computational purposes.

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