On the Hydrodynamic Stability of Two Viscous Incompressible Fluids in Parallel Uniform Shearing Motion

Author: Feldman, Saul

Year: 1955

Degree: Dissertation (Ph.D.)

Advisor: Rannie, W. Duncan

Committee Member: Unknown, Unknown

Option: Mechanical Engineering; Mathematics

DOI: 10.7907/X62Y-2070

Abstract

A new problem in hydrodynamic stability is investigated. Given two contiguous plane sheets of viscous incompressible fluids, bounded on one side by a solid wall and unbounded on the other, the problem is to study the hydrodynamic stability when the fluids are in longitudinal, laminar, uniform shearing motion. The mathematical analysis, based on small disturbance theory, leads to a characteristic vague problem in a system of two linear ordinary differential equations. The case for which forces due to gravity and surface tension are negligible compared with inertia and viscous forces is studied in detail, and the results are presented graphically for all fluid combinations of possible interest.

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