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Introduction to Hydrodynamic Stability

Mark J. McCready
Organization: University of Notre Dame
Department: Department of Chemical Engineering
URL: http://www.nd.edu/~mjm
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This notebook is intended to give a first introduction to hydrodynamic instability. This includes both the physical concepts and several useful mathematical manipulations.

There are three parts. The first discusses the concept of linear instability theory and uses a simple wave equation to demonstrate the linearization and calculation of temporal and spatial growth.

The second part derives the stability relation for a two-layer inviscid flow, the Kelvin-Helmoltz instability.

The third part shows how to derive the basic equation of hydrodynamic stability for Newtonian fluids, the Orr-Sommerfeld equation.

*Science > Physics > Fluid Mechanics

linear stability analysis, hydrodynamic stability, interfacial waves, gas-liquid flows, multifluid flows
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linstab.nb (548.3 KB) - Mathematica notebook