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On the nonlinear stability of rotating Newtonian and non-Newtonian fluids

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Summary

The effect of superimposed rigid body rotations on the nonlinear stability of an arbitrary base flow is examined from a theoretical standpoint for incompressible Newtonian and non-Newtonian fluids. It is proven mathematically, from an analysis of the full nonlinear equations of motion, that instabilities which depend on the state of rotation of the fluid must arise from variations in the velocity disturbances along the axis of rotation of the fluid. Consequently, it follows that Squire's theorem cannot, under any circumstances, apply to rotationally dependent instabilities. The consistency of these results with previous work on Couette flow and rotating plane Poiseuille flow is discussed briefly.

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  1. Stevens Institute of Technology, 07030, Hoboken, NJ, U.S.A

    C. G. Speziale

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  1. C. G. Speziale
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Speziale, C.G. On the nonlinear stability of rotating Newtonian and non-Newtonian fluids. Acta Mechanica 49, 263–273 (1983). https://doi.org/10.1007/BF01236356

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