Eigenvalues of the Orr-Sommerfeld Equation

Milan Miklavcic
Department of Mathematics
Michigan State University
East Lansing, MI 48824-1027

Published in Differential and Integral Equations, 4(1991), 731-737.


Abstract:

A very simple proof is presented of the fact that the Orr-Sommerfeld equation for flows that approach exponentially to a constant at infinity has at most finitely many eigenvalues. A completely elementary argument shows that the Orr-Sommerfeld equation has no eigenvalues when the product of the Reynolds number and the wave number is small enough.

Here is the whole article in the PDF format.

For my other publications related to the Orr-Sommerfeld equation see:

  1. Stability of mean flows over an infinite flat plate,
    Arch. Rational Mech. Anal. 80(1982), 57-69.
    This is a joint work with M. Williams.

  2. Eigenvalues of the Orr-Sommerfeld equation in an unbounded domain,
    Arch. Rational Mech. Anal. 83 (1983), 221-228.

  3. Nonlinear stability of asymptotic suction
    AMS Transactions 281(1984),215-231.
    Also in IMA Preprint Series 5, 1982.

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