Green Function and Integral Equation Method for the Orr-Sommerfeld Equation

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Li Jia-chun. Green Function and Integral Equation Method for the Orr-Sommerfeld Equation[J]. Applied Mathematics and Mechanics, 1982, 3(5): 597-604.

Citation:

Li Jia-chun. Green Function and Integral Equation Method for the Orr-Sommerfeld Equation[J]. Applied Mathematics and Mechanics, 1982, 3(5): 597-604.

Citation:

Li Jia-chun. Green Function and Integral Equation Method for the Orr-Sommerfeld Equation[J]. Applied Mathematics and Mechanics, 1982, 3(5): 597-604.

Abstract

In this paper, an alternative method has been presented to solve the Orr-Sommerfeld equation in the linear theory of stability. To begin with, we define a Green function which is expressed in terms of matrix. Subsequently, its reciprocity has been shown. Finally, a linear integral equation equivalent to the original Orr-Sommerfeld equation is derived. The method is applied to the cases with two solid walls and any velocity distribution of the main flow at any Reynolds number.

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