Applied Mathematics and Mechanics (English Edition) ›› 1982, Vol. 3 ›› Issue (5): 647-655.

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SOLVING THE ORR-SOMMERFELD EQUATION WITH INTEGRAL EQUATION METHOD IN TERMS OF THE GREEN FUNCTION

Li Jia-chun   

  1. Institute of Mechanics, Academia Sinica, Beijing
  • Received:1981-10-01 Online:1982-09-18 Published:1982-09-18

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.

Key words: left ventricle, end diastolic volume, mechanical periodicity, nonlinear dynamics

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