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

In this paper,an alternative method has been presented tosolve the Orr-Sommerfeld equation in the linear theory ofstability.To begin with,We define a Green function whichis expressed in terms of matrix.Subsequently,its reci-procity has been shown.Finally,a linear integral equa-tion equivalent to the original Orr-Sommerfeld equation isderived.The method is applied to the cases with two solidwalls and any velocity distribution of the main flow at anyReynolds number.