L. Brevdo, INITIAL-BOUNDARY-VALUE STABILITY PROBLEM FOR THE BLASIUS BOUNDARY-LAYER, Zeitschrift fur angewandte Mathematik und Mechanik, 75(5), 1995, pp. 371-378
The initial-boundary-value linear stability problem for two-dimensiona
l disturbances in the Blasius boundary layer is treated formally by me
ans of Fourier-Laplace transform. The resulting nonhomogeneous boundar
y-value problem for the Orr-Sommerfeld equation is studied analyticall
y. At infinity of the boundary layer the ''outgoing wave'' conditions
are applied. A fundamental set of solutions for the homogeneous bounda
ry-value problem is defined formally, and the inhomogeneous problem is
solved by means of a variation of parameters. We show by using this f
undamental set that the dispersion relation function of the problem D(
k,omega) has the form D(k,omega) = P(k,omega) + root k(2) + iR(k-omega
), where Q(k,omega) and P(k,omega) are analytic functions of (k,omega)
, k is a wave number, omega is a frequency, and R is the Reynolds numb
er. Consequently, a simple proof of the discreteness of the eigenvalue
spectrum is given. The solution of the initial-boundary-value problem
is expressed as an inverse Fourier-Laplace transform of the solution
of the inhomogeneous Orr-Sommerfeld problem. Based on this solution th
e unstable wave packets in the Blasius boundary layer are studied in B
REVDO [5].