INITIAL-BOUNDARY-VALUE STABILITY PROBLEM FOR THE BLASIUS BOUNDARY-LAYER

The initial-boundary-value linear stability problem for two-dimensional disturbances in the Blasius boundary layer is treated formally by means of Fourier-Laplace transform. The resulting nonhomogeneous boundary-value problem for the Orr-Sommerfeld equation is studied analytically. At infinity of the boundary layer the ''outgoing wave'' conditions are applied. A fundamental set of solutions for the homogeneous boundary-value problem is defined formally, and the inhomogeneous problem is solved by means of a variation of parameters. We show by using this fundamental 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 number. 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 the unstable wave packets in the Blasius boundary layer are studied in BREVDO [5].