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

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].