Using WKB method for solving the problem of the stability of slowly diverging jet flows
A modification of WKB method for approximate solving the linear complex fourth order
differential equation for a small deviation from the steady-state stream function is
given. This equation is derived from the Navier--Stokes equations for a slowly diverging
plane flow. It contains a large parameter proportional to the root square from the
The method under consideration
allows us to find the complex eigenvalues and eigenfunctions. The real
part of the eigenvalue describes the real wave number of a hydrodynamical
wave of a certain frequency, and the imaginary part determines its gain factor.
The latter determines the stability of the flow.
The solution found may be used as a generating one for using the
asymptotic Krylov--Bogolyubov method.