Root
/
Conference Proceedings
/
6th EUROMECH Nonlinear Dynamics Conference (ENOC 2008)
/
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

Reynolds number.

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.

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

Reynolds number.

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.