I want to solve the Rayleigh eq. about inviscid free shear flow in the spatial instabiltiy. All references I have are about the temporal stability solution. How can I solve the spatial stability Rayleigh eq. ?? Same method with temporal stability ? (Only change of the unknowns) If you know the references or method, please let me know.

Thanks in advance.

Best regards.

I thought that the Kelvin Helmholtz instability describes shear flows. And the Rayleigh inviscid criterion describes a circulation gradient condition for rotating flows to go unstable.

What is Rayleighs inviscid free shear instability?

It's just a change of unknowns as you state; i.e. fix the frequency and treat the wavenumber as the unknown.

Look at Drazin & Reid Hydrodynamic stability and, if you can find a copy, the book by C.C. Lin,

Tom.