Exact solutions of Rayleigh's equation and sufficient conditions for inviscid instability of parallel, bounded shear flows
The object is to specify sufficient conditions for the inviscid instability of a general class of plane parallel flows. For a given complex eigenvalue and a real wave number, and for the real part of the adjoint eigenfunction, the Rayleigh's equation is converted into a nonlinear integral equation, if the basic velocity profile \(U(y)\) is given. Then the author deduces sufficient conditions for the existence and uniqueness of solution to this integral equation (for homogeneous boundary conditions) and shows that the velocity is unstable. Again, a method is given to obtain a general class of new exact neutrally stable solutions of the Rayleigh's equation for a given complex eigenvalue, a real wave number, and a function \(U(y)\). The paper is of theoretical nature.
scientific article; zbMATH DE number 690942