The General Kelvin–Helmholtz Stability Model

In this chapter, the character of hydrodynamic stability is given and some examples of well-known instabilities are pointed out. The Kelin–Helmholtz (KH) instability is described by its historical background and by presenting its theoretical flow model, followed by stating the classical result of the stability analysis of the flow system. A multilayer flow system is defined and the equations for KH stability analysis of the system are established. The theoretical stability result—the General Kelvin–Helmholtz (GKH) stability model—is derived and commented. Some consistency checks on the GKH are performed, by comparing GKH applications to known results such as the eigenvalues of a stationary multilayer system, waves on the surface of a deep free surface flow, and the conventional KH stability result for a flow system of two layers of finite depth. Finally the GKH model is applied to a finite depth two-layer system with free surface.