Multimode Coupling Theory for Kelvin-Helmholtz Instability in Incompressible Fluid

A weakly nonlinear model is proposed for multimode Kelvin-Helmholtz instability. The second-order mode coupling formula for Kelvin-Helmholtz instability in two-dimensional incompressible fluid is presented by expanding the perturbation velocity potential to second order. It is found that there is an important resonance in the course of the sum frequency mode coupling but the difference frequency mode coupling does not have. This resonance makes the sum frequency mode coupling process relatively complex. The sum frequency mode coupling is strongly dependent on time especially when the density of the two fluids is adjacent and the difference frequency mode coupling is not.