Resonant Interactions of Dean Vortices in a Curved Channel Flow

Stability of the flow in a curved channel is investigated with the Dean approximation by using the weakly nonlinear stability theory. A set of amplitude equations lor the Dean vortices of wavenumber ratio 1:2 is derived. The amplitude equations describe the resonant interactions between the fundamental mode and the higher harmonic. The equilibrium amplitudes of the Dean vortices are evaluated from the set of amplitude equations numerically. It is concluded that the phenomena of the coalescence of two vortices and the splitting of one large vortex into two are explained from the 1:2 resonance.