RESONANT INTERACTIONS OF DEAN VORTICES IN A CURVED CHANNEL FLOW

Stability of the flow in a curved channel is investigated with the Dea n approximation by using the weakly nonlinear stability theory. A set of amplitude equations for the Dean vortices of wavenumber ratio 1:2 i s 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 amplitud e equations numerically. it is concluded that the phenomena of the coa lescence of two vortices and the splitting of one large vortex into tw o are explained from the 1:2 resonance.