Secondary fluid flows driven electromagnetically in a two-dimensional extended duct

This study focuses on two-dimensional fluid flows in a straight duct with free-slip boundary conditions applied on the channel walls y=0 and y=2?N with N>1. In this extended wall-bounded fluid motion problem, secondary fluid flow patterns resulting from steady-state and Hopf bifurcations are examined and shown to be dependent on the choice of longitudinal wave numbers. Some secondary steady-state flows appear at specific wave numbers, whereas at other wave numbers, both secondary steady-state and self-oscillation flows coexist. These results, derived through analytical arguments and truncation series approximation, are confirmed by simple numerical experiments supporting the findings observed from laboratory experiments