The steady and unsteady backwash vortices

A circulatory flow called a ‘backwash vortex’ forms under waves running up a sloping bed. The backwash vortex is classified into two types: the ‘steady backwash vortex’ and the ‘unsteady backwash vortex ‘. The former is a steady streaming formed when Re₂< 90, and the latter an unsteady separated flow formed when Re₂> 90, where Re₂is a form of Reynolds number. The ratio of the lengthscale of the backwash vortex to the swash length is proportional to Re₂^½R when Re₂≪ 30, and becomes constant when Re₂is sufficiently large.