Self-similar asymptotics in non-symmetrical convergent viscous gravity currents

Abstract

We investigate the evolution of the ridge produced by the non-symmetrical convergent motion of two substrates over which an initially uniform layer of a Newtonian liquid rests. The lack of symmetry of the flow arises because the substrates move with different velocities. We focus on the self-similar regimes that occur in this process. For short times, within the linear regime, the height and the width increase as t1/2 and the profile is symmetric, independently of degree of asymmetry of the motion of the substrates. In the self-similar regime for large time, the height and the width of the ridge follow the same power laws as in the symmetric case, but the profiles are asymmetric. © 2009 IOP Publishing Ltd.