Vortex dynamics of passive and active interfaces

Abstract Two classes of interface motion are exemplified. In the first example the advection of a line of passive marker particles by the unsteady flow due to a pair of vortex agitators is considered. The qualitative nature of the subsequent motion of the line depends sensitively on the parameters governing the unsteady flow. The advection of the particles determines either an integrable or a non-integrable dynamical system. The consequences of the transition from one regime to the other are explored by numerical experiments. In the second example a calculation of piecewise potential flow with a sharp interface is presented. The flow of two immiscible fluids of different but constant density and viscosity in a Hele-Shaw cell is considered. The interface separating the fluids is formally a tangential discontinuity of velocity and, thus, may be modelled as a vortex sheet. The evolution of fingers on the interface and the variability of the finger topology with the control parameters in the problem are accessible to numerical computation using a variant of the vortex-in-cell method. Results of numerical experiments employing such a code are presented and discussed. The paper concludes with some general speculations on the dynamics of interfaces.