Vorticity generation and conservation on generalised interfaces in three-dimensional flows

Abstract

This article presents a three-dimensional theory of vorticity creation on generalised interfaces, including both non-slip and free-slip boundaries, which generalises a previous two-dimensional formulation (Terrington et al., J. Fluid Mech., vol. 890, 2020, p. A5). Under this description, vorticity may be created on a boundary by the inviscid relative acceleration between fluid elements on each side of the boundary, driven by either tangential pressure gradients or body forces. Viscosity acts to transfer circulation between the vortex sheet representing the slip velocity on the interface, and the fluid interior, but is not responsible for the creation of vorticity on the interface. This formulation also describes a principle of vorticity conservation for interfacial and free-surface flows: in many flow configurations, the net generation of vorticity on the interface is zero, and the total circulation remains constant throughout flow evolution.