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.
Highlights
This article presents a general description of vorticity generation on interfaces and boundaries in three-dimensional flows, which is a direct extension of our previous two-dimensional description of vorticity generation (Terrington, Hourigan & Thompson 2020)
Vorticity generation on 3-D generalised interfaces circulation is generated by the inviscid relative acceleration between fluid elements on each side of the interface, due to either tangential pressure gradients or body forces
In the special case of an incompressible flow, where no vorticity is generated in the fluid interior, is the total vorticity generation given by tangential pressure gradients and body forces on the interface
Summary
This article presents a general description of vorticity generation on interfaces and boundaries in three-dimensional flows, which is a direct extension of our previous two-dimensional description of vorticity generation (Terrington, Hourigan & Thompson 2020) This formulation considers a generalised interface, which may represent a wide range of boundaries, including no-slip and free-slip walls, free surfaces and fluid–fluid interfaces. Vorticity generation on 3-D generalised interfaces circulation is generated by the inviscid relative acceleration between fluid elements on each side of the interface, due to either tangential pressure gradients or body forces Under this interpretation, viscosity is not responsible for the creation of vorticity; viscosity is responsible for the diffusion of vorticity into the fluid interior, after it has been generated by the inviscid mechanism.
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