Whither vortex tubes?

Abstract

We review research aimed at the development of an analytical and numerical framework for tracking the evolution, in an incompressible viscous fluid, of scalar fields, called `vortex surface fields' (VSFs), whose instantaneous isosurfaces always contain continuous vortex lines. A set of equations describing the evolution of VSFs starting from a known initial condition is proposed and discussed. Non-uniqueness in the initial-value problem is resolved with the introduction of evolution in a pseudo-time variable where the vorticity, frozen in real time, plays the role of an advecting field. A numerical method for following both the real and pseudo-time evolution is described and its regularization properties are discussed. Examples are given of following VSFs in a viscous Taylor-Green flow (Taylor and Green 1937 Proc. R. Soc. A 158 499-521). The prospects for extending these ideas to fully turbulent flows are discussed.

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