The viscous modulation of Lamb’s dipole vortex

Abstract

A description of the adiabatic decay of the Lamb dipolar vortex is motivated by a variational characterization of the dipole. The parameters in the description are the values of the entrophy and linear momentum integrals, which change in time due to the dissipation. It is observed that the dipole dilates during the decay process [radius R∼(νt)1/2], while the amplitude of the vortex and its translation speed diminish in time proportional to (νt)−3/2 and (νt)−1.

The decay of a dipolar vortex in a weakly dispersive environment

“…The model is extended to weakly viscous flows in § 6 by including viscous dissipation of vortex energy and viscous dissipation of centre vorticity. In the dispersionless limit this model approximates the results of van de Fliert (1996) and Nielsen & Rasmussen (1997) for a homogeneous fluid but unlike their determinations, based on impulse conservation and enstrophy decay respectively, also reproduces the inviscid, dispersive results. The relative importance of the two effects, for small here, is measured by D = 3 Re: when D 1 wave drag dominates and when D 1 viscous dissipation dominates.…”

“…As a and U evolve the value of D changes and the dominant decay mechanism can change. van de Fliert (1996) combines the dispersionless ( = 0) version of (6.2) with conservation of the impulse μ and Nielsen & Rasmussen (1997) combine the dispersionless version of (6.2) with an equivalent equation for the viscous decay of enstrophy. Both derive equivalent models where the LC dipole slows with speed U ∼ t −1 but radius expanding with a ∼ t 1/2 .…”

“…Section 6 extends the model to include viscous dissipation, relating the results to the homogeneous-fluid results of van de Fliert (1996) and Nielsen & Rasmussen (1997), and § 7 discusses the results briefly.…”