The spiral wind-up and dissipation of vorticity and a passive scalar in a strained planar vortex

Abstract

The response of a Gaussian vortex to a weak time-dependent external strain field is studied numerically. The cases of an impulsive strain, an on-off step function, and a continuous random strain are considered. Transfers of enstrophy between mean and azimuthal components are observed, and the results are compared with an analogous passive scalar model and with Kida's elliptical vortex model.A 'rebound' phenomenon is seen: after enstrophy is transferred from mean to azimuthal component by the external straining field, there is a subsequent transfer of enstrophy back from the azimuthal component to the mean. Analytical support is given for this phenomenon using Lundgren's asymptotic formulation of the spiral wind-up of vorticity. Finally the decay of the vortex under a continuous random external strain is studied numerically and compared with the passive scalar model. The vorticity distribution decays more slowly than the scalar because of the rebound phenomenon.

Elementary Vortex Processes in Thermal Superfluid Turbulence

“…Finally, sufficiently perturbed axisymmetric vortices [47] lead to classical spiral vortices that are also employed as models of the finest turbulence structure [48]. There is a notable similarity between the computed quantized vorticity spiral and spiraling patterns of passive scalar dispersion by these classical spiral vortices [48,49]. Notably, at final time, the superfluid tangle is so dense that the kinematic description of the normal fluid is not appropriate.…”

A Lagrangian Trajectory View on Transport and Mixing Processes between the Eye, Eyewall, and Environment Using a High-Resolution Simulation of Hurricane Bonnie (1998)

“…The details of these flows are quite different, yet the tendency for vortices to act as mixing barriers to environmental fluid is believed central to both their emergence and long lifetimes in complex flows (e.g., McWilliams 1984;Mizuta and Yoden 2001). This vortex robustness can be traced to the quasi-elastic behavior of vortices, which results from having mechanisms that can oppose disturbances that are either axisymmetric [via centrifugal restoration (Howard and Gupta 1962;Charney 1973)] or nonaxisymmetric [via realness of discrete spectra (Vladimirov and Tarasov 1980) or via a tendency to axisymmetrize (Melander et al 1987;Montgomery and Kallenbach 1997;Bassom and Gilbert 1999;Reasor et al 2004;Schecter and Montgomery 2004)]. If the robustness of a vortex core were to be reduced, however, this could have important consequences on the maintenance of that vortex.…”

A Formal Theory for Vortex Rossby Waves and Vortex Evolution

“…The motivations for having such a theory are manifold. Among the phenomena that may be addressed by applications of this theory are the following: horizontal vortex axisymmetrization (McCalpin, 1987;Melander et al, 1987;Sutyrin, 1989;MK97;Bassom and Gilbert, 1998;Brunet and Montgomery, 2002); vortex spiral evolution (Lundgren, 1982;Moffat, 1986;Gilbert, 1988); vertical alignment (i.e., relaxation of perturbations that tilt the vortex axis away from the vertical Sutyrin et al, 1998;Polvani and Saravanan, 2000;Reasor and Montgomery, 2001;; evolutionary parity selection of either anticyclonic vortices away from boundaries (CushmanRoisin and Tang, 1990;Polvani et al, 1994;Arai and Yamagata, 1994;Yavneh et al, 1997;Stegner and Dritschel, 2000) or cyclonic vortices adjacent to solid horizontal boundaries (Simmons and Hoskins, 1978;Snyder et al, 1991;Rotunno et al, 2000;Hakim et al, 2002), both due to their greater robustness to perturbations at finite Rossby number; conservative vortex dynamics in shearing or straining flows (Marcus, 1990;Bassom and Gilbert, 1999); tropical cyclone development and potential vorticity redistribution (Guinn and Schubert, 1993;Montgomery and Enagonio, 1998;Schubert et al, 1999;Montgomery, 1999, 2000); and astrophysical accretion and protoplanetary disks (Bracco et al, 1999;Mayer et al, 2002;Nauta, 1999). It is not our present purpose to report particular solutions of the formal theory required for these various applications.…”