Merger and alignment in a reduced model for three-dimensional quasigeostrophic ellipsoidal vortices

Abstract

We investigate the interaction of two ellipsoidal vortices in the three-dimensional quasigeostrophic fluid equations by first studying a reduced model of vortex interaction, the ellipsoidal moment model, and second by comparing the results to corresponding numerical simulations. The ellipsoidal moment model approximates the interaction of two ellipsoidal lumps of potential vorticity by a finite-degree-of-freedom Hamiltonian system. This approximation is derived explicitly in the natural moment coordinate system to first order in the ratio of the size of the vortices to their separation. Using this Hamiltonian system for the case of initially spheroidal identical vortices, the linear stability of vertically aligned vortices is analyzed. A new dynamical criterion for vortex merger and alignment is proposed and shown to give a clear and reasonable boundary for vortex merger. A similar boundary is shown to exist in the size of the largest Lyapunov exponent, although not in the chaotic region as measured by the 0-1 test of Gottwald and Melbourne ͓Proc. R. Soc. London, Ser. A 460, 603 ͑2004͔͒. There is no such sharp boundary for vortex alignment in this reduced model. A series of numerical experiments confirms the accuracy of the merger criterion used in the ellipsoidal moment model. The numerical simulations also suggest a mechanism for understanding the process of vortex alignment in terms of vortex Rossby waves.

Models of interacting pairs of thin, quasi-geostrophic vortices: steady-state solutions and nonlinear stability

“…In general, strong vortex interactions only occur when the vortex centers are sufficiently close (depending on parameters), irrespective of the sign, shape and intensity of the vortices (see, e.g. Viera 1995, Sutyrin et al 1998, Dritschel 2002, Reinaud and Dritschel 2005, Martinsen-Burrell et al 2006, Bambrey et al 2007, Ozugurlu et al 2008, Reinaud and Carton 2009, Reinaud and Dritschel 2009.…”

The Ellipsoidal Vortex: A Novel Approach to Geophysical Turbulence

“…While the single vortex case provides great insight into vortex behaviour, in order to understand some of the dynamics that precipitate strong interactions and vortex mergers, one must consider a multivortex scenario. There are a number of works that have generalized the single ellipsoidal vortex solution to a multivortex scenario [35][36][37][38]. However, because of the form of the external stream function (24) generated by a vortex, in general it can induce nonellipsoidal disturbances on external vortices.…”

Can large eddy simulation techniques improve mesoscale rich ocean models?

“…Bracco et al [2004] show that many of the Lagrangian statistics of 3D qg turbulence are virtually identical to 2D turbulence for short to intermediate timescales (a few eddy turnovers). At longer times, vertical effects become important, such as vertical vortex alignment [e.g., Martinsen-Burrell et al, 2006].…”