Predicting the aftermath of vortex breakup in rotating flow

• Published in: Journal of fluid mechanics Vol. 669; pp. 90 - 119
• Main Authors: CARNEVALE, G. F., KLOOSTERZIEL, R. C., ORLANDI, P., van SOMMEREN, D. D. J. A.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.02.2011
• Subjects: Breakup; Computational fluid dynamics; Earth, ocean, space; Exact sciences and technology; External geophysics; Flow velocity; Fluid flow; Fluid mechanics; Geophysics; Geophysics. Techniques, methods, instrumentation and models; Instability; Mathematical models; Navier-Stokes equations; Stability; Turbulent flow; Vortices; turbulent flows; geophysical and geological flows; vortex flows; Barotropic instability; Swirling flow; Hydrodynamic instability; Vorticity; turbulent flow; Centrifugal force; digital simulation; Vortex; Geophysical fluid dynamics; Modeling
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112010004945

A method for predicting the outcome of vortex breakup in a rotating flow is introduced. The vortices dealt with here are subject to both centrifugal and barotropic instabilities. The prediction of the aftermath of the breakup relies on knowing how both centrifugal and barotropic instabilities would equilibrate separately. A theoretical model for non-linear equilibration in centrifugal instability is wedded to two-dimensional simulation of barotropic instability to predict the final vortices that emerge from the debris of the original vortex. This prediction method is tested against three-dimensional Navier–Stokes simulations. For vortices in which a rapid centrifugal instability triggers a slower barotropic instability, the method is successful both qualitatively and quantitatively. The skill of the prediction method decreases as the time scales of the two instabilities become comparable.