On the evolution and saturation of instabilities of two-dimensional isolated circular vortices

Citation:
Kloosterziel, RC, Carnevale GF.  1999.  On the evolution and saturation of instabilities of two-dimensional isolated circular vortices. Journal of Fluid Mechanics. 388:217-257.

Date Published:

Jun

Keywords:

2-dimensional incompressible flows, emergence, rotating fluid, stability, tripoles, turbulence, vortex

Abstract:

Laboratory observations and numerical experiments have shown that a variety of compound vortices can emerge in two-dimensional flow due to the instability of isolated circular vortices. The simple geometrical features of these compound vortices suggest that their description may take a simple form if an appropriately chosen set of functions is used. We employ a set which is complete on the infinite plane for vorticity distributions with finite total enstrophy. Through projection of the vorticity equation (Galerkin method) and subsequent truncation we derive a dynamical system which is used to model the observed behaviour in as simple as possible a fashion. It is found that at relatively low-order truncations the observed behaviour is qualitatively captured by the dynamical system. We determine what the necessary ingredients are for saturation of instabilities at finite amplitude in terms of wave-wave interactions and feedback between various azimuthal components of the vorticity field.

Notes:

n/a

Website

DOI:

10.1017/s0022112099004760