ON THE NATURE OF VORTEX INTERACTIONS AND MODELS IN UNFORCED NEARLY-INVISCID 2-DIMENSIONAL TURBULENCE

A powerful feature-tracking tool is applied to several high-resolution , very long-duration, regularized contour dynamics (contour surgery) s imulations of unforced nearly-inviscid two-dimensional turbulence (2DT ) on the surface of a sphere. Particularly low density gases of vortic es (i.e. on average, very widely separated vortices) are examined to a scertain the nature of their interactions. The simplest (minimal) mode l system is studied, namely a set of vortex patches of just two vortic ity values, +/- omega(0), whose total circulation is zero. The areas o f the patches are selected initially from a pre-assigned, stable (near ly time invariant) power-law distribution. When the vorticity occupati on fraction f> 0.01, often more than three vortices are found relative ly close together at the onset of a strong interaction. But, when f le ss than or similar to 0.01, all such interactions involve only three n earby vortex patches, not all having the same sign of vorticity. This is related to the well-known collapse of three singular (point) vortic es. Thus, under these conditions, isolated two-vortex interactions, wh ich have figured in recent nd hoc theories and models for decaying 2DT , cannot occur. Taking into account these results, we propose an asymp totically-motivated and computationally-efficient ''reduced'' model. ( C) 1996 American Institute of Physics.