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

Laboratory observations and numerical experiments have shown that a variety of compound vortices can emerge in two-dimensional flow due to the instabi lity of isolated circular vortices. The simple geometrical features of thes e compound vortices suggest that their description may take a simple form i f an appropriately chosen set of functions is used. We employ a set which i s complete on the infinite plane for vorticity distributions with finite to tal enstrophy. Through projection of the vorticity equation (Galerkin metho d) 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 foun d that at relatively low-order truncations the observed behaviour is qualit atively captured by the dynamical system. We determine what the necessary i ngredients are for saturation of instabilities at finite amplitude in terms of wave-wave interactions and feedback between various azimuthal component s of the vorticity field.