Nonlinear stationary vortices in gravitating fluid
The problem of nonlinear self-organization of perturbations in differentially rotating, nonuniform, gravitating systems is studied. Two types of stationary nonlinear solutions, in the form of tripolar vortices and vortex chains of gravitational potential and density, dependent on the spatial profiles of the basic state quantities, are found. They propagate with a constant velocity perpendicularly to the basic state gradients, and characteristic time scales for the creation of such vortical structures are shown to be much shorter than the corresponding intervals for gravitational contraction.
Static configurations and nonlinear waves in rotating nonuniform self-gravitating fluids.
The equilibrium states and low-frequency waves in rotating nonuniform self-gravitating fluids are studied. The effect of a central object is included. Two-dimensional static configurations accounting for self-gravity, external gravity, and nonuniform rotation are considered for three models connecting the pressure with the mass density: thermodynamic equilibrium, polytropic pressure, and constant mass density. Explicit analytical solutions for equilibrium have been found in some cases. The low-frequency waves arising due to the vertical and horizontal fluid inhomogeneities are considered in the linear and nonlinear regimes. The relationship between the background pressure and mass density is supposed to be arbitrary in the wave analysis. It is shown that the waves considered can be unstable in the cases of polytropic pressure and constant mass density. The additional nonlinear term proportional to the product of the pressure and mass density perturbations, which is usually omitted, is kept in our nonlinear equations. There have been found conditions for this term to be important. Stationary nonlinear wave equations having solutions in the form of coherent vortex structures are obtained in a general form. The importance of involving real static configurations in the consideration of wave perturbations is emphasized.
Tripolar vortices in a rotating fluid
THE emergence of coherent flow structures is a well-known feature of quasi-geostrophic or two-dimensional turbulence, and because of their relevance to large-scale geophysical flows the dynamics of these structures have been studied increasingly over the past decade1–5 The most common coherent structures are the axisymmetric (monopolar) vortex, with circular streamlines, and the vortex dipole, both of which have been found to arise in a variety of situations under different (sometimes nondescript) forcing conditions. The emergence of vortex dipoles, for example, has been observed in turbulence in soap films3, in electrically forced magnetohydrodynamic flows5 and in collapsing turbulence in a continuously stratified fluid6. There is growing evidence4,7–9 that, in addition to the monopolar and dipolar vortices, a tripolar coherent flow structure exists. Here we describe a laboratory experiment in which a tripolar structure is found to emerge from an unstable cyclonic vortex in a homogeneous rotating fluid. The tripole seems to be a very stable structure, even persisting in a highly sheared fluid environment, and might therefore be found in natural geophysical flows.