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.
Nonlinear kink modes in the presence of charged dust grains
A set of coupled nonlinear equations, which govern the dynamics of electromagnetic perturbations in the presence of a spatially nonuniform electron current in a magnetized dusty plasma, is derived. The linear stability of such a system is discussed. It is shown that in the presence of the dust an oscillatory, kink-type instability can develop with a threshold for the instability far exceeding the value for an ordinary electron–ion plasma. In the nonlinear regime, the possibility for several types of stationary, coherent solutions is demonstrated. For specific profiles of spatially dependent functions describing the basic state, traveling dipolar and tripolar vortices, and vortex chains are found.
Vortex streets driven by sheared flow and applications to black aurora
Black aurora often exhibits the signature of vortex structures. In this paper, it is proposed that pseudo-three-dimensional drift-like electrostatic modes can play a very important role in those phenomena. Employing a two-fluid model, we derive a set of nonlinear equations governing the dynamics of long wavelength inertial convective cells and coupled drift-acoustic waves in the presence of geomagnetic field-aligned plasma flows. It is shown that free energy stored in the latter can cause purely growing and oscillatory instabilities in the auroral ionosphere. The threshold conditions as well as expressions for the linear growth rates are presented. Furthermore, it is found that possible stationary solutions of the nonlinear equations can be represented in the form of vortex structures. It is, therefore, likely that the nonlinear low-frequency electrostatic modes, as described here, may possibly account for the coherent vortex structures within black aurora, as they are often observed during the late recovery phase of a substorm.