Anatoly Tur

Point vortices with a rational necklace: New exact stationary solutions of the two-dimensional Euler equation

In this paper we find a new class of explicit exact stationary solutions of the two-dimensional (2D) Euler equation which describe vortex patterns of necklace type with N+1-fold symmetry in rotational shear flow. The point vortex with a strength equal to ±4πN (where N-integer number) is situated in the center of the vortex structure. The vorticity distribution outside of the center is smooth and is described by a two-parametric family of rational functions which are known in explicit form for any N. In the centers of vortex satellites the vorticity does not have any singularity and remains of finite value. When N is increasing, the solutions describe the transition layer in 2D–rotational shear flow.

Point vortices in two dimensional-plasma hydrodynamics

An exact theory of point vortices in two dimensional (2D) electron-ion plasma hydrodynamics is presented. This theory is a logical generalization of the classical theory of point vortices in a 2D Euler equation. The existence of two types of point vortices is shown: ion and electron, and their structure is described in detail. Ion vortices interact over long distances, while electron vortices interact over short distances. A dynamic system is obtained, which describes the common motion of an arbitrary number of electron and ion vortices. The proposed theory can be used to construct finite dimensional dynamical models of plasma motion, as well as for the construction of finite dimensional statistical models of turbulence, transport processes and filaments.

Nonlinear vortex dynamo in a rotating stratified moist atmosphere

We have found a new type of large-scale instability in a rotating stratified moist atmosphere with small-scale turbulence. The turbulence is excited by an external small-scale force with a low Reynolds number. We have constructed the theory based on the method of multiscale asymptotic expansions. The nonlinear equations for large-scale motion have been derived in the third order of the perturbation theory. We have investigated the linear instability and stationary nonlinear regimes. Solutions in the form of localized vortex structures or kinks of a new type have been obtained.

Large-scale convective instability in an electroconducting medium with small-scale helicity

A large-scale instability occurring in a stratified conducting medium with small-scale helicity of the velocity field and magnetic fields is detected using an asymptotic many-scale method. Such a helicity is sustained by small external sources for small Reynolds numbers. Two regimes of instability with zero and nonzero frequencies are detected. The criteria for the occurrence of large-scale instability in such a medium are formulated.