The problem with peaking in the atmospheric magnetohydrodynamics. Limiting cases

G. Bystrai - I. Lykov - S. Okhotnikov

Ural Federal University, Yekaterinburg, Russia

Abstract
For the mathematical modelling of highly nonequilibrium and nonlinear processes in the atmosphere based on the equations of momentum and charge transfer, a thermodynamic approach is used with the model function of sources and sinks, which is characteristic for problems with peaking, where the maximum of the velocity distribution and charge distribution in space can increase without bound for a limited time. It allows to consider the general case, taking into account the interaction between the components of the velocity vector and the electromagnetic field in the presence of sources and sinks of momentum in a flat layer. As a limiting case, we consider the transfer of momentum when its source in a nonlinear medium leads to the regime with peaking, and the development of the regime generated by a nonlinear medium itself leads to self-organization. The competition between the process increment and the propagation of momentum and charge can result in appearance of new medium characteristics, such as the spatial diameter of tornado (lightning core), in which these processes balance each other. Another limiting case is the process of charge transfer in an atmosphere considered. As a result, a more general problem may be formulated, and a joint system of equations, which not only describes the behaviour of the velocity vector for an incompressible medium in the form of parabolic equation of momentum, but also takes into account the influence of electromagnetic field, may be derived. Tables 1, Figs 4, Refs 21.