Transformation of Two-Dimensional Stationary Equations of Magnetic Hydrodynamics in Arbitrary Orthogonal Coordinate System to Physical Variables. Jet Streams

摘要

We consider two-dimensional stationary equations of magnetic hydrodynamics in arbitrary orthogonal coordinate system (x_1, x_2, x_3). Starting from validity of the equations div pv = 0, div B = 0, we introduce the stream function Ψ(x_1,x_2) and the function of magnetic flow Χ(x_1,x_2), which are accepted as new independent variables, and realize the transformation x_1 = x_1 (Ψ, Χ), x_2=x_2(Ψ, Χ). Under the condition that magnetic field is orthogonal to field of velocities we obtained two integral magnetic hydrodynamics equations. Taking into account these integrals we considered "solar wind" flow, for which in contrast to the known solution the dipole field of the Sun is considered. Generalization of the Grad-Shafranov and Bragg-Hawthorne equations was obtained as well.