Collision of a solar wind shock wave with the Earth’s bow shock. Wave flow pattern

Abstract

The wave pattern of the flow developed when a solar wind shock wave propagates along the surface of the Earth's bow shock is studied. The investigation is carried out in the three-dimensional non-plane-polarized formulation within the framework of the ideal magneto- hydrodynamic model in which the medium is assumed to be inviscid and non-heat-conducting and to have the infinite conductivity. The global three-dimensional pattern of the interaction which is a function of the latitude and longitude of elements on the surface of the bow shock is constructed as a mosaic of solutions to the problem of breakdown of a discontinuity developed between the states behind the impinging and bow shocks on the moving curve of intersection of their fronts. The investigation is carried out for typical solar wind parameters and interplanetary magnetic field strength in the Earth's orbit and for several Mach numbers of the interplanetary shock wave, which makes it possible to trace the evolution of the flow developed as a function of the intensity of the shock perturbation of the solar wind. The solution obtained is necessary for interpreting measurements carried out by spacecraft located in the neighborhood of the Lagrange point and the Earth's magnetosphere. At present, spacecraft located in the solar wind in the neighborhood of the Lagrange point L1 at distances of approximately 250 Earth's radii RE from the Earth (Wind, SOHO, and ACE) and groups of spacecraft in the neighborhood of the Earth's bow shock, in the magnetosheath, and in the outer magnetosphere (THEMIS, Cluster, and Double Star) are measuring the state of the interplanetary medium and magnetic field and transferring the data to the Earth. The measurements are used to identify sharp jumpwise changes occurring in the solar wind and related to shock waves, rotational and tangential discontinuities, and their manifestations recorded on spacecraft in the neighborhood of the Earth with the aim to forecast the cosmic weather in the form of sudden storm commencements, magnetic substorms, and sudden impulses in the Earth's magnetosphere (1-4). The results of numerical MHD simulations carried out by means of various methods (2-6) are used in analyzing the events. However, the simulations have insufficient spatial resolution, and due to this fact several MHD waves merge with one another and can hardly be identified; for example, slow or Alfven waves are unified with the contact discontinuity (5). For the correct interpretation of measurements it is necessary to use the exact solutions to the problem of interaction between a solar wind discontinuity and the Earth's bow shock Sb (7-11). The quasi-steady-state method of finding them within the framework of magnetohydrodynamics of an ideally conducting medium was first proposed in (7, 8) as the solution to the problem of breakdown of a discontinuity between the states behind the interacting waves on the moving curve of intersection of their fronts. The wave flow pattern and the dependences of the physical parameters of the medium and the magnetic field were first obtained as functions of the angle of inclination of Sb to the solar wind velocity Vsw in the