Numerical Simulation of a Viscous Flow Interaction of the Solar Wind with the Magnetic Polar Regions of the Venus Ionosphere

A numerical code has been developed to simulate the flow of the solar wind as it interacts with the magnetic polar regions of the Venus ionosphere in the presence of viscous-fluid forces. The geometry of the flow suggests that a flat plate immersed in a supersonic hydrodynamic flow is a suitable model to study the conditions encountered near the magnetic polar regions of the Venus ionosphere where the solar wind directly interacts with the upper ionospheric plasma. In its preliminary form the code does not take into account the presence of a magnetic field nor curvature effects associated with flow motion around the dayside ionosphere and it is basically directed to analyse the effects of viscous force terms in the flow. The velocity, density, pressure and temperature profiles derived from the numerical simulation have been compared with the position of the bow shock and the intermediate transition as measured by the Mariner 5 and the Venera 10 spacecraft along the flanks of the Venus ionosheath. Values in the 10 < R < 100 range for the Reynolds number and in the 2 < M < 3 range for the local Mach number are found as most suitable to account for the observed relative position of both transitions. These values are comparable to those inferred for the terminator region from the velocity and temperature diagrams derived from the analysis of the momentum equation of an MHD flow subject to viscous forces. The results of the numerical simulation also provide evidence that the incident plasma accumulates above the leading edge of the flat plate representing the response of the fluid to the drastic drop of the ~300 km/s solar wind velocity to conform with a very small velocity as boundary condition set at the plate and that represents the main effect of the viscous transport of solar wind momentum to the Venus ionosphere where the speed is only 2-3 km/s.