Engineering topics

Ratkiewicz, R.

Publications and source records attributed to Ratkiewicz, R..

3 records

NASA NTRS1995

Multi-dimensional MHD simple waves

In this paper we consider a formalism for multi-dimensional simple MHD waves using ideas developed by Boillat. For simple wave solutions one assumes that all the physical variables (the density rho, gas pressure p, fluid velocity V, gas entropy S, and magnetic induction B in the MHD case) depend on a single phase function phi(r,t). The simple wave solution ansatz and the MHD equations then require that the phase function has the form phi = r x n(phi) - lambda(phi)t, where = n(phi) = Delta phi / (absolute value of Delta phi) is the wave normal and lambda(phi) = omega/k = -phi t / (absolute value of Delta phi) is the normal speed of the wave front. The formalism allows for more general simple waves than that usually dealt with in which n(phi) is a constant unit vector that does not vary along the wave front. The formalism has implications for shock formation for multi-dimensional waves.

Webb, G. M.↗

NASA NTRS1995

Global aspects of the motion of the heliospheric termination shock: A gasdynamic model

The heliospheric termination shock is expected to move in response to variation in upstream solar wind conditions. Using numerical techniques, we extend an earlier strictly one-dimensional analytic gas dynamic model of shock motion to two dimensions, to investigate the qualitative features of global behavior of shock motion, and the consequences of latitudinal variation in dynamic pressure. The boundary conditions of the calculation are given by the solar wind parameters as a function of latitude and time on an inner spherical boundary, and a constant pressure (roughly simulating the effect of the local interstellar medium) on an outer boundary. Density variations, specified at the inner boundary as a function of time, are convected into the termination shock. Immediately after the interaction, the shock moves with speeds given by the earlier analytic model. However, as the termination shock propagates outward (or inward), it begins to slow down. After about 2 to 10 years, depending on details of boundary conditions, the signal from the shock interaction has reached the outer boundary and propagates inward to the position of the termination shock, strongly affecting the behavior of the shock. Assuming no further disturbances in the solar wind, the termination shock will reach its new equilibrium after some tens of years. In reality, large-scale variations in solar wind dynamic pressure occur on time scales short in comparison with the eleven year solar cycle, so that one expects that the termination shock is never in an equilibrium position, but rather oscillates inward and outward; this oscillation will vary with heliographic latitude. The effects of a variety of types of solar wind disturbances are investigated and summarized.

Ratkiewicz, R.↗

NASA NTRS1995

Heliospheric Termination Shock Motion Due to Fluctuations in the Solar Wind Upstream Conditions: Spherically Symmetric Model

Large-scale fluctuations in the solar wind plasma upstream of the heliospheric termination shock (TS) will cause inward and outward motions of the shock. Using numerical techniques, we extend an earlier strictly one-dimensional (planar) analytic gas dynamic model to spherical symmetry to investigate the features of global behavior of shock motion. Our starting point is to establish a steady numerical solution of the gasdynamic equations describing the interaction between the solar wind and the interstellar medium. We then introduce disturbances of the solar wind dynamic pressure at an inner boundary, and follow the subsequent evolution of the system, especially the motion of the termination shock. Our model solves spherically symmetric gasdynamic equations as an initial-boundary value problem. The equations in conservative form are solved using a fully implicit Total Variation Diminishing (TVD) upwind scheme with Roe-type Riemann solver. Boundary conditions are given by the solar wind parameters on an inner spherical boundary, where they are allowed to vary with time for unsteady calculations, and by a constant pressure (roughly simulating the effect of the local interstellar medium) on an outer boundary. We find that immediately after the interaction, the shock moves with speeds given by the earlier analogous analytic models. However, as the termination shock propagates it begins to slow down, seeking a new equilibrium position. In addition, the disturbance transmitted through the TS, either a shock or rarefaction wave, will encounter the heliopause boundary and be reflected back. The reflected signal will encounter the TS, causing it to oscillate. The phenomenon may be repeated for a number of reflections, resulting in a "ringing" of the outer heliosphere.

Ratkiewicz, R.↗