Properties of mass-loading shocks: 1. Hydrodynamic considerations

The one-dimensional hydrodynamics of flows subjected to mass loading are considered anew, with particular emphasis placed on determining the properties of mass-loading shocks. This work has been motivated by recent observations of the outbound Halley bow shock (Neubauer et al., 1990), which cannot be understood in terms of simple hydrodynamical or magnetohydrodynamical descriptions. By including mass injection at the shock, we have investigated the properties of the Rankine-Hugoniot conditions on the basis of a geometric formulation of the entropy condition. Such a condition, which is more powerful than the usual thermodynamical formulation, serves to determine those solutions to the Rankine-Hugoniot conditions which correspond to a physically realizable downstream state. On this basis a concise theoretical description of hydrodynamic mass-loading shocks is obtained. We show that mass-loading shocks have more in common with combustion shocks than with ordinary nonreacting gas dynamical shocks. It is shown that for decelerated solutions to the Rankine-Hugoniot conditions to exist, the upstream flow speed u0 must satisfy u0 > ucrit > cs, where cs is the sound speed. Besides the usual supersonic-subsonic transition, mass-loading fronts can also admit a decelerating supersonic-supersonic transition, the structure of which consists of a sharp decrease in the flow velocity preceding a recovery and an increase in the final downstream flow speed. We suggest the possibility that such structures may describe the inbound Halley bow shock (Coates et al., 1987a). Both parallel and oblique shocks are considered, the primary difference being that oblique shocks are subjected to a shearing stress due to mass loading. It is conjectured that such a shearing may destabilize the shock

Phenomenology of hydromagnetic turbulence in a uniformly expanding medium

A simple phenomenology is developed for the decay and transport of turbulence in a constant-speed, uniformly expanding medium. The fluctuations are assumed to be locally incompressible, and either of the hydrodynamic or non-Alfvénic magnetohydrodynamic (MHD) type. In order to represent local effects of nonlinearities, a simple model of the Kaármá-Dryden type for locally homogeneous turbulent decay is adopted. A detailed discussion of the parameters of this familiar one-point hydrodynamic closure is given, which has been shown recently to be applicable to non-Alfvénic MHD as well. The effects of the large-scale flow and expansion are incorporated using a two-scale approach, in which assumptions of particular turbulence symmetries provide simplifications. The derived model is tractable and provides a basis for understanding turbulence in the outer heliosphere, as well as in other astrophysical applications

Mass-loading and parallel magnetized shocks

Recent observations at comets Giacobini-Zinner and Halley suggest that simple non-reacting gas dynamics or MHD is an inappropriate description for the bow shock. The thickness of the observed (sub)shock implies that mass-loading is an important dynamical process within the shock itself, thereby requiring that the Rankine-Hugoniot conditions possess source terms. This leads to shocks with properties similar to those of combustion shocks. We consider parallel magnetized shocks subjected to mass-loading, describe some properties which distinguish them from classical MHD parallel shocks, and establish the existence of a new kind of MHD compound shock. These results will be of importance both to observations and numerical simulations of the comet-solar wind interaction

Termination Shock Asymmetries as Seen by the Voyager Spacecraft: The Role of the Interstellar Magnetic Field and Neutral Hydrogen

We show that asymmetries of the termination shock due to the influence of the interstellar magnetic field (ISMF) are considerably smaller in the presence of neutral hydrogen atoms, which tend to symmetrize the heliopause, the termination shock, and the bow shock due to charge exchange with charged particles. This leads to a much stronger restriction on the ISMF direction and its strength. We demonstrate that in the presence of the interplanetary magnetic field the plane defined by the local interstellar medium (LISM) velocity and magnetic field vectors does not exactly coincide with the plane defined by the interstellar neutral helium and hydrogen velocity vectors in the supersonic solar wind region, which limits the accuracy of the inferred direction of the ISMF. We take into account the tilt of the LISM velocity vector with respect to the ecliptic plane and show that magnetic fields as strong as 3 μG or greater may be necessary to account for the observed asymmetry. Estimates are made of the longitudinal streaming anisotropy of energetic charged particles at the termination shock caused by the nonalignment of the interplanetary magnetic field with its surface. By investigating the behavior of interplanetary magnetic field lines that cross the Voyager 1 trajectory in the inner heliosheath, we estimate the length of the trajectory segment that is directly connected by these lines to the termination shock. A possible effect of the ISMF draping over the heliopause is discussed in connection with radio emission generated in the outer heliosheath

Properties of mass-loading shocks, 2. Magnetohydrodynamics

The one-dimensional magnetohydrodynamics of shocked flows subjected to significant mass loading are considered. Recent observations at comets Giacobini-Zinner and Halley suggest that simple nonreacting MHD is an inappropriate description for active cometary bow shocks. The thickness of the observed cometary shock implies that mass loading represents an important dynamical process within the shock itself, thereby requiring that the Rankine-Hugoniot condition for the mass flux possess a source term. In a formal sense, this renders mass-loading shocks qualitatively similar to combustion shocks, except that mass loading induces the shocked flow to shear. Nevertheless, a large class of stable shocks exist, identified by means of the Lax conditions appropriate to MHD. Thus mass-loading shocks represent a new and interesting class of shocks, which, although found frequently in the solar system, both at the head of comets and, under suitable conditions, upsteam of weakly magnetized and nonmagnetized planets, has not been discussed in any detail. Owing to the shearing of the flow, mass-loading shocks can behave like switch-on shocks regardless of the magnitude of the plasma beta. Thus the behavior of the magnetic field in mass-loading shocks is significantly different from that occurring in nonreacting classical MHD shocks. It is demonstrated that there exist two types of mass-loading fronts for which no classical MHD analogue exists, these being the fast and slow compound mass-loading shocks. These shocks are characterized by an initial deceleration of the fluid flow to either the fast or the slow magnetosonic speed followed by an isentropic expansion to the final decelerated downstream state. Thus these transitions take the flow from a supersonic to a supersonic, although decelerated, downstream state, unlike shocks which occur in classical MHD or gasdynamics. It is possible that such structures have been observed during the Giotto-Halley encounter, and a brief discussion of the appropriate Halley parameters is therefore given, together with a short discussion of the determination of the shock normal from observations. A further interesting new form of mass-loading shock is the “slow-intermediate” shock, a stable shock which possesses many of the properties of intermediate MHD shocks yet which propagates like a slow mode MHD shock. An important property of mass-loading shocks is the large parameter regime (compared with classical MHD) which does not admit simple or stable transitions from a given upstream to a downstream state. This suggests that it is often necessary to construct compound structures consisting of shocks, slip waves, rarefactions, and fast and slow compound waves in order to connect given upstream and downstream states. Thus the Riemann problem is significantly different from that of classical MHD

Turbulence, spatial transport, and heating of the solar wind

A phenomenological theory describes radial evolution of plasma turbulence in the solar wind from 1 to 50 astronomical units. The theory includes a simple closure for local anisotropic magnetohydrodynamic turbulence, spatial transport, and driving by large-scale shear and pickup ions. Results compare well to plasma and magnetic field data from the Voyager 2 spacecraft, providing a basis for a concise, tractable description of turbulent energy transport in a variety of astrophysical plasmas