A three‐dimensional model of corotating streams in the solar wind, 1. Theoretical foundations

Abstract

This paper is concerned with the development of the theoretical and mathematical background pertinent to the study of steady, corotating solar wind structure in all three spatial dimensions. The dynamical evolution of the plasma in interplanetary space (defined as the region beyond roughly 35 Rs where the flow is supersonic) is approximately described by the nonlinear, single‐fluid, polytropic magnetohydrodynamic or hydrodynamic equations. We outline efficient numerical techniques for solving this complex system of coupled, hyperbolic partial differential equations. The present formulation is inviscid and nonmagnetic, but our methods allow for the potential inclusion of both features with only modest modifications. We examine one simple, highly idealized hydrodynamic model stream to illustrate the fundamental processes involved in the three‐dimensional dynamics of stream evolution. We find that spatial variations in the rotational stream interaction mechanism produce small nonradial flows on a global scale that lead to the transport of mass, energy, and momentum away from regions of relative compression and into regions of relative rarefaction. The magnitude of this transport is small, but inside 1 AU the nonradial flow can significantly retard shock formation by allowing fluid in the compressions to slip laterally, thereby partially relieving the stresses built up in the stream interaction. Comparison with simpler models demonstrates the essential nonlinear, multidimensional nature of the interplanetary dynamics. A subsequent paper will be devoted to the investigation of a wide range of more realistic model streams.

Solar Wind Collisional Age From a Global Magnetohydrodynamics Simulation

“…In the inner region, steady-state solutions of one-fluid, polytropic (γ=1.08) solar wind equations with WKB Alfvén waves are obtained by time relaxation initiated with a Parker-type flow in a dipole magnetic field (Usmanov et al 2000;Usmanov & Goldstein 2003). Two-fluid steady-state equations for protons and electrons with Hollwegʼs electron heat flux and WKB Alfvén waves are solved in the intermediate region (Pizzo 1978(Pizzo , 1982Usmanov 1993). In the outer region, we solve three-fluid (thermal protons, electrons, and pickup protons) Reynolds-averaged solar wind equations simultaneously with transport equations for turbulence energy, cross helicity, and correlation length.…”

Global MHD Modeling of the Solar Corona and Inner Heliosphere for the Whole Heliosphere Interval

“…Over the years they have become progressively more sophisticated (e.g., Mikić and Linker, 1994), culminating in models that include the photospheric field as a boundary condition (e.g., Roussev et al, 2003). Complementary efforts focusing on heliospheric models, where the inner boundary was placed beyond the outermost critical point, were also pursued (e.g., Pizzo, 1978;Odstrcil, 1994). Most recently, coronal and heliospheric models have been coupled (e.g., Riley, Mikić, and Linker, 2003;Odstrcil et al, 2004;Manchester et al, 2006;Riley et al, 2007), and more sophisticated descriptions of energy-transport processes have been included (e.g., Lionello, Linker, and Mikić, 2009).…”

Statistics of counter-streaming solar wind suprathermal electrons at solar minimum: STEREO observations

“…Counter-streaming beam patterns may occur owing to the presence of magnetic field enhancements, e.g., within corotating interaction regions and at their bounding shocks (CIR; cf. Pizzo, 1978;Gosling and Pizzo, 1999), downstream along magnetic field lines from the observation point. The backscattering there likely results from wave-particle interactions and shock heating combined with simple adiabatic mirroring and particle leakage into the upstream regions of the CIR (Gosling et al, 1993;Steinberg et al, 2005;Skoug et al, 2006).…”