A three‐dimensional model of corotating streams in the solar wind 2. Hydrodynamic streams
Authors: Pizzo Victor J. 
Published: February 2008

This paper explores theoretical aspects of corotating solar wind dynamics on a global scale by means of numerical simulations executed with a nonlinear, inviscid, adiabatic, single‐fluid, three‐dimensional (3‐D) hydrodynamic formulation. The study begins with a simple hypothetical 3‐D stream structure defined on a source surface located at 35 RS and carefully documents its evolution to 1 AU under the influence of solar rotation. By manipulating the structure of this prototype configuration at the source surface, it is possible to elucidate the factors most strongly affecting stream evolution: (1) the intrinsic correlations among density, temperature, and velocity existing near the source; (2) the amplitude of the stream; (3) the longitudinal breadth of the stream; (4) the latitudinal breadth of the stream; and (5) the heliographic latitude of the centroid of the stream. The action of these factors is best understood in terms of momentum arguments of relative simplicity and general application (to the extent that waves, conduction, and kinetic effects may be ignored). Corotating structure is viewed as a spiral standing wave (in the rotating frame) in which there is an ongoing competition between the kinematic tendency of the stream to steepen (as high‐speed material overtakes slow) and the dynamical reaction of the gas to resist compression (through acceleration and tangential deflection of material by pressure gradients in the interaction region). Longitudinal gradients in the radial velocity distribution determine how fast material is brought into the interaction region, but the detailed momentum balance as a function of position within the stream dictates what happens when the material collides. Reasonable specifications of the five factors mentioned above can so affect this kinematic‐dynamic balance that even a high‐amplitude stream (e.g., peak‐to‐trough velocity differences at 1 AU ≅ 480 km/s) may be prevented from shocking inside 1 AU, where the nonradial flow‐broadening mechanism operates most efficiently. The nonlinear 3‐D capabilities of the model allow quantitative study of the global development of this induced tangential flow in some detail. The nonradial motions lead to the net latitudinal transport of small amounts (a few percent) of mass, energy, and momentum. The effects of the latitudinal transport upon the evolution within an east‐west plane are minimal, and the latitudinal spreading of stream material in interplanetary space, even in the presence of steep meridional gradients (up to 30 km/s/deg), is limited to a few degrees. Thus for corotating structures, with their favorable spiral geometry, the two‐dimensional approximation adequately describes the dynamical interaction. However, certain important research topics can only be approached in the full 3‐D formulation. For example, the systematic pattern of the meridional flow changes across stream fronts contains information on the 3‐D structure of the stream and thus offers promise as a practical diagnostic tool. Also, since the magnetic field is tied to the flow, it is to be expected that stream‐driven meridional motions should have a noticeable effect upon the north‐south magnetic fluctuations and may be of consequence to angular momentum studies. Proper discussion of these subjects demands a 3‐D magnetohydrodynamic model and will be considered in a subsequent paper.