Solar wind frequency spectra show a distinct steepening of the ƒ−5/3 power law inertial range spectrum at frequencies above the Doppler‐shifted ion cyclotron frequency. This is commonly attributed to dissipation due to wave‐particle interactions. We consider the extent to which this steepening can be described, using a magnetohydrodynamic formulation that includes the Hall term. An important characteristic of Hall MHD is that although the ion cyclotron resonance is included, there is no wave‐particle dissipation of energy. In this study we use a compressible Hall MHD code with a constant magnetic field and a polytropic equation of state. Artificial dissipation in the form of a bi‐Laplacian operator is used to suppress numerical instabilities, allowing for a clear separation of the dissipative scales from the ion cyclotron scales. A distinct steepening appears in the simulation power spectra near the cyclotron resonance for certain types of initial conditions. This steepening is associated with the appearance of right circularly polarized fluctuations at frequencies above the ion cyclotron resonance. Similar steepenings and polarization enhancements are observed in solar wind magnetic field data.
A quasifluid formalism designed to capture some effects of cyclotron interactions is presented. Starting from the contractions of exact moments of the Vlasov equation, a closure for cyclotron interactions is achieved by using kinetic information directly. This nonperturbative approach does not require a priori assumptions about zeroth-order particle velocity distributions. The nonlinear coupling between field-aligned particle thermal velocities and transverse cyclotron wave and thermal motions are described by off-diagonal elements of the pressure tensor. These elements are related to the growth and damping of cyclotron wave energy. A functional form for an effective wave–particle momentum transport coefficient is derived from the requirement of consistency between the energy and momentum moment equations, but its specific magnitude and sign, determined by threshold temperature anisotropy levels, must be input from kinetic theory. This effective transport coefficient has a nondefinite sign, reminiscent of the gyroviscous coefficients of classical transport, and is consistent with the time reversibility of the Vlasov equation. A coupled set of cyclotron equations of state for the evolution of the parallel and perpendicular pressures are derived. This formalism provides a connection between known kinetic solutions of cyclotron interactions and fluid plasma equations.
We study a transverse ("meridional" in heliocentric coordinates) plasma flow induced by the evolution of a Karman vortex street using a Chebyshev-Fourier spectral algorithm to solve both the compressible Navier-Stokes and magnetohydrodynamic (MHD) equations. The evolving vortex street is formed by the nonlinear interaction of two vortex sheets initially in equilibrium, such as are naturall• found either side of the heliospheric current sheet at solar minimum. We study spatial profiles of the total plasma velocity, the density, the meridional flow angle and the location of sector boundaries and find generally good agreement with Voyager 2 measurements of quasi-periodic transverse flow in the outer heliosphere. The pressure pulses associated with the meridional flows in the simulation are too small, although they are correctly located, and this may be due to the lack of any "warp" in the current sheet in this model. A strong, flowaligned magnetic field, such as would occur in the inner heliosphere, is shown to lead to weak effects that would be masked by the background interplanetary turbulence. We also study the plasma and magnetic transport resulting from the meridional flow, and find that deficits of magnetic quantities do occur near the ecliptic and that while the effect is relatively small, it is in general agreement with the most recent analysis of 'flux deficit' in the outer heliosphere. 1. INTRODUCTION The Plasma Science experiment on board Voyager 2 revealed a surprising quasi-periodic meridional solar wind plas•na flow in the outer heliosphere [Lazarus et al., 1988; McNutt, 1988] during a long interval near solar minimum. From 1986 to early 1988, Voyager 2 was in the ecliptic and near the heliospheric equatorial plane (within 2 ø) and located between 20 AND 25 A•. The period of flow variations was close to 25.5 days or about one solar rotation period, and the deflection angle of the flow was as much as 5 ø . Over such large distances, the observation of this regularity in the turbulent solar wind is remarkable. The high-speed streams flowing either side of the heliospheric current sheet provide a natural source for the periodicity of the N-S variations in the flow. However, as with the problem of interplanetary turbulence [Roberts and Goldstein, 1991] a significant question is the degree to which the streams lead to compressire effects as compared to shear effects. While high-speed wind will compress slower flow in front of it, it is not clear that this should lead to meridional excursions of the flow. The detailed model of Pizzo and Goldstein [1987] that uses the pressure built up by the streams to drive meridional flow predicts that there will be two N-S excursions of the flow vector each solar rotation, and these will both be accompanied by latitude variations. Although two maxima are observed in the solar wind speed for each period of the pattern, only one cycle of transverse flow is seen and it is nearly always perpendicular to the ecliptic; this implies that although the Pizzo and Goldstein model un...
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