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Alfven waves are a ubiquitous feature of the solar wind. One approach to studying the evolution of such waves has been to study exact solutions to approximate evolution equations. Here we compare soliton solutions of the Derivative Nonlinear Schrodinger evolution equation (DNLS) to solutions of the compressible MHD equations.
Nonlinear dynamics, of large-amplitude circularly polarized Alfvenic wave packets, is investigated using a one-dimensional hybrid model.
A hybrid numerical code is employed to trace the evolution of rotational discontinuities (RDs). An extensive parameter variation is carried out, with particular emphasis on beta, Ti/Te, theta sub B (the angle between the normal and total magnetic field), and the helicity of the RD. The RD structure is shown to have features in common with the evolution of both strongly modulated nonlinear wave packets and linear dispersive wave propagation in oblique magnetic fields. For small theta sub B, the RD disperses linearly, giving fast and Alfven waves upstream and downstream, respectively, and the familiar S-shaped hodograms. At larger theta sub B, nonlinearity becomes important and strong coupling to a compressional (sonic) component can occur in the main current layer. The results are applied to RDs observed in the solar wind and at the magnetopause.
Recently we have restructured our approach to simulating magnetohydrodynamic (MHD) turbulence in the solar wind. Previously, we had defined a 'virtual' heliosphere that contained, for example, a tilted rotating current sheet, microstreams, quasi-two-dimensional fluctuations as well as Alfven waves. In this new version of the code, we use the global, time-stationary, WKB Alfven wave-driven solar wind model developed by Usmanov and described in Usmanov and Goldstein [2003] to define the initial state of the system. Consequently, current sheets, and fast and slow streams are computed self-consistently from an inner, photospheric, boundary. To this steady-state configuration, we add fluctuations close to, but above, the surface where the flow become super-Alfvenic. The time-dependent MHD equations are then solved using a semi-discrete third-order Central Weighted Essentially Non-Oscillatory (CWENO) numerical scheme. The computational domain now includes the entire sphere; the geometrical singularity at the poles is removed using the multiple grid approach described in Usmanov [1996]. Wave packets are introduced at the inner boundary such as to satisfy Faraday's Law [Yeh and Dryer, 1985] and their nonlinear evolution are followed in time.