CHARACTERISTICS OF OBLIQUELY PROPAGATING, NONLINEAR ALFVEN WAVES

Properties of obliquely propagating (with respect to the large scale magnetic field) nonlinear Alfven and fast magnetosonic waves as described by the derivative nonlinear Schrodinger equation are considered. Attention is restricted to those waves which in the parallel-propagating limit are circularly polarized, exact solutions to the magnetohydrodynamic (MHD) equations. A study is made of the changes in the structure of these waves as the propagation angle is increased. In addition, numerical studies are made of the evolution of initial conditions which do not correspond to stationary wave solutions. The principal conclusions of this investigation are as follows. (1) As the propagation angle with respect to the mean field increases, the functional forms of the wave magnetic field components in the two directions orthogonal to the propagation direction become increasingly dissimilar. This fact may be the basis for the "polarization evolution" of large amplitude MHD waves observed in space. (2) The angle about the mean field within which stationary waves resemble parallel-propagating, circularly polarized waves becomes smaller as the wavelength increases. (3) Numerical investigations of the evolution of large amplitude, circularly polarized wave packets show that if the "initial condition" wave train is close to parallel-propagating (where the criterion for "close" is developed in this paper), then there is little subsequent evolution in its form. However, if the propagation angle is sufficiently large, the wave steepens, undergoes polarization evolution, and can generate high-frequency wavelets. The relevance of these results for the large amplitude MHD waves near the Earth's bow shock is briefly discussed.