Oblique propagation of nonlinear hydromagnetic waves: One‐ and two‐dimensional behavior

The one‐ and two‐dimensional behavior of obliquely propagating hydromagnetic waves is analyzed by means of analytical theory and numerical simulations. It is shown that the nonlinear evolution of a one‐dimensional MHD wave leads to the formation of a rotational discontinuity and a compressive steepened quasi‐linearly polarized pulse whose structure is similar to that of a finite amplitude magnetosonic simple wave. For small propagation angles, the pulse mode (fast or slow) depends on the value of β with respect to unity while for large propagation angles the wave mode is fixed by the sign of the initial density‐field correlation. The two‐dimensional evolution shows that an MHD wave is unstable against a small‐amplitude long‐wavelength modulation in the direction transverse to the wave propagation direction. A “two‐dimensional magnetosonic wave” solution is found, in which the density fluctuation is driven by the corresponding total pressure fluctuation, exactly as in the one‐dimensional simple wave. Along with the steepening effect, the wave experiences both wave front deformation and a self‐focusing effect which may eventually lead to the “collapse” of the wave. The results compare well with observations of MHD waves in the Earth's foreshock and at comets.