Propagation of three‐dimensional Alfvén waves and its nonlinear effects in the solar wind

Abstract

We consider propagation of three‐dimensional, adiabatic magnetohydrodynamic (MHD) perturbations in a background radial MHD solar wind which is spherically symmetric. In the linear approximation, three‐dimensional propagation of Alfvén waves decouples from three‐dimensional propagation of MHD fast and slow perturbations in the wind. For Alfvén waves, we extend previous analytical WKB, non‐WKB, and asymptotic solutions at large distances as well as numerical results to explicit three‐dimensional versions; as to three‐dimensional MHD fast and slow perturbations, we generalize the prior perturbation scheme for a purely hydrodynamic solar wind by including a magnetic field. In general, Alfvén wave flux in the solar wind is not conserved; we further study the following second‐order nonlinear effects due to a three‐dimensional propagation of Alfvén waves in the wind, namely, (1) the driving of compressible MHD wind flow and thermodynamic variations; (2) the generation of MHD fast and slow waves; (3) the generation of Alfvén waves; and (4) the formation of steady, incompressible vortex and current structures. Therefore in the absence of direct dissipative mechanisms, the energy flux of Alfvén waves in the solar wind is consumed to produce these nonlinear effects. For typical solar wind parameters in the absence of dissipations, the Alfvén wave flux density at the solar coronal base inferred from that observed at 1 AU is thus 1 to 2 orders of magnitude less than what is needed (5 ∼ 8 × 105 ergs cm−2 s−1) if a solar wind stream would be entirely driven and maintained by Alfvén waves. We discuss several relevant heliospheric applications of our results.