On the properties of hydromagnetic waves in the vicinity of critical levels and transition layers

Abstract

We consider magnetosonic-gravity waves, in an isothermal atmosphere, under a uniform, horizontal magnetic field, with horizontal wavevector in the plane of gravity and the magnetic field. It is shown (Section 2) that the logarithmic singularity, at the critical level (of type I, i.e. singular layer), only occurs for acoustically evanescent waves, of “large” horizontal wavenumber k >Ω/c_o , whose frequency Ω<c_o k lies within the continuous spectrum of slow modes; for fast modes, which have a discrete spectrum, in the opposite case k<Ω/c_o , when a purely acoustic wave could propagate, the “logarithmic singularity” appears as a leading term of a divergent series expansion that cancels it, and the magnetosonic-gravity waves have finite amplitude and phase everywhere (Section 3). The altitude z=z_c , corresponding when k>Ω/c_o to the critical level (of type I, or singular layer), gives way when k<Ω/c_o to a transition layer (or critical level of type II), i.e. a singularity away from the real axis, which determines the regions of convergence of low-altitude z <z_c and high-altitude z >z_c solutions (Section 4). The waveform of magnetosonic-gravity waves evolves continuously across the transition layer z=z_c , from nearly acoustic-gravity waves far below z<z_c , to compressive Alfvèn type far above z≫z_c , the process of “mode conversion” being illustrated in Figures 1 to 5, for vertical waves k=0, which are not strongly reflected. Oblique k=0 magnetosonic-gravity waves are strongly reflected at the critical level z=z_c , which is of type III or reflection layer, corresponding to evanescent waves above, and below to the superposition of upward (i.e. incident) plus downward (i.e. reflected) propagating fields.

Key Words:

• Critical levels
• hydromagnetic waves
• magnetohydrodynamics
• transition layer
• solar physics
• astrophysics