On oblique Alfven waves in a viscous and resistive atmosphere

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Abstract
Considers Alfven waves propagating obliquely in an atmosphere, subject to a uniform magnetic field of arbitrary direction, in the presence of viscous stresses and electrical resistance. This problem is fundamental to theories of atmospheric heating by dissipation of Alfven waves, on which there is a relatively substantial literature. The Alfven wave equation is deduced for an atmosphere with non-uniform diffusivities and propagation speed. The wave equation is solved exactly in the case of an isothermal atmosphere, for which the Alfven speed increases exponentially on twice the scale height and the dynamic viscosity increases exponentially on the scale height; the rate of ionisation is assumed uniform, leading to a constant electrical diffusivity. The exact solution includes, as particular cases, those obtained before for Alfven waves in an isothermal atmosphere, in the non-dissipative case with vertical (Ferraro and Plumpton, 1958) and oblique (Schwartz et al., 1984) magnetic field, and in the case of resistive dissipation along (Campos, 1983). The wave fields are expressed at all altitudes in the terms of hypergeometric functions, which are used to plot the amplitudes and phases for several combinations of wave frequency, horizontal wavenumber, inclination of the magnetic field to the vertical and viscous and resistive diffusivities. It is shown that, for certain ranges of values of the parameters, intense localised dissipation of waves can occur.

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