On oblique magnetohydrodynamic waves in an atmosphere under a magnetic field of arbitrary direction

Abstract

Abstract We consider magneto-acoustic-gravity waves in an isothermal atmosphere, in a uniform magnetic field tilted at an arbitrary angle to the vertical, and with wavevector in the plane of gravity and the magnetic field. It is shown that the velocity perturbation transverse to the magnetic field and gravity satisfies a decoupled second-order Alfven wave equation, and the fourth-order wave equation for the coupled slow-fast mode is solved exactly, using as variable the velocity perturbation transverse to the magnetic field, in the plane of the latter and gravity. The solution uses the method of two characteristic polynomials (Campos, 1987; Campos and Leitao 1988), and is checked by comparison with particular cases in the literature expressible in terms of elementary, Bessel or hypergeometric functions. It is shown that there is no critical layer, both for vertical and oblique waves, except in the case of a horizontal magnetic field; it is shown that for oblique waves in an oblique magnetic field there ar...