ON OBLIQUE MAGNETOHYDRODYNAMIC WAVES IN AN ATMOSPHERE UNDER A MAGNETIC-FIELD OF ARBITRARY DIRECTION

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 Alfvén 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 Leitão 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 are three cut-off frequencies, namely the gravity, acoustic and magnetic cut-offs. The ranges of the frequency spectrum is which there are standing modes or propagating waves are discussed for the dynamic and magnetic components of the wave field, the latter are expressed in terms of generalized hypergeometric functions of type 2F3, and plotted for different values of the wave frequency, horizontal wavenumber, plasma β and inclination of the magnetic field to the vertical. © 1991 Gordon and Breach Science Publishers S.A.