The propagation of internal Alfven-inertio-gravitational waves in a Boussinesq inviscid adiabatic perfectly conducting shear flow with rotation is investigatedudin the presence of a transverse magnetic field. It is shown that the effect of the rotational nature of electromagnetic force and Coriolisforce is that linear momentum is not conserved anywhere in the fluid even at critical levels, whereas the angular momentum flux is conserved everywhere in the fluid except at the critical levels at which the Doppler-shifted frequency ad = 0, rt: SZ,, or & Q rf: ( SZ2 + a:)*, where QA is the Alfvhn frequency and SZ is the Coriolis frequency,and the angular momentum is transferred to the mean flow there by Alfvhn-inertio-gravitational waves. Asymptotic solutions to the wave equationudare obtained near the critical levels and it is shown that the effect of the Lorentz force on the waves at the critical levels is to increase the process of critical layerudabsorption. The condition for neglection of rotation for higher frequency waves is also obtained and is found to be the same in both hydrodynamic and hydromagneticudflows.
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