The critical level behaviour of internal Alf#xE9;n-gravity waves in a perfectly conducting shear flow in the presence of an aligned magnetic field is re-examined. A new form of the governing wave equation is given which has only two singularities #x3A9;d= #xB1;#x3A9;A, where #x3A9;dis the Doppler-shifted frequency and #x3A9;Ais the Alfv#xE9;n frequency. (Previously a form with three singularities has been used.) When the shear flow profile is linear, hydromagnetic waves propagating across the critical levels are attenuated at the hydromagnetic critical levels #x3A9;d= #xB1;#x3A9;A. As the wave approaches the first critical level, the wave momentum decreases by a factor of exp(-2#x3BC;0#x3C0;)1 +coth(#x3BC;0#x3C0;); as it approaches the second there is a further decrease by a factor 1+coth(#x3BC;0#x3C0;)#x2212;1, where #x3BC;0= (JH#x2212;#xBC;)#xBD;. andJHis the hydrodynamic Richardson number. Unlike in the work of Rudraiah and Venkatachalappa (1972) where two gross attenuation factors are obtained, this yields just one gross attenuation factor exp(-2#x3BC;0#x3C0;). These results are also confirmed by numerical integration. Numerical solutions are also obtained for the hyperbolic tangent shear flow profile. It is observed that the waves are attenuated at the critical levels, the total attenuation being increased by the magnetic field. It is also found that the waves are reflected in the regions of varying vorticity. The amount of reflection decreases with the horizontal wave number.
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