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For understanding magnetic effects on dynamical tides, we study the rotatingmagneto-hydrodynamic (MHD) flow driven by harmonic forcing. The linearresponses are analytically derived in a periodic box under the local WKBapproximation. Both the kinetic and Ohmic dissipations at the resonantfrequencies are calculated and the various parameters are investigated.Although magnetic pressure may be negligible compared to thermal pressure,magnetic field can be important for the first-order perturbation, e.g.dynamical tides. It is found that magnetic field splits the resonant frequency,namely the rotating hydrodynamic flow has only one resonant frequency but therotating MHD flow has two, one positive and the other negative. In the weakfield regime the dissipations are asymmetric around the two resonantfrequencies and this asymmetry is more striking with a weaker magnetic field.It is also found that both the kinetic and Ohmic dissipations at the resonantfrequencies are inversely proportional to the Ekman number and the square ofwavenumber. The dissipation at the resonant frequency on small scales is almostequal to the dissipation at the non-resonant frequencies, namely the resonancetakes its effect on the dissipation at intermediate length scales. Moreover,the waves with phase propagation perpendicular to magnetic field are much moredamped. It is also interesting to find that the frequency-averaged dissipationis constant. This result suggests that in compact objects magnetic effects ontidal dissipation should be considered.

Calculating rotating hydrodynamic and magneto-hydrodynamic waves to understand magnetic effects on dynamical tides