We calculate and analyze the longevity of magnetohydrodynamic ( MHD ) wave modes that occur in the plane of a magnetic thin sheet .
Initial turbulent conditions applied to a magnetically subcritical cloud are shown to lead to relatively rapid energy decay if ambipolar diffusion is introduced at a level corresponding to partial ionization primarily by cosmic rays .
However , in the flux-freezing limit , as may be applicable to photoionized molecular cloud envelopes , the turbulence persists at “ nonlinear ” levels in comparison with the isothermal sound speed c _ { s } , with one-dimensional rms material motions in the range of \approx 2 c _ { s } -5 c _ { s } for cloud sizes in the range of \approx 2 pc - 16 pc .
These fluctuations persist indefinitely , maintaining a significant portion of the initial turbulent kinetic energy .
We find the analytic explanation for these persistent fluctuations .
They are magnetic-tension-driven modes associated with the interaction of the sheet with the external magnetic field .
The phase speed of such modes is quite large , allowing residual motions to persist without dissipation in the flux-freezing limit , even as they are nonlinear with respect to the sound speed .
We speculate that long-lived large-scale MHD modes such as these may provide the key to understanding observed supersonic motions in molecular clouds .