Coronal loop heating by torsional Alfven waves directly driven by footpoint motions: Harmonic driving versus stochastic driving

Two scenarios of coronal loop heating by directly driven torsional Alfven w aves are considered. In the first scenario the driving is assumed to be har monic. In the steady state of oscillations, wave energy dissipation mainly occurs in a narrow dissipative layer embracing an ideal resonant magnetic s urface. The wave motion in the dissipative layer is characterized by very l arge amplitudes. It is assumed that the radiative and thermoconductive loss es from loops are exactly covered by wave energy dissipation. This assumpti on allows expression of the maximum value of the velocity in the dissipativ e layer in terms of the energy losses and the loop parameters. It turns out that this maximum velocity is proportional to R-1/3, where R is the total Reynolds number accounting for both viscosity and resistivity. For typical coronal loops and R = 10(6), the maximum velocity in the dissipative layer is between 800 and 1000 km s(-1). In the second scenario the driving is ass umed to be a stationary stochastic process. Once again it is assumed that e nergy losses from the loop are covered by wave energy dissipation. The maxi mum value of the mean square velocity turns out to be proportional to R-1/6 . This value is also very sensitive to the width of the driver frequency sp ectrum. In two considered examples, one with a narrow spectrum and another with a wide spectrum, the maximum values of the mean square velocity betwee n 300 and 400 km s(-1) and between 150 and 200 km s(-1) were obtained, resp ectively, for typical coronal loops and R = 10(6). Since the observed nonth ermal velocities in coronal loops never exceed a few tens of km s(-1), thes e results lead to the conclusion that both scenarios do not satisfy the obs ervational constraints.