A study is made on the resonance of Alfven waves in a coronal loop excited at its footpoints by the photospheric convective motion. The driving velocity field at the footpoints is modeled by random wave trains. The nonuniformity of the Alfven velocity in the loop is taken ito account so that the Alfven surface wave resonance and the phase mixing of Alfven body waves take place. The derived dissipation rate of wave energy, which turns out to be sufficient to heat the corona, depends neither on the values of resistivity and viscosity, in agreement with Ionson (1978, 1982) nor on whether the Alfven velocity is uniform or not. The velocity amplitude in the loop, however, depends on the resistivity and the viscosity as well as on the degree of nonuniformity. When the phase mixing is in operation, the expected velocity amplitude is smaller than in the case of uniform medium and lies within the range of the linear treatment of waves.
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Sakurai et al. (1984) studied this question.