We solve the nonlinear three-dimensional MHD equations for fully compressible, low-β, resistive plasma to model resonant Alfven wave heating of a coronal loop. Alfven waves are driven in the loop by a (pseudo)random time-dependent forcing with a bounded amplitude. We find that global modes are excited and resonantly heat the loop in the nonlinear regime in three dimensions. Resonant heating occurs in several narrow layers accompanied by high velocity and magnetic field shear. The narrow dissipation layers are affected by the self-consistent velocity shear and are carried around by the flow. Consequently, the topology of the perpendicular magnetic field and the ohmic heating regions differs significantly from the linear or single-frequency driver regimes, and the heating is spread more uniformly inside the loop. The heating rate varies significantly on a timescale of one to several global mode periods. We conclude that, in solar active regions, random field-line motions can excite global mode oscillations and resonantly heat the loops with a time-varying heating rate.
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