The dissipation of internal energy in the turbulent boundary layer under pack ice is determined using a time-varying boundary layer model with an eddy coefficient closure scheme. The magnitude of the eddy coefficient is determined by the ice drift velocity, which is assumed greater than the rms water velocity induced by internal waves. The Arctic Ocean internal wave velocity spectrum is represented by a line spectrum with 44 rotary frequency components. The energy at a given frequency is set equal to the energy in a band about the frequency in the continuous spectrum. The dissipation spectrum is found to have an ω-2 shape. For an internal wave energy level representative of Arctic Ocean conditions (energy parameter r equal to 50 m2 cph) the total dissipation is 0.16 mW m-2. This corresponds to a dissipation time scale of 32 days and suggests that underice dissipation is important. The surface boundary layer dissipation process is unique to ice-covered regions, and the predicted amount of dissipation appears to be great enough to explain earlier observations that the internal wave energies in the Arctic Ocean are low compared to internal wave energies measured in ice-free oceans.