The atmosphere exerts a direct torque on the Earth, perturbing its rotation. Additionally, the atmosphere exerts pressure, gravitational, and friction forces on the ocean, which induce an indirect effect of the atmosphere on the Earth. The oceanic response consists of variable currents and mass fluxes. These effects change the oceanic torque on the Earth. As the atmosphere has a large diurnal cycle, the indirect torque also presents a large diurnal component. This indirect diurnal torque is investigated using a numerical barotropic ocean model. In particular, we show that a dynamic ocean model is essential to compute the indirect effect of the atmosphere on nutation, as the oceanic response is far from that predicted by a static model. We also point out that the response of the ocean is nevertheless highly correlated with the atmospheric signal for the diurnal timescale but with a large amplification. The amount of ocean bottom friction is found to have a substantial influence on the indirect diurnal torque acting on the Earth. The effect of this indirect torque on the Earth nutation is computed and found to be much larger than the precision of current nutation observations, but results are uncertain in light of discrepancies in the angular momentum and torque balance.