Constraints on viscous dissipation of plate bending from compressible mantle convection

Tectonic plates on the Earthʹs surface bend at plate boundaries as they subduct into the mantle, thus generating viscous dissipation. It has been proposed that viscous dissipation due to plate bending accounts for more than 40% of the total viscous dissipation in mantle convection. The proposed large bending dissipation at subduction zones may have significant effects on the Earthʹs thermal evolution history. However, recent studies show that viscous dissipation from plate bending may not be as significant as previously suggested. Here based on an energetics argument of mantle convection and previously estimated bending dissipation for present-day Earthʹs subduction zones, we show that the total dissipation in the Earthʹs mantle is 10.0–15.5 TW and that the bending dissipation only accounts for < 10% of the total dissipation in the Earthʹs mantle convection. We also determine the ratio of the bending dissipation to the total viscous dissipation using compressible mantle convection models within a large parameter space. The bending dissipation accounts for 10% to 20% of the total dissipation for cases with only temperature-dependent viscosity. For cases with a weak upper mantle, the bending dissipation accounts for less than 10% of the total dissipation. These results from numerical models further support the conclusion that the bending dissipation only accounts for a small fraction (< 10%) of the total viscous dissipation. Our results suggest that in studying plate motions and long-term thermal evolution of the Earth, other convective processes in the mantle play probably more important roles than plate bending.