Characterization of Viscous Dissipative Heating in the Earths Mantle Caused by Exogenic Forces

Viscous dissipative heating has long been discussed as a heat source in solid celestial bodies undergoing exogenic forces such as tidal forcing or surface loading (Hanyk et al., 2005; Jaupart & Labrosse, 2007; Nakada & Yokose, 1992; Ross & Schubert, 1987; Segatz et al., 1988). In this study, we investigate viscous dissipative heating of a Newtonian, Maxwell viscoelastic solid under a surface load in a 2D Cartesian box, using a finite element formulation as in Zhong et al. 2003. The solutions are examined to determine the controlling parameters for viscous dissipative heating under surface deformation. We scale our results to some common climate mass movement and tidal processes on Earth to assess when and how these processes might contribute heat to the mantle via viscous dissipation. We find that at present day, a long period, high amplitude load, such as glaciation-deglaciation, can produce up to about 0.03 TW of heat within the mantle, while a short period, low amplitude load, such as seasonal hydrological variations in the Amazon basin, results in a very small amount of dissipative heating compared to the total heat flux from Earth. Tidal forcing produces about 0.2 TW of heat at present day. If these results are scaled for smaller mantle viscosities as expected for the early Earth, we find that long period processes, such as glaciation and deglaciation, would not produce significant amounts of heat. Short period processes such as tidal forcing, however, could produce enough heat to significantly contribute to early Earths energy budget. It is thus concluded that viscous dissipation as a result of exogenic forces has the capacity to contribute significantly to Earths energy budget, especially for the early Earth.