Limits of tidal energy dissipation by fluid flow in subsea formations

Tidal loading causes fluid flow through permeable seafloor and between regions of contrasting elastic properties or porosity within subsea formations. We examine theoretically the dissipation of energy by these flows and its global significance as a mechanism for tidal energy dissipation. Expressions are given for energy dissipation rates in layered formations due to vertical flow caused by tidal loading, but the results can be used to constrain dissipation by other flow patterns. We consider flow near the seafloor, in gas-bearing sediments, and in highly fractured permeable igneous crust. Energy dissipation by the first two mechanisms is negligibly small globally, although it may be locally significant under extreme conditions. Under favourable conditions, flow in fractured crust may have greater energy dissipation, but the total amount is limited by the thickness of the permeable layer. Based on our current understanding of subsea hydrogeology, tidally induced flow in subsea formations appears to make little contribution to the observed global tidal energy dissipation.     

On the penetration of a hot diapir through a strongly temperature-dependent viscosity medium

Summary. The ascent of a hot spherical body through a fluid with a strongly temperature-dependent viscosity has been studied using an axisymmetric finite element method. Numerical solutions range over Peclet numbers of 10⁻¹– 10³ from constant viscosity up to viscosity variations of 10⁵. Both rigid and stress-free boundary conditions were applied at the surface of the sphere. The dependence of drag on viscosity variation was shown to have no dependence on the stress boundary condition except for a Stokes flow scaling factor. A Nusselt number parameterization based on the stress-free constant viscosity functional dependence on the Peclet number scaled by a parameter depending on the viscosity structure fits both stress-free and rigid boundary condition data above viscosity variations of 100. The temperature scale height was determined as a function of sphere radius. For the simple physical model studied in this paper pre-heating is required to reduce the ambient viscosity of the country rock to less than 10²² cm² s⁻¹ in order for a 10 km diapir to penetrate a distance of several radii.