Effects of elasticity on the Rayleigh-Taylor instability: implications for large-scale geodynamics

Although parts of the lithosphere may be expected to behave elastically over certain timescales, this effect is commonly ignored in models of large-scale mantle dynamics. Recently it has been demonstrated that elasticity, and in particular viscoelasticity, may have a significant effect on the buckling instability and on the creation of lithospheric-scale shearzones. It is, however, less clear whether elasticity also has an effect on mantle convection and density-driven lithospheric instabilities. The focus of this work is, therefore, to study the effects of elasticity on the two-layer Rayleigh-Taylor (RT) instability, consisting of a Maxwell viscoelastic layer overlying a viscous layer of lower density. We analyse this problem by performing systematic numerical simulations that are compared with newly derived analytical solutions. It is demonstrated that elasticity can be important for certain parameter combinations; it leads to a speedup of the RT instability. The cause for this speedup is that the RT instability is only sensitive to the viscous fraction of deformation in the viscoelastic layer. Elasticity reduces the viscous fraction of deformation at timescales shorter than the Maxwell relaxation time t(M)(t(M) = mu/G, where mu is the viscosity and G the elastic shear module). For plate tectonics on Earth, the parameters are such that the effect of elasticity on instability growth is negligible for most boundary conditions. Whereas elasticity does not (or only slightly) change the timescales for lithospheric detachment of the upper mantle, it does significantly alter the response and stress build-up in the overlying crust. Numerical simulations illustrate this effect for lithospheric detachment and show that peak stresses in a viscoelastic crust are smaller than stresses that develop in a viscous crust. Moreover, if the timescale for delamination of the mantle lithosphere is equal or smaller than the Maxwell relaxation time of the crust, the topography of the crust is increased compared to viscous models.