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

Elasticity is typically ignored in models of mantle convection which has resulted in vigorous debates about the appropriateness of this simplification in the past. In order to obtain a better understanding of the effects of elasticity on geodynamic processes, we have analyzed the Rayleigh-Taylor (RT) instability for Maxwell viscoelastic rheology. Both an analytical thick-plate perturbation technique and direct numerical, finite element simulations have been employed. Results for a two-layer setup of a viscoelastic layer overlying a lower, less dense viscous layer show that elasticity may influence the growth rate of the instability significantly. If started from an initially relaxed stress-state, the effect of elasticity is to speed up the instability. Alternatively, if the initial setup is pre-stressed, the opposite effect may occur. This behavior may be understood on the basis of a simple analysis of a Maxwell body under different load conditions. The importance of elasticity can be measured by the Deborah number, which, for the present setup, can be defined as De=Δ ρ g H / G (where Δ ρ denotes the density difference, g gravitational acceleration, H total height of the system and G elastic shear module). For typical Earth-like parameters, De=10-3--1. For a two-layer system with a free-slip upper boundary condition, the critical Deborah number for elasticity to become important is ~ 1--10, hinting at negligible contributions from elasticity in lithospheric systems. If, however, a fast erosion/mass redistribution boundary condition is present, the critical Deborah number may decrease significantly for large viscosity contrasts. Under these conditions, elastic effects may influence lithospheric and mantle dynamics. Results for a three-layer setup with various upper boundary conditions (free-surface, free-slip, no-slip and fast erosion) were tested additionally; they show very similar behavior. The insights gained from the theoretical analysis of the RT-instability are then applied to geodynamic examples such as subduction of slabs and plume-lithosphere interactions. We show how the dynamics of these setups may be influenced by elasticity for a range of plausible scenarios.