Rayleigh-Taylor instability under a shear stress free top boundary condition and its relevance to removal of mantle lithosphere from beneath the Sierra Nevada

The separation of zones of apparent downwelling flow at the ends of the Sierra Nevada suggests a relatively large wavelength (∼500 km) of unstable growth, but Rayleigh-Taylor instabilities for plausible rheological structures with a fixed top boundary condition require much shorter wavelengths (<100 km) for maximum growth rates. To understand this difference, we analyze analytical solutions and perform numerical 2-D plane strain experiments for Rayleigh-Taylor instability of a dense layer overlying a less dense substratum, representing the instability between the mantle lithosphere and the underlying asthenosphere, focusing on the effects of a shear stress free boundary condition at the top. The overall effect of this condition is an enhancement of growth rate factors at long wavelengths, which depends greatly on the exponential viscosity variation with depth of the layer. With large or little variation across the unstable layer, the solutions approximate those with a fixed top boundary condition or for constant viscosity, respectively. An intermediate zone showing the enhanced growth rates includes ratios of layer thickness to viscosity e-folding length, h/L, of ∼-8 for Newtonian viscosity and ∼-4 for nonlinear viscosity. The free top condition is likely applicable to geologic situations where the lower crust is weak. Olivine flow laws and low-temperature estimates at 35 km depth (255-355°C) place the Sierra Nevada viscosity scaling ratio, h/L, between 5 and 9. Thus longer wavelengths than commonly assumed for Rayleigh-Taylor instabilities seem permissible when viscosity decreases with depth and the top surface of the layer is only weakly constrained.