Linear stability analysis of the onset of sublithospheric convection

Abstract

We consider the onset of small scale convection associated with the cooling of the oceanic lithosphere. This process is investigated by examining the linear stability of a 2-D shear flow that is cooled from the top and obeys an Arrhenius rheology. The perturbation equations are derived assuming a parallel flow, local 1-D analysis. The linear stability results are able to reproduce the structure and growth rate produced by solving the full non-linear equations. In addition, linear stability analysis predicts a similar dependence of onset times on activation energy and Rayleigh number as previous studies when small plate velocities are specified. Our linear stability analysis predicts a significant increase in the onset time with increasing plate velocity. Suggestions are given for the dynamical influence of plate velocity in reducing the convective forcing and delaying onset times. © 2012 The Authors Geophysical Journal International © 2012 RAS.