Convective instability of a thickened boundary layer and its relevance for the thermal evolution of continental convergent belts


  • G. A. Houseman,

  • D. P. McKenzie,

  • Peter Molnar


When crust thickens during crustal shortening, the underlying mantle lithosphere must shorten and thicken also, causing the submersion of cold, dense material into the surrounding asthenosphere. For a range of physical parameters the thickened boundary layer that forms the transition from the strong lithosphere to the convecting asthenosphere may become unstable, detach, and sink into the asthenosphere, to be replaced by hotter asthenospheric material. We have studied the instability of a thickened boundary layer for a range of physical parameters (Rayleigh number), amounts of thickening, and boundary conditions. In all cases the fluid was overlain by a rigid, conducting layer. Extensive numerical experiments were made for fluids with stress-free boundary conditions, heated either from below or from within. From a simple physical description of the observed pattern of flow we derived expressions that related the growth of the instability and the time needed to remove the thickened boundary layer as a function of the amount of horizontal shortening (f), the Rayleigh number (R), and the ratio (a/d) of the thicknesses of the rigid and fluid layers. In our opinion, observations and theory agree well (within 10% for R > 105) and show that the speed with which the thickened boundary layer is removed increases with increasing f, R, and a/d. A limited series of runs with no-slip boundary conditions suggests approximately the same functional relationships but with the process 0–30% slower than with stress-free boundaries. For Rayleigh numbers comparable to those appropriate for upper mantle convection (105–107) the removal of the boundary layer occurs rapidly, in times less than the thermal time constant of the overlying rigid plate. Using typical values for the physical parameters in the earth, the boundary layer is removed in times less than the duration of deformation in some collision zones (30–50 m.y.). Thus we suspect that often the lower lithosphere is removed during the process of crustal shortening, causing the overlying crust and uppermost mantle to warm rapidly. This process is likely to contribute to the development of regional metamorphism and to the generation of latetectonic or posttectonic granites. We suspect, in fact, that in some cases the entire mantle lithosphere may detach from the lower crust during crustal shortening, exposing the crust to asthenospheric temperatures.