Low viscosity channels and the stability of long wavelength convection

Mantle convection simulations with a low viscosity channel, akin to the Earth's asthenosphere, are characterized by long wavelength flow structure. Boundary layer theory predicts that as the viscosity of the channel decreases, the wavelength that maximizes heat transfer increases. As a pattern selection criterion, this analysis is not complete. It provides no mechanism to relate the optimal heat transfer wavelength to the wavelength that is realized in nature. We present numerical simulation suites, for bottom and internally heated end-members, to demonstrate that the cell wavelengths that maximize heat transfer are also the most stable. This does not rule out the possibility of multiple wavelengths being realizable but it does imply that wavelengths near the stability peak will be preferred and, for the configurations we explore, the stability peak corresponds to the energetically most efficient flow configuration.