Frictional convergence, atmospheric convection, and causality

Frictional convergence in an atmospheric boundary layer topped by a stable free troposphere is considered. In agreement with extensive previous work, we find that atmospheric stability reduces the vertical scale of the free tropospheric secondary circulation associated with frictional convergence. Associated with this reduction in vertical scale is a proportional reduction in the time scale for the frictional spindown of an atmospheric circulation. This reduction in time scale alters the balance between terms in the component of the momentum equation along the isobars. In particular, for disturbance scales less than a few hundred kilometers in typical tropical conditions, the momentum tendency term comes into approximate balance with the friction term, with the Coriolis term becoming less important. This reduces the magnitude of the cross-isobaric flow and the strength of the ascent in regions where this flow converges. If some other mechanism such as moist convection produces enough boundary layer convergence to nullify the spindown of the disturbance in question, then the magnitude of the convergence equals that predicted by the steady-state frictional convergence formulation. However, in this case the arrow of causality is reversed from that assumed in a naive treatment of frictional convergence. 254 D. J. Raymond and M. J. Herman Frictional convergence is not “causing” the convection; the convection is actually causing the convergence, and the mechanism forcing the convection must be sought elsewhere. This distinction is crucial in understanding what drives deep convection. The present analysis is linearized and the picture may change when nonlinear effects become important. It is also limited to situations in which the boundary layer winds are relatively weak. Tropical cyclones, with their strong winds and nonlinear behavior, thus deserve an independent analysis.