How Does the Boundary Layer Contribute to Eyewall Replacement Cycles in Axisymmetric Tropical Cyclones?

Three diagnostic models of the axisymmetric tropical cyclone boundary layer, with different levels of approximation, are applied to the problem of tropical cyclones with concentric eyewalls. The outer eyewall is shown to have an inherently stronger frictional updraft than the inner because it is in an environment of lower vorticity. Similarly, a relatively weak local enhancement of the radial vorticity gradient outside the primary radius of maximum winds can produce a significant frictional updraft, even if there is no outer wind maximum. Based on these results, it is proposed that the boundary layer contributes to the formation of outer eyewalls through a positive feedback among the local enhancement of the radial vorticity gradient, the frictional updraft, and convection. The friction-induced secondary circulation associated with the inner eyewall is shown to weaken as the outer wind maximum strengthens and/or contracts, so boundary layer processes will contribute, along with the heating-induced secondary circulation, to the weakening of the inner eyewall during an eyewall replacement cycle. An integral mass constraint on the friction-induced secondary circulation is derived and used to examine the oft-stated proposition that the outer eyewall uses up the inflowing energy-rich boundary layer air. Using the integral constraint, the author argues that formation of a secondary eyewall will tend to increase the total friction-induced secondary circulation and that, if the moat between the two eyewalls has a local vorticity minimum, then sufficient subsidence may occur there to maintain the primary eyewall's updraft. It is noted, however, that the enthalpy of the updraft is important as well as its mass.