Time and Space Scales in the Tropical Cyclone Boundary Layer, and the Location of the Eyewall Updraft

The transient response of the tropical cyclone boundary layer is studied using linearized and nonlinear models, with particular focus on the frictionally forced vertical motion. The impulsively started, linearized tropical cyclone boundary layer is shown to adjust to its equilibrium solution via a series of decaying oscillations with the inertial period 2p/ I. In the nonlinear case, the oscillation period is slightly lengthened by inward advection of the slower-evolving flow from larger radii, but the oscillations decay more quickly. In an idealized cyclone with small sinusoidal oscillations superimposed on the gradient wind, the equilibrium nonlinear boundary layer acts as a low-pass filter with pass length scaling as 2u10/ I, where 2u10 is the 10-m frictional inflow. This filter is absent from the linearized boundary layer. The eyewall frictional updraft is similarly displaced inward of the radius of maximum winds (RMW) by a distance that scales with 2u10/ I, owing to nonlinear overshoot of the inflowing air as it crosses the relatively sharp increase in I near the eyewall. This displacement is smaller (other things being equal) when theRMWis small, and greater when it is large, including in secondary eyewalls. The dependence of this distance on 2u10/ I may explain, at least partially, why observedRMWare seldom less than 20 km, why storms with relatively peaked radial profiles of wind speed can intensify more rapidly, and why some secondary eyewalls initially contract rapidly with little intensification, then contract more slowly while intensifying.