Relaxation of SST in the cool wake of a hurricane

Satellite imagery and in situ ocean data show that SST in the cooled wake of a moving hurricane returns to pre-hurricane values in one to two weeks, typically. The cool wake seen in satellite imagery fades away while remaining in place, suggesting that the warming is a relaxation process driven by air-sea heat fluxes. A model of this relaxation process requires only two pieces: 1) a heat flux anomaly, Q, assumed to be proportional to the amplitude of SST cooling, Q ~ B*SST, where B is estimated from bulk formulae to be about 70 W m*m/C for nominal trade wind conditions, and 2) the thickness of the surface layer that absorbs this heat flux anomaly is set by the thickness of the diurnal warm layer, D, typically about ten meters for late summer trade wind conditions, but dependent upon the noon heat flux, Qmax, and the wind stress, tau. The e-folding time of the relaxation process is then expected to be given by tau/B*sqrt(Qmax). This very simple model gives plausible estimates of the observed relaxation time in the wake of Fabian, approx. 5 days, where prevailing winds were light, and in the wake of Frances, approx. ten days to two weeks, because winds were fresher and variable. It is notable that the relaxation time depends upon two aspects of the air-sea heat flux, the slowly-varying anomaly due to the depressed SST, and the noon maximum value, which is due mainly to solar insolation.