An analytical model of maximum potential intensity for tropical cyclones incorporating the effect of ocean mixing

The theoretical study of Emanuel (1986) developed a potential intensity (E-PI) theory for tropical cyclones (TCs). Although the theory considers a highly idealized system, the PI theory appears to capture the upper bound of real TC intensity for most storms (e.g., Emanuel 2000). The E-PI, however, does not account for potential cooling of the sea surface temperature (SST). Although observations can be used to include the effects of ocean cooling in an empirical PI equation (e.g., Lin et al. 2013), few studies have made an attempt to analytically derive PI formulae incorporating the effects of ocean cooling. This presentation will describe a PI theory that accounts for ocean cooling due to vertical turbulent mixing. We present a quantitative theory of the atmospheric and oceanic parameters that affect PI, and examine the degree of diminishment of PI due to the ocean cooling.

The theory considers a simple atmosphere-ocean coupled system; the atmospheric part is a translating TC vortex, and the ocean is a vertical one-dimensional, two-layer fluid. The theory is based on the following key assumptions: I) the TC moves with a constant speed, II) the upper ocean is vertically well mixed with colder water below, and III) the mixing is integrated during the TC passage at the local point at which the PI is calculated.

The resulting PI (hereafter, O–PI) is evaluated at a local point at which the SST is cooled up to the arrival of TC. The derived formulae for oceanic quantities are basically similar to those by Schade (1997), but we explicitly incorporate the vortex structure outside the RMW and the time scale for mixing. As expected, the O-PI approaches the E-PI in the limit of infinite TC translation speed, zero radial extent of vortex (i.e., mixing occurs only at the RMW), or infinite mixed layer depth. It was also shown that the O-PI is weaker than the E-PI in case of a larger vortex size, slower translation speed, or shallower mixed layer. The degree of SST cooling (or diminishment of PI compared to the E-PI) depends only on one nondimensional quantity, as in Schade (1997), but our formulation incorporates the time scale for mixing, and also the surface stress obtained from an explicit representation of vortex structure.