Potential Intensity Theory of Tropical Cyclone Incorporating Ocean Cooling

Tropical cyclones (TCs) are powered by capturing large amounts of water vapor from the ocean and converting it into kinetic energy. TC has a potential intensity (PI) that can develop the most under the environment in which it exists. Emanuel (1988) deduced the potential strength by devising a theoretical model representing the structure of the TC in equilibrium by applying neutral assumptions to humid oblique convection. Miyamoto et al. (2017, hereafter referred to as M17) formulated the cooling process of sea surface temperature due to vertical mixing caused by strong winds under TC, and derived a PI equation using the water temperature after cooling. However, it is known that when the TC movement speed is slow, not only vertical mixing but also the effects of upwelling cannot be ignored. Therefore, the purpose of this study is to formulate the effect of upwelling in addition to the vertical mixing derived in M17, and to derive a PI equation that takes this effect into account.

In this study, like M17, we consider a TC that has no non-axisymmetric component and moves at a constant speed, and a two-layer ocean on the f-plane (mixed layer and layer below it). In the mixed layer, the water temperature is constant vertically, and in the layer below it decreases with depth. We assume that the sea surface temperature gradually cools as the TC moves, while the structure of the TC does not change. Regarding cooling of water temperature, consider only the sea surface stress inside the radius of maximum wind (RMW), assume a steady response, and consider the cooled water temperature at RMW.

For cooling of sea surface temperature due to ocean mixing, winds outside the RMW play an important role, but for upwelling, the sea surface stress inside the RMW was more important (cf. Lu et al. 2021). Therefore, considering the coordinates relative to the TC, water temperature cooling starts from each point on the RMW at the front in the direction of travel and ends at the point at the rear of the RMW in the direction of travel. The degree of cooling is calculated as the integrated value during the TC passage. We first estimate the degree of cooling of the sea surface temperature at each angle, and then find the azimuthal average. Since the water temperature differs at each angle, the amount of flux flowing into the atmosphere also differs at each angle, but near the RMW of a developed TC, the tangential wind speed is high and the fluctuations in the angular flux can be regarded as the average value in the angular direction. When calculating the flux, use the water temperature value averaged in the angular direction.

Based on the assumptions, we derived an analytical PI model considering the effects of ocean cooling. We have examined the sensitivity of PI to key parameters in the developed model and conducted a set of numerical experiments.