The maximum potential intensity of a tropical cyclone is the theoretical limit of the strength of a tropical cyclone.
Maximum potential intensity Due to surface friction, the inflow only partially conserves angular momentum. Thus, the sea surface lower boundary acts as both a source (evaporation) and sink (friction) of energy for the system. This fact leads to the existence of a theoretical upper bound on the strongest wind speed that a tropical cyclone can attain. Because evaporation increases linearly with wind speed (just as climbing out of a pool feels much colder on a windy day), there is a positive feedback on energy input into the system known as the Wind-Induced Surface Heat Exchange (WISHE) feedback. This feedback is offset when frictional dissipation, which increases with the cube of the wind speed, becomes sufficiently large. This upper bound is called the "maximum potential intensity", v p {\displaystyle v_{p}} , and is given by
v p 2 = C k C d T s − T o T o Δ k {\displaystyle v_{p}^{2}={\frac {C_{k}}{C_{d}}}{\frac {T_{s}-T_{o}}{T_{o}}}\Delta k}
where T s {\displaystyle T_{s}} is the temperature of the sea surface, T o {\displaystyle T_{o}} is the temperature of the outflow ([K]), Δ k {\displaystyle \Delta k} is the enthalpy difference between the surface and the overlying air ([J/kg]), and C k {\displaystyle C_{k}} and C d {\displaystyle C_{d}} are the surface exchange coefficients (dimensionless) of enthalpy and momentum, respectively. The surface-air enthalpy difference is taken as Δ k = k s ∗ − k {\displaystyle \Delta k=k_{s}^{*}-k} , where k s ∗ {\displaystyle k_{s}^{*}} is the saturation enthalpy of air at sea surface temperature and sea-level pressure and k {\displaystyle k} is the enthalpy of boundary layer air overlying the surface. The maximum potential intensity is predominantly a function of the background environment alone (i.e. without a tropical cyclone), and thus this quantity can be used to determine which regions on Earth can support tropical cyclones of a given intensity, and how these regions may evolve in time. Specifically, the maximum potential intensity has three components, but its variability in space and time is due predominantly to the variability in the surface-air enthalpy difference component Δ k {\displaystyle \Delta k} .
Derivation A tropical cyclone may be viewed as a heat engine that converts input heat energy from the surface into mechanical energy that can be used to do mechanical work against surface friction. At equilibrium, the rate of net energy production in the system must equal the rate of energy loss due to frictional dissipation at the surface, i.e.
W i n = W o u t {\displaystyle W_{in}=W_{out}}
The rate of energy loss per unit surface area from surface friction, W o u t {\displaystyle W_{out}} , is given by
W o u t = C d ρ | u | 3 {\displaystyle W_{out}=C_{d}\rho |\mathbf {u} |^{3}}
where ρ {\displaystyle \rho } is the density of near-surface air ([kg/m3]) and | u | {\displaystyle |\mathbf {u} |} is the near surface wind speed ([m/s]). The rate of energy production per unit surface area, W i n {\displaystyle W_{in}} is given by
W i n = ϵ Q i n {\displaystyle W_{in}=\epsilon Q_{in}}
where ϵ {\displaystyle \epsilon } is the heat engine efficiency and Q i n {\displaystyle Q_{in}} is the total rate of heat input into the system per unit surface area. Given that a tropical cyclone may be idealized as a Carnot heat engine, the Carnot heat engine efficiency is given by
… excerpt ends here. Continue reading the full article.
