USTropics wrote:There are a lot of questions on how deep can Melissa get, or in other words what is the theoretical minimum pressure that this system can achieve. The answer is called
maximum potential intensity (MPI). This is quite literally the most dangerous part of the Atlantic ocean in terms of MPI due to the sea surface temperatures (and the depth it goes to). Melissa could park over this region for days, and it would not upwell cooler waters:
https://i.imgur.com/iU4gpjr.gif If you want to know the exact details (it's a bit of a read), but here is a post I made a while ago that outlines the mechanics of a hurricane and how to calculate MPI.
Determining the maximum wind speed a tropical cyclone can reach involves applying some thermodynamics, namely we model the mechanisms of a tropical cyclone as a Carnot heat engine (not too dissimilar from a motor/car engine). This allows us to determine the MPI (maximum potential intensity) as others have mentioned by using the Carnot cycle. But what exactly is a Carnot cycle and how does this physically look?
The Carnot cycle is characterized by four stages of expansion and compression. I created a crude diagram below to better show these stages in a cross-section of a mature hurricane:
The first stage (A→B) is isothermal expansion. In this stage, air flows inward towards the low pressure center for the storm.
The second stage (B→C) is adiabatic expansion. Air begins to rise adiabatically up the eyewall to the top of the atmosphere (TOA).
The third stage (C→D) is isothermal compression. Air now flows outward at this point and radiative cooling begins.
The fourth stage (D→A) is adiabatic compression, as air now sinks and begins to warm. Pressure increases, and the cycle begins again.
https://i.imgur.com/1UYbPBt.jpeg Now that we can identify the inner mechanisms of a hurricane, what are we really trying to show here? First, we now know the ocean-hurricane interaction provides the fuel pump, and as a hurricane intensifies, a feedback loop begins. As wind speeds begin to increase, this also increases the evaporation rate, which in turn increases the latent heat supply that drives our Carnot engine.
Secondly, we can now apply some math equations to quantify what this value is. From our previous statement, we know our main source of latent heat/warm reservoir is our sea surface temperatures (i.e., through the evaporation process, latent heat is released). If we also treat our TOA as the outflow (think cool reservoir), we can now mathematically model a hurricane using the Carnot efficiency ratio. Skipping some of the setup using the First Law of Thermodynamics and determining work done for each leg of the cycle, we arrive at our most simplified equation:
https://i.imgur.com/ZwQOzhG.png Where Ts is our inflow surface temperature of the ocean (hot reservoir), To is our TOA outflow temperature (cold reservoir), and E is a ratio of enthalpy and surface drag (i.e., heat exchange coefficients). In this sense, we can state the mechanical energy produced by our heat engine (V, or work done) is the energy of the winds (hurricane intensity)!
If we consider E to be constant (not the safest assumption, but will do for now), our maximum potential intensity, as stated by thermodynamics, is simply governed by the outflow temperature and the inflow temperature. In other words, this means changes in our cloud top convection or sea surface temperature strictly dictates the maximum wind speeds a tropical cyclone can reach.
With all that said, it’s important to note that we’re discussing the theoretical maximum potential intensity. Cyclones rarely reach this intensity because this requires ideal atmosphere and oceanic conditions—in other words, environmental factors rarely allow a system to reach MPI. This includes
Land interaction: this obviously removes our fuel source (latent heat release from the ocean surface)
Vertical wind shear: This causes the cyclones core to become asymmetrical, weakening the convective pattern or even creating an absence of convection on the upshear side of the cyclone (this raises our To)
Ocean interaction: As stated previously, increased wind speed can increase evaporation, but too much wind speed over a very specific area of the ocean can also cause upwelling. This localized cooling of the ocean layer decreases our Ts variable.
Dry air entrainment: If our adiabatic cooling/expansion leg of the cycle becomes disrupted by dry air, this decreases the convective potential of our cyclone and To.
