Is there an upper bound on sustained wind speed in a hurricane?

[al78]

Just a theoretical question thinking about what is the strongest a tropical cyclone can theoretically get given the best conditions possible in the current climate. I was wondering if there is a theoretical upper bound on how fast the near-surface wind can blow.

My thinking is that at the ground, wind speed is always zero, so at the standard 10 meter anemometer height, as the wind speed increases, the near-surface wind shear also increases. As the wind shear increases, this increases mechanical turbulence which transports and mixes lower momentum air from closer to the ground, acting to oppose the increase in wind speed. Is there a point where if you had a theoretical hurricane with perfect atmospheric conditions and the oceanic heat content under the storm was slowly increased, the peak 1-minute sustained wind would initially increase but would stop increasing beyond some theoretical limit.

I guess this lead onto the question as to whether storms like Patricia (2015) with 200 mph sustained winds at its peak could represent the strongest a tropical cyclone can get on this planet, without increasing the sea surface temperatures to unrealistic levels.

[Hurricane2022]

This question is one of those that seems easy to answer, but when we really stop to think about it, we even think about other planets, like Jupiter and its Armageddonian brown hurricane... But in a way, I don't think there exactly a limit... because records in this regard were broken successively by Tip, Haiyan, Patricia... Furthermore, 2023 was the 4th year in a row that the West Pacific saw a system with winds of 190+ mph.

I think what we may have is a broken conclusion,
since the vast majority of super C5s normally always reach winds around 190 - 200 mph, but we can still see exceptions like Haiyan (in my opinion) and Patrícia. I think it won't be long before we see something like Patrícia, but the lack of recon and satellite-only observations in parts of the world also makes us wonder about other cyclones that could briefly rival Pat and Haiyan or perhaps even surpass them, like Typhoons Nora '73, Rita '78, Hagibis '19, Cyclone Olaf '05, etc....

These are questions that always deserve study, but given the short time since reliable observations began to appear, they are very difficult to answer...

Do we have more professional meteorologists or more specialized members who can come up with more theories here?

[storm_in_a_teacup]

As far as I can tell, there is: https://en.wikipedia.org/wiki/Maximum_potential_intensity.

But I'm an astrophysicist not a meteorologist so I might be wrong

[mitchell]

In theory there should be, I think. A maximum sea surface temperature and atmospheric latent energy potential could be assumed. Friction reduced to lowest possible value, and other factors plugged in, all set at values that are the highest (or lowest) that a location can support, aimed at values that lead to highest wind speeds.

Its a similar exercise to calculating the "Probable Maximum Precipitation (PMP)" value that Dam safety engineers use to design dams. (they use a % of PMP in design). PMP is based on the concept that theoretical maximum precipitation for a given duration under modern meteorological conditions. An engineer described it as taking the most water that the atmosphere can accumulate in a given location based on local factors, squeezed out as rapidly as is theoretically possible.

[ChrisH-UK]

There isn't a upper limit as such it's just a case of needing more power, for a tropical cyclone that power is from the sea and the energy that it contains. The problem is that it's exponential for instance for a car to do 200 mph your taking of 700 bhp to do 250 mph you need over a 1000 bhp to go supersonic well that 100,000 bhp. Its the dame for cyclones I read a study once (I can't remember where it was) but they theorised that you would need 50c waters to get a 300 mph cyclone, you need a ton more power for a cyclone to get faster in order to the huge amount of mass that the air is and the friction that is created.

I think you would probably see that about 200 mph been the about that practical limit to the speed of cyclones not saying they you could get some a bit faster if they was perfect conditions.

[al78]

There isn't a upper limit as such it's just a case of needing more power, for a tropical cyclone that power is from the sea and the energy that it contains. The problem is that it's exponential for instance for a car to do 200 mph your taking of 700 bhp to do 250 mph you need over a 1000 bhp to go supersonic well that 100,000 bhp. Its the dame for cyclones I read a study once (I can't remember where it was) but they theorised that you would need 50c waters to get a 300 mph cyclone, you need a ton more power for a cyclone to get faster in order to the huge amount of mass that the air is and the friction that is created.

I think you would probably see that about 200 mph been the about that practical limit to the speed of cyclones not saying they you could get some a bit faster if they was perfect conditions.

That is why I added the condition of restricting the sea surface temperatures to realistic levels. There is little short of an asteroid impact or super-volcanic eruption that could raise sea surface temperatures that high. The concept of a hypercane has been put forward if sea temperatures reached 50C where the energy balance equilibrium equation (energy input vs energy dissipation) has no solution.

https://hypothetical-events.fandom.com/wiki/Hypercane

With the car analogy the restriction on speed comes from wind resistance which goes up as the cube of the wind velocity relative to the car so to double the speed requires of the order of eight times the energy input. Beyond a certain speed the car would burn up due to friction with the air.

[LarryWx]

As far as I can tell, there is: https://en.wikipedia.org/wiki/Maximum_potential_intensity.

But I'm an astrophysicist not a meteorologist so I might be wrong

So, is the general idea that friction increases as waves get higher as winds increase, thus imposing a limit as to how high the winds can get?

[kronotsky]

As far as I can tell, there is: https://en.wikipedia.org/wiki/Maximum_potential_intensity.

But I'm an astrophysicist not a meteorologist so I might be wrong

So, is the general idea that friction increases as waves get higher as winds increase, thus imposing a limit as to how high the winds can get?

Basically yes, although waves don't necessarily have anything to do with it in the formulation described in the article. You're just balancing the potential energy, per unit area, of moving heat from the surface to the upper troposphere with the energy, per unit area, that is dissipated by friction. Friction depends on a higher power of wind speed than does energy advection, so you can solve for it when you balance them. Of course, you can't calculate the exact MPI from first principles because there are some fudge factors (the "C" coefficients), and those do depend a lot on the details of the boundary between the air and the ocean.

[USTropics]

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.



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:



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.

[LarryWx]

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.

What about increases in friction over the ocean helping to limit how high the winds can get because as a storm gets stronger wave heights increase? Don’t the higher waves exert more friction meaning negative feedback against strengthening?

[USTropics]

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.

What about increases in friction over the ocean helping to limit how high the winds can get because as a storm gets stronger wave heights increase? Don’t the higher waves exert more friction meaning negative feedback against strengthening?

Our equation does account for frictional drag forcing (ratio of enthalpy and drag, or E). However, frictional dissipation over the ocean occurs primarily in the inflow layer. This is actually another positive feedback loop, where the power of the winds is converted back into heat which then flows back into the system. This is where the Carnot cycle of a cyclone differs from a typical heat engine (like a car), in that the recycling of waste heat acts to increase the strength/intensity of a cyclone. Wave height definitely acts to churn up the water/increases entrainment of cooler waters from the thermocline into the mixed layer. I believe wave height would be localized/microscale to not really provide much in the way of frictional drag to reduce wind speed, however.

[storm_in_a_teacup]

Ah yes the famous Carnot heat engine diagram...I learned about it in my thermodynamics class...except we had to combine it with quantum mechanics and it was called statistical mechanics, and the textbook was impenetrable. Oh physics undergrad days