<p>This perhaps only indirectly addresses the question, but maybe it might be helpful. According to Kerry Emmanuel's book "Divine Wind", a hurricane can, in a sense, achieve super-Carnot efficiency without violating the Second Law of Thermodynamics. A hurricane's heat reservoir is the ocean surface at temperature Th and its cold reservoir is the tropopause at temperature Tc. Heat flow Q, mainly via water evaporating from the warm ocean and condensing in the cold upper troposphere is, according to the Carnot efficiency (Th - Tc)/Th, converted into work W as per W = Q(Th - Tc)/Th. But a hurricane's work output is the kinetic energy generation for its winds. With a hurricane in steady sate (constant wind speeds) kinetic energy generation is matched by frictional dissipation. Frictional dissipation of W into the hot reservoir reduces the net heat input required from the hot reservoir from Qh to Qh - W = Qc and raises the hurricane's efficiency to (Th - Tc)/Th X Qh/(Qh - W) = (Th - Tc)/Th X Qh/Qc = (Th - Tc)/Th X Th/Tc = (Th - Tc)/Tc. The Second Law of Thermodynamics is not violated because it allows work to be dissipated via friction as heat at any temperature --- at Th as well as at Tc. Of course the above assumes perfect or reversible operation. Like all real heat engines, hurricanes are imperfect. But perhaps it at least illustrates the point.</p>

CC BY-SA 3.0
2017-09-12T23:35:17.827Z
2017-09-12T23:35:17.827Z
Jack Denur
<p>The maximum potential intensity (<a href="https://en.wikipedia.org/wiki/Tropical_cyclone#Maximum_potential_intensity" rel="nofollow noreferrer">MPI</a>) is a computed quantity that often sets a maximum bound for maximum hurricane wind speed, though rarely, the wind speeds observed can exceed it. MPI is based off of the idea that hurricanes effectively work as Carnot engines. Has there been a table produced with historic MPI calculations (reanalysis or forecast based)?</p>
<p>Also, is there a source that calculates MPI for each model and each hurricane?</p>
<p>For reference, <span class="math-container">$$v_{MPI}=\sqrt{\frac{C_k(T_s-T_0)}{C_dT_0}\Delta k}=\sqrt{\frac{T_sC_k}{T_0C_d}(CAPE_s-CAPE_b)}$$</span>
where <span class="math-container">$v_{MPI}$</span> is the theoretical maximum speed (MPI), <span class="math-container">$C_k$</span> is the surface drag coefficient of enthalpy, <span class="math-container">$C_D$</span> is the surface drag coefficient, <span class="math-container">$\Delta k$</span> is the change in enthalpy between the surface and environment, <span class="math-container">$T_s$</span> is the sea surface temperature, <span class="math-container">$T_0$</span> is the outflow temperature, <span class="math-container">$CAPE_s$</span> is the convective available potential energy (CAPE) from sea level and <span class="math-container">$CAPE_b$</span> is the
CAPE of the boundary layer air.</p>

<wind><tropical-cyclone><thermodynamics>
Is there a table available for the maximum potential intensity of hurricanes?
BarocliniCplusplus
# Is there a table available for the maximum potential intensity of hurricanes?

(Asked by: username_0 on 2017-09-08)

The maximum potential intensity ([MPI](https://en.wikipedia.org/wiki/Tropical_cyclone#Maximum_potential_intensity)) is a computed quantity that often sets a maximum bound for maximum hurricane wind speed, though rarely, the wind speeds observed can exceed it. MPI is based off of the idea that hurricanes effectively work as Carnot engines. Has there been a table produced with historic MPI calculations (reanalysis or forecast based)?

Also, is there a source that calculates MPI for each model and each hurricane?

For reference, $$v\_{MPI}=\sqrt{\frac{C\_k(T\_s-T\_0)}{C\_dT\_0}\Delta k}=\sqrt{\frac{T\_sC\_k}{T\_0C\_d}(CAPE\_s-CAPE\_b)}$$
where $v\_{MPI}$ is the theoretical maximum speed (MPI), $C\_k$ is the surface drag coefficient of enthalpy, $C\_D$ is the surface drag coefficient, $\Delta k$ is the change in enthalpy between the surface and environment, $T\_s$ is the sea surface temperature, $T\_0$ is the outflow temperature, $CAPE\_s$ is the convective available potential energy (CAPE) from sea level and $CAPE\_b$ is the
CAPE of the boundary layer air.

**Tags:** wind, tropical-cyclone, thermodynamics


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## 1 answers

### Answer by username_1 on 2017-09-12. Score: 1

This perhaps only indirectly addresses the question, but maybe it might be helpful. According to Kerry Emmanuel's book "Divine Wind", a hurricane can, in a sense, achieve super-Carnot efficiency without violating the Second Law of Thermodynamics. A hurricane's heat reservoir is the ocean surface at temperature Th and its cold reservoir is the tropopause at temperature Tc. Heat flow Q, mainly via water evaporating from the warm ocean and condensing in the cold upper troposphere is, according to the Carnot efficiency (Th - Tc)/Th, converted into work W as per W = Q(Th - Tc)/Th. But a hurricane's work output is the kinetic energy generation for its winds. With a hurricane in steady sate (constant wind speeds) kinetic energy generation is matched by frictional dissipation. Frictional dissipation of W into the hot reservoir reduces the net heat input required from the hot reservoir from Qh to Qh - W = Qc and raises the hurricane's efficiency to (Th - Tc)/Th X Qh/(Qh - W) = (Th - Tc)/Th X Qh/Qc = (Th - Tc)/Th X Th/Tc = (Th - Tc)/Tc. The Second Law of Thermodynamics is not violated because it allows work to be dissipated via friction as heat at any temperature --- at Th as well as at Tc. Of course the above assumes perfect or reversible operation. Like all real heat engines, hurricanes are imperfect. But perhaps it at least illustrates the point.


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