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Sunday, November 10, 2013

Typhoon Haiyan may have killed 10,000. 3D structure of typhoons; Carnot engine theory

Boat in debris in Tacloban on November 10
Photo by Aaron Favila/AP from here
Although confirmed estimates of deaths due to Typhoon Haiyan remain around 1200, there are now credible speculations that there may be as many as 10,000 dead in just one village. My condolences to the people of the Philippines, and best wishes that supplies reach you quickly.
       According to this Reuters.com article, 70-80% of the structures in the path of the typhoon were destroyed. Most of the deaths appear to have been caused by a debris-laden storm surge that swept away whole villages. The capital of Leyte province, Tacloban, lies in a narrow cove where storm surges can be focused toward the city. The storm surge appears to have surged at least a half mile inland.
Tacloban location

November 9, 2013 Super Typhoon Haiyan imaged by NASA Astronaut Karen Nyberg on NASA's ISS.
The country was not unprepared for this event, and it is sobering that so much damage could still occur.  A question not often addressed is: Are there storms simply too strong for even modern engineering to provide safety?  The heartbreaking scenes from this storm are so similar to those of the tsunami damage from the 2011 Tohoku tsunami that it appears the answer may be "yes."  Could people have survived if all buildings had been made of concrete, and made so tall that people could take refuge above the 15' high storm surge reported? Can concrete buildings be designed to withstand 250 kilometer per hour (155 mph) winds?
       What determines the intensity of a tropical cyclone? Remember: typhoon, hurricane, cyclone are just different words for the same phenomenon.  Tropical intensity is usually measured by the value of the maximum wind speed.  Here's a table of cyclone wind speeds from The Guardian:
From TheGuardian.com November 9, 2013
Haiyan, although the strongest cyclone to make landfall is the fourth strongest in terms of measured wind speeds.
       Kerry Emanuel, Professor of Atmospheric Science at MIT, specializes in hurricane physics (see several references to his work at ** below). A tropical cyclone is driven principally by heat transfer from the ocean. They generally develop over water whose surface temperature exceeds 26 C. They occur in three main belts generally within 5 degrees latitude. The cyclones then move westward and poleward at speeds on the order of a few meters per second. Cold water kills them as can unfavorable atmospheric winds.
       Emanuel is famous for, amongst other things, his analysis of hurricanes as a Carnot heat engine. The Carnot cycle is a basic concept in thermodynamics. A thermodynamic cycle is the set of thermodynamic conditions (such as pressure, temperature, entropy, enthalpy) reached in a system as energy is transferred from warm to cool regions. In the process, some of the energy is converted to mechanical work.
The Carnot heat engine of Emmanuel
Taken from the Physics Today article referenced at **

In the cross-section diagram to the left, the horizontal axis shows distance from the center of a cyclone, and the vertical axis shows altitude. The colors, from deep blue to dark red represent entropy, with the cooler colors indicating lower entropy. Evaporating sea water transfers energy and entropy from sea to air, and this causes air to spiral inward from A to B.  As it moves, the temperature of the air is nearly constant (an isothermal process), its volume increases as it flows toward the low-pressure core of the cyclone, and its entropy increases. The air then rises rapidly upward (in the eyewall) and outward, from B to C, so rapidly that the process can be considered adiabatic and isentropic (note how the path B-C lies within the constant yellow color). Once away from the storm center at C, the air generally mixes with other storms and is lost from the system, but in idealized models, the air radiates in the infrared wavelengths into space, a process Emanuel considers nearly isothermal, and so it loses entropy. The air then sinks again (D-A) and warms through (nearly) adiabatic compression (in the deep blues of constant entropy). This closes the Carnot cycle.
       Emanuel then shows that the velocity of the surface winds is proportional to the difference in temperature between the ocean surface and the high-level outflow (conveniently, 100 C in the figure shown) and the thermodynamic disequilibrium between the ocean and atmosphere, E, which is the difference between the enthalpy of air near the surface and of air in contact with the ocean.  Using these concepts, Kerry then showed (in a 2003) paper, that a limit on maximum sustained wind speeds is about 85 m/s or 195 mph. (He did not comment on the possibility of higher winds as shown in the table above.) He also showed that the average cyclone dissipates about 3E12 watts, equal to the total electrical power consumption in the US in 2000, and that an exceptionally large storm can generate an order of magnitude more power.

**K. Emanuel, Tropical Cyclones, Annual Reviews of Earth and Planetary Sciences, 31, 75, 2003.
**K. Emanuel, Divine Wind: The History and Science of Hurricanes, Oxford U. Press, New York, 2005.
**K. Emanuel, Hurricanes: Tempests in a greenhouse, pp. 74-75, Physics Today, August 2006.

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