Power Dissipation in Cyclones Such as Hurricanes, Typhoons and Tornadoes
http://applet-magic.com/hurricanepower.htm
applet-magic.com
Thayer Watkins
Silicon Valley
& Tornado Alley
USA
Power Dissipation in Cyclones
Such as Hurricanes, Typhoons and Tornadoes
It is alleged, notably by Kerry Emmanuel a meteorologist at the Massachusetts Institute of
Technology, that the rate of power dissipation in hurricanes, and therefore in other wind
storms, is given by the formula
P = CDρv³
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Power Dissipation in Cyclones Such as Hurricanes, Typhoons and Tornadoes
http://applet-magic.com/hurricanepower.htm
In this equation P is the rate of energy dissipation per unit time per unit horizontal surface area,
v is the wind speed, ρ is the air mass density and CD is a coefficient depending upon the surface
irregularities.
Kerry Emmanuel developed a theory about thirty years ago that tropical cyclones are
essentially heat engines power by the difference in the temperature of the sea surface and the
upper atmosphere. (Hurricanes, typhoons and cyclones are the same thing but just given
different names in different oceans.)
Any equation or theory should be viewed as a hypothesis or conjecture in search of empirical
verification. There are even theories which have verification in the laboratory which are not
valid for in nature because they leave out phenomena which are important in nature but are
eliminated in the controlled setting of the laboratory. This point is driven home in the book
Useless Arithmetic by Orrin H. Pilkey and Linda Pilkey-Jarvis. (The subtitle of this book is Why
Environmental Scientists Cannot Predict the Future.)
Proposed theories concerning natural phenomena must always be supported empirically. This is
always true but is more crucial in this day and age when purported scientific results are
presented to support an ideological agenda. Kerry Emmanuel's work got tied to the issue of
global warming in that if global warming increased sea surface temperature there would be
more energy to dissipate in terms of more hurricane and typhoons and/or greater severity of
these phenomena. Kerry Emmanuel has spent about the last twenty five years trying to
empirically verify his model. However he was not able to establish a trend in number of
hurricanes or in the severity of hurricanes to correspond with the upward trend in sea surface
temperature. About five years ago Emmanuel took a different approach. He asserted that the
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Power Dissipation in Cyclones Such as Hurricanes, Typhoons and Tornadoes
http://applet-magic.com/hurricanepower.htm
power dissipation in a hurricane is proportional to the cube of its wind velocity. Thus the
severity of a hurricane would be proportional to the cumulative sum of the cube of its wind
velocity over time. This material examines the assertion that the rate of power dissipation of a
cyclone satisfies the equation given previously.
Theoretical justification of an equation is significant in that it lends support for seeking the
empirical verification. Here is a theoretical justication for the above power dissapation
equation. Let m be the mass of a gas molecule which is traveling at a group velocity v. The
kinetic energy of that molecule is ½mv². Suppose the collision of the molecule with an upright
surface is inelastic; i.e., the molecule loses all of its forward motion. The energy loss in that
collision would be ½mv². Now the problem is determining the number of such molecules hitting
a unit area of vertical surface per unit time. That number would be the number of molecules
contained in a prism having a unit area base and a length equal to v. The number would be the
number density of the molecules times the volume, which in this case is v. The product of the
number density and the mass per molecule is the mass density of the air, ρ. The energy
dissipation per unit area per unit time is thus ρv³.
The coefficient CD then accounts for the amount of vertical surface area per unit of horizontal
surface area.
Thus the velocity cubed law for power dissipation for hurricanes and typhoons has a simple and
solid theoretical justification and justifies an effort at empirical verification.
Consider some of the implications of the equation. A category 5 hurricane has wind speeds in
excess of 155 miles per hour (mph). A category 4 hurricane has wind speeds in the range of 131
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Power Dissipation in Cyclones Such as Hurricanes, Typhoons and Tornadoes
http://applet-magic.com/hurricanepower.htm
to 155 mph. A category 5 hurricane with winds of 170 mph would have a rate of destructive
power almost 80 percent greater than that of a category 4 hurricane with wind speeds of 140
mph. A tornado with a wind speed of 300 (F5 on the Fujita scale) would have a rate of
destructive power per unit area nearly ten times that of a 140 mph hurricane and about 5.5
times that of a 170 mhp hurricane.
Thus Kerry Emmanuel's formula for the power dissipation of a wind has a solid justification.
The question of whether his heat engine model of tropical cyclones is verified or not is a
different question. For that see Global Warming and Cyclones and Moving Averaging.
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