FacebookTwitterRedditEmail

The Energy of a Hurricane

In Fidel Castro’s account of Hurricane Gustav’s impact on Cuba, he speculates about the energy such a storm can hold:

In all honesty, I daresay that the photos and film footage shown on national television on Sunday reminded me of the desolation I saw when I visited Hiroshima, victim of the first nuclear strike in August 1945. With good reason, it is said that hurricanes release an enormous amount of energy, equal, perhaps, to thousands of nuclear weapons like the ones used on the cities of Hiroshima and Nagasaki. It would be worthwhile for a Cuban physicist or mathematician to do the relevant calculations and make a comprehensible presentation.

Being Cuban (from New York) , and a physicist (when I was employed), I felt challenged to provide details. What follows are the results of a simple model.

I consider a hurricane to be a vortex with a local rotational speed that increases as the point of observation moves to smaller radius. The center of the hurricane is a zone of low pressure, while the exterior of the hurricane is a region of high pressure; air is drawn radially inward by this pressure gradient. Air drawn into the outer radius of the hurricane, Ro,  rotates with angular (or circular) speed vo. Let us say this condition applies to a ring (inward along the radial direction) of thickness dr. This ring has a height L, from sea level up to the top of the storm (what satellite cameras photograph). The rotation of this large cylindrical shell carries a total angular momentum (the product of total air-mass in the shell times average rotational speed), which we will label Mr.

The air in the outermost shell moves inward to the next nested shell of thickness dr (these shells are arbitrary mathematical conceptions), which must also carry momentum Mr since there is no significant force to impede the flow (this is the law of conservation of angular momentum). However, since there is less volume in this next inner ring, and since the air is not significantly compressed as it moves, the circular velocity of the flow must increase (the radial velocity also increases, but is of lower magnitude). This effect continues so that the circular wind speed, vi, at the inner radius, Ri, is very high. The total number of rings in the storm is given by (Ro-Ri)/dr, or simply Ro/dr when Ro is much larger than Ri. Since each ring has the same momentum Mr, the total momentum of the storm is equal to the product M = Mr x (Ro-Ri)/dr, or to a reasonable approximation M = Mr x (Ro/dr). [x has been used as the multiplication sign.]

The circular speed v at any radius r can be expressed as the product v = w x r, where w is the rotational or circular frequency. This frequency is low at the outer edge of the hurricane and increases as the point of observation moves inward. From the model here, one can find that the circular frequency varies with radius as follows,

w = M/(2 pi rho Ro L r r).

[I have dropped the x for multiplication.] This quantity is the total momentum of the storm, M, divided by the product of 2, pi = 3.14159…, rho = density of air, Ro, L, and the square of the radius in question.

Hang on, we’re almost there.

Because M, 2, pi, rho, Ro and L are constants, the angular frequency can be written as w = A/(r r), where A is a constant equal to M/(2 pi rho Ro L). Notice that for any pair (r1, w1), where perhaps these specific values were measured at radius r1, that

A = r1 r1 w1,

the product of w1 times the square of r1. So, once we measure the wind speed at any given radius, we can infer the rotational frequency there (w1 = v1/r1), and then we can define constant A and use this in the formulas shown to get w and v at any radius.

Now, we find the kinetic energy of every layer (shell), which is essentially the product of its mass times the square of its average circular velocity, divided by 2. Then, we add up all the layers for the total energy of the storm. I do this with differential layers and form the double integral, radially and vertically, but we will skip over that discussion. The result for the total energy of the storm is

E = pi rho L A A LOGe(Ro/Ri)

in units of energy called joules (if you fell asleep, this is the answer).

E is the product of five factors, the four leading ones being: pi, rho, L and the square of A; and the product of these four is multiplied by the mathematical function called the natural logarithm (LOGe) of the ratio Ro/Ri. The natural logarithm of 1 is equal to 0; LOGe(2.7182818…) = 1; LOGe(10) = 2.3026; LOGe(100) = 4.6052.

Let’s list parameters, choose values and find some numerical answers:

pi = 3.14159…

rho = 1.2 kilogram/(cubic meter)
[air at sea level]

L = 5000 meters (5 km)
[height]

A = 4,000,000 (meters squared)/seconds
[value chosen for rotational acceleration parameter]

Ro = 400,000 meters (400 km)
[outer radius]

Ri = 40,000 meters (40 km)
[inner radius].

Our choice for the value of A is consistent with:

v1 = 10 m/s,
r1 = 400,000 m (400 km) and
w1 = 0.000025 radians/s; and/or

v1 = 20 m/s,
r1 = 200,000 m (200 km) and
w1 = 0.0001 radians/s; and/or

v1 = 100 m/s,
r1 = 40,000 m (40 km) and
w1 = 0.0025 radians/s.

[There are 6.283 radians along a circle,
so 57.3 degrees/radian;
recall 360 degrees = 1 circle]

Note that 1 m/s = 2.24 mph (miles per hour);
1.61 km = 1 mile;
1 km = 0.62 mile.

For the values shown,

E = 6.944 x (10 to the 17th power) joules.

The energy released by the explosion of 1000 tons of TNT (a kiloton, abbreviated kt) is 4.182 x (10 to the 12th power) joules. So, E = 166,055 kt (or equivalently, 166.05 megatons). The atomic bomb exploded at Hiroshima on August 6, 1945 produced about 15 kt, so the model storm has the energy equivalent of 11,070 Hiroshima bombs. Most of the energy of a hurricane is dissipated as atmospheric turbulence and heating, and friction along the Earth’s surface, only a very tiny portion of it is absorbed by the structures built by humans.

Bear in mind that the energy of the hurricane is spread over a much larger volume than that of a nuclear explosion (so hurricane energy per unit volume is smaller), and it is released over a much longer period of time. But it is of awesome scale, and we are still as powerless before it as were our first ancestors four million years ago.

MANUEL GARCIA, Jr./strong>. is a retired physicist; e-mail = mango@idiom.com

 

Your Ad Here
 

 

 

 

More articles by:

Manuel Garcia, Jr, once a physicist, is now a lazy househusband who writes out his analyses of physical or societal problems or interactions. He can be reached at mangogarcia@att.net

bernie-the-sandernistas-cover-344x550

April 18, 2019
Gerald Sussman
Russiagate is Dead! Long Live Russiagate!
Lance Olsen
Perverse Housing Policy Perverts Forest Policy
Richard Ward
All Will be Punished
Jonathan Cook
Annexation of West Bank May Provide Key to Unlocking Netanyahu’s Legal Troubles
Judith Deutsch
People Music: Malignant Phallic Narcissism v. Being Ordinary
Jan Oberg
The Iran Floods and US Sanctions: 10 Million at Risk, But Who Cares?
Manuel E. Yepe
Assange: Between Gratitude and Betrayal
Ralph Nader
Children’s Moral Power Can Challenge Corporate Power on Climate Crisis
ADRIAN KUZMINSKI
Your Check is in the Mail
Binoy Kampmark
The European Union and Refugees in the Mediterranean
Arnold R. Isaacs
Looking Back at 1919: Immigration, Race, and Women’s Rights, Then and Now
Andrew Moss
Immigration and the Shock Doctrine
Michael Howard
Assange and the Cowardice of Power
Jesse Jackson
Making Wall Street Pay for the Financial Crisis
Mel Gurtov
At Risk—the Idea of America
April 17, 2019
James Bovard
Washington’s Biggest Fairy Tale: “Truth Will Out”
Yoav Litvin
The Ilhan Omar Gambit: Anti-Semitism as a Reactionary Political Tool
Evaggelos Vallianatos
Hawai’i in Trouble
Vijay Prashad
To Ola Bini, a Political Prisoner Caught Up in the Assange Debacle
Hans Muilerman and Jonathan Latham
EU Threatens to Legalize Human Harm From Pesticides
Binoy Kampmark
Delegitimising Journalism: The Effort to Relabel Julian Assange
Jack Rasmus
Trump Whacks the Middle Class
Kollibri terre Sonnenblume
The Burning Cathedral and the Dead Turtle
Kenneth Surin
Insurgencies in Malaysia and Vietnam: Boyhood Reflections
Rev. William Alberts
Opening Tombs and Resurrecting Lives
Tom Engelhardt
How the U.S. Military Feeds at the Terror Trough
Norman Solomon
The Toxic Lure of “Guns and Butter”
George Wuerthner
How to Stop Grazing on Public Lands: Buy Out the Permits
George Ochenski
Vote-Trading for Big Coal
John Stanton
The Price of Participating in Society is the Sacrifice of Privacy and Self
April 16, 2019
Richard Rubenstein
Julian and Martin: Reflections on the Arrest of Assange
Geoff Dutton
Talking Trash: Unfortunate Truths About Recycling
Kenn Orphan
A Land Uncharted: the Persecution of Julian Assange
Patrick Cockburn
Netanyahu’s Victory in Israel Tells Us About the Balance of Power in the Middle East
Robert Fisk
No More Excuses: Israeli Voters Have Chosen a Country that Will Mirror the Brutal Regimes of its Arab Neighbours
Jonah Raskin
The French (Bread) Connection in a Bourgeois California Town
Denis Rogatyuk
The Ordeal of Julian Assange
David Swanson
Exporting Dictators
Ted Rall
Self-Censorship is Credibility Suicide
Robert Koehler
War Crimes and National Security
Lee Ballinger
None Dare Call It Fascism
April 15, 2019
Bruce Neuburger
The Border, Trumpian Madness and the Clash of Demographics
Patrick Cockburn
Calling Assange a Narcissist Misses the Point
Conn Hallinan
Diego Garcia: The “Unsinkable Carrier” Springs a Leak
Dan Corjescu
State of Apocalyptic Nature: A Contract with Gaia
FacebookTwitterRedditEmail