• Monthly
  • $25
  • $50
  • $100
  • $other
  • use PayPal

ONE WEEK TO DOUBLE YOUR DONATION!

A generous CounterPuncher has offered a $25,000 matching grant. So for this week only, whatever you can donate will be doubled up to $25,000! If you have the means, please donate! If you already have done so, thank you for your support. All contributions are tax-deductible.
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
October 16, 2019
Patrick Cockburn
How Turkey’s Invasion of Syria Backfired on Erdogan
Chitrangada Choudhury – Aniket Aga
How Cotton Became a Headache in the Age of Climate Chaos
Jack Rasmus
US-China Mini-Trade Deal: Trump Takes the Money and Runs
Michael Welton
Communist Dictatorship in Our Midst
Robert Hunziker
Extinction Rebellion Sweeps the World
Peter A. Coclanis
Donald Trump as Artist
Chris Floyd
Byzantium Now: Time-Warping From Justinian to Trump
Steve Klinger
In For a Dime, in For a Dollar
Gary Leupp
The Maria Ramirez Story
Kim C. Domenico
It Serves Us Right To Suffer: Breaking Down Neoliberal Complacency
Kiley Blackman
Wildlife Killing Contests are Unethical
Colin Todhunter
Bayer Shareholders: Put Health and Nature First and Stop Funding This Company!
Andrés Castro
Looking Normal in Kew Gardens
October 15, 2019
Victor Grossman
The Berlin Wall, Thirty Years Later
Raouf Halaby
Kurdish Massacres: One of Britain’s Many Original Sins
Robert Fisk
Trump and Erdogan have Much in Common – and the Kurds will be the Tragic Victims of Their Idiocy
Ron Jacobs
Betrayal in the Levant
Wilma Salgado
Ecuador: Lenin Moreno’s Government Sacrifices the Poor to Satisfy the IMF
Ralph Nader
The Congress Has to Draw the Line
William A. Cohn
The Don Fought the Law…
John W. Whitehead
One Man Against the Monster: John Lennon vs. the Deep State
Lara Merling – Leo Baunach
Sovereign Debt Restructuring: Not Falling Prey to Vultures
Norman Solomon
The More Joe Biden Stumbles, the More Corporate Democrats Freak Out
Jim Britell
The Problem With Partnerships and Roundtables
Howard Lisnoff
More Incitement to Violence by Trump’s Fellow Travelers
Binoy Kampmark
University Woes: the Managerial Class Gets Uppity
Joe Emersberger
Media Smears, Political Persecution Set the Stage for Austerity and the Backlash Against It in Ecuador
Thomas Mountain
Ethiopia’s Abiy Ahmed Wins Nobel Peace Prize, But It Takes Two to Make Peace
Wim Laven
Citizens Must Remove Trump From Office
October 14, 2019
Ann Robertson - Bill Leumer
Class Struggle is Still the Issue
Mike Miller
Global Climate Strike: From Protest To Power?
Patrick Cockburn
As Turkey Prepares to Slice Through Syria, the US has Cleared a New Breeding Ground for Isis
John Feffer
Trump’s Undeclared State of Emergency
Dean Baker
The Economics and Politics of Financial Transactions Taxes and Wealth Taxes
Jonah Raskin
What Evil Empire?
Nino Pagliccia
The Apotheosis of Emperors
Evaggelos Vallianatos
A Passion for Writing
Basav Sen
The Oil Despots
Brett Wilkins
‘No Friend But the Mountains’: A History of US Betrayal of the Kurds
John Kendall Hawkins
Assange: Enema of the State
Scott Owen
Truth, Justice and Life
Thomas Knapp
“The Grid” is the Problem, Not the Solution
Rob Kall
Republicans Are Going to Remove Trump Soon
Cesar Chelala
Lebanon, Dreamland
Weekend Edition
October 11, 2019
Friday - Sunday
Becky Grant
CounterPunch in Peril?
FacebookTwitterRedditEmail