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This is just a blog to document the energy produced by tornadoes and hurricanes, and by extension the energy required to be able to create them. Note: These calcs were not done by me, they have just been moved here for easier access.

Tornado Energy

The calculation for this can be found here and has been moved here for convenience.

Most energy of a tornado is energy of motion: kinetic energy.

KE = 1/2mv^2

Where m = mass (of air in tornado) and v = velocity (wind velocity in tornado). Let's assume that wind velocity is typical of an F3 tornado, around 300 km/hr.

v = 300km/hr^-1 = 80m/s^-1

To get the mass, recall that m = rV, where r = density and V = volume. The appropriate density is that of air: r = 1kg m^-3.

To estimate the volume, make a simplifying assumption: approximate the tornado shape by a vertical cylinder with height h and radius r. The volume of the cylinder is:

V = p r^2 h

Assume the cylinder is 1 km in height and 1 km in radius. Substituting volume and density into the equation for mass, then substituting for mass in the expression for kinetic energy,

KE = 1/2p r^2 h v^2

= 1/2p (103m)^2 (103m)(80m/s^-1)^2

= 3e+12 J

Hurricane Energy

Both of these calculations were originally done here, and have been moved here for convenience.

Total kinetic energy (wind energy) generated: For a mature hurricane, the amount of kinetic energy generated is equal to that being dissipated due to friction. The dissipation rate per unit area is air density times the drag coefficient times the windspeed cubed. One could either integrate a typical wind profile over a range of radii from the hurricane’s center to the outer radius encompassing the storm, or assume an average windspeed for the inner core of the hurricane. Doing the latter and using 40 m/s winds on a scale of radius 60 km, one gets a wind dissipation rate (wind generation rate) of 1.3e+17 Joules/day, or 1.5e+12 J/s.

Total energy released through cloud/rain formation: An average hurricane produces 1.5 cm/day of rain inside a circle of radius 665 km. Converting this to a volume of rain gives 2.1e+16 cm^3/day. A cubic cm of rain weighs 1 gm. Using the latent heat of condensation, this amount of rain produced gives 5.2e+19 Joules/day, or 6.01e+14 J/s.

Conclusion:

Energy produced by a Tornado/Energy to produce a Tornado: 3e+12 J / 717.017208413 Tons of TNT, Multi-City Block level+

Energy to create Hurricane Force winds: 1.5e+12 J / 358.508604207 Tons of TNT, Multi-City Block level+

Energy to create a full Hurricane: 6.01e+14 J / 143.642447418938 Kilotons of TNT, Large Town level