Tsunami effects of a nuclear explosion

Question

Sea surface nuclear explosion arouses a tidal wave of water.

How does this kind of wave compare to naturally occurring tsunamis? E.g. what would be the potential of a 100KT bomb 100km away the from shore to flood that shore?

Answer 1

You asked a similar question on worldbuilding for a story.

Hit youtube for Operation Crossroads, Baker test. The US Navy detonated a 21kt device 90 feet underwater. Produced a nice fountain but no overly-destructive wave action after a few kilometers.

A few years later, Castle Bravo (15Mt) also failed to produce any significant damage* outside the immediate vicinity.

Natural tsunamis, like the one that damaged Japan a few years ago, release far, far more energy than man has learned to control.

• Yes, I'm deliberately ignoring radiological damage. Go find his question on worldbuilding.

Answer 2

Yes, destructive tsunamis can be created by current warheads.

This source provides in Chapter VII an equation to obtain the amolitude of the biggest wave in a nuclear tsunami, which I have turned into a more convenient form.

Amplitude(m) × radius(km) ≈ 15 × yield(kt)^0.54

For a 10 meter wave without shoaling at 100km this gives 2.4Mt, or <5% of Tsar Bomba.

The tsunami will however be different from a tectonuc one.

1. This tsunami is made of many short period waves rather then a few long ones

2. The shortness of wavelength in comparison to the water depth causes dispersion, which means:

2a. The number of waves in the wavetrain increases with time

2b. So the energy gets split along more and more waves, causing amplitude to decay faster then for a long wave, with radius rather than it's square root

Answer 3

Typical Tsunami arises when Earth tectonic plates transfers kinetic movement energy to the ocean water. The thing that earthquake can "bypass" big ocean water & earth mantle pressure, says a lot of about earthquake power. For example 2011 Tōhoku earthquake has originated at the shallow depth of about $30~\text{km}$ in the Pacific Ocean. So this earthquake has to get over through $\approx 4~km$ of water (Pacific ocean mean depth) and about $\approx 26~km$ of upper mantle. Having this we can calculate approximate opposing pressure which seismic waves had to conquer :

$$ P_{at\_origin} = \rho_{water} ~g~h_{ocean} + \rho_{mantle}~g~h_{mantle} $$

Substituting water column and soil column heights, and taking for soil density $2.5~g/cm^3$ (which is not constant, but depends on depth too), we can deduce that above mentioned pressure is: $$ P_{at\_origin} \approx \frac 23 GPa$$

If you were to put typical A-bomb at the same depth in the mantle and detonate, it would be like a "nasal hissing",- nothing comparable to the processes going at the Earth core. Such A-bomb detonation would be quickly swallowed by Earth deep soil pressure, so that water surface would by reached only by "toy" seismic waves, if any at all. The point is that it's not worth to compare Earth core processes / earthquakes power to nuclear bombs power, because they are of very different scale.

For comparison. There was some research which analyzed underground nuclear blast effects. They have derived couple of formulas, how blast spreads in soil. For example one can calculate, blast cavity,- region where due to nuclear explosion soil would melt :

$$ R_c = \frac {52~W^{1/3}}{(\rho g h + C_s)^{1/3~\gamma}}~, $$

Where $W$- A-bomb power in kT of TNT; $~\rho g h$ term is pressure in soil (depends on depth), substituted in bars; $C_s$ some adjustable explosion strength term in bars also,- given to vary between $[120,320]~\text{bars}$; $\gamma = 1.03$ - some dimensionless constant. So, substituting soil pressure at $26~km$, which would be about $6374~\text{bars}$ into the formula, assuming average parameter $C_s$, gives that $100~\text{kt}~\text{TNT}$ A-bomb would melt rock just in $12~m$ blast radius sphere. Really, not a big deal in underground world. So final conclusion is that A-bombs can't induce major earthquakes.