Natural disaster in the South Pacific has evolved into tragedy along the Samoan islands. Just 2 days ago we first heard the news of the tsunami that was generated just offshore of Samoa. So far, it has resulted in over +100 deaths. Contrary to what many people believe, the impact of a tsunami, also referred to as a seismic wave, has less to do with its actual wave height and more to do with its energetics. In this case, energy is related to the square of the wave speed. Let’s take a look at how wave speed is generated and how that is translated into energy…..
First, a seismic wave results from a shift at the bottom of the ocean floor caused by an earthquake. The earthquake acts to physically shift the ocean bottom surface, which then vertically shifts a mass of water located directly above the quake zone. This vertical liquid displacement reaches the surface and then propagates outwards as a wave.
The resulting wave is known as a low frequency dispersive wave. Period and frequency are indirectly related, such that a low frequency (units of 1/seconds) wave has a high wave period (units of seconds). And, wave speed is directly related to wave period. In this case, a low frequency wave with a high period ends up having a very high wave speed.
Energy, the main culprit of a tsunami, is a function of wave speed. More specifically, energy is the sum of kinetic energy plus potential energy. Kinetic energy is a function of mass and wave speed or velocity while potential energy is a function of vertical displacement or height. Using equations we can say that:
TOTAL ENERGY = Kinetic Energy + Potential Energy
TOTAL ENERGY = 1/2 (mass)*(velocity)2 + (mass*gravity*height)
From the above equation, we immediately see that energy is related to the square of the wave velocity times the mass. There is an enormous amount of mass involved in a seismic wave (remember that it originated from the vertical displacement from an underwater earthquake). More precisely, every cubic meter of water has a mass of 1,000kg, or weighs 2,200 pounds. Speeds of a tsunami can reach up to 400 miles per hour! Sir Isaac Newton told us many years ago that the force of an object is related to the product of the mass and its acceleration. If every cubic meter of water weighs 2,200 lbs and it is traveling at speeds up to 400mph, you can quickly understand the force that is related to a tsunami.
So as we can now see, the destructive nature of a tsunami is related to the extreme energy that is created by the quake. There are many surf spots throughout the world that regularly exceed wave heights that are associated with tsunamis, but their formation and related energetics are vastly different, thus the reason why we find big wave surf spots all over the world that do not harness the power and destruction of a tsunami.
Meteos sends his best wishes to those in the South Pacific and to those abroad who have loved ones in both American and Western Samoa.