How Far Do Waves In the Ocean Travel Before They Lose Energy and Why Do Waves Get Smaller After a While?

Waves traveling in a fluid are not infinite.

They lose energy because the passing of a wave causes an upwards and downwards displacement of the water, and hence there is always an associated dissipation of energy due to viscous forces.

In addition, as the wave spreads, its energy gets distributed out over a greater and greater perimeter, causing the energy density to drop until it would become unmeasurable against background noise.

Waves traveling in deep water do not cause a very large displacement, and so the rate of energy dissipation is relatively slow. This is why tsunamis can travel such great distances.

However, in a shallow puddle or even the relatively shallow waters of the Mediterranean, energy is dissipated much more quickly.

Ripples spread out in an ever-increasing concentric circle.

Making the rather unrealistic assumption that the height of a ripple is directly proportional to the energy that creates and sustains it and that there are no losses to friction, the height of these ripples is inversely proportional to their radius.

This is because the energy associated with the ripple at any point has to be shared around the whole circumference of this ever-enlarging circle.

So, by the time the ripple passes through the Strait of Gibraltar 620 miles away, its radius has increased a million-fold and its amplitude would be a million times smaller than when the circular ripple had a radius of only 3 feet. A ripple 4 inches high would already be an imperceptible 100 nanometers high as it left the Mediterranean.

In principle, ripples should be able to pass through other waves undisturbed.

But, if the ripple were to break onto an American beach 4,000 miles further away, it would only be about 10 nanometers high, equivalent to the thickness of 100 atoms. Even this height would not actually be achieved because of air friction and the viscosity of the water itself.

To make matters worse, the Strait of Gibraltar is not on a line of sight from Ciutadella so the ripple would need to be reflected off North Africa or a passing ship and this would involve an even greater loss of energy.

Waves normally have a source of energy, the wind, to sustain them.

The ripples from a stone would have to survive on the tiny morsel of energy as you tossed them. To make matters worse, the rate at which a wave loses its energy is inversely related to its wavelength so, with their tiny wavelengths, your ripples quickly lose the small amount of energy they start with.

On the other hand, a tsunami such as the disastrous one that occurred in the Indian Ocean in late 2004 is created by the release of a huge amount of energy associated with events like submarine earthquakes.

They have typical wavelengths of 300 miles, so they lose very little energy as they head for distant landfall. In deep water they can outrun a jet aircraft, but with a wave height of a yard or so, they go unnoticed aboard ships. However, when they reach shallow water they slow down and start “shoaling,” often reaching many feet in height and sometimes traveling far inland.

This is probably the scale equivalent of dropping stones into a rock pool.

Have you ever seen the waves in a still pond die out a short while after you’ve tossed in a pebble? The viscosity of the water will dampen the wave you started so that it dies out long before it reaches the Straits, unless you toss in a truly gigantic stone.

Even if an initially circular wave front encounters no shores, the height of its wave crest diminishes in inverse proportion to the square root of its distance from its origin.

Initially, the entire wave formed by a small rock dropped directly down into deep water has a circular pattern. But this pattern is broken up if segments of the wave front are reflected from various shorelines at various angles and times.

If a shoreline is very shallow and sandy, or marsh-like, practically all the energy of such a wave’s front segment reaching it is apt to be absorbed by the elements of the shore, and so there is no significant reflection.

Near-perfect reflection in a single main direction without significant energy loss can only be expected when a segment of the wave front strikes something like a smooth, hard cliff side in deep water. But if the horizontal contour of the cliff side at water level is jagged rather than smooth at the scale size of the wave crest, the wave segment becomes scattered, with fragments being reflected off in different directions.

Looking at detailed maps of the Mediterranean, it is obvious that no segment of a wave front originating from a rock dropped in the harbor of Ciutadella in Menorca could travel to the Strait of Gibraltar and out into the Atlantic Ocean without first striking a good number of shores and being reflected by each.

Another factor is wind. Most surface waves in bodies of water are created by the wind. If a wave front created by a rock falling into water travels in the same direction as a gentle wind, it may become larger.

But a strong wind can completely deform it to the point where its identity becomes lost.

It seems unlikely that any significant part of the original wave from a rock dropped in Ciutadella harbor would ever reach the Strait of Gibraltar, let alone North America.

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