How waves are formed

When wind blows across water, sea or a lake, some of the energy is absorbed due to friction and this causes the top layer of the water to move, the stronger the wind, the greater the expanse of water and the longer the period the wind blows for, the larger the waves get. Starting from a flat sea, you start with ripples, and the windward side of each ripple is effected then more than the sheltered side of the ripple, causing the ripple or wave to grow. As a wave grows so does it speed,  so the speed difference between the water and wind is decreased, and you get to a balancing point where the wave does not get any larger. The wave may also role right over and break dissipating some of the energy.

Size of individual waves

 A wave is measured from the bottom of the trough to the top of the crest.

The wave length is the distance from the bottom of one trough to the next or the distance from one crest to the next. As waves get larger both the size and wavelength increases. In theory a wave that has grown in height to one seventh of its wave length will break, but because some of the energy is absorbed then in following waves, and waves combine,  once  the height of waves get to about one twentieth they tend to break. In open ocean winds above force 7 are likely to give breaking waves.

Charts are available that allow using nautical miles of sea over which a wind blows, the wind speed, and the time it blows for, to get the normal wave size for coastal waters. Deep ocean is 10 - 20% greater. The wave height given is what is classed as significant wave height, this is computed by producing an average of the largest third of the waves.

Within the ocean all waves are not the same size, some combine and other variables occur so that there is a considerable variation, but most are about the same size. Observation exercises have shown that 1 wave in 23, is twice the average height, 1 in 1175 three times, and 1 in 300,000 (about a month at sea) is four times the average. The average is about 0.6 times what is known as the significant wave height, which is normally the wave heights quoted.

Swell

Swell can be created by pressure differences, and will exist for some time and distance after the cause stops. When troughs or crests of swells combine waves form. If a storm, or wind then develops large waves and disturbed water can develop quickly.

Movement within a wave

As a wave passes any particle of water will move in a circular motion,  and move only slightly forward, this is why when you see an item in the sea, it tends to ride the wave, bobbing up and down, rather than moving rapidly forward. Particles below the surface also move in a near circular orbit ending up to near to where they started. The size of this orbit reduce as you go further down until at about two thirds of the wavelength there is no or very little movement.

Waves in shallow water

When the depth of water becomes less than two thirds of the wavelength, friction on the bottom of the orbital movements start to have an effect, the wave is slowed down but becomes steeper, forcing it to break, destroying the wave and releasing a lot of kinetic energy, and this is the force people ride while surfing. This force can move structures of great weight.

Waves around an obstruction

When waves hit an island, the effect is to slow the wave, and therefore further away it is running faster. The effect of this is that the waves wrap around the island causing an interference pattern where they overlap behind the island. Where you may have expected to have calm water in the shadow of an island, you can often find far rougher water, than clear of the island.

Tsunamis

Waves created from an underwater earthquake or similar, mostly occurring in the Pacific ocean, can be over 100 miles long, traveling at speeds of 500 knots at a height of only a few feet. At sea they present no danger, but on reaching land considerable damage can be done. Often the sea level drops a few minutes before the first wave, then a series of large waves at a few minute intervals with often the 3rd or 8th being the largest.

Relevance to a floating island

Sea defenses need to be able to cope with the largest waves, and the islands stand up under the variety of wavelengths.

Structurally ships or islands need to be able to be supported by any combination of parts of waves, so heading into a wave a ship will often only be supported at one point in the middle or at the two ends. If the wave is not hit exactly squarely you also get a twisting effect.

Given a freak wave of 60 feet in height, the wave length could be 20 times that 1200 feet. Therefore an island just over this length could be a bridge between two waves suspended at each end and a second later held up just in the center. As islands get larger than any possible wave then they will experience increased buoyancy and have over hanging parts alternately. They have to be strong enough to stand this constant flexing for ever.

Waves in the position we have chosen

We propose to put the new country near the center of a constant high pressure zone, so the sea normally is calm with waves of only 2 to 3 feet, gales are extremely rare and can occasionally result in waves of up to 30 feet. Given what we have said above that, there are a small number of larger waves, we could expect to get a 60 foot wave around once in a thousand years. The odds therefore of a 60 foot wave hitting the kingdom is much smaller than New York being wiped out by a large wave or  San Francisco being flattened by an earthquake.

Storm force 10 on land uproots tress and does considerable damage to property.

Hurricanes are major storms that hit the coast of the Caribbean and USA, start lower in the Atlantic and move around the edge of the extended high pressure area, usually going to the west of Bermuda. The position we have chosen, the center of the high pressure area, is the safest place to be and should have far fewer bad storms than land or sea areas away from this position.

As large waves are often a combination of waves, and only occur for seconds before collapsing, or others neutralizing them,  the wavelength or gap between waves  is unlikely ever to be be as large as mathematical theoretical computations, and therefore structural bridging distances will be far shorter than the theoretical amounts. With a very large item with stabilizers, it is more likely to damp out much of the effect and sit mid wave. Pointed front ends also tend to split the wave, reducing the actual ride height so we see with large ships waves breaking over the front and not bobbing up and down as predicted mathematically. The sea defense wall will break the large waves cut most of the wave off, so within the wall there should be a very much smaller wave height, as in a harbor that is well protected by a sea wall.

One answer was to have sea defenses that can handle normal maximums and island structures that can take a very occasional wave over the defenses without causing too much damage, another is to build defenses that can handle anything, and a third that says you defend against what is likely to happen over several lifetimes and then design structures that if they break cause minimal risk to life and stay afloat.

Our solution

Ultra safe, a sea wall that is very large, with a basic structure able to take a 60 foot wave and a wall on top of this 120 foot high. The sea wall is usable space, so this overbuilding provides a lot of shelter for the islands but also are commercial units in their own right. Islands designed to withstand any sea condition, so even if the sea wall broke up they would survive intact, but also designed as  multiple compartments so if a failure did occur each part would stay afloat, and could be repaired.

The outer wall is constructed of  a large number of individual units.

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Last updated: October 09, 2002.