# The Naked Scientists Forum

### Author Topic: Sea waves high speed  (Read 1262 times)

#### saspinski

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##### Sea waves high speed
« on: 27/04/2016 23:51:53 »
This month, part of a new bike path in Rio de Janeiro was destroyed by the upward force of strong sea waves.
The lane is parallel to a road along a rocky shore, and at 50m above sea level, and can be modelled as a collection of beams, being supported by pillars.
It was designed to support its own weight, bycicles and people, all downward forces. The water simply pushed it upward disconnecting it from the pillars.
Of course there is no 50m high waves here. The waves crushed the inclined rock wall, and were reflected upward.

If the water could reach 50m, mgh = 1/2mv2 means a speed about 30m/s or 100km/h.
Is it right? I have never known that the impact of waves on shores could reach such a high speed.

#### Colin2B

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##### Re: Sea waves high speed
« Reply #1 on: 28/04/2016 12:52:20 »
The speed of an ocean wave depends on its wavelength and in deep water has been recorded at over 140km/h.
However, as a wave approaches shallow water the wavelength shortens and the wave slows. In 3m of water a wave will have a max speed of around 10knots, 18km/h.
Most sea defences try to shelve the water to reduce the speed and ideally make the waves break before hitting the wall.
The power in a breaking wave is delivered faster than a roller and so the momentum transfer is much greater. Also the breaker compresses the air trapped in the wave front and this is responsible for the huge plumes of spray that can reach considerable heights and carry a lot of energy. I suspect that if the wall was crushed it would have been a breaker and the plume - which would contain rock debris - probably did the damage to the bike path. As you say, paths like these are only designed to take downward force and the shock upward load would easily cause failure.
« Last Edit: 28/04/2016 14:23:44 by Colin2B »

#### saspinski

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##### Re: Sea waves high speed
« Reply #2 on: 29/04/2016 23:13:10 »
Just a correction, I think the news of 50m high are exagerated, but as the photo in annex shows, the road (over the arcs, the photo is old before the bike path) may have 25m at least. Even so, it would require a kinectic energy of a water flow with 80 km/h against the rocks.
The energy stored and soon released by the trapped air should be delivered by the kinectic energy of the water, so I understand it can not be responsible any additional power.

#### Colin2B

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##### Re: Sea waves high speed
« Reply #3 on: 30/04/2016 09:13:17 »
.... it would require a kinectic energy of a water flow with 80 km/h against the rocks.
What wave height did you assume? Remember that although wave energy is proportional group velocity it is also proportional to height squared.
Although compression etc won't give extra energy you also have to consider the change of momentum and the time over which the energy is delivered which can result in considerable shock loads. A plunging wave will deliver its energy in a much shorter time than a surge up a beach. Looking at the photo, the slope below the arches is very steep and would encourage a very short energy transfer.

EDIT: sorry, did t have a lot of time when I posted that, so bit rushed.
If you know the wind speed at the time and the duration it is possible to calculate the average wave height. For eg, for 90km/h wind, if you assume a fully arisen sea (not fetch or time limited) the deep water waves would be about 15m average. As they come to shore and feel bottom the wavelength shortens and the waves get higher - because you still have the same amount of water. Even for a relatively shallow slope of 10% the wave height will increase by 1.7, so your 15m wave could easily reach 25m, add to that the high velocity spume generated at impact and you have a lot of pressure on the underside of the bikeway.
Of course, the exact situation will depend on many more factors including the seabed profile as the waves approach shore and their angle of incidence, height of tide, distance from storm centre, duration, fetch, etc, but it doesn't seem unreasonable that even a slow moving wave could reach the bikeway.
« Last Edit: 30/04/2016 14:21:01 by Colin2B »

#### The Naked Scientists Forum

##### Re: Sea waves high speed
« Reply #3 on: 30/04/2016 09:13:17 »