I am not sure if this is the correct forum to post this in, but I am hopeful someone can give me a direction to move in. I am in a debate with a friend of mine. We are arguing over the amount of damage a wake from a boat causes when it impacts a shoreline on a steady grade.

The main thrust of the argument, is velocity of the wave a factor? I think that a faster moving wave would generate more energy than a slower moving wave, therby causing more damage. So does a boat's wake moving at 22mph (assume the wakes are the same size) do less damage than a wake that is sent by a boat moving at 34mph?

Does this change if the wake is larger (let's say the slower wake is 6 inches taller). Obviously a larger wake would do damage to more of an area, but which one would have stronger forces?

Is there any truth to the following? In the same scenerio above with a shore line on a 1/10 slope (1 inch up to every 10 inches in run). I noticed the taller slower moving wakes tend to break much earlier and disspate more over a shorter distance. Could someone explain in the "for dummies" version why this is either a mis-perception on my part or a correct oberservation?

Thanks for any help in resolving this question, David

I can't answer your main question, but I was observing wakes near a marina while picnicing yesterday. We were eating near a "no wake" zone.

... So does a boat's wake moving at 22mph (assume the wakes are the same size) do less damage than a wake that is sent by a boat moving at 34mph? ...

The boats were going through at less than walking speed in order to keep the wakes to the ripple level. When they reached the buoy a couple of hundred yards out, they "put the throttle to the wall" and started generating a large wave (3-4 feet?). So the size of the wake does change with the speed of the boat.

Looking forward to seeing what other observers can add to this.

See if my explanation is reasonable:

The damage/impact of a wave to the wall/coast depends on how the wall/coast line feels the wave.

A bigger wake/wave will be more energetic than a smaller one.

But if the bottom slope of the coast is sufficiently gentle (say 1:20), the a wave will break at the point where the waveheight/depth ratio approximate 0.78, hence a bigger wave will break earlier than a smaller wave(assume same wave period and wavelength), and after breaking, the wave height will be dissipated, and undertow will be generated. That means the bottom will spend a longer distance to feel the coming wave. As the wave finally reaches the coastline, it may be very small already. So hard to say whether the bigger wave will make more damage to the coast line.

While for a very steep slope, or a perpendicular wall, standing wave will be formed and the waves are not going to break, and the waveheight will be nearly doubled, and so does the pressure on the wall, in this case, a bigger wave/wake will make more damage.

If somebody punch on my chin, I'll feel painful, but on my hip, may be not too bad.

wen

Perhaps there is some confusion regarding speed of the waves compared to the speed of the boat. When the water depth is much smaller than the wave length, as is the case beyond some point on a slope, the wave speed depends on depth. For example the speed is 3 m/s if depth is 1 m (and the wave length >> 1m). And, as Wen points out, if the wave height was about 80 cm the wave would break at depth=1 m.

The speed of the boat controls both the wave height and the wave length. Generally, and as one would guess, the wave height grows with increasing boat speed. But at some speed the boat generates the biggest waves and if it goes faster the wave height decreases again. Therefore it is possible that a boat emits smaller waves at higher speed.

The boat type (hull form, weight etc) govern the dependancy of wave height on boat speed. The wave length also increases with boat speed, but there is no maximum wave length: the faster the boat the longer the waves. (As the wave length depends on depth on shallow water, wave period is often used instead of wave length. The wave period does not depend on depth.)

If the boat moves in shallow water and at the same speed as the waves, for instance at 3 m/s on 1 m depth, the waves can become very large.