>I am trying to learn more about how waves break. i.e. what equations >drive how a wave will break. Do you know of any books on the subject >and how to order them?

In short, In shallow water There is a limit on how steep a wave can be, when it gets beyond this it starts to break, thus reducing the height. This tends to produce spilling breakers.

Combined with this, as I said the speed of the wave depends on the water depth, so the crests of the waves travel faster than the troughs, [because the water is deeper] so the waves become asymmetric, with steeper fronts than backs. this increases the steepness of the face of the wave. Eventually the wave becomes unstable and the faster crest tries to overtake the trough and the wave breaks. This process tends towards producing plunging breakers, especially when it happens rapidly.

These two processes act together, [along with other smaller and even more complex ones]. The extent of each depends on things like the rate of shoaling, hence you see plunging breakers [+ tubes] on steep beaches where the depth changes rapidly.

h = water depth, L = wavelength, H = wave height.

I have not gone into the equations too much, I can send you some if you wish {:^)

But for more detail I would recommend: Introductory Dynamical Oceanography, 2nd Ed. 1983 Pond S. and Pickard G.L. Butterworth-Heineman Ltd, [Reed Elseiver] ISBN 0 7506 2496 5

Regards, Ric

From: Ric
Newsgroups: alt.surfing
Subject: Re: The Push (??)
Date: Wed, 22 Jan 1997

>Here on the West coast of the UK, waves are affected by a phenomenon >called "The Push". As the tide comes up, the waves get bigger. As the tide drops away, so does the swell. >>I think this is due to our big (30 foot) tidal range, rushing up the >Bristol Channel.

Mainly, yes. The large tidal range causes large tidal streams. Here's a paragraph that Graham wrote for wavelength last year. Why do we get bigger waves on an incoming tide? Basically there are two reasons, the effect of sand bars and the tidal water movement itself. If a wave travels at 15mph and the tide is coming in at 5mph, the actual wave speed increases to 20mph and on the dropping tide a 5mph flow in the opposite direction against the swell slows the swell to 10mph.

The effect is greatest when the swell direction is similar to tide direction, spring tides also boost this effect. It is possible for the effect of an outgoing tide to stop the swell from reaching the beach. Gary Lewis of Black Rock Surf Shop, Porthcawl confirmed that the area sees probably the most dramatic example of these phenomena. Porthcawl is situated in the funnel of the Bristol Channel. "With a consistent swell, a 2' wave at low water will build to 3-4' at high water on a neap tide and as much as 6' on a spring tide."

Gary also pointed out that the effect is further emphasised by sandbars off Porthcawl which kill the wave energy at low tide while at high tide are completely covered and have little effect. Constantine beach has a similar thing with the banks. It doesn't break until near high tide when the wave clears the outer banks. The tide stream thing increases as you move further up the Bristol Channel. It makes little difference south of Newquay, but increases up to the figures quoted for Porthcawl above. I can send you a ~12k .xls graph of the tidal stream directions for our area if you like.

Interestingly, around Padstow the tide direction is about 90\dg out of phase with the height, [ie: the tide does not start flooding till 3 hours after LW.] and it is actually this that counts.

>Or is it a universal thing?

No, it depends on the local tidal characteristics.

>Another thing. Are these big tides, the reason why we don't get good >sandbanks in these parts?

Partly. Many aspects of the coastline are defined in some way by the tidal range and wave climate. I could type all day on this one, but I have to do some work today. If you really want to know a lot more I'd recommend reading the OU book listed in the FAQ. If you want to see a copy I have one. Get your tail down to Plymouth for a beer and a chat.

>Perhaps our resident oceanographers, Ric and Tim, could enlighten me.

From: tbmaddux@alumnae.caltech.edu (Timothy B. Maddux) Newsgroups: alt.surfing
Subject: Re: Fetch for wave height
Date: 11 Apr 1997

>Why would the period of waves increase as they travel?

Good question. The increase of wave period within a fetch is known as frequency downshifting -- a decrease in frequency is an increase in period.

Here's how it works: The wind starts blowing on a flat sea, and short little waves form. They grow in height as high as they can until they can grow no further and begin to break. There's still a bunch of wind energy out there, though, and it can't go into the short waves any more. So, longer waves start forming and they grow until they break, and the process repeats itself. This continues until the waves being formed are so long that they are moving as fast as or even faster than the wind is blowing, at which point the wind cannot push on them to make them larger.

Growth stops and you have a "fully developed sea." The waves are as big as they'll ever get for the wind speed that is present. If the fetch is short, the waves never get to be fully developed, and they move away from the wind smaller and shorter than waves from a long fetch. The result is similar for winds that blow for a short period of time. After the storm passes, the waves are free and move across the ocean.

The heights of the waves diminish due to directional spreading across the ocean. The longer waves move out faster than the shorter ones, causing the whole wave train to spread, which causes the waves to shrink even more. The shortest-period waves get left behind and become so small that they are undetectable. The result is an increase in the average wave period that we see when they reach us. Take a look at Kinsman's "Wind Waves" (1984, ISBN 0-486-64652-1), for a solid and difficult discussion of all this. Pages 408-409 on Pierson-Neumann forecasting nail it down in plain English pretty well.

>I think they would start out as sine waves with troughs >and crests.

Yes... in deep water swells are very well-approximated by pure sine waves. As waves come in to shallow water their shape changes to something called a 'cnoid' which has a short, steep crest and a long shallow trough -- those are what we see as lines of corduroy ahoooooooo.

-- .-``'. Timothy B. Maddux, Ocean Engineering Lab, UCSB .` .`~ http://www.engineering.ucsb.edu/~tbmaddux/ _.-' '._ "From the essence of pure stoke springs all creation."