Dockhead
Well-Known Member
Your post is astounding in its arrogance and ignorance. You haven't bothered to make an effort to understand what I'm saying and are too lazy to look at the source material I've quoted. I've spent seven or eight hours over the last couple of weeks going through modules on the web and have simplified it down to a what is still quite a lengthy post, but I've condensed an awful lot of detail.
The whole point is to try to understand it mathematically. They're not difficult formulae. I've also provided worked examples to help illustrate the points, but you don't seem to have looked at them in any detail.
I'm not sure I can even simplify it to your terms. You're looking for a one dimensional answer to something that is not one dimensional. I guess you read abridged versions of the classics.
So anyway, here goes in noddy terms.
1) waves are generated by the wind. The period and height depend upon the wind speed, fetch, which is the distance over which the waves are affected by the wind not the distance from the nearest land, and time. Sometimes they develop from scratch and sometimes they develop from existing waves already created by a gentler wind.
2) After generation is finished waves propagate as swell (I'm not going into that as it's a whole area in itself). Swell is generally less steep because energy transfer and dispersion causes swell period (hence wavelength) to increase and height to decrease.
3) Wave speed in deep water is proportional to period, in shallow water it is proportional to water depth.
4) The period of a wave does not change when it enters shallow water so its wavelength decreases as it slows down. That again is a whole area in itself and I'll skip that to keep it simple as my earlier posts confined themselves to deep water.
5) I must've already posted this three or four times, but here goes again. WIND OVER TIDE IS NOT IN ITSELF THE MAJOR CAUSE OF THE STEEP WAVES YOU ENCOUNTER IN 'WIND OVER TIDE' CONDITIONS. In other words, although the wind opposing the tide causes bigger waves to be generated, it is not the major factor.
6) When an existing wave enters an area of water that is flowing in the opposite direction its period remains the same. It slows down and the wavelength decreases. It's height increases by a proportionate amount. In other words it becomes much steeper. THAT IS THE MAJOR CAUSE.
7) The wave energy is a mixture of kinetic and potential energy. Although energy is lost to the sea bed in shallow water, we're not considering that case, so as the wave slows down kinetic energy is transferred into potential energy. The potential energy is the gravational potential energy of the wave crests.
Now we're getting somewhere. At least 90% of this verbiage is irrelevant to the question (Waves are generated by wind? You don't say!) but at long last (!) a clear thesis emerges, in Point 6 - so it is, according to you, the transition between areas of water moving in relation to one another, which causes the foreshortening of the wavelength. So for the Gulfstream, you have swell built up over a long fetch which is then caught up short against the moving mass of the Stream.
I think all of us "noddies" know that the water in waves moves up and down (or in circles), contrary to appearances. So I think we can imagine that if you impart a real horizontal moment to this whole system, you might have something like a Doppler shift in the wavelength. Hmm.