The pressure differential will change from zero at the surface (well, a very minor shift there due to atmospheric) to twice the amplitude of the wave at the bottom.
I think I'm probably splitting hairs now and we're well outside the scope of practical diving physics but I'm not sure I can agree (or understand) this statement. As sschlesi pointed out in
this and
this post, the effect of a swell on the pressure at the bottom of the sea is not as directly coupled as this statement suggests. The pressure at any point is not a function of the distance from that point and a point directly above it an on the surface, it is rather a more complex function of the average distance between that point and a number of points spread out over the surface roughly above that point.
Like I said, I don't think this even resembles anything applicable to diving really. I'm not even sure I'm coming across clearly so never mind if I don't
A tire is soft so a portion of it conforms to the flatness of the road. That portion which is constantly changing has to move horizontally to the direction of travel of the car.
So if you're using the word "movement" do you refer to movement relative to the car or movement relative to the road? If you're referring to movement relative to the car then I would agree with the statement but I also then don't understand how it applies to the model of a point moving in water as a result of wave motion.
Think of the track on an army tank. A different part of the track is constantly coming into contact with ground and leaving contact with the ground. Although no part of the track moves in relation to where it touches the ground the length of the track is moving in a horizontal direction with the direction of movement of the tank.
Again, I'll agree with this because we're measuring movement on the track relative to the tank not relative to the ground (ie. movement on the track as viewed by an observer on the tank, not an observer on the road). To be more exact, the point on the track that is touching the ground will be moving
backwards relative to the tank at
exactly the same speed that the tank is moving
forward relative to the ground - because now the tank is motionless and the ground is moving backwards (as opposed to the ground being motionless and the tank moving forward).
If you took the wheel in the cycloid link and flattened it at the contact point, the point on the wheel would form a straight line parallel to the surface from the time it contacted the flat surface until it left the flat surface and there would be a straight line connecting the semi circles rather than them touching
No it wouldn't. If a point touches the ground, it can not move relative to the ground (unless the weel is slipping of course, which is not the case here). For a horizontal line to exist on the bottom of the cycloid curve the point has to undergo horizontal movement and like you said in the bolded section above, no point of the tank's track (or the flattened wheel) moves in relation to where it touches the ground. In other words the point on the ground where that point first touches is exactly the same point where it will eventually leave the ground. If it is a perfectly round wheel then the point will leave the ground instantaneously, if it is a flattened wheel the point will remain on the ground a little bit longer before it leaves the ground and if it is a tank's track, the point wil remain on the ground for quite a bit longer. But for as long as the point touches the ground it will never move horizontally.
Again though, this is merely a mental exercise in physics/mathematics. I don't think it has any bearing anymore on describing a diver's situation under a swell so if you don't feel like agreeing with me, I don't think it's important to convince you.
