Scroll down to figure 10.1.3, and view the animation. This is what I imagine I'm feeling.
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There is movement in both directions, plus up and down. Under six miles of fetch, it's an
interesting ride.
That makes perfect sense. The water does move forward, albeit much slower than the actual speed of the wave, and likely your paddling rate too in most circumstances.
I think
@chrisrezac's observation about boat length, relative to wave length, is critical. At least with respect to
trailing waves that might be traveling faster than your paddling speed: If the boat is long and the wavelength is short, then the bow gets buried in the backside of the forward wave, while the stern is being pushed with more force by the trailing wave. So if you're not perfectly perpendicular to the waves, then the trailing wave pushes your stern sideways much more easily than it can push your whole canoe up the backside of the forward wave. That's why quartering waves can be a viable option in that scenario: because you're effectively shortening the length of your boat relative to the vector of the wave, which reduces the force differential along the length of your boat. That said, if the waves are really that tight, even if you're quartering, you're still probably going to need to pry to keep your stern planted at the moment of the trailing wave's engagement with your boat because it is still going to meet your stern before the bow.
With nice big rollers, like
@lowangle al's example, the wavelength is much longer and so the force differential isn't quiet as stark, so there is less relative lateral push on the stern, and its easier to maintain your intended direction.
You all know far more than I do about the performance characteristics of hull shape within any given length, but earlier observations about a rockered hull being easier to navigate in waves makes sense to me. By comparison, a seakindly sailboat would have a lot of volume amidships, with high ends that would gently lift the ship up and over the seas, rather than digging in. Though, I suppose a sailboat's rudder and keel go a long way too...