The Decelerating Wave-Form

A shoaling wave is constantly slowing down.

All shoaling waves decelerate.  This deceleration is often imperceptible to an observer, but it can be quite dramatic - as if the wave seemingly just stopped and "jacked".

The deceleration is the result of a frictional interaction of the water particles currently experiencing the wave action in the very lowest portion of the wave-form with the bottom topography. This slowing down will continue to increase as long as the wave-form continues to move into shallower and shallower water.

Communication between the upper and lower regions of the wave-form is not instantaneous.

The deceleration currently experienced by the lower portions of a shoaling wave is not instantaneously transmitted to the upper regions.  This is why waves break they way they do. The uppermost portions, attempting to continue move forward, slide up and over the lower portions which continue to decelerate.  When the difference in deceleration between the upper and lower portions of the wave-form is sufficiently great - the wave "breaks".

As the wave shoals the height of the wave-form increases.

As a wave starts to shoal, a large portion of the kinetic energy (energy by virtue of relative motion) of the participating water particles is transformed into potential energy (energy by virtue of relative position, here, position in the gravitational field of the Earth) as the upper-most particles continue to slide up and over the lower portions. (Some energy will be lost due to frictional interaction.)  This increase in height results in another acceleration which is of paramount importance to surfers – an accelerating upward flow of water, which on the leading or forward face of the wave-form, manifests itself as a flow up the 'wave-face'.

Drag keeps a surfer connected to the deceleration wave-form.

But if a shoaling  wave-form is constantly slowing down, what exactly keeps surfers from being seemingly launched forward, that is leaving the forward wave-face in the direction in which the wave-form is progressing?

Newton's First Law states,

"Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it."

(If you like you may insert 'constant velocity' for uniform motion. During Newton's time, he and other scientists of his day, saw them as one in the same thing.)  Therefore, if the surfer is to remain connected to a decelerating wave-face, there must be some force or set of forces that similarly slow down the surfer, or similarly decelerate him, at least in the direction in which the wave-form is moving.

There are a number of forces that can be at play here, but the dominant force that keeps a surfer on the wave-face is drag. In particular, the drag which is generated from the interaction of the surfboards wetted-surface (which  might include fins, etc.) and the flow of water past that surface.

Some of the other forces might include wind-resistance (another source of drag), or the surface tension, or that from material interaction (surfboard surface and water in this case). But by far, the largest contributor is the drag generated by the wetted-surface and the flow of the water up the wave-face.

The curl region is decelerating faster than the shoulder region.

The 'curl' (the region where the wave appears to be breaking or where breaking appears to be imminent) is an important region to surfers. Curiously, this region however, relative to the unbroken portions of the wave, is decelerating faster. That is, the 'shoulder' region, that part of the wave-form which has yet to break, is actually moving faster than the curl.  The transition between the two regions generally appears quite smooth and continuous. at least for most of the breaks that surfers frequent. So smooth, as to be almost imperceptible in terms of the difference in deceleration as you move from shoulder to curl.

The flow up the wave-face is greater in the curl region.

And in a manner similar to that described above, the degree of upward acceleration of the wave-form is different for these different regions too. Slowest for the shoulder regions, becoming increasingly more rapid as you move towards the curl.

So surfers have to contend with at least two kinds of acceleration; a deceleration which is greatest in the curl region, and an upward acceleration which is also greatest in the curl region. Both of these accelerations becoming progressively lesser magnitude as you move out onto the shoulder.

As mentioned above, the dominant forces that keeps a surfer on the wave-face is drag, and that drag is generated by the interaction of the surfboards wetted-surfaces with the flow of water up the wave-face. So the acceleration of the flow up the wave-face is used in part as a way for the surfer to stay connected to the wave-form - allowing him to decelerate in kind as the wave continues to shoal.