Water waves accelerate in deeper water.

[barfllwyd]

A standard demonstration of refraction is to show water ripples traveling from deeper to shallow water. The frequency remains constant and the wavelength is observed to be shorter and the velocity lower. BUT when the water wave travels from shollow to deeper water the opposite happens and the wave increases its speed. What causes these changes in speed and in particular what's accelerating the wave. What's happened to Newton's Second Law? A common analogy is a car traveling from tarmac to sand which would slow the car but what force would accelerate the car when traveling from sand to tarmac.
How would any explanation then be related to the refraction of light?

 

[Dadface]

I think it has something to do with viscosity this being greatest in the shallow water.The wave speed is determined by how quickly the transverse vibrations are carried from one layer to the next and I think this transfer occurs more quickly where viscous forces are smaller.I would like to hear other opinions,it is an interesting question.

 

[cesiumfrog]

Newtons laws apply to the individual parcels of water that, moving up and down, make up the wave, rather than to the wave itself. (Similarly, you might think a gyroscope behaves anomalously if you treat it as a whole rather than accounting for the dynamics of its constituents. Likewise, we can make a shadow move across a wall faster than the speed of light without violating relativity.)

 

[Gear300]

Deeper water does have higher pressure. I'm not sure how, but this might have an effect on the elastic modulus, which could account for the higher wave speeds.