Wave speed and water depth.

[Yuqing]

I have trouble understanding why water waves tend to speed up for waters deeper than 1/2 wavelength and slow down for waters shallower. I have read it has something to do with how the particle orbit changes to elliptical in shallow waters.

Why does the particle orbit become a flat ellipse in shallow water and is that the factor influencing the slower wave speed? If not not, what is?

 

[Yuqing]

Does anyone have an answer for this?

 

[nlightner]

The relationship between wave speed and water depth can be explained by the concept of wave dispersion. In shallow water, the depth is less than half of the wavelength of the wave, which causes the wave to interact with the sea floor. This interaction results in a change in the shape of the wave, causing it to become more elongated and flatter, with a smaller amplitude.

This change in the shape of the wave also affects the movement of the water particles within the wave. In deep water, the particles move in a circular motion, but in shallow water, they move in a more elliptical motion. This change in particle motion requires more energy to maintain the wave, resulting in a slower wave speed.

In addition, the shallower water also has a higher drag force due to the interaction with the sea floor, which further decreases the wave speed. This increase in drag force is also a result of the change in particle motion from circular to elliptical.

Therefore, the factor influencing the slower wave speed in shallow water is a combination of the change in wave shape and particle motion, as well as the increase in drag force. I hope this explanation helps to clarify the concept of wave speed and water depth.