Conservative Transport and Waves
Joel L. Plawsky · 2020
The momentum equation exhibits the feedback relationship between generation and accumulation that is the hallmark of a conservative process. The moment a water wave begins to crest for example, the motion is no longer irrotational, and the rotation within the flow causes the wave to break and collapse. There are two types of water waves to consider. The first case, called tidal waves, results when the wavelength of the motion is much larger than the depth of the channel. The amplitude of the wave is also much less than the channel depth. In these cases, the vertical acceleration of the fluid is negligible when compared to the horizontal acceleration, so all the fluid in a vertical plane moves synchronously. The second type of wave is called a surface wave and its wavelength is much less than the depth of the fluid.