I took some photos of water waves having clear boundaries. It is amazing that the boundaries of the waves are sharp.
In this article, I will discuss an idea that I came up in 2013.
Capillary Surface Gravity Wave
On observation from the images is that the boundaries don’t depend on the angle a lot. Surface gravity wave amplitudes decrease exponentially. That being said, boundaries would be sharp if the source has a sharp boundary since the waves by the source won’t propagate far.
The source of the wave can be quite different. The wind is probably one of the most popular sources. If the wind is stronger in some regions, it creates messy waves with wavelength of several centimeters. In other regions with lower wind speed, the waves would remain parallel and clean. The boundaries will appear. The key insights of the wind-driven theory are
- capillary surface gravity wave where the wavelength is small,
- wind is the source,
- the wind field projection on to the water surface is not homogeneous.
How does the wind drive the waves? There is a layer of water vapor which can be driven by wind. The water vapor is then driving the water beneath using surface tension.
We explain the capillary waves a bit here. Using a coordinate system where water wave is static. In the following chart, wave peak B will experience surface tension, gravity, and from part of the Bernoulli equation due to wave moving below the wave. We assume water is incompressible, the relative velocity of water at the peak is smaller than the relative velocity at the crest. This difference generates a restoring force.
Turbulent spot like the footprint of a whale?
Lei Ma (2020). 'Clear Cut Water Wave Boundaries', Intelligence, 10 April. Available at: https://intelligence.leima.is/toolbox/physics/clear-cut-water-wave-boundaries/.