I am confused by success.
Below is a picture I have sought for months, yet, I don’t understand why I was able to get it now. It is a simple illustration of the dispersion of gravity waves on water.
On more than one occasion, this blog has treated the subject of water waves — what can I say, the blog’s theme is that of exploring a lake. Water waves possess many interesting behaviours, some of which I have treated over the years. Recent ones relevant to this posting are 23 cm/s (which illustrated that when a water disturbance moves at less than 23 cm/s, no waves are created) and making waves (which showed both gravity waves and ripples, and that it is the shortest ripples that travel fastest).
The term, wave dispersion, describes the situation where waves of different lengths travel at different speeds. On water, both ripples and gravity waves are dispersive: for ripples, the shortest waves travel fastest; for gravity waves, the longest waves travel fastest.
To my mind, these are all really interesting features of the natural world around the Lake. But, while it was easy to illustrate the fact that for ripples (surface tension is the restoring force) it is the shortest waves that travel fastest, I found it really challenging to illustrate that for gravity waves (gravity is the restoring force) it is the longest waves that travel fastest. While the behaviour is undeniable, taking a single picture to illustrate the latter simply proved a challenge. Alas, often such scenes are really cluttered, such as the jumble of waves generated by the wind. A boat’s wake is also rather complex. How might I capture a simple illustration?
Then I saw it illustrated clearly in the waves made by the cable of a cable ferry.
Why the cable provided such simple waves is not obvious to me. However, the disturbance caused by a small cable rising out of the water is different than that of an object moving across the water. The simplicity of the situation merits more exploration.
As the (Harrop) cable ferry crosses the Lake, the (orange) cable rises out of the water ahead of the ferry off the picture to the lower left. This disturbs the water and creates gravity waves which are seen spreading towards the upper left. What the picture makes clear is that the longest waves have travelled farthest (towards the upper left) as a result of having travelled fastest. (The wake of the turbulent bow wave of the ferry itself is seen on the right.)
Reading your insights into the wave movement over the past few years leads me to wonder how often artists who do studies of the surfaces of ponds, say, get these things right – or rather, how often they get them wrong. Probably more often than not when one looks closely. Just a thought.
Trevor, yours is a perceptive thought. Leaving aside artistic licence (e.g., the Picasso school of faces), it is often possible to know that the objective was to be representational. For example there are websites that explain how to use photo editing to add realistic raindrop ripples to a picture of water. Those I have read botch the realism by creating spreading waves that are equally spaced. However, the most unfortunate case I encountered was that of a custom furniture maker and wood carver. He was working on a commission of a rather grand table for a ski resort. Endless work had gone into carving the table top to represent the surface of a pond during a rain shower. (A heavy transparent lacquer would be used to render the table top flat.) When I saw it, it was a large, beautiful, and intricate carving of rain on water — except that all the ripples across the table top were equally spaced. Alas, nature does not behave that way. A simple observation, photograph, or image search would have allowed the artist to succeed in his objective of representing reality. And don’t get me started on the unnatural rainbows that ‘representational’ artists manufacture.