Sunday, September 18, 2011

The Miles-Phillips Mechanism

Two distinct mechanisms have been proposed to explain the means by which the wind is capable of generating waves and perturbations on the surface of lakes and oceans: Kelvin-Helmholtz instability (KHI), and the Miles-Phillips Mechanism.

Now, KHI reputedly requires a minimum wind speed of 6 m s-1 to make waves grow against the competing effects of gravity and surface tension. Thus, whilst KHI is relevant to the generation of large wavelength perturbations, it is the Miles-Phillips Mechanism which is relevant to low wind speeds, and short-wavelength perturbations. In particular, the Miles-Phillips Mechanism involves a resonant interaction between the surface of the water and turbulent fluctuations in the air.

So, in the interests of science, I wandered down acorn-strewn paths to my local lake, to see if I could identify the Miles-Phillips Mechanism in action. What I observed over the course of several days, were a complex sequence of meta-stable and transient patterns. All the photos here were taken at the same time of day, around 2pm.

The first couple of pictures are from Friday 16th September. There was a light breeze blowing from left-to-right here, and this appeared to maintain a band of short wavelength perturbations in the middle of the lake. There is a clearly-defined transition, however, towards the margins of the lake, where the ripples were of a visibly longer wavelength. The shorter modes completely disrupt the reflective properties of the lake, but you can still see distorted images of the surrounding trees in the areas with the longer wavelength disturbances.

This is in sharp contrast with the pattern exhibited on two days previously, when a stable pattern of short-wavelength perturbations covered most of the lake. Note the absence of any reflective images at all.

On Sunday 18th September, the breeze was light, but rapidly fluctuating, and bands of short-wavelength perturbations would arise, and then dissipate, over a timescale of just a few minutes. In the first photo here, virtually the entire surface is smooth and reflective...

But within little more than five minutes, a band of short-wavelength ripples had covered the middle of the lake.

Such patterns would rise and fall, and drift back and forth across the lake as the local wind shifted and fluctuated. The wind variation was imperceptible from the viewpoint of the observer, and the patterns became as inexplicable and mesmerising as a mere screen-saver.


Doug said...

Nice pun at the end there.

BBC did a documentary on waves not so long ago. It wasn't overly scientific, but did raise some interesting ideas, such as the idea that in one sense, all objects are waves - it is just more convenient for us to think of them as objects from the perspective of our brief lives. The final idea it put forward was that we are waves too: we are born, we make ripples and then, we die.

Gordon McCabe said...

In fact, I wrote a post about that programme earlier this year: Waves are not made of water.

Along with irony, puns are a difficult commodity for the internet, where many of the readers will not have English as their first language.

Doug said...

My apologies. I did read that article but I did not connect it with what I was watching.

This is what happens when you rely on iplayer for your televisual fix.

One further thing that struck me on this documentary, was the illustration of waves occurring at the boundary between two media - air and water, or water and thickened water? What about light waves though? What is the medium they propagate through - and is it really the boundary between two media, and if so what are they?

Please educate me!

Gordon McCabe said...

No need for any apologies Doug.

Light is ultimately composed of photons, which are quite happy to propagate through empty space. When there's lots of photons together, under certain conditions their emergent collective behaviour is nicely described by the electromagnetic waves of Maxwell's classical theory, which again doesn't require any underlying medium.

There are subtle issues here, however. For further thoughts, there's my rather terse post, What is laser light?, and Richard Healey's article, Physical Composition, contains some really good stuff. See Section 3, The Decomposition of light.