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Treebeard's Stumper Answer
7 May 1999

Wind Ripples

It's sure been windy this Spring! Julie and I were at Surf Beach beyond Lompoc recently on a day when the wind was howling onshore. There was a thin layer of sand flying over the beach in the wind, enough to sandblast our legs! In the midst of this windy chaos, I noticed regular rows of ripple marks in the sand along the beach, evenly spaced about 3 inches apart perpendicular to the wind, like tiny sand dunes. How can wind produce such regular sand ripples? What does the spacing depend on? Where else in nature does something similar occur?

Wind ripples at Surf Beach.
Regular wind ripples at Surf Beach, with my pocket knife for scale.
The wind is blowing from the top to the bottom.


Wind ripples in the sand show how close the frontiers of science can be. The exact mechanism is not well understood. Sand doesn't really fly in the wind. Grains bounce along in a process called saltation, and bump other grains into the air when they land, called reptation. Somehow millions of these micro-events make visible ripples, a fine example of self-organization in nature. Rivers also make ripples on the bottom. Wind makes waves. Are washboard dirt roads another example? Maybe everything is just fleeting patterns of quantum chaos at an atomic level!

Notes:

I don't really have an answer for this stumper. I find it satisfying that such a humble phenomenon as sand ripples is so puzzling! My impression is that this is an area of active research, with work being done on modeling ripple formation using massively parallel super computers to simulate the behavior of individual sand grains acting independently. It might be easier to create ripples than to understand them?! By changing the variables of wind speed and sand particle mass and shape, understanding may come from such a model. This would be a fun programming project on the right platform.

The hard question for me is why sand ripples have such a surprisingly regular wavelength, about 3 inches in the photo. It can only depend on the density of air, the wind speed and dynamics, and the physical properties of individual sand grains such as their weight, size, and shape. There's nothing else to consider!

Wind ripples have a regular amplitude and wavelength, but they're not perfect. Examine the photo to see that several ripples bifurcate. The rows are visible in the photo because of shadows, but also because larger grains tend to collect along the tops of the ripples and change the albedo. Windward slopes are less steep than leeward slopes. A model should explain these phenomena too.

There seem to be two main contenders for explaining wind ripples:

I favor the latter. The first explanation seems too much like a rabbit from the hat, and I'm not sure it's true. Even if they exist, what determines the spacing of the wind eddies? This just pushes the problem back to even smaller particles of air. I don't buy it. Here's my best shot at understanding how sand can make ripples on its own.

Sand grains bounce along for several inches or meters at a time by the process of saltation. They follow characteristic elongate trajectories taking off at a fairly steep angle and coming down at a flatter angle. They land with enough force at a low angle of impact to knock several or many other sand grains into the air on short hops in the process of reptation. Sand grains that are too big to blow away might still get bumped along.

Saltation and Reptation
Saltation and Reptation of Sand Grains.

If there are already slight ridges present on the beach, sand grains on the windward slopes will be more likely to be picked up by the wind. The leeward side of the ridge is actually protected from the wind, so sand that falls there will stay there. (Maybe there's also an eddy effect?) This is the mechanism by which ripples move. They erode on the windward side and grow on the leeward side. In time, they creep downwind.

If the wind speed and the size/shape/weight of the sand grains are fairly constant, then maybe sand grains will tend to jump about the same distance each time. Then one ripple will tend to make more ripples downwind about that far away, and they will be more likely to land on the ripple slope that faces the wind, like a catcher's mitt, so the ripples will grow. The large grains will tend to stay high on the windward slopes since they are too heavy to bounce away and they will be pushed up by reptation. The short reptation hops will move many sand grains further up the windward slope of the ripple. Some will cascade down the steeper leeward side adding to the accumulation. The longer saltation bounces will move sand to other ripples downwind, jumping over the valleys between.

This will create a "sand shadow" behind each ripple where few sand grains land because they are intercepted by the windward face of the slope. Stronger winds result in a more stretched out saltation trajectory, so the sand grains will land at a flatter angle and be even more likely to land on the windward slope of an existing ripple. This creates a larger sand shadow, and so gives a longer wavelength.

Formation of Sand Shadow
Formation of a Sand Shadow Between Ripples.

I still don't understand how this process gets started in the first place. Maybe any random bump (e.g. an ocean wave) is enough to get it going. Does straight wind over a flat surface really tend to produce eddies and turbulence with a regular wavelength all by itself? Maybe both wind and sand explanations are part of the story?

This mechanism makes some sense. I tried wiping a small section of beach clean, and it was satisfying to watch the ripples rebuild in a matter of minutes. But there were other ripples downwind to launch new sand to rebuild them. What if I wiped a section of beach clean all the way down to the water. Would the ripples rebuild as quickly? Would the wavelength of the ripples be the same? I can think of lots of experiments to do.

I noticed another interesting wind-sand phenomena. At Surf Beach, the flat beach sand extends back to a place where permanent dunes fixed with deep-rooted plants start. At the border I noticed a small depressed trench that runs all along the base of the dunes.

Wind depression at base of dune.
Wind depression at base of dune.

I didn't notice when I took this picture, but it sure looks like the ripples are running parallel to the wind blowing towards the base of the dunes from right to left. Maybe the dune is turning the wind sideways in a large eddy?

It takes a tough plant to anchor the sand against the howling beach winds. One of those plants is Sticky Sand Verbena, Abronia maritima. Here's a picture taken after the wind exposed its secret massive root system. Those roots are about six inches thick!

Exposed Sand Verbena Root System.
Exposed Sand Verbena Root System.

It's easier to notice similar phenomena and raise questions than to answer them! Every one of these is a good stumper by itself.

When I was a philosophy grad student at UC Santa Barbara many years ago, we used to argue about "emergent properties" as part of the "mind-body problem". I'm not sure now what we were arguing about, but it had something to do with trying to deny Cartesian dualism and still say that the pain itself is something other than the various neurons and muscles involved. Now I'm old enough to deal with real mind and body problems, and it all seems less important! Maybe sand ripples and these other phenomena show genuine emergent properties of matter.

Here are a few Web links for further research to explore:

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Copyright © 1999 by Marc Kummel / mkummel@rain.org