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?

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:

• It's the wind.
  Wind or water flowing over a flat surface "trips over itself" because of friction with the bottom that slows it down. This creates rolling vortices of tubulence, an eddy effect that in turn produces ripples.

• It's the sand.
  Wind ripples result from just the saltation and reptation of individual sand grains.

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 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 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.

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.

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

• Sand dunes have a lot in common with sand ripples, and raise some of the same questions and many more of their own. Dunes have ripples on their faces, a kind of fractal structure-within-a-structure. Dunes can be stable for generations, for example there's a huge dune near Mussel Rock between Point Sal and Guadalupe Beach that appears on some maps. Dunes can quickly disappear when the wind changes. Dunes usually run perpendicular to the wind, but they can also run parallel to the wind, or form complicated arc and star shapes. They can be stationary or move. The slopes can be the same on each side or different. Do dunes form by the same process as ripples, or are they something different?

• How can steady winds over the deep ocean organize water into great waves with a regular wavelength? Why don't they make chop instead? Every surfer knows that afternoon winds will blow out the surf into unridable chop. Yet storm winds make big swells??? I never understood this as a surfer, and I still don't.

• On Dunn Middle School Hike Club, we waded across the mouth of the Santa Ynez River at Surf Beach where the river cuts across the sand between the estuary and the ocean. It's fast water. There were regular waves spaced a few feet apart on the surface. We found by wading that there are also regular sand ripples several inches high on the bottom. I assume the water waves are following the contour of the bottom, and that these ripples are formed by bouncing sand grains in the river current just like saltating sand grains in the wind. Really, wind and water are just different fluids with a different density (and Reynolds number). I've always wanted to tube this section of water, but it's been too polluted since last year's El Niño deluge, which is really disturbing. The San Juan River along the Utah/Arizona boarder in the Four Corners region is famous among river rafters for sand waves many feet high. I've rafted that river and never seen the sand waves, but I've been swimming in it and I know it has a sandy bottom. I guess it's the same phenomena on a larger scale.

• I've long noticed regular bands of clouds that form parallel to the east-west Santa Ynez Mountains. This is caused by marine air that is uplifted up the west face of the mountains and then bounces up and down on the inland eastern side. See my fog stumper for details. Is this a similar mechanism? High cirrus clouds often show longitudinal banding, and a Mackerel Sky is like chop.

• I'm really intrigued by washboard roads. Probably the worst we've seen are in the Scammon's Lagoon area of Baja California in Mexico. Forty miles of washboard road is not inviting! You can either creep along at 5 mph (40/5=8!), or try to find a higher speed that evens out the bumps. Why are washboard ridges so regular in amplitude and wavelength? Why do they get worse as more cars go over them? I'd expect more traffic to even out the bumps, but it seems just the opposite. Do cars act like giant sand grains hopping from ripple to ripple? I've always assumed this has to do with the springs of the vehicles. The wheels hit one bump and lift up and back down on to the next, so the spacing depends on speed and the suspension. But maybe not. Is there a model here for sand ripples? (Or vica-versa!)

• A steady wind will keep a flag fluttering back and forth rather than standing straight. What's the amplitude and period of the fluttering? Is this something similar?

• How about the wind blowing across a field of oats or wheat? Even in a steady wind, I see regular waves of grass marching across the fields. Or are these just stronger gusts I didn't notice?

• Global economic patterns emerge from countless individual exchanges every day in a way we would all love to predict!

• There are many other familiar examples of self-organization. Walk along a beach or river and you will find places with sandy beach, gravel beach, or cobbles and rocks. How can moving water like surf or a river so carefully sort the rocks? Wind does the same thing on a smaller scale. My favorite example is to shake up a can of mixed nuts (or nuts and bolts). The small nuts end up at the bottom, with the big ones on top. How can randomly shaking the can actually organize the contents? Isn't this something for nothing?

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:

• Scientific American has an Ask The Experts feature about sand ripples. The answer by Robert Anderson explains why it's the sand.

• The Canadian radio show Quirks and Quarks for January 3, 1998 has a discussion on sand ripples by Bruce Parsons who says it's the wind. The show is available on the Web in Real Audio format.

• Lenard Milich of the University of Arizona has useful pages on sand dunes and ripples.

• The Rio Hondo Prep School has an excellent page on the Eastern Mojave Desert with information on the Kelso Dunes area and general information on sand behavior, including ripples. We've camped in this beautiful desert in the Devil's Triangle of the Mojave between Barstow, Needles, and Las Vegas. The Kelso Dunes and the Eureka Dunes between Death Valley and the Sierra are famous for their booming sounds when you walk on them. That's another stumper!

• The Web page Geomorphology by Micromechanical Simulations discusses supercomputer research by the Caltech Concurrent Computation Group. The goal is to use "dynamical and computer simulations at the level of individual grains in order to elucidate some of the basic mechanical properties of granular materials."

• I haven't found much on the Web (or anywhere) about washboard roads. One interesting post on the Alaska Science Forum describes a simple apparatus to make your own washboards with a rotating wheel. There is also a Q&A with Tom & Ray radio transcript about driving fast over washboard bumps. The gritty 1952 French film The Wages of Fear by H.-G.Clouzot has an intense sequence with Yves Montand and others trying to transport sensitive nitroglycerine across a long washboard road in some South American desert. They decide to go fast to minimize bumps. Then come mountains and jungle... The opening shot of vultures on the village street helps set the unique mood. This is one of my favorite movies ever. William Friedkin remade the film in 1977 as Sorcerer.

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