Dust flux, Vostok ice core

Dust flux, Vostok ice core
Two dimensional phase space reconstruction of dust flux from the Vostok core over the period 186-4 ka using the time derivative method. Dust flux on the x-axis, rate of change is on the y-axis. From Gipp (2001).

Saturday, January 15, 2011

Self-organization in geological phenomena, part 1: Rhomboidal rills

Beaches in Ghana commonly show an amazing pattern of light and dark sands which are caused by the interaction of water flows as waves recede from the beach.

Rhomboidal rills on a beach in Ghana. The sea is toward the top of the photo. 
The light scuff mark at lower right is part of a footprint for scale.

The patterning is composed of regions of black sands, which are heavier minerals (and usually small grains), whereas the lighter-coloured grains are lower-density, rounded silica grains.

I have never observed this sort of patterning on beaches anywhere else. However there is something of a geological literature on these features dating back to the 1840s.

Oblique view of rhomboidal rills on beach surface, western region of Ghana.

Based on the paper referenced above (which appears to be a class project), the features form during the waning flow phase (as the wave finishes retreating) over a deforming bed.

The last point is significant, as it implies that the deforming bed (in this case, sand) is affected by the flow in a manner that feeds back and influences the flow.

What observations support this conclusion?

First of all, rhomboidal rills don't form on all beaches. In Ghana we observe them on beaches with a very low gradient, and the grain size is usually in the fine sand range. In my experience on some Great Lakes beaches, the beach gradient is high and the material is very coarse, but such beaches have no rhomboidal rillls.

My own observations of these forms occurring on beaches led me to conclude that they form under laminar flow conditions, when the flow thickness is small.

Photo taken as wave flows out, showing organization in the flow. 

The principal idea in the paper referenced above is that the organization in the flow arises from a random assortment of "rises" on the surface of  the water at the moment the wave has reached its high point on the beach. The "rises", or area where the water flow is a little thicker than elsewhere, result from random motion within the wave.

When the wave begins to recede, relaxation of the flow causes a local flow of water away from the centre of the each of the rises, while simultaneously the entire wave begins to flow back towards the sea.

In the diagram above, the small circe at the top represents the rise in the brief moment the wave is at rest and before it begins to flow back towards the sea. Water flows away from the centre of the rise (circles) but also flows downslope, resulting in a thin triangular flow defined by a characteristic angle, which is probably related to the gradient of the beach.

If the gradient were steep and the flow thick, the sides of the flow would form a parabola, and such forms are seen on beaches where fixed objects (say rocks) are washed by waves. As the wave flows around such a fixed obstacle, we observe a parabolic flow seaward of the object. On these Ghanaian beaches, the flow characteristics are such that the water flow is a thin film, flowing at low speed, and viscous drag reduces the acceleration so that the edges of the flow appear to be straight.

Now let us imagine two of these angular sheet flows interacting. At the point of intersection there is a sudden acceleration in the flow, as we now have twice as much water moving over a given area. This can only be accommodated by an increase in flow velocity, or an increase in thickness. Momentarily, both are observed. The increased flow results in erosion (E), preferentially of lighter material.

On the Ghanaian beaches in question, the sands are comprised of brown quartz sands (light) mixed with fine heavier black sands (including higher-density magnetite, ilmenite, rutile, zircon, garnet, and sapphire). The erosion removes the quartz sand, leaving behind the darker heavy minerals.

Immediately downslope of the intersection, the angular flows diverge, and the flow thins and slows. As it slows, the quartz sand grains picked up by the flow are deposited.

In this figure I have drawn in the edges of some of the thin angular flows that generated the rhomboidal rills in the photograph. Note the darker sands occur near the intersection of the angular flows, and the lighter sands farther downslope and often to one side of the divergent flow.

Rhomboidal rills are formed by self-organization in wave flow.

The features are destroyed and reformed by subsequent waves.

Hints of organization in the receding wave.

The organization in the receding wave is apparent at the right of the following video (all in the first four seconds).

I spent half an hour filming every wave that came in and none of the videos where I tried to capture the self-organization in the water flow worked except for the one video shown here. And when I filmed this one, I thought at the time that I had missed it!

Unfortunately the loss of resolution in posting this video makes it unconvincing

Screen capture of video 2 seconds in. Note overlapping angular flows at right.

Update: more photos of rhomboidal rills here.

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