The D ynamics of T raffic J ams
(Shock waves in a 2D Granular Flow)

by S. Hørlück and P. Dimon

Paris Exhibition poster text

Intro page

This is an experiment in the field of granular physics. Granular materials are composed of small hard objects such as powder, sand, grain, gravel, medicine pills and corn flakes. Granular materials may behave like solids, liquids and gases in different situations and understanding their properties poses many challenges. In addition to the intriguing physics issues, such materials are also of great technological interest hence the field is rapidly growing.

The flow of steel balls takes place between two walls which form a small-angle funnel. Shock waves (traffic jams) are created in the funnel and move upstream opposite the flow.

When the angle is changed the properties of both the flow and the shock waves also change significantly.

By turning the handle you may change this angle and see the effects. A detailed description can be found on the right side of the experiment.

For further information, see:

Traffic jams

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Some phenomena in granular physics are similar to those observed in traffic. In particular, shock waves which propagate against the flow have strong parallels with some types of traffic jams.

In rush-hour or holiday traffic the number of cars may become so large that the traffic occasionally stops - sometimes for no apparent reason. The place where the cars stop (enter the "queue") will often move backwards because the incoming traffic is fast, while the cars in the queue move very slowly. This phenomenon is illustrated with toy cars in an image sequence above. Time progresses from left to right.

Following individual balls

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The graph above (second picture) shows a reconstructed flow sequence from the larger original experiment in Copenhagen. The flow was filmed and the motion of each ball tracked on a computer. In this sequence each ball is assigned a specific color so it can be easily tracked by eye.

On the vertical axis you see the distance from the lower end of the funnel. On the horizontal axis time increases from left to right.

A shock wave is observed to propagate from the lower left corner to the upper right corner (approx. 12 cm in 0.13 seconds).

Try to find, for example, a yellow ball in the upper part of the first image and see what happens to it as it moves downstream and encounters the shock wave in the next images.

A propagating shock wave

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The third picture shows a 0.75 second film sequence of the flow in the lower 36 cm of the funnel. At first there are no shock waves. Then a shock wave is formed 10 cm from the bottom which moves upstream at approximately 70 cm/sec.

By tracking all the balls in such a film sequence (as illustrated in the former picture) we can deduce information about how and why the shock waves are formed and how they propagate.

If you look at the picture above from a distance it is impossible to follow individual balls and difficult to separate individual images, but you can still see the shock wave move upstream as a "dark diagonal edge". This way of looking at the shock wave without focusing on individual balls led to another simpler way of examining the flow.

Different types of shock waves

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(For films showing the different flow types with shock waves see here.)

The fourth picture contains three graphs each showing 100 cm of the funnel for 10 seconds. Only the density of balls at each position at the funnel is shown: BLACK signifies high density (shock waves), WHITE signifies low density.

The three graphs show the three flow types with shock waves. There are two flow types without shock waves. The flow types below are listed in order of increasing funnel angle: (And "assigned" the color of the text describing them.)

A fast flow at low density. No shock waves are observed. This flow type is only observed at very low funnel angles (almost parallel walls). (Not shown in picture)

A fast flow at low density. Very pronounced shock waves (traffic jams) are observed, but they stand still or move very slowly upstream at around 10 cm/sec. They never reach the "top" of the funnel.

A strongly fluctuating flow with pronounced, moderately fast shock waves. Typical speeds are 50-100 cm/sec.

The flow is consistently rather dense and slow. Weak but very fast shock waves constantly move upstream. Typical speeds are 1-4 m/sec. In addition to the shock waves many packing patternscan be seen.

The flow is dense and very slow. No shock waves are seen. You only see many shifting packing patterns. (Not shown in picture)

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May 10 , 1998
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