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Complainant Name:
Mr Richard Holyroyd

Clauses Noted: 1

Publication: New Scientist


Mr Richard Holroyd complained that the Last Word section of the magazine carried inaccurate answers to a question about why waves formed on rainwater running down a road.


The complaint was resolved when the magazine published the following response from the complainant:

The waves shown in Robert Johnstone's photograph are a classic example of what are know as roll waves. Other examples are those spotted by Tony Cowley in the "gents" and rain water flowing down a window (which are effectively the same thing) and, on a larger scale, they sometimes appear on spillways discharging the overflow from reservoirs where they can become large enough to overtop the sides of the channel that would comfortably contain a uniform, steady flow. In extreme cases the flow effectively moves in surges with very little water in between which gives the phenomenon another name, slug flow. Roll waves occur on the free surface of liquids, liquids carrying solid particles in suspension, even slurries, and also at the interface of immiscible liquids (such as oil on water).

Contrary to what your other correspondents suggest, they are quite different from solitons which are essentially discrete pulses of liquid moving on top of the otherwise undisturbed flow beneath them, nor are they miniature waterfalls over static bands of silt. If these existed, they would obscure PART OF the line in the road running from top right to bottom left of the photograph.

Roll waves have been studied for just over 80 years. For a gentle slope the flow will be slow and deep, what is known as subcritical flow, while for a steep slope the flow will be shallow and fast moving, or supercritical. The difference between these two states is given by the Froude number, named after the 19th century fluid dynamicist William Froude. The Froude number is the ratio of the velocity of the flow to the speed of very small waves that invariably appear on the liquids surface and can be greater than or less than one. For supercritical flow it is greater than one which means that the waves move slower than the flow and therefore can only travel downstream.

The speed of waves increases with their height so larger waves will overtake and absorb the smaller ones (which also increases the speed of the large ones). Gradually the many tiny waves become fewer, larger ones. Eventually the flow in their vicinity becomes subcritical, the wave fronts steepen and they break in much the same way as waves break on a beach.

Roll waves do not appear at regular intervals and there is no way of calculating even the average distance between them. They appear spontaneously even when the flow is over a smooth surface provided the Froude number is greater than two. A slightly rough surface appears to promote their appearance but further increasing the roughness has the opposite effect and ultimately will prevent them occurring altogether.

Report: 76

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