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While cycling in Ireland I had ample opportunity to observe rain and puddles. I took a photo (right) of muddy water running across a road. Why has it separated into bands, and what determines their spacing? (Continued)
In January I dropped some bricks into my pond, which is a metre deep. In March the pond froze over and an image of the bricks appeared like a hologram in the ice. What caused this? (Continued)
● The waves shown in the photograph are a classic example of what are known as roll waves. Other examples are those spotted by your correspondent who was using a urinal and rainwater 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, 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, and nor are they miniature waterfalls over static bands of silt. If these existed, they would obscure the line in the road running from top right to bottom left of the photograph. Roll waves have been studied for more than 80 years. For a gentle slope
● A previous correspondent states: “Because of the physical properties of water, the colder it is the less gas per unit volume it can hold.” Actually, the opposite is true: water holds more gas as it gets colder. This is why opening a bottle of fizzy drink on a hot summer day releases more fizz than opening one out of the fridge. What does happen is that water releases most of its dissolved gas when it freezes. In the case of this question, the layer of water on top of the pond releases bubbles of gas when it freezes, which is why the water below becomes supersaturated with gas. Tim Patru By email, no address supplied
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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. This
“Roll waves do not appear at regular intervals and there is no way of calculating the average distance between them” number is the ratio of the velocity of the flow to the speed of very small waves that invariably appear on the liquid’s surface, and can be greater than or less than 1. For supercritical flow it is greater than 1, 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 the average distance between them. They appear spontaneously even when the flow is over a smooth surface, provided the Froude number is greater than 2. 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. Richard Holroyd Cambridge, UK
THIS WEEK’S QUESTION Chain gang My father used to hang a chain which dragged along the road from the back of our car. He said it would prevent my sister from getting car sick. I thought it was some kind of placebo effect but later I discovered that my husband’s family did this for their car-sick dog. Does it work and, if so, how? Ginette Andress Allambie Heights, New South Wales, Australia
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