Wave Front Shapes in Flowing Water
Date: Winter 2013-14
On a recent quiz in Physics we had a question that asked. When you drop a stone into smoothly flowing water (meaning that there are no previously existing waves) what shape will the waves it creates be and what will happen to the. My teacher claims that the waves will be circular and flow down stream. However most of the class thinks that the waves will form an ellipse because the rock will either A) make the pond more shallow thus interfering with the wave frequency or B) the rock will slow down the flow of the water and delay the back of the circle from flowing for a short amount of time and thus creating an ellipse. Who is correct?
Run an experiment and measure (or watch) what happens.
Create a simple channel in which you can have laminar flow, put a rock in your stream. Maybe sprinkle some finely cut dried grass to help visualize the flow. Measure flow rates, take pictures of the flow, analyze the pictures.
Leslie Kanat, Ph.D.
Since the waves are the manifestation of the energy of the rock falling into the water, the waves should maintain their circular shape as they propagate out and as they pass down stream.
However, rocks in the stream may cause a turbulence that delays (or accelerates) a portion of the water column through which the wave is passing at the time and may distort the circle.
If the depth of the stream shallows to the point that the bottom interferes with the wave's propagation, it would not effect the frequency. As waves at the ocean front roll in from the deep sea to the shallow beach, the bottom of the wave starts to drag on the sand and slow down while the top of the wave continues on its original speed causing the top to curl over (as it is moving faster than the bottom) like a Smurf's hat. But still, if the wave started out as a circle it would keep that shape unless, as discussed above, something caused a turbulence.
As with so many physics-class questions, it somewhat depends on what
simplifying assumptions you make. In the simplest case -- which I am
assuming is your circumstance -- If the rock is assumed to be
spherical, then the wave shape (when viewed from above) will be
spherical. The effects you describe (A) and (B) do not make sense to
me. If you want to create an elliptical pattern, use an elongated rock
(or a stick). If you are looking at the water waves from the side, the
physics are entirely different... but the shape depends on the
amplitude of the wave and the water depth. I assume this is not your
question, but I included just to make sure readers are using the same
frame of reference.
Hope this helps,
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Update: November 2011