Resumen de Cats, dogs, and roll waves
On a hot afternoon in western North Carolina, the heavens opened and (to mix metaphors) it started raining “cats and dogs.”1 The rain was torrential, and soon a river of water was flowing downhill into the parking lot. In rivers and dam spillways, these are known as flood waves. The picture shows a particular type of flood waves known as roll waves—shock-like patterns separated by smooth profiles. In a steady-state situation, the drag forces on the water in the channel are balanced by the down-slope gravitational force. The dimensionless friction coefficient is C, the stream depth is h, v is the average speed of the water, g is the gravitational acceleration, and α is the angle of the slope (assumed to be small so that sin α ≈ α). In a steady state, Cv2 = ghα.
