If you make a small model of a river, what special rule helps you match the way waves and ripples move in the model to the real river?

The special rule that helps match the way waves and ripples move in a small model of a river to the real river is called Froude similarity, or Froude scaling. This rule requires that the Froude number of the model must be equal to the Froude number of the real river, which is known as the prototype. The Froude number is a dimensionless quantity that represents the ratio of inertial forces to gravitational forces acting on the fluid. Inertial forces are associated with the fluid's mass and its resistance to changes in motion, while gravitational forces are due to the pull of gravity on the fluid. For flow in open channels, where the water has a free surface exposed to air, gravitational forces significantly influence the behavior of the flow, including the formation and propagation of waves and ripples. By ensuring the Froude number is the same in both the model and the prototype, the relative importance of these forces is maintained, accurately replicating free surface phenomena like waves and ripples. This means that if the model is, for example, 1/100th the length of the real river, the velocity of the water in the model must be reduced by a factor of the square root of 100, or 10, compared to the real river's velocity, to correctly simulate the wave and ripple movement.