If I fill a bathtub with water to the point that it is spilling out of the far end of the tub, the waves in the tub caused by the water coming into the basin stabilize at a given height -- roughly two centimeters in the couple tubs that I've tested.

What I want to know is how the waves change if I were to get larger and larger bathtub setups. So if I made a 2x scale bathroom, I'd have a larger faucet dumping water into a larger tub. Assume the "volume of water through a square centimeter of faucet exit" across the exit of the faucet is constant as scale increases. Clearly the waves would be larger as well, but how much larger? Would the waves scale linearly? Or does some volume-surface area ratio get involved to drive it nonlinearly?

Photos may help. In image 1, I have slowed the faucet to a trickle. With this lighting, you can see the waves making their way along the surface of the water. At a trickle, the waves are barely moving vertically, but they create enough disturbance to see in light.

In image 2, I turn the water up full. Now the waves are much bigger. Right by the faucet, I measure about 2.0cm of bounce once the water gets deep enough, and about 1/3 of the way down the tub, they fall off to about 0.5cm. They flatten almost completely at the far end of the tub.

I want to know the rough height of those waves at the faucet and at 1/3 distance if the tub were magnified by 2x... 4x... 350x... 1000x, etc.