Distorting Mirrors, Bernoulli & Kelvin

Myles Duffy took this from a boat on Two Medicine Lake, Montana looking amidships and downwards to the water.

At top the landscape with Rising Wolf Mountain is inverted in the glassy water. Nearer the boat something strange happens, the mountain appears again but this time the right way up.

Closer still is the familiar wake

All images ©Myles Duffy, shown with permission
Waves & Wakes

To move forward a boat must displace water from forward to aft. The water moves backwards at each side and at increased velocity.

Fluids moving faster have lower pressure than elsewhere - Bernoulli principle. This in turn produces a standing wave pattern, a depression of the water surface amidships.

The surface there changes from flat to convex and then concave at the most depressed area. Glass smooth water and reflections reveal this otherwise oft unnoticed effect.

Superimposed is the familiar Kelvin wake first explained by William Thompson, Lord Kelvin, in the 1880s. Leading waves may contribute to the reflection.
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Accurate computer ray tracings for a sinusoidal hollow are at right.

The topmost shows rays from the green arrow reflected off the convex edge of the depression towards the eye. The eye sees an inverted image in the water.

Closer in the surface becomes concave. Rays reaching the eye cross each other before reflection. Ray crossing, as in mirages, always creates an inversion. A second inversion occurs at the actual reflection finally giving an erect image in the water.

Even closer in the depression goes convex again. It would give another inverted reflection but that one is obscured by the boat's Kelvin wake.

Sky pools do this too.