The shapes of waves of ships and ducks

The wake of a duck, a ship, or anything in between, all have the same shape. To explain why, we need to discover a few things about the mathematics of water waves.

This video is submitted to the 2022 Summer of Math Exposition #SoME2

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The description of ship waves is a common topic in textbooks on hydrodynamics, for example [James Lighthill. Waves in Fluids. Cambridge University Press, 1978]

The first mathematical treatment of ship wakes was given by William Thomson (Lord Kelvin). The result is mentioned in a remarkable lecture of his in Edinburgh in 1887. A transcript can be found here: https://books.google.co.uk/books?id=Q...

If you're looking for an explanation that is less mathematical and more visual, MinutePhysics has also done a video on this topic: Why Do Boats Make This Shape?

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Background music: The Inner Sound by Jesse GallagherThe animations were made in manim community.

Source code for the animations is available at https://github.com/mvermeeren/SoME2-W...

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00:00 Intro
00:57 Speed depends on wavelength
02:49 Formula for a sine wave
04:43 Group velocity
08:18 A Duck
09:49 Why a V-shape?
12:43 Conclusions