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• If you look at the wake behind a duck, or a kayak, or a ship, you might notice two unusual

• things: first, the wake isn't simple (like the perfectly straight shock wake of a supersonic

• projectile is) - it's a fascinating, feathery, ripple-y pattern.

• And second, that feathery pattern looks the same - same angle, same repeating pattern

• of ripples along the edge, same reverse arcs in the middle - it looks more or less the

• same regardless of whether it's made by a duck, a kayak or a ship, even though they're

• all moving at different speeds and the waves are very different sizes.

• The reason water wakes always have this particular shape and pattern is because of the surprising

• physics of water waves.

• While there's a single speed of light waves, and a single speed of sound waves, there's

• no single speed of water waves.

• In water, longer waves travel faster, while shorter waves travel slower.

• This phenomenon where different wavelength waves travel at different speeds is known

• as dispersion, and it makes water waves both interesting and complicated.

• Like a boat wake.

• To explain the shape of a boat wake, we'll start by looking at water waves of just a

• single wavelength (and speed).

• A boat traveling across this simpler water creates a series of circular waves - if the

• water waves are faster than the boat, the waves encircle it, but you don't get a wake.

• If the waves are slower than the boat, the boat outruns them and the circles all add

• together to create a V-shaped wake.

• And if the waves are even slower, the boat will outrun them even more and they'll add

• together to a narrower V shape.

• Slower waves make narrower wakes.

• Faster waves make wider wakes.

• But we need to remember that water waves are waves, that is, they repeat themselves.

• So every circular wave is really the first of a series of circular waves.

• This means that instead of creating just one v-shaped wake, a moving boat creates a train

• of v-shaped wakes that are each exactly one wavelength apart.

• The reason a real boat doesn't make straight v-shaped wakes is that a real boat makes waves

• of many different wavelengths.

• And because of dispersion, different wavelengths travel at different speeds: the longer ones

• travel faster and shorter ones travel slower.

• Faster waves create wider wakes, and because faster waves also have longer wavelengths,

• that means that wider wakes are further apart.

• Similarly, slower waves create narrower wakes, and because slower waves also have shorter

• wavelengths, narrower wakes are closer together.

• When you add together narrow, closely spaced wakes, with wider, more widely spaced wakes,

• with even wider, even more widely separated wakes, and so on, voilá!

• The shape of a boat wake!

• Look at the beautiful repeating feathery ripples out on the edge, and the wider repeating arcs

• inside the wake itself.

• If you replace these sharp lines with smoother waves at the appropriate angles and spacings,

• you get an even more convincing boat wake.

• And we can do the same again in 3D to get a really realistic-looking boat wake.

• So in summary: wakes have the shape they do because water waves travel at different speeds.

• Slower water waves create narrow, closely spaced V-shaped wakes, and faster water waves

• create wider V-shaped wakes that are further apart.

• When you add all these different v-shaped patterns together, at the correct angles and

• spacings determined by water's dispersion relation, you end up with the unique shape

• of a water wake.

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• Ok, there are some caveats to the science in this video, and you can find out about

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If you look at the wake behind a duck, or a kayak, or a ship, you might notice two unusual

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# Why Do Boats Make THIS Pattern?

• 3 1
Summer posted on 2021/03/21
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