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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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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?

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    Summer posted on 2021/03/21
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