INSPIRATIONAL: The infamous Navier-Stokes equations

Hard Science — February 8, 2023
Solved: 500-year-old mystery about bubbles that puzzled Leonardo da Vinci

  • The solution involves the infamous Navier-Stokes equations, which are so difficult, there is a $1-million prize for solving them.
  • Small bubbles shoot straight up in water, but larger bubbles dance and zigzag.
  • This effect has intrigued scientists, beginning with Leonardo da Vinci.
  • A new study finds a solution that we can understand intuitively. 

Tom Hartsfield

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Pour water — or another tasty, bubbly liquid — into a clear glass. Carefully watch bubbles as they nucleate and then float up in the glass: You’ll notice that some of them rise differently than others. The tiniest ones shoot straight up, while bigger bubbles rhythmically bounce back and forth, slowing their trip. If you’ve ever wondered why this occurs, you’re not alone. No less a natural philosopher than Leonardo da Vinci was confounded by it.

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I guess we can say Leonardo da Vinci’s genius had its limits.  Took 500 years, modern math, advance computers, and some fudging to get close to an answer.  So we can forgive poor old da Vinci for flubbing it.

Found it fascinating that a bubble can become an oval.

Wonder what other mysteries are out there?  We know so little.


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