We care about your data, and we'd like to use cookies to give you a smooth browsing experience. Please agree and read more about our privacy policy.
Quanta Homepage
  • Physics
  • Mathematics
  • Biology
  • Computer Science
  • Topics
  • Archive
The Trouble With Turbulence
Comment
Read Later
Share
Facebook
Twitter
Copied!
Copy link
Email
Pocket
Reddit
Ycombinator
Flipboard
    • Comment
      Comments
    • Read Later
    In Theory

    The Trouble With Turbulence

    By Michael Moyer

    January 28, 2019

    Turbulence is everywhere, yet it is one of the most difficult concepts for physicists to understand.
    Comment
    Read Later
    Art for "The Trouble With Turbulence"

    Qais Sarhan for Quanta Magazine

    Michael Moyer
    By Michael Moyer

    Deputy Editor


    January 28, 2019


    View PDF/Print Mode
    fluid dynamicsIn TheorymathematicsmultimediaNavier-Stokes equationspartial differential equationsphysicsturbulenceAll topics
    Watch and Learn Watch and Learn

    Introduction

    Fluids should be easy. They’re ordinary, classical things — water, air currents, maple syrup — described by physical laws first written down nearly two centuries ago. And yet when a tornado rips open the roof of the table-tennis factory, just try to predict where all the pingpong balls are going to land.

    This is hard because of turbulence, a problem that gives physicists and mathematicians more trouble than you might think. On the physical side, turbulence happens when a smooth fluid flow starts to split into smaller eddies and vortices. These swirls then break into smaller swirls, with those swirls begetting ever-smaller whorls, an unpredictable cascade that dissipates the energy from the original smooth stream. These whorls all affect one another, making it impossible to precisely predict what is going to happen to any particular particle in the fluid you’re measuring. On the large scale, energy dissipates gradually and with a semblance of order. On the small scale, chaos abounds.

    The mathematics of turbulence would at first appear to present a simpler case. The Navier-Stokes equations have been used to describe fluid flows since the early 19th century. They take into account properties of the fluid such as its density and viscosity, along with any forces acting on it. And for all practical purposes — and so long as we don’t ask the equations to predict the exact motions of all the eddies in a turbulent fluid — we know that they work. But “for all practical purposes” is not the same as a proof.

    Share this article
    Facebook
    Twitter
    Copied!
    Copy link
    Email
    Pocket
    Reddit
    Ycombinator
    Flipboard

    Newsletter

    Get Quanta Magazine delivered to your inbox

    Recent newsletters
    Physicists use the Navier-Stokes equations to describe fluid flows, taking into account viscosity, velocity, pressure and density. But because of turbulence in fluids, proving that the equations always make sense is one of the hardest problems in physics and mathematics.

    Video: Physicists use the Navier-Stokes equations to describe fluid flows, taking into account viscosity, velocity, pressure and density. But because of turbulence in fluids, proving that the equations always make sense is one of the hardest problems in physics and mathematics.

    Directed by Emily Driscoll and animated by Qais Sarhan for Quanta Magazine

    Introduction

    What is there to prove? For one thing, that the Navier-Stokes equations will always behave nicely. That is, given any initial state of the fluid, mathematicians want to be able to prove that the equations will never lead to a nonsensical result. You might imagine a scenario in which all those swirls and whorls conspire to concentrate all their energy at a particular point in the fluid, and in doing so accelerate the flow at that point to infinite velocity. That’s unlikely, but mathematically possible (so far as we know). The proof that such a scenario is impossible — or the opposite, a demonstration of how it might happen — is so coveted that it stands as one of the $1 million Millennium Prize Problems.

    This fourth episode from season two of Quanta’s In Theory video series covers the trouble with turbulence. It follows videos on universality, quantum gravity and emergence — like turbulence, never easy, but frequently fascinating.

    Michael Moyer
    By Michael Moyer

    Deputy Editor


    January 28, 2019


    View PDF/Print Mode
    fluid dynamicsIn TheorymathematicsmultimediaNavier-Stokes equationspartial differential equationsphysicsturbulenceAll topics
    Watch and Learn Watch and Learn
    Share this article
    Facebook
    Twitter
    Copied!
    Copy link
    Email
    Pocket
    Reddit
    Ycombinator
    Flipboard

    Newsletter

    Get Quanta Magazine delivered to your inbox

    Recent newsletters
    The Quanta Newsletter

    Get highlights of the most important news delivered to your email inbox

    Recent newsletters

    Comment on this article

    Quanta Magazine moderates comments to facilitate an informed, substantive, civil conversation. Abusive, profane, self-promotional, misleading, incoherent or off-topic comments will be rejected. Moderators are staffed during regular business hours (New York time) and can only accept comments written in English. 

    Next article

    A Child’s Puzzle Has Helped Unlock the Secrets of Magnetism
    Quanta Homepage
    Facebook
    Twitter
    Youtube
    Instagram

    • About Quanta
    • Archive
    • Contact Us
    • Terms & Conditions
    • Privacy Policy
    • Simons Foundation
    All Rights Reserved © 2023