Why does orderly fluid flow become turbulent at higher speeds?

What is it about?

Explaining why fluid flow behaviour changes from orderly and regular at low speed, to turbulent at high speed, remains one of the great challenges of classical applied mathematics and physics. It is generally assumed that this transitional behaviour can be explained using the Navier-Stokes equations of fluid mechanics, which generally provide an excellent model for the behaviour of viscous fluid flow. But according to Navier-Stokes theory, viscous fluid flow in a pipe should always be stable to small disturbances; this would say that the flow would never become turbulent unless it were given a sufficiently large-amplitude disturbance initially. This paper examines the key assumption of Navier-Stokes theory - that the stress/strain-rate relation is linear - and replaces this with a more general nonlinear stress/strain-rate relation. Then, it is found that the flow does indeed become unstable at a critical speed (Reynolds number). Furthermore, it does so in a manner that is so complicated that perhaps it might, in fact, explain the precise nature of turbulence, and account for why the transition to turbulence takes place.

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Why is it important?

Understanding what turbulence is, and why fluid flows become turbulent at a critical speed, remains one of the big outstanding problems of classical physics. This paper provides one possible explanation for this phenomenon.