Transition to turbulence in shear flows

5 problems

• What selects the angle and wavelength of transitional turbulent bands?

  Partially resolved

  In flows between parallel plates near the onset of turbulence, turbulent and smooth regions arrange themselves into tilted stripes with a definite angle and spacing. A theory that predicts these numbers from the flow equations is incomplete.

• When is the onset of shear-flow turbulence discontinuous?

  Open

  Adding forces such as buoyancy, pipe curvature or magnetic fields to a pipe or channel flow can turn the gradual onset of turbulence into an abrupt jump with hysteresis, like boiling. No rule predicts which flows behave which way.

• Direct measurement of directed-percolation exponents in pipe flow

  Partially resolved

  Near the onset of turbulence in a pipe, turbulent patches called puffs either decay or split, much like sick individuals recovering or infecting others. Pipe flow has now been placed in the class of this epidemic-type transition (directed percolation), but its critical exponents have not been measured directly in a pipe.

• Is uniform pipe turbulence permanent or an extremely long transient?

  Open

  Single turbulent puffs in a pipe always decay eventually, with lifetimes that grow faster than exponentially with flow speed. Whether fully turbulent flow at high speed is truly permanent, or also only a very long-lived transient, is unknown.

• Reynolds-number scaling of the turbulence-triggering threshold in pipes

  Partially resolved

  The faster the flow in a pipe, the smaller the disturbance needed to make it turbulent. How exactly this minimum disturbance shrinks with flow speed is not agreed.