Elastic turbulence and polymer drag reduction

4 problems

• Are elasto-inertial and purely elastic turbulence the same state?

  Partially resolved

  Polymer solutions show chaotic flow both at moderate speeds, where inertia helps, and at vanishing speeds, from elasticity alone. Whether these are two forms of one state is unknown.

• Origin and universality of the maximum drag reduction asymptote

  Contested

  Polymers can cut pipe friction a great deal, but adding more stops helping beyond a limiting friction curve that is the same for all polymers. Why this limit exists and is universal is not understood.

• How does purely elastic turbulence arise in straight channels and pipes?

  Partially resolved

  Polymer solutions can become chaotic even when flowing too slowly for ordinary turbulence, because stretched molecules store and release elastic energy. In curved flows the cause is known, but in straight pipes and channels it is still debated.

• Is the velocity spectrum of elastic turbulence universal?

  Open

  The chaotic flow of polymer solutions has an energy spectrum that falls off steeply toward small eddies. Whether its slope is the same in all flows is unknown.