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Area of Science:

  • Fluid Dynamics
  • Polymer Physics
  • Nonlinear Dynamics

Background:

  • Elasto-inertial turbulence (EIT) is a recently identified chaotic flow state in polymer solutions.
  • Its relationship to Newtonian turbulence and inertialess elastic turbulence is unclear.
  • Previous research identified an elasto-inertial linear instability at high Weissenberg numbers.

Purpose of the Study:

  • To investigate the origins of elasto-inertial turbulence.
  • To establish a dynamical connection between EIT and previously identified elasto-inertial linear instabilities.
  • To explore the role of coherent structures in EIT.

Main Methods:

  • Isolation and tracking of exact coherent structures (nonlinear elasto-inertial traveling waves) in viscoelastic parallel flows.
  • Analysis of these structures from high Weissenberg numbers down to the regime where EIT exists.
  • Comparison of traveling wave dynamics with observed EIT behavior.

Main Results:

  • The first exact coherent structures in viscoelastic parallel flows, nonlinear elasto-inertial traveling waves (TWs), were identified.
  • These TWs originate from the elasto-inertial linear instability.
  • TWs with a distinctive "arrowhead" polymer stretch structure were found to persist at lower Weissenberg numbers, characterizing EIT and acting as attractors.

Conclusions:

  • The origins of elasto-inertial turbulence are fundamentally different from Newtonian turbulence, stemming from an elastic instability.
  • Nonlinear traveling waves are crucial coherent structures linking the linear instability to the chaotic EIT state.
  • The dynamical systems framework, involving invariant solutions, applies to EIT, with elasticity being essential for these solutions.