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Extensional channel flow revisited: a dynamical systems perspective.

Francisco Marques1, Alvaro Meseguer1, Fernando Mellibovsky1

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Summary
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This study numerically explores self-similar channel flows under wall acceleration. Complex dynamics emerge at intermediate Reynolds numbers, offering insights into realistic fluid behavior.

Keywords:
bifurcationsfluid dynamicsself-similar solutionsspectral continuation methods

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Area of Science:

  • Fluid dynamics
  • Nonlinear dynamics
  • Computational physics

Background:

  • Previous research analyzed steady solutions for specific wall stretching-shrinking rates.
  • Recent studies have begun exploring the dynamical aspects of these flows.
  • A dynamical systems perspective is crucial for understanding flow instabilities.

Purpose of the Study:

  • To numerically investigate extensional self-similar flows in a channel with arbitrary wall stretching-shrinking rates.
  • To analyze the instabilities and bifurcations of the base state as the Reynolds number increases.
  • To characterize the complex dynamics in the transitional flow regime.

Main Methods:

  • Numerical exploration of extensional self-similar flows.
  • Time integrations and continuation of steady and periodic solutions.
  • Dynamical systems analysis of base state instabilities and bifurcations.

Main Results:

  • The base state becomes unstable at low Reynolds numbers.
  • A transitional region with complex dynamics is observed at intermediate Reynolds numbers, dependent on wall acceleration.
  • Codimension-two bifurcations govern the dynamics in the parameter space.

Conclusions:

  • Self-similar flows at high Reynolds numbers lack realistic behavior.
  • Flows in the transitional region provide valuable insights into realistic Navier-Stokes solutions.
  • Understanding bifurcations is key to controlling channel flow dynamics.