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Minimal nonlinear dynamical system for the interaction between vorticity waves and shear flows.

Erik Gengel1, Eyal Heifetz1

  • 1Department of Geophysics, Porter School of the Environment and Earth Sciences, Tel Aviv University, Tel Aviv 69978, Israel.

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Summary

This study enhances a minimal nonlinear dynamical system by adding wave-mean-flow interactions. The research reveals oscillatory Hamiltonian dynamics and wave behaviors in shear instability.

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Area of Science:

  • Fluid dynamics
  • Nonlinear dynamics
  • Plasma physics

Background:

  • Builds upon prior work on linearized two-dimensional shear instability.
  • Previous models described wave interactions via action at a distance.

Purpose of the Study:

  • To incorporate mutual interactions between vorticity waves and the mean flow.
  • To investigate the resulting oscillatory Hamiltonian dynamics.
  • To analyze phase slipping and libration phenomena.

Main Methods:

  • Extension of a minimal nonlinear dynamical system.
  • Analysis of wave-mean-flow feedback mechanisms.
  • Mathematical modeling of Hamiltonian dynamics.

Main Results:

  • Introduction of mutual wave-mean-flow interaction leads to oscillatory dynamics.
  • Observed phenomena include phase slipping and finite-size wave amplitude oscillations.
  • Unstable normal modes evolve into librating states around an antiphased neutral configuration.

Conclusions:

  • The enhanced model exhibits complex oscillatory behavior not present in simpler models.
  • Wave-mean-flow dynamics are characterized by mutual hindrance and libration.
  • The findings offer insights into phase oscillator models.