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Nicolas Périnet1, Claudio Falcón1, Jalel Chergui2

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This study investigates subcritical bifurcations in shallow fluid layers, revealing how small surface waves transition to large, nonlinear ones. Hysteresis is linked to shear stress changes, confirmed by numerical and theoretical analysis.

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Area of Science:

  • Fluid dynamics
  • Nonlinear wave phenomena
  • Bifurcation theory

Background:

  • Parametrically amplified waves at fluid interfaces are crucial in various physical systems.
  • Understanding nonlinear wave behavior in shallow fluid layers presents unique challenges.
  • Subcritical bifurcations can lead to sudden, large amplitude changes in wave dynamics.

Purpose of the Study:

  • To numerically and theoretically study the subcritical bifurcation of parametrically amplified waves.
  • To investigate wave behavior at the interface of two immiscible fluids with a very shallow lower layer.
  • To understand the underlying mechanisms causing hysteresis in wave amplitude.

Main Methods:

  • Numerical simulations of fluid dynamics.
  • Theoretical analysis of wave propagation and stability.
  • Application of stress balance principles to explain observed phenomena.

Main Results:

  • Observed subcritical bifurcation where small amplitude waves transition to highly nonlinear waves with twice the amplitude.
  • Identified hysteresis in the wave response as a critical control parameter is surpassed.
  • Established a correlation between hysteresis and changes in shear stress.

Conclusions:

  • The study elucidates the mechanism of subcritical bifurcation in shallow fluid systems.
  • Shear stress variations are identified as the key factor driving hysteresis in parametrically amplified waves.
  • Numerical and theoretical findings are consistent, validating the proposed stress balance model.