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Time-delayed interactions on acoustically driven bubbly screens.

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Compressibility effects and time delays influence bubbly screen dynamics. Finite screens exhibit resonances limiting effective medium theory (EMT), while nonlinear analysis reveals optimal distances for subharmonic emission.

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Area of Science:

  • Acoustics
  • Fluid Dynamics
  • Wave Propagation

Background:

  • Bubbly screens are crucial in acoustics and fluid dynamics.
  • Understanding their dynamics under compressibility and time-delay effects is essential.
  • Existing models like effective medium theory (EMT) have limitations.

Purpose of the Study:

  • To investigate the influence of compressibility and time delays on acoustically excited bubbly screens.
  • To analyze the validity and limitations of effective medium theory (EMT) for bubbly screens.
  • To explore nonlinear dynamics and resonance phenomena in bubbly screen structures.

Main Methods:

  • Development of a theoretical model for bubbly screen dynamics.
  • Linear and nonlinear analysis of the model, including delay differential equations.
  • Numerical solutions for the nonlinear regime.
  • Comparison with effective medium theory (EMT).

Main Results:

  • The model recovers EMT results for infinite screens in the linear regime.
  • Boundary effects on finite screens introduce local resonances and periodic structures, limiting EMT applicability.
  • Local resonance is observed in liquid spacings for crystal structures, vanishing upon perturbation.
  • Nonlinear analysis reveals an optimal bubble distance for subharmonic emission in crystal structures.

Conclusions:

  • Compressibility and time delays significantly impact bubbly screen dynamics.
  • EMT is accurate for infinite screens at large wavelengths but limited for finite screens due to boundary effects.
  • Resonance phenomena are sensitive to the crystalline structure of the bubbly screen.
  • Nonlinear dynamics offer insights into phenomena like optimal distances for subharmonic emission.