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Multistability for nonlinear acoustic-gravity waves in a rotating atmosphere.

N C Pati1, Paulo C Rech2, G C Layek1

  • 1Department of Mathematics, The University of Burdwan, Burdwan 713104, West Bengal, India.

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Summary

Earth's rotation causes complex behaviors in acoustic-gravity waves, leading to unpredictable dynamics and multistable states in a rotating atmosphere. This study explores these phenomena under specific atmospheric conditions.

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Area of Science:

  • Atmospheric physics
  • Fluid dynamics
  • Nonlinear dynamics

Background:

  • Nonlinear acoustic-gravity waves are crucial for understanding atmospheric phenomena.
  • The influence of rotation on wave dynamics is complex and requires detailed study.
  • Previous research has not fully explored multistability in rotating stratified atmospheres.

Purpose of the Study:

  • To investigate the multistable states of nonlinear acoustic-gravity waves in a rotating atmosphere.
  • To analyze bifurcation patterns and long-term dynamics under varying parameters.
  • To understand the role of Earth's rotation in wave behavior and stability.

Main Methods:

  • Exploration of low-frequency, short-wavelength nonlinear acoustic-gravity waves.
  • Analysis of a low-order nonlinear model system with varying air Prandtl number (σ).
  • Study of bifurcation patterns and long-term dynamics, considering rotation and slope parameters.

Main Results:

  • Earth's rotation induces both catastrophic and non-catastrophic transitions to unsteady motion.
  • Hysteresis-induced multistability observed, with coexisting multi-periodic and chaotic attractors.
  • Rotation parameter is key in generating heterogeneous attractors and unpredictable dynamics.

Conclusions:

  • The study highlights the significant impact of rotation on wave dynamics and stability.
  • Multistability and complex attractors arise due to rotational effects.
  • Findings are relevant for weakly stratified atmospheres with small slopes and wavelengths.