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Irrotational flow is characterized by fluid motion where particles do not rotate around their axes, resulting in zero vorticity. For a flow to be irrotational, the curl of the velocity field must be zero. This imposes specific conditions on velocity gradients. For instance, to maintain zero rotation about the z-axis, the gradient condition:
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A wave is a disturbance that propagates from its source, repeating itself periodically, and is typically associated with simple harmonic motion. Mechanical waves are governed by Newton's laws and require a medium to travel. A medium is a substance in which a mechanical wave propagates, and the medium produces an elastic restoring force when it is deformed.
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Generation of nonlinear internal waves by flow over topography: Rotational effects.

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This study explores internal wave generation using the forced Ostrovsky equation, revealing how background currents and topography influence wave patterns. Findings detail steady and unsteady wave behaviors influenced by rotation and current speed.

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Area of Science:

  • Fluid dynamics
  • Oceanography
  • Nonlinear wave phenomena

Background:

  • Internal waves are crucial in oceanic mixing and transport.
  • Previous studies focused on wave generation without background rotation.
  • The forced Ostrovsky equation models wave dynamics in rotating fluids.

Purpose of the Study:

  • To investigate internal wave generation by a background current over topography with rotation.
  • To analyze the influence of rotation, topography, and current speed on wave characteristics.
  • To understand the transition between subcritical, transcritical, and supercritical flow regimes.

Main Methods:

  • Utilized the forced Ostrovsky equation for theoretical analysis.
  • Employed linearized response analysis to categorize waves.
  • Conducted numerical simulations to validate theoretical predictions.

Main Results:

  • Identified steady waves downstream and unsteady waves upstream under specific conditions (negative group velocity minimum).
  • Demonstrated that increased background current reduces steady wave numbers.
  • Highlighted the significant roles of topographic concavity, width, and rotation strength in wave generation.

Conclusions:

  • The study provides a comprehensive framework for understanding rotating internal wave generation.
  • Nonlinear effects lead to amplitude modulation and coherent wave packet formation.
  • Findings are robustly supported by numerical simulations, offering insights into geophysical fluid dynamics.