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Related Experiment Videos

Strongly nonlinear long gravity waves in uniform shear flows.

Wooyoung Choi1

  • 1Department of Naval Architecture & Marine Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2003
PubMed
Summary

This study models finite-amplitude surface gravity waves in shear flows. Shear flows alter solitary wave properties, creating eddies or peaked profiles depending on propagation direction.

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Area of Science:

  • Fluid dynamics
  • Oceanography
  • Wave theory

Background:

  • Surface gravity waves are crucial in oceanographic phenomena.
  • Understanding wave behavior in shear flows is complex due to vorticity.
  • Previous models often limited by wave amplitude assumptions.

Purpose of the Study:

  • To develop an asymptotic model for finite-amplitude surface gravity waves in uniform shear flows.
  • To analyze the impact of shear flows on solitary wave characteristics.
  • To investigate wave amplitude effects on solitary wave profiles and stability.

Main Methods:

  • Asymptotic analysis based on a small wavelength-to-depth ratio.
  • Model applicable to arbitrary wave amplitudes.
  • Comparison with numerical solutions and observational data.

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Main Results:

  • The model accurately captures nonlinear solitary wave features in shear flows.
  • Upstream-propagating solitary waves are wider and can form bottom eddies.
  • Downstream-propagating solitary waves are narrower, more peaked, and may exhibit cusps or round profiles.

Conclusions:

  • Uniform shear flows significantly modify solitary wave dynamics compared to zero vorticity cases.
  • The model provides insights into wave-vortex interactions and nonlinear wave phenomena.
  • Despite model limitations, results align qualitatively with existing observations and numerical findings.