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Updated: Jun 29, 2025

Preparation of Free-Surface Hyperbolic Water Vortices
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Atmospheric undular bores.

A Constantin1, R S Johnson2

  • 1Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.

Mathematische Annalen
|March 26, 2024
PubMed
Summary
This summary is machine-generated.

Nonlinear atmospheric waves can form undular bores, which are waves with damped oscillations behind a front. This wave generation requires a heat source jump, aligning with observational data.

Keywords:
34C1535C0786A10

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Area of Science:

  • Atmospheric science
  • Fluid dynamics
  • Wave propagation

Background:

  • Nonlinear wave phenomena in the atmosphere are complex and not fully understood.
  • Previous models have not fully captured the dynamics of specific wave structures like undular bores.

Purpose of the Study:

  • To investigate the existence and characteristics of undular bores as traveling-wave solutions within a new atmospheric wave propagation model.
  • To identify the necessary conditions for the generation of these specific wave profiles.

Main Methods:

  • Utilized a recently-derived mathematical model for nonlinear wave propagation in the atmosphere.
  • Analyzed the model to identify traveling-wave solutions representing undular bores.

Main Results:

  • The model admits undular bores as valid traveling-wave solutions.
  • These solutions describe waves with damped oscillations following a leading front.
  • A jump in the heat source across the wave's leading front is identified as a requirement for generation.

Conclusions:

  • The derived model successfully predicts undular bores, validating its applicability to atmospheric wave dynamics.
  • The identified heat source jump mechanism provides a plausible explanation for observed undular bore generation.