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Related Concept Videos

Travelling Waves01:04

Travelling Waves

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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.
Water waves, sound waves, and seismic waves are some examples of mechanical waves. For water waves, the wave propagation medium is...
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Wave Parameters01:10

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The simplest mechanical waves are associated with simple harmonic motion and repeat themselves for several cycles. These simple harmonic waves can be modeled using a combination of sine and cosine functions. Consider a simplified surface water wave that moves across the water's surface. Unlike complex ocean waves, in surface water waves, water moves vertically, oscillating up and down, whereas the disturbance of the wave moves horizontally through the medium. If a seagull is floating on the...
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Standing Waves01:17

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Sometimes waves do not seem to move; rather, they just vibrate in place. Unmoving waves can be seen on the surface of a glass of milk kept in a refrigerator, which is one example of standing waves. Vibrations from the refrigerator motor create waves on the milk that oscillate up and down but do not seem to move across the surface. These waves are formed or created by the superposition of two or more identical moving waves in opposite directions. The waves move through each other, with their...
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Standing Waves in a Cavity01:28

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A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
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Sound as Pressure Waves01:17

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Sound waves, which are longitudinal waves, can be modeled as the displacement amplitude varying as a function of the spatial and temporal coordinates. As a column of the medium is displaced, its successive columns are also displaced. As the successive displacements differ relatively, a pressure difference with the surrounding pressure is created. The gauge pressure varies across the medium.
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Propagation of Waves01:07

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When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second medium. In such a case, the interface of the two mediums can be considered as a boundary that is neither fixed nor free.
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Updated: May 4, 2026

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
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Transversally periodic solitary gravity-capillary waves.

Paul A Milewski1, Zhan Wang2

  • 1Department of Mathematical Sciences , University of Bath , Bath BA2 7AY, UK.

Proceedings. Mathematical, Physical, and Engineering Sciences
|January 9, 2014
PubMed
Summary

This study explores gravity-capillary solitary waves in fluids, revealing new wave types that bridge 2D and 3D cases. These waves exhibit unique behaviors depending on their transverse period and stability.

Keywords:
breathergravity–capillaryperiodic wavesolitary wave

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Area of Science:

  • Fluid dynamics
  • Wave phenomena
  • Nonlinear physics

Background:

  • Surface solitary water waves are known in 2D and 3D fluids under gravity and surface tension.
  • Existing research primarily focuses on fully 2D or 3D solitary waves.

Purpose of the Study:

  • To describe novel traveling waves bridging 2D and 3D solitary water waves.
  • To investigate the characteristics and stability of these transversally periodic waves.

Main Methods:

  • Numerical analysis within a Hamiltonian system for water waves.
  • Utilizing a cubic truncation of the Dirichlet-to-Neumann operator for approximation.
  • Investigating stability through time evolution of perturbed wave profiles.

Main Results:

  • Discovered transversally periodic gravity-capillary solitary waves of elevation or depression type.
  • Observed transitions to plane waves (below critical period) and solitary lumps (infinite period).
  • Validated the accuracy of the numerical approximation for 2D and 3D solitary waves.

Conclusions:

  • The study successfully identified and characterized a new class of solitary water waves.
  • The findings contribute to understanding the complex behavior of surface waves under combined gravity and surface tension.
  • The numerical methods employed proved effective for analyzing these complex wave phenomena.