Related Experiment Video
Updated: May 18, 2026
08:54
Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
Published on: February 13, 2018
Nonlinear shallow ocean-wave soliton interactions on flat beaches
Mark J Ablowitz1, Douglas E Baldwin
1Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526, USA.
Summary
Nonlinear ocean wave interactions, once thought rare, occur daily near low tide. These events, resembling X or Y shapes, are linked to soliton solutions and can influence tsunami wave behavior.
Area of Science:
- Fluid dynamics
- Oceanography
- Nonlinear physics
Background:
- Ocean waves exhibit complex behaviors, with most interactions being linear.
- Nonlinear wave interactions can generate waves significantly taller than the sum of individual wave heights.
Purpose of the Study:
- To investigate the frequency and characteristics of nonlinear ocean wave interactions.
- To determine if these nonlinear events are rare or common occurrences.
- To explore the relationship between observed wave interactions and theoretical models.
Main Methods:
- Field observations of ocean waves on two flat beaches approximately 2000 km apart.
- Analysis of wave interaction patterns, including shapes like X, Y, and multiple lines.
- Comparison of observed phenomena with analytic soliton solutions of nonlinear wave equations.
Main Results:
- Nonlinear wave interactions are not rare but occur daily, particularly near low tide.
- Observed interaction patterns closely resemble theoretical soliton solutions.
- The findings suggest a broader applicability of these nonlinear dynamics, potentially including large-scale phenomena like tsunami wave merging.
Conclusions:
- Nonlinear wave interactions are a common, predictable feature of shallow-water wave dynamics.
- The study validates theoretical models of nonlinear waves through empirical observation.
- Understanding these interactions is crucial for predicting wave behavior, from beaches to tsunamis.
Related Concept Videos
01:17Standing Waves
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...
01:10Wave Parameters
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...
01:07Propagation of Waves
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.
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
01:04Travelling Waves
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 water;...
Water waves, sound waves, and seismic waves are some examples of mechanical waves. For water waves, the wave propagation medium is water;...
01:07Interference and Superposition of Waves
When two waves of the same nature occur in the same region simultaneously, they result in interference. Interference of waves implies that the net effect of the waves is the sum of the individual waves' effects. However, it does not imply that the individual waves affect the propagation of other waves.
Interference occurs in mechanical waves, such as sound waves, waves on a string, and surface water waves. Mechanical waves correspond to the physical displacement of particles. Hence,...
Interference occurs in mechanical waves, such as sound waves, waves on a string, and surface water waves. Mechanical waves correspond to the physical displacement of particles. Hence,...
02:18Interference and Diffraction
Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.