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Propagation of Waves01:07

Propagation of Waves

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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.
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...
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Velocity and Acceleration of a Wave00:51

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A wave propagates through a medium with a constant speed, known as a wave velocity. It is different from the speed of the particles of the medium, which is not constant. In addition, the velocity of the medium is perpendicular to the velocity of the wave. The variable speed of the particles of the medium implies that there must be acceleration associated with it. 
The velocity of the particles can be obtained by taking the partial derivative of the position equation with respect to time....
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Equations of Wave Motion01:02

Equations of Wave Motion

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Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a period T. The wave on the string is sinusoidal and is translated in the positive x-direction as time progresses. Sine is a function of the angle θ, oscillating between +A and −A and repeating every 2π radians. To construct a wave model, the ratio of the angle θ and the position x is considered.
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Travelling Waves01:04

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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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Interference and Diffraction02:18

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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.
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Traveling Waves: Lossless Lines01:27

Traveling Waves: Lossless Lines

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The provided content explores the behavior of traveling waves on single-phase lossless transmission lines. It begins with a single-phase two-wire lossless transmission line of length Δx, characterized by a loop inductance LH/m and a line-to-line capacitance C F/m. These parameters result in a series inductance LΔx  and a shunt capacitance CΔx.
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Related Experiment Video

Updated: Sep 25, 2025

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
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Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

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Nonlinear wave evolution with data-driven breaking.

D Eeltink1,2, H Branger3, C Luneau3

  • 1Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, United States. eeltink@mit.edu.

Nature Communications
|April 29, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a blended machine learning framework to accurately predict ocean wave breaking, a key process in marine energy dissipation. The model combines physics-based simulations with recurrent neural networks for improved forecasting.

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Area of Science:

  • Fluid dynamics
  • Oceanography
  • Machine learning

Background:

  • Wave breaking is the primary mechanism for ocean wave energy dissipation and influences sea state properties.
  • Its turbulent nature makes direct numerical simulations computationally prohibitive for complex scenarios.
  • Accurate prediction of wave breaking is vital for understanding ocean-atmosphere interactions, pollution, and rogue waves.

Purpose of the Study:

  • To develop a computationally efficient and accurate method for predicting ocean wave breaking.
  • To overcome the limitations of traditional numerical simulations for turbulent wave breaking.
  • To enhance the understanding of wave evolution and its impact on marine environments.

Main Methods:

  • A blended machine learning framework combining a physics-based nonlinear evolution model with a recurrent neural network (RNN).
  • Utilized wave tank measurements for training data, avoiding computationally intensive simulations.
  • Employed a long short-term memory (LSTM) neural network for finite-domain corrections to the evolution model.

Main Results:

  • The blended framework accurately predicts wave breaking events and their effects on wave evolution.
  • Demonstrated excellent predictive performance even with external, previously unseen data.
  • Successfully integrated physics-based models with machine learning for complex fluid dynamics problems.

Conclusions:

  • The developed machine learning framework offers a powerful tool for predicting ocean wave breaking.
  • This approach significantly reduces computational demands compared to traditional methods.
  • The findings have implications for oceanography, marine engineering, and climate modeling.