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Related Concept Videos

Shock Waves01:16

Shock Waves

While deriving the Doppler formula for the observed frequency of a sound wave, it is assumed that the speed of sound in the medium is greater than the source's speed through it. When this condition is breached, a shock wave occurs.
When the source's speed approaches the speed of sound, constructive interference between successive wavefronts emitted by the source occurs immediately behind it. Initially, scientists believed that this constructive interference would result in such high pressures...
Design Example: Creating a Hydraulic Model of a Dam Spillway01:21

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Scaled hydraulic models of dam spillways provide a practical way to replicate and study the intricate flow dynamics of these structures. Often built to a 1:15 ratio, these models allow for observing critical water behavior, such as velocity distribution, flow patterns, and energy dissipation.
Standing Waves01:17

Standing 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...
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Propagation of Waves01:07

Propagation of Waves

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Sound Waves: Interference00:53

Sound Waves: Interference

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Related Experiment Video

Updated: May 13, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Model for shock wave chaos.

Aslan R Kasimov1, Luiz M Faria, Rodolfo R Rosales

  • 1Division of Computer, Electrical, and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia. aslan.kasimov@kaust.edu.sa

Physical Review Letters
|March 26, 2013
PubMed
Summary
This summary is machine-generated.

We developed a new model equation to predict chaotic shock waves, mimicking detonations. This first-of-its-kind scalar partial differential equation captures essential physics like instability and chaos onset in reactive mixtures.

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Area of Science:

  • Fluid Dynamics
  • Nonlinear Dynamics
  • Chemical Physics

Background:

  • Detonations in chemically reacting mixtures exhibit complex phenomena, including chaotic shock waves.
  • Understanding the underlying physics of these shock waves is crucial for predicting their behavior.

Purpose of the Study:

  • To propose a novel mathematical model for predicting chaotic shock waves.
  • To investigate the essential physics governing detonations using a simplified equation.

Main Methods:

  • Development of a scalar first-order partial differential equation.
  • Incorporation of a nonlocal forcing term mimicking chemical energy release.
  • Analysis of the interplay between nonlinearity and the forcing term.

Main Results:

  • The model equation successfully predicts chaotic shock waves.
  • It reproduces key detonation properties: steady traveling waves, instability, and chaos onset.
  • Demonstrates chaos arising from the nonlinear inviscid Burgers equation and a novel nonlocal forcing term.

Conclusions:

  • This model is the first to describe chaos in shock waves using a scalar first-order PDE.
  • The equation captures essential physics of detonations in gaseous reactive mixtures.
  • The interplay between nonlinearity and the nonlocal forcing term is key to generating chaos.