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Related Concept Videos

Elastic Collisions: Introduction01:00

Elastic Collisions: Introduction

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An elastic collision is one that conserves both internal kinetic energy and momentum. Internal kinetic energy is the sum of the kinetic energies of the objects in a system. Truly elastic collisions can only be achieved with subatomic particles, such as electrons striking nuclei. Macroscopic collisions can be very nearly, but not quite, elastic, as some kinetic energy is always converted into other forms of energy such as heat transfer due to friction and sound. An example of a nearly...
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Turbulent Flow01:24

Turbulent Flow

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Turbulent flow is characterized by unpredictable fluctuations in velocity and pressure, which result in a chaotic fluid movement distinct from the orderly patterns of laminar flow. While laminar flow is governed by smooth, parallel layers with minimal mixing, turbulent flow exhibits highly irregular, three-dimensional patterns. This behavior arises due to instabilities in the fluid's velocity profile, and amplifies as the flow velocity increases. Minor disturbances, known as turbulent...
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Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

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As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
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Laminar and Turbulent Flow01:07

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Fluid dynamics is the study of fluids in motion. Velocity vectors are often used to illustrate fluid motion in applications like meteorology. For example, wind—the fluid motion of air in the atmosphere—can be represented by vectors indicating the speed and direction of the wind at any given point on a map. Another method for representing fluid motion is a streamline. A streamline represents the path of a small volume of fluid as it flows. When the flow pattern changes with time, the...
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Elastic Strain Energy for Normal Stresses01:22

Elastic Strain Energy for Normal Stresses

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Strain energy quantifies the energy stored within a material due to deformation under loading conditions, a fundamental concept in materials science and engineering. The strain energy can be modeled when a material is subjected to axial loading with uniformly distributed stress. In this scenario, the stress experienced by the material is the internal force divided by the cross-sectional area, and the strain induced is directly proportional to this stress through the modulus of elasticity.
If...
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Elastic Collisions: Case Study01:15

Elastic Collisions: Case Study

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Elastic collision of a system demands conservation of both momentum and kinetic energy. To solve problems involving one-dimensional elastic collisions between two objects, the equations for conservation of momentum and conservation of internal kinetic energy can be used. For the two objects, the sum of momentum before the collision equals the total momentum after the collision. An elastic collision conserves internal kinetic energy, and so the sum of kinetic energies before the collision equals...
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Related Experiment Video

Updated: Jun 25, 2025

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
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Intermittency in the not-so-smooth elastic turbulence.

Rahul K Singh1, Prasad Perlekar2, Dhrubaditya Mitra3

  • 1Complex Fluids and Flows Unit, Okinawa Institute of Science and Technology Graduate University, Okinawa, Japan.

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|May 27, 2024
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Summary

Elastic turbulence, a low Reynolds number phenomenon, shares similarities with Newtonian turbulence. Direct simulations reveal power-law energy spectra and evidence of intermittency, challenging previous assumptions.

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Area of Science:

  • Fluid Dynamics
  • Polymer Physics
  • Non-Newtonian Flows

Background:

  • Elastic turbulence arises from elastic instabilities in viscoelastic fluids at low Reynolds numbers.
  • Classical turbulence is well-understood in Newtonian fluids but its relation to elastic turbulence is less clear.

Purpose of the Study:

  • To investigate the characteristics of elastic turbulence using direct numerical simulations.
  • To compare elastic turbulence with Newtonian turbulence.
  • To identify power-law spectra and evidence of intermittency in elastic turbulence.

Main Methods:

  • Direct numerical simulations of viscoelastic fluid flow.
  • Analysis of kinetic and polymeric energy spectra.
  • Scale-by-scale energy budget calculations.
  • Structure function analysis of velocity differences.
  • Calculation of multifractal spectra from energy dissipation rates.

Main Results:

  • Identified power-law spectra for kinetic energy (E(k) ~ k^-4) and polymeric energy (Ep(k) ~ k^-3/2), independent of Deborah number.
  • Demonstrated a balance between viscous and polymeric terms in the momentum equation.
  • Observed a non-trivial sub-leading contribution in velocity differences, indicating intermittency.
  • Structure functions and energy dissipation rates provided evidence of multifractality.

Conclusions:

  • Elastic turbulence exhibits more similarities to Newtonian turbulence than previously assumed.
  • The findings support an intermittent and multifractal nature of elastic turbulence.
  • Direct numerical simulations are effective in elucidating complex turbulent phenomena in viscoelastic flows.