Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Couette Flow01:22

Couette Flow

1.3K
Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...
1.3K
Bernoulli's Equation for Flow Normal to a Streamline01:16

Bernoulli's Equation for Flow Normal to a Streamline

1.4K
Bernoulli's equation for flow normal to a streamline explains how pressure varies across curved streamlines due to the outward centrifugal forces induced by the fluid's curvature. The pressure is higher on the inner side of the curve, near the center of curvature, and decreases outward to balance these centrifugal forces.
The pressure difference depends on the fluid's velocity and radius of curvature. The pressure variation is minimal in flows with nearly straight streamlines. However, the...
1.4K
Bernoulli's Equation for Flow Along a Streamline01:30

Bernoulli's Equation for Flow Along a Streamline

1.7K
Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
1.7K
Plane Potential Flows01:23

Plane Potential Flows

1.1K
Plane potential flows simplify fluid motion by assuming the fluid to be irrotational and incompressible. These characteristics allow these flows to be described by a velocity potential function, ϕ, representing the flow speed in a given direction, and a stream function, ψ, that visualizes the flow path, both governed by Laplace's equation. These parameters help in estimating flow patterns, velocity distributions, and pressure fields around various hydraulic structures.
Uniform...
1.1K
Eulerian and Lagrangian Flow Descriptions01:22

Eulerian and Lagrangian Flow Descriptions

2.2K
Fluid flow analysis is critical in many scientific and engineering disciplines, and two principal approaches are used to describe this flow: the Eulerian and Lagrangian methods. These methods offer different perspectives on monitoring and analyzing the motion of fluids, each with distinct advantages depending on the scenario.
The Eulerian method focuses on fixed points in space where fluid properties, such as velocity, pressure, and temperature, are observed as the fluid moves between these...
2.2K
Laminar and Turbulent Flow01:07

Laminar and Turbulent Flow

12.0K
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...
12.0K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Spontaneous atopic dermatitis due to immune dysregulation in mice lacking Adamts2 and 14.

Matrix biology : journal of the International Society for Matrix Biology·2018
Same author

An optimization approach for analysing nonlinear stability with transition to turbulence in fluids as an exemplar.

Reports on progress in physics. Physical Society (Great Britain)·2014
Same author

Genesis of streamwise-localized solutions from globally periodic traveling waves in pipe flow.

Physical review letters·2014
Same author

Balancing a cylinder on a thin vertical layer of viscous fluid.

Physical review. E, Statistical, nonlinear, and soft matter physics·2013
Same author

Experimental and theoretical progress in pipe flow transition.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2008
Same author

Variational principle for the Navier-Stokes equations.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics·2002

Related Experiment Video

Updated: Apr 12, 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

12.0K

Localization in a spanwise-extended model of plane Couette flow.

M Chantry1, R R Kerswell1

  • 1School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 15, 2015
PubMed
Summary

Localized, time-periodic solutions in plane Couette flow were discovered. These solutions transition smoothly from domain-filling to spanwise-localized states, challenging traditional instability theories for fluid localization.

More Related Videos

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

9.2K
Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
13:02

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

Published on: February 27, 2016

13.2K

Related Experiment Videos

Last Updated: Apr 12, 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

12.0K
The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

9.2K
Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
13:02

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

Published on: February 27, 2016

13.2K

Area of Science:

  • Fluid Dynamics
  • Nonlinear Dynamics
  • Computational Physics

Background:

  • Plane Couette flow is a fundamental fluid dynamics model.
  • Understanding flow localization is crucial for predicting complex fluid behavior.
  • Previous studies focused on modulational instabilities for localization.

Purpose of the Study:

  • To investigate spanwise localization phenomena in plane Couette flow.
  • To explore the nature of localized states beyond traditional instabilities.
  • To analyze the transition from global to localized flow structures.

Main Methods:

  • A reduced nine-partial-differential-equation model of plane Couette flow was employed.
  • Analysis focused on restricted degrees of freedom in streamwise and cross-stream directions.
  • Numerical investigation of steady states and bifurcations in Reynolds number was performed.

Main Results:

  • No steady Eckhaus instabilities led to localized states.
  • Spatially localized, time-periodic solutions were identified via saddle node bifurcations.
  • These solutions exhibited smooth transitions from global to spanwise-localized states with increasing domain width.

Conclusions:

  • Localized, time-periodic solutions are a key feature of plane Couette flow.
  • Flow localization can occur without preceding modulational instabilities.
  • The smooth localization behavior suggests a different mechanism for pattern formation in wide domains.