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Couette Flow

Couette Flow

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...

Turbulent Flow

Turbulent Flow

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 spots,...

Plane Potential Flows

Plane Potential Flows

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Uniform Flow
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Steady, Laminar Flow Between Parallel Plates

Steady, Laminar Flow Between Parallel Plates

Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.

Laminar and Turbulent Flow

Laminar and Turbulent Flow

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Turbulent Flow: Problem Solving

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Related Experiment Video

Updated: Jun 2, 2026

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

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

Published on: February 27, 2016

From temporal to spatiotemporal dynamics in transitional plane Couette flow.

Jimmy Philip¹, Paul Manneville

¹Laboratoire d'Hydrodynamique, Ecole Polytechnique, 91128 Palaiseau, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 27, 2011

Summary

Turbulence in plane Couette flow transitions from temporal to spatiotemporal behavior as system size increases. Large systems exhibit oblique patterns, while smaller ones show chaotic transients before laminar flow.

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Spatial Temporal Analysis of Fieldwise Flow in Microvasculature

Spatial Temporal Analysis of Fieldwise Flow in Microvasculature

Published on: November 18, 2019

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Last Updated: Jun 2, 2026

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

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

Published on: February 27, 2016

Spatial Temporal Analysis of Fieldwise Flow in Microvasculature

Spatial Temporal Analysis of Fieldwise Flow in Microvasculature

Published on: November 18, 2019

Area of Science:

Fluid dynamics
Turbulence theory
Computational physics

Background:

Plane Couette flow (PCF) exhibits laminar-turbulent patterns at varying Reynolds numbers.
Previous studies often used small-aspect-ratio systems with periodic boundary conditions, unlike experimental large-aspect-ratio setups.

Purpose of the Study:

To investigate the transition from temporal to spatiotemporal behavior in PCF using direct numerical simulations.
To identify the critical system size influencing this transition and the nature of observed patterns.

Main Methods:

Fully resolved direct numerical simulations of Navier-Stokes equations at decreasing Reynolds numbers.
Analysis of flow behavior in systems of intermediate sizes to bridge temporal and spatiotemporal regimes.

Main Results:

A streamwise crossover size (Lx ~70-80h) was identified, distinguishing temporal and spatiotemporal transitions.
Above this size, transitions involve oblique patterns (turbulent→riddled→oblique pattern→laminar).
Below this size, transitions are temporal (chaotic flow→laminar flow via chaotic transients), skipping the oblique pattern stage.

Conclusions:

The transition to or from turbulence in PCF is fundamentally spatiotemporal for large enough systems.
Accurate modeling of experimental patterns requires accounting for streamwise correlations at scales around the crossover size.