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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...

Steady, Laminar Flow Between Parallel Plates

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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.

Bernoulli's Equation for Flow Normal to a Streamline

Bernoulli's Equation for Flow Normal to a Streamline

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...

Bernoulli's Equation for Flow Along a Streamline

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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:

Steady, Laminar Flow in Circular Tubes

Steady, Laminar Flow in Circular Tubes

Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is purely axial,...

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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 Flow
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Related Experiment Video

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

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Towards minimal perturbations in transitional plane Couette flow.

Yohann Duguet¹, Luca Brandt, B Robin J Larsson

¹Linné Flow Centre, KTH Mekanik, Osquars Backe 18, SE-10044 Stockholm, Sweden.

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

|September 28, 2010

Summary

Researchers identified the least energetic initial disturbances that trigger turbulence in parallel shear flows. This minimal perturbation approach, applied to plane Couette flow, reveals insights into transition dynamics and energy thresholds.

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Area of Science:

Fluid Dynamics
Turbulence Transition

Background:

Parallel shear flows require perturbations of significant amplitude to transition to turbulence.
Understanding minimal energy disturbances is crucial for predicting transition onset.

Purpose of the Study:

To develop and apply a numerical method for identifying the least energetic initial disturbances leading to turbulence.
To investigate these minimal perturbations in the context of plane Couette flow.

Main Methods:

An optimization approach was used to find minimal perturbations as a linear combination of optimal modes.
The study focused on plane Couette flow at a Reynolds number (Re) of 400.

Main Results:

The minimal perturbation's energy threshold was found to be only 2% lower than that of symmetric oblique waves.
The transition scenario involved a prolonged approach to a symmetric steady state.
Modal analysis revealed how adding oblique modes can optimize the transition mechanism.

Conclusions:

The study provides a method for finding minimal energy disturbances in shear flows.
Results offer insights into the dynamics of turbulence transition and energy scaling.
Evidence suggests an O(Re(-2)) scaling for energy thresholds in both oblique wave and streamwise vortex scenarios.