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Related Concept Videos

Couette Flow01:22

Couette Flow

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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...
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Steady, Laminar Flow in Circular Tubes01:23

Steady, Laminar Flow in Circular Tubes

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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...
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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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Steady, Laminar Flow Between Parallel Plates01:17

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.
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Laminar and Turbulent Flow01:07

Laminar and Turbulent Flow

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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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Bernoulli's Equation for Flow Along a Streamline01:30

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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:
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Updated: Aug 7, 2025

Measurements of Local Instantaneous Convective Heat Transfer in a Pipe - Single and Two-phase Flow
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Taylor-Couette flow for astrophysical purposes.

H Ji1,2, J Goodman1

  • 1Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|March 12, 2023
PubMed
Summary

Astrophysical Taylor-Couette flow, when hydrodynamically stable, shows no turbulence from radial shear. Magnetohydrodynamic instabilities like the standard magnetorotational instability (SMRI) are key to understanding astrophysical discs.

Keywords:
MHD flowTaylor–Couette flowmagnetorotational instability

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Area of Science:

  • Fluid Dynamics
  • Astrophysics
  • Magnetohydrodynamics (MHD)

Background:

  • Taylor-Couette flow with differential rotation (inner cylinder faster) is linearly stable against inviscid centrifugal instability.
  • Quasi-Keplerian flows at high shear Reynolds numbers appear nonlinearly stable, with turbulence linked to axial boundaries, not radial shear.

Purpose of the Study:

  • To review experimental and theoretical research on astrophysically motivated Taylor-Couette flow.
  • To investigate the origins of accretion-disc turbulence and the role of magnetohydrodynamics.
  • To discuss the challenges and successes in experimentally demonstrating the standard magnetorotational instability (SMRI).

Main Methods:

  • Review of existing experimental and theoretical research.
  • Analysis of direct numerical simulations of Taylor-Couette flow.
  • Discussion of magnetohydrodynamic (MHD) Taylor-Couette experiments.

Main Results:

  • Hydrodynamic Taylor-Couette flows are nonlinearly stable, indicating accretion-disc turbulence is not solely from radial shear.
  • Theoretical predictions of linear MHD instabilities, such as SMRI, in astrophysical discs.
  • Experimental challenges due to low magnetic Prandtl numbers in liquid metals, requiring high Reynolds numbers and controlled axial boundaries.

Conclusions:

  • Accretion-disc turbulence likely involves magnetohydrodynamic effects, not just hydrodynamic shear.
  • Recent experiments have successfully demonstrated SMRI using conducting axial boundaries.
  • Further research is needed to address outstanding questions and explore near-future prospects in astrophysics.