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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...

Magnetostatic Boundary Conditions

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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 purely axial,...

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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Navier–Stokes Equations

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For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...

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Updated: May 29, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

Instabilities in magnetized spherical Couette flow.

Christophe Gissinger¹, Hantao Ji, Jeremy Goodman

¹Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544, USA.

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

|September 21, 2011

Summary

Numerical simulations reveal that boundary-induced instabilities in rotating, electrically conducting fluids under magnetic fields resemble magnetorotational instability (MRI). This study compares these findings to experimental observations.

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Area of Science:

Magnetohydrodynamics
Fluid Dynamics
Plasma Physics

Background:

Investigating the behavior of electrically conducting fluids in spherical shells under magnetic fields is crucial for understanding astrophysical phenomena and fusion energy concepts.
Spherical Couette flow, with applied magnetic fields, presents complex dynamics influenced by rotation ratios and boundary conditions.

Purpose of the Study:

To conduct three-dimensional numerical simulations of electrically conducting fluid flow in a spherical shell with an applied magnetic field.
To explore various spherical Couette configurations by altering rotation ratios, magnetic field geometries, and inner sphere magnetic boundary conditions.
To analyze the similarities between observed boundary-induced instabilities and the magnetorotational instability (MRI).

Main Methods:

Employed three-dimensional numerical simulations to model fluid flow.
Investigated different spherical Couette configurations, systematically varying parameters such as rotation ratio, magnetic field geometry, and magnetic boundary conditions.
Compared simulation results with experimental data from the Maryland experiment.

Main Results:

Observed the generation of either a Stewartson layer or a Shercliff layer, along with a radial jet, contingent on rotation speeds and magnetic field strength.
Documented various nonaxisymmetric destabilizations of the flow.
Identified striking similarities between boundary-induced instabilities and the magnetorotational instability (MRI).

Conclusions:

The study demonstrates that instabilities in this configuration share significant resemblances with the magnetorotational instability (MRI).
Numerical findings provide a basis for comparison with experimental claims of MRI observation in similar setups, such as the Maryland experiment.