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Updated: May 22, 2026
08:01
The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Bilateral shear layer between two parallel Couette flows
Vagesh D Narasimhamurthy1, Simen Å Ellingsen, Helge I Andersson
1Fluids Engineering Division, Department of Energy and Process Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway.
Summary
An unusual shear layer between parallel Couette flows shows lateral width variation, not streamwise. An analytical solution, validated by Navier-Stokes simulations, provides a formula for shear zone width.
Area of Science:
- Fluid Dynamics
- Computational Fluid Dynamics
- Aerodynamics
Background:
- Classical free shear layers exhibit streamwise width variation.
- Couette flow involves fluid layers moving parallel to each other at different velocities.
- Understanding shear layer dynamics is crucial for various engineering applications.
Purpose of the Study:
- To investigate an unusual shear layer between two parallel Couette flows.
- To derive an analytical solution for this unique shear layer.
- To compare the analytical solution with numerical simulations of the Navier-Stokes equations.
Main Methods:
- Development of a simplified analytical model for the shear layer.
- Numerical solutions of the full Navier-Stokes equations for validation.
- Analysis of shear zone width variation in the wall-normal coordinate.
Main Results:
- The shear zone width varies laterally, not streamwise, unlike classical shear layers.
- The analytical solution accurately predicts the shear layer behavior, with deviations less than 1% from numerical results.
- An explicit formula for shear zone width as a function of wall-normal coordinate was derived.
- In the laminar regime, shear zone width is independent of wall velocities.
Conclusions:
- The study successfully models an unusual shear layer with lateral width variation.
- The analytical solution provides a reliable and efficient method for analyzing this flow phenomenon.
- Preliminary results indicate shear-layer instabilities can lead to unsteady mixing in cocurrent laminar-turbulent flows.
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