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Some similarity solutions for three-dimensional boundary layers
1Department of Mathematics, Imperial College London, London SW7 2AZ, UK.
Proceedings. Mathematical, Physical, and Engineering Sciences
|October 16, 2019
Summary
Researchers investigated three-dimensional boundary layer similarity solutions for Navier-Stokes equations. Two distinct solutions were found, revealing non-unique behaviors similar to Falkner-Skan flows.
Area of Science:
- Fluid Dynamics
- Boundary Layer Theory
- Navier-Stokes Equations
Background:
- Investigates similarity solutions for three-dimensional boundary layers.
- Outer flow defined by U = (-xz, -yz, z^2), an exact Navier-Stokes solution.
- Focuses on boundary layer development along a wall at y=0.
Purpose of the Study:
- To determine if similarity reduction to ordinary differential equations (ODEs) is possible for this 3D boundary layer.
- To find and analyze distinct solutions and their stability.
- To generalize findings for outer flows with varying powers of z.
Main Methods:
- Similarity reduction of the three-dimensional boundary layer equations to a system of ODEs.
- Numerical path-continuation to find one of the distinct solutions.
- Stability analysis of the identified solutions.
Main Results:
- Demonstrated the possibility of similarity reduction to ODEs.
- Identified two distinct three-dimensional boundary layer solutions.
- Found similar results when generalizing for outer flows scaling with different powers of z.
Conclusions:
- The non-uniqueness of solutions is analogous to the Falkner-Skan problem in a 3D context.
- The behavior is linked to the presence of a transverse wall-jet.
- This study contributes to understanding complex fluid flow phenomena.
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