Math Department (Thesis/2008-09)

Jet Flow and Karman Vortex Street

Under the direction of: Jue Wang

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Stuart vortices are a family of solutions to the 2D inviscid, incompressible Euler equations given by the streamfunction

$\Psi = \ln(\cosh y + \sqrt{1-\epsilon^2} \cos x), \quad 0 < \epsilon < 1$

When $\epsilon=1$, this is the hyperbolic tangent shear flow $U(y) = \tanh y$; when $\epsilon=0$, this is a row of point vortices.

We would like to investigate and find other such families of solutions. In particular, we'd like to find a family that connects the 2D jet flow $U(y)=\sec h^2 y$ to the Karman vortex street. Asymptotic expansions and perturbation analysis need to be performed.

Students need to know (or will have to learn) some fluid dynamics and techniques on numerical analysis.

This topic is suitable for a two-term thesis.

Math Department web pages Created: 25 Apr 2003 Last modified: 25 Apr 2008 15:20:45 Comments to: math@union.edu

Thesis Topics - K. Zimmermann Thesis Topics for 2008-2009 Thesis Topics -J. Wang