Dwight Barkley
This
research concerns the fundamental issue of vortex shedding from
a bluff body |
Onset of vortex shedding |
Below the critical Reynolds number (Rec = 46) the flow past a circular cylinder is steady and reflection symmetric. (Shown to the left is vorticity and separating streamlines at Re=40) |
Above Rec the flow is time periodic. One observes the famous Benard-von-Kaman vortex street. (Shown to the left is a snapshot of the flow at Re=100) |
A large body of research has been devoted to understanding this curve. |
Linear Stability Analysis of Base Flows |
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One can approach this problem by computing eigenvalues of steady solutions of the Navier-Stokes equations. These steady solutions are commonly referred to as base flows.
(Shown to the right are two base flows: Re=40 top and Re=100 bottom. Both are steady solutions to the Naiver-Stokes equation. The top one is linearly stable while the bottom one is linearly unstable.) |
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The eigenvalues from linear stability analysis correctly give the wake frequency at onset, but rapidly diverge from St above onset.
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Mean flows |
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Rather than computing eigenvalue for the base flows, one can compute eigenvalue of mean flows - time-averaged solutions of the Navier-Stokes equations. (Shown to the right is the mean flow at Re=100.) |
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The eigenvalues from linear analysis of mean flows correctly give the wake frequency in the nonlinear regime. Moreover, the mean flows are marginally stable.
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Nonlinear Selection |
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