Thursday 26 Feb 2015Colloquium: Can frequencies be predicted from mean fields?

Prof Laurette Tuckermann - PMMH France

H103 15:00-16:00

The von Karman vortex street is one of the most striking visual images
in fluid dynamics. Immersed in a uniform flow of sufficient strength,
a circular cylinder periodically sheds propagating vortices of
alternating sign on either side of the "street". Although the von
Karman vortex street can be simulated numerically with great accuracy,
predicting its properties from general theoretical principles has
proved elusive. It has been shown that the vortex-shedding frequency
can be obtained by carrying out a linear stability analysis about the
temporal mean, but there is no understanding of why the correct answer
emerges from such an unorthodox procedure.

We have carried out a similar analysis of thermosolutal convection,
which is driven by opposing thermal and solutal gradients. In a
spatially periodic domain, branches of traveling waves and standing
waves are created simultaneously by a Hopf bifurcation. We find that
linearization about the mean fields of the traveling waves yields an
eigenvalue whose real part is almost zero and whose imaginary part
corresponds very closely to the nonlinear frequency, consistent with
the cylinder wake. In marked contrast, linearization about the mean
field of the standing waves yields neither zero growth nor the
nonlinear frequency. It is shown that this difference can be
attributed to the fact that the temporal power spectrum for the
traveling waves is peaked, while that of the standing waves is
broad. We give a general demonstration that the frequency of any
quasi-monochromatic oscillation can be predicted from its temporal
mean.

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