Abstract
Results are reported on direct numerical simulations of transition
from
two-dimensional to three-dimensional states due to secondary instability
in
the wake of a
circular cylinder. These calculations quantify the nonlinear response of
the system to three-dimensional perturbations near threshold for the two
separate
linear instabilities
of the wake: mode A and mode B. The objectives are to classify the nonlinear
form
of the bifurcation to mode A and mode B and to identify the conditions
under which
the wake evolves to periodic, quasi-periodic, or chaotic states with
respect to changes
in spanwise dimension and Reynolds number. The onset of mode A is shown
to occur
through a subcritical bifurcation that causes a
reduction in the primary oscillation
frequency of the wake at saturation. In contrast, the onset of mode B occurs
through
a supercritical bifurcation with no frequency shift
near threshold. Simulations of the
three-dimensional wake for fixed Reynolds number and increasing spanwise
dimension show that large systems evolve to a state of spatiotemporal chaos,
and suggest that three-dimensionality in the wake leads to irregular states
and fast transition to
turbulence at Reynolds numbers just beyond the onset of the secondary instability.
A
key feature of these ‘turbulent’ states is the
competition between self-excited, three-dimensional instability modes
(global modes) in the mode A wavenumber band. These
instability modes produce irregular spatiotemporal patterns and large-scale
‘spot-like’ disturbances in the wake during the breakdown of
the
regular mode A pattern. Simulations at higher Reynolds number show
that long-wavelength interactions modulate
fluctuating forces and cause variations in phase along the span of the
cylinder that
reduce the fluctuating amplitude of lift and drag. Results of both two-dimensional
and three-dimensional simulations are presented for a range of Reynolds
number
from about 10 up to 1000.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
303 articles.
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