https://doi.org/10.1140/epjb/e2004-00302-y
Stability of oscillatory flows past compliant surfaces
Department of Chemical Engineering Indian
Institute of Science Bangalore 560 012, India
Corresponding author: a kumaran@chemeng.iisc.ernet.in
Received:
19
December
2003
Revised:
17
March
2004
Published online:
30
September
2004
The stability of oscillatory flows over compliant surfaces is
studied analytically and numerically. The types of compliant surfaces
studied are the spring backed wall model, which permits tangential motion
of the surface, and the incompressible viscoelastic gel model. The stability
is determined using the Floquet analysis, where amplitude of perturbations
at time intervals separated by one time period is examined to determine
whether perturbations grow or decay. The oscillatory flows past
both the spring backed wall model and the viscoelastic gel model exhibit an
instability in the limit of zero Reynolds number, and the transition amplitude
of the oscillatory velocity
increases with the frequency of oscillations. The transition amplitude has
a minimum at zero wave number for the spring backed plate model, whereas the
minimum occurs at finite wavenumber for the viscoelastic gel model.
For the spring backed plate model,
it is shown that the instability due to steady mean flow and the purely
oscillatory instability reinforce each other, and the regions of instability
are mapped in the () plane, where Λ is the steady strain rate and
A is the oscillatory strain rate.
For the viscoelastic gel model, the instability is found to depend strongly
on the gel viscosity
, and the effect of oscillations on the
continuation of viscous modes at intermediate Reynolds number shows a complicated
dependence on the oscillation frequency.
PACS: 47.20.Ft – Instability of shear flows / 83.50.-v – Deformation and flow / 87.19.Tt – Rheology of body fluids
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2004