The Effect of Wall Compliance on the Stability of Jets and Wakes

The 1950s experiments of Kramer into modelling dolphin skin using compliant
coatings lead to a surge in research on the validity of said experiments,
as well as the general stability characteristics of such coatings. These stability
characteristics were consisted by bounding channel flows by two identical compliant
walls. This approach lead to a rich array of instabilities, since the wall
can now carry its own wave and can thus interact with the fluid instabilities.
In this talk, we discuss the effects of bounding a 2D jet/wake flow with two
identical compliant walls. Dispersion relations, which are 4th order polynomials
in the wave frequency ω, and transcendental in wave number α, are derived
for both varicose and sinuous flows, which we use to determine the temporal
and absolute instability characteristics of the flow for a range of flow and wall
parameters.
Solving the dispersion relations leads to 4 solutions, two related to the flow,
and 2 that depend on the walls. We find the addition of the walls leads to
additional instabilities unseen in the case when the flow is bounded by rigid
walls, this is true for both temporal and absolute instability. We also find that
we are able to increase and decrease the magnitude of the absolute instabilities,
as well as increase the range of parameter space where absolute instability exists.