In this thesis, we study the effectiveness of compliant boundaries on the absolute instability (AI) of

confined 2D inviscid jets and wakes, and compare the results with the effects of rigid impermeable

boundaries. We consider symmetric and asymmetric configurations. We define AI in the long time

limit after an impulsive perturbation has been made to the flow. If we see growth in time as well

as in space, both upstream and downstream of the initial perturbation than this constitutes an AI.

The characteristics of the AI is quantified by the sign and magnitude of the imaginary part of the

temporal frequency ω.

We construct the governing boundary conditions for the compliant walls, and derive analytic dis-

persion relations D(α, ω) = 0 for the flow for both varicose and sinuous modes in the case of

symmetric flows. Furthermore, we initially consider the limit of zero shear layer thickness but go on

to consider more realistic flow configurations with finite thickness shear layers and smooth velocity

profiles. We plot contours of constant ωi into the complex α-plane through the dispersion relation

to locate modes of instability, which take the form of saddle points. Using Brigg’s Criterion, we de-

termine which saddle points contribute to the AI characteristics of the flow, known as pinch points.

We use numerical techniques to determine the precise values of α and ω associated with each pinch

point, and to explore how these values evolve as we modify flow or wall parameters.

It is shown that compliant walls modify existing shear-induced modes (SI), while also inducing new

wall-induced (WI) modes. These new modes are able to dominate the flow’s AI response. By

asymmetrically confining the flow, we find that the location of the closest bounding wall is usually

key in determining the flow’s instability characteristics. When the wall is placed in an optimum

position, WI modes are able to persist with even larger growth rates even when one of the two

walls is taken away. This behaviour is also seen when the walls are rigid, but the mechanism behind

this behaviour is not driven by wall compliance in this case. By making the walls non-identical in

construction, on the other hand, we observe a family of AI modes associated with each wall. When

one wall is taken to be rigid, the WI modes associated with the wall stabilize, while the modes

associated with the remaining compliant wall remain unstable, suggesting that only one compliant

wall is sufficient to generate strong WI modes.

Compliant boundaries can readily influence the flow’s stability characteristics, both in a symmetric

and asymmetric configuration. This has practical applications in engineering for use in cases which

could benefit from modifying the flow’s instability, such as improving the mixing between shear

layers, or as a means of reducing sound pollution.