Oscillatory sensitivity patterns for global modes in wakes

Abstract

AbstractGlobally unstable wakes with co-flow at intermediate Reynolds numbers are studied, to quantify important spatial regions for the development and control of the global instability. One region of high structural sensitivity is found close to the inlet for all wakes, in agreement with previous findings for cylinder wakes. A second, elongated region of high structural sensitivity is seen downstream of the first one for unconfined wakes at $\mathit{Re}= 400$. When base-flow modifications are considered, a spatially oscillating sensitivity pattern is found inside the downstream high-structural-sensitivity region. This implies that the same change in the base flow can either destabilize or stabilize the flow, depending on the exact position where it is applied. It is shown that the sensitivity pattern remains unchanged for different choices of streamwise boundary conditions and numerical resolution. The actual base-flow is modified in selected configurations, and the linear global modes recomputed. It is confirmed that the linear global eigenvalues move according to the predicted sensitivity pattern for small-amplitude base-flow modifications, for which the theory applies. We also look at the implications of a small control cylinder for the flow. Only the upstream high-sensitivity region proves to be robust in terms of control, but one should be careful not to disturb the flow in the downstream high-sensitivity region, in order to achieve control. The findings can have direct implications for the numerical resolution requirements for wakes at higher Reynolds numbers. Furthermore, they provide one more possible explanation for why confined wakes have a more narrow frequency spectrum than unconfined wakes.