• control
• fluid instabilities
• Lagrange problem
• optimization
• sensitivity
• turbine wake
• vortex

In this thesis the sensitivity of flow instabilities in swirling wakes is investigated. In particular, the present work aims to understand how the instability of the hub-vortex of the wake of a wind turbine is affected by a modification of the near-wake conditions. A sensitivity model is formulated and first applied to the case of the laminar Batchelor vortex and then to the turbulent hub-vortex of a wind turbine wake.
In particular, an adjoint based method is proposed to study how a mean-flow modification at a given section in the near-wake affects the stability of the overall wake. The sensitivity of the flow is obtained by means of a lagragian analysis. Leveraging on boundary layer assumptions, an alternative lagrangian formulation, based on a set of quasi-cylindrical flow equations, is then presented.
A main result obtained are the sensitivity maps which prescribe the shape and the magnitude of the optimal mean-flow disturbances to be applied in the near wake so as to damp or enhance the hub-vortex instability. The sensitivity maps can be interpreted as the first step towards the design of a control strategy in the near-wake.