The use of global modes to understand transition and perform flow control

Authors: Henningson, D.S.H., Åkervik, E.Å.
Document Type: Article
Pubstate: Published
Journal: Physics of Fluids
Volume: 20   031302
Year: 2008


The stability of non-parallel flows is considered using superposition of global modes. When perturbed by the worst case initial condition these flows often exhibit a large transient growth associated with the development of wavepackets. The global modes of the systems also provide a good starting point for the design of reduced order models used to control the growing disturbances. Three recent investigations are reviewed. The first example is the growth of a wavepacket on a falling liquid sheet. The optimal perturbation analysis shows that the worst case initial condition is a localized disturbance that creates a propagating wave packet that hits the downstream end, regenerating a wavepacket upstream through a global pressure pulse. Second, we consider two-dimensional disturbances in the Blasius boundary layer. It is found that a wavepacket is optimally excited by an initial condition consisting of localized backward leaning Orr-structures. Finally, the control of a globally unstable boundary-layer flow along a shallow cavity is considered. The disturbance propagation is associated with the development of a wavepacket along the cavity shear layer, unstable to the Kelvin-Helmholtz mechanism, followed by a global cycle related to the two unstable global modes. Direct numerical simulations of this flow are coupled to a measurement feedback controller, which senses the wall shear stress at the downstream lip of the cavity and provides the actuation at the upstream lip. A reduced order model for the control is obtained by a projection on the least stable global eigenmodes. The linear-quadratic-Gaussian controller is run in parallel to the Navier-Stokes equations time integration and it is shown to damp out the global oscillations.