Recent studies of transition to turbulence in linearly stable shear flows have been dominated by finding, and characterising, so-called exact coherent structures which exist as either equilibrium or travelling wave solutions of the governing Navier-Stokes equations. These structures have been shown to act as either edge states between laminar and turbulent flow or become associated with attractors for turbulent flows, making the quest to understand these structures equally as mathematically interesting as it is industrially relevant. In this thesis, vortex-wave interaction theory, an asymptotic approach based on the assumption of large Reynolds number, is used as a means of finding such structures in plane Couette flow. A new, iterative, numerical method will be developed to solve the governing interaction equations that will allow us to circumvent many of the difficulties in calculating such structures (in particular at high Reynolds numbers) and perform analyses into the state-space of solutions, as well as explore their stability properties. A number of previously found exact coherent structures will be shown to be vortex-wave interaction states, including the so-called upper branch sinuous mode and the class of solutions called mirror-symmetric modes. A number of receptivity type problems will also be considered. Namely, the use of periodic blowing/suction on the channel walls and the introduction of variations in the wall shape. The effect of these two techniques on the skin friction drag and the wave amplitude will be discussed in the context of whether they are beneficial in terms of laminar flow control. Further, it will be shown that the use of periodic blowing/suction leads to a new class of synchronous mirror-symmetric modes and variations in the wall shape lead to a new class of inhomogeneous vortex-wave interaction states.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:724125 |
| Date | January 2015 |
| Creators | Maestri, Joseph |
| Contributors | Hall, Philip |
| Publisher | Imperial College London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/10044/1/51109 |
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