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Title: The effects of rotation and wall compliance on hydrodynamic stability
Author: Cooper, Alison Jane
ISNI:       0000 0001 3562 1278
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1996
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The effects of system rotation and passive wall compliance on hydrodynamic stability is investigated. Rotating channel flow is studied where a Coriolis force instability mechanism produces streamwise rolls at modest Reynolds numbers and rotation rates. The linear stability of mean flow states consisting of a combination of plane Poiseuille and Couette flows is considered using spectral Chebyshev collocation with a staggered grid. A Newton algorithm is implemented in three-dimensional parameter space to calculate minimum points of the neutral surfaces. Weakly nonlinear behaviour of the rolls is studied using a Ginzburg-Landau formulation and accurate numerical values for the equation coefficients indicate supercritical instability. Effects of external pressure gradient and three-dimensionality on boundary layer stability over compliant walls is examined. In these cases an inflexion point in the boundary layer profile promotes a powerful inviscid instability mechanism. Two-dimensional profiles, including a Falkner-Skan representation, are considered in inviscid and viscous analyses with plate-spring and viscoelastic compliant wall models. Walls which are rendered stable with respect to hydroelastic instabilities are shown to reduce maximum spatial growth rates by up to 60%. This work is extended to consider the three-dimensional boundary layer over a rotating disc where inviscid (Type 1) and viscous (Type 2) instabilities can coexist. A single layer viscoelastic wall model coupled to a sixth order system of fluid equations, which accounts for Coriolis and streamline curvature effects, is solved by a spectral Chebyshev tau technique. The Type 1 stationary instability is found to be significantly stabilised, whilst the effect on the Type 2 mode is complex but can be destabilising. For travelling-wave modes, across a band of positive frequencies, evidence of modal coalescence between the Type 1 and 2 instabilities leading to absolute instability is presented. This would constitute a major route to transition and appears to be caused by large values of viscous stress work at the wall/flow interface.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: TC Hydraulic engineering. Ocean engineering