Cooper, Alison Jane (1996) The effects of rotation and wall compliance on hydrodynamic stability. PhD thesis, University of Warwick.

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Abstract

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.

Item Type:	Thesis (PhD)
Subjects:	T Technology > TC Hydraulic engineering. Ocean engineering
Library of Congress Subject Headings (LCSH):	Hydrodynamics, Stability, Rotational motion, Boundary layer
Official Date:	January 1996
Dates:	Date Event January 1996 Submitted
Institution:	University of Warwick
Theses Department:	Department of Engineering
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Carpenter, P. W. (Peter William), 1942-
Sponsors:	Engineering and Physical Sciences Research Council
Format of File:	pdf
Extent:	xi, 219 leaves : charts
Language:	eng

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