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Title: Exact invariant solutions for grooved Couette and channel flows
Author: Vadarevu, Sabarish Bharadwaz
ISNI:       0000 0004 6500 693X
Awarding Body: University of Southampton
Current Institution: University of Southampton
Date of Award: 2017
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The dynamical systems approach to turbulence has gained a lot of traction since the turn of the century. A large set of exact invariant solutions for canonical wall-bounded flows such as Couette, channel, and pipe flows has been found by researchers. These solutions, and their connections, are thought to form a skeleton for trajectories of turbulent flow. However, this vision of turbulence has not been extended to rough-walled flows despite the practical signficance of such flows in engineering applications. This thesis describes continuation, by numerical homotopy, of known equilibria from smooth-walled plane shear flows to grooved plane shear flows using a domain transformation method, with the hope that this exploratory work would inform later efforts to extend such solutions to rough-walled flows. As a precursor to computing non-laminar equilibria, laminar solutions are computed for grooved channel flows for transverse, longitudinal, and oblique grooves. In addition to the numerical solutions, analytical solutions are also derived for asymptotically long groove-wavelengths, employing the Stokes-flow approximation for transverse and oblique grooves. Exact invariant solutions can indeed be continued from plane Couette flow (PCoF) with smooth walls to grooved PCoF with longitudinal grooves using a simple domain transformation method. However, smooth PCoF equilibria exist as continuous families of solutions that are identical up to a translational shift; the loss of spanwise homogeneity due to the grooves restricts such continuous families to discrete families due to symmetry-breaking. This phase-based restriction can also be expected to be reflected in turbulent statistics. Continuation of equilibria in grooves of different wavelengths shows a drag increasing tendency for grooves of the same wavelength as the vortex-streak structure, and a drag reducing tendency for grooves of significantly smaller wavelengths. This can relate the optimal spacing of riblets for maximal drag reduction to the spanwise spacing of the vortex-streak structures observed in the self-sustaining near-wall cycle.
Supervisor: Sharma, Atul Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available