DSpace Collection:http://hdl.handle.net/2440/10872017-05-26T16:37:14Z2017-05-26T16:37:14ZLocalisation of Rayleigh-Bloch waves and damping of resonant loads on arrays of vertical cylindersBennetts, L.Peter, M.Montiel, F.http://hdl.handle.net/2440/1052172017-05-17T00:20:09Z2017-01-01T00:00:00ZTitle: Localisation of Rayleigh-Bloch waves and damping of resonant loads on arrays of vertical cylinders
Author: Bennetts, L.; Peter, M.; Montiel, F.
Abstract: Linear potential-flow theory is used to study loads imposed on finite line arrays of rigid, bottom-mounted, surface-piercing, vertical cylinders by surface water waves. Perturbations in the cylinder locations are shown to damp the resonant loads experienced by the unperturbed array. A relationship is established between the damping and the phenomenon of Anderson localisation. Specifically, the Rayleigh–Bloch waves responsible for the resonant loads are shown to attenuate along the array when perturbations are introduced, resulting in localisation when the attenuation rate is sufficiently large with respect to the array length. Further, an efficient solution method for line arrays is introduced that captures the Rayleigh–Bloch wave modes supported by unperturbed arrays from the scattering characteristics of an individual cylinder.2017-01-01T00:00:00ZThin-film flow in helically wound shallow channels of arbitrary cross-sectional shapeArnold, D.Stokes, Y.Green, J.http://hdl.handle.net/2440/1050812017-05-11T03:18:48Z2017-01-01T00:00:00ZTitle: Thin-film flow in helically wound shallow channels of arbitrary cross-sectional shape
Author: Arnold, D.; Stokes, Y.; Green, J.
Abstract: We consider the steady, gravity-driven flow of a thin film of viscous fluid down a helically wound shallow channel of arbitrary cross-sectional shape with arbitrary torsion and curvature. This extends our previous work [D. J. Arnold et al., “Thin-film flow in helically-wound rectangular channels of arbitrary torsion and curvature,” J. Fluid Mech. 764, 76–94 (2015)] on channels of rectangular cross section. The Navier-Stokes equations are expressed in a novel, non-orthogonal coordinate system fitted to the channel bottom. By assuming that the channel depth is small compared to its width and that the fluid depth in the vertical direction is also small compared to its typical horizontal extent, we are able to solve for the velocity components and pressure analytically. Using these results, a differential equation for the free surface shape is obtained, which must in general be solved numerically. Motivated by the aim of understanding flows in static spiral particle separators used in mineral processing, we investigate the effect of cross-sectional shape on the secondary flow in the channel cross section. We show that the competition between gravity and inertia in non-rectangular channels is qualitatively similar to that in rectangular channels, but that the cross-sectional shape has a strong influence on the breakup of the secondary flow into multiple clockwise-rotating cells. This may be triggered by small changes to the channel geometry, such as one or more bumps in the channel bottom that are small relative to the fluid depth. In contrast to the secondary flow which is quite sensitive to small bumps in the channel bottom, the free-surface profile is relatively insensitive to these. The sensitivity of the flow to the channel geometry may have important implications for the design of efficient spiral particle separators.2017-01-01T00:00:00ZFeedback control: two-sided Markov-modulated Brownian motion with instantaneous change of phase at boundariesLatouche, G.Nguyen, G.http://hdl.handle.net/2440/1049542017-05-08T23:39:07Z2016-01-01T00:00:00ZTitle: Feedback control: two-sided Markov-modulated Brownian motion with instantaneous change of phase at boundaries
Author: Latouche, G.; Nguyen, G.
Abstract: Abstract not available2016-01-01T00:00:00ZA numerical scheme for computing stable and unstable manifolds in nonautonomous flowsBalasuriya, S.http://hdl.handle.net/2440/1049192017-05-07T23:58:08Z2016-01-01T00:00:00ZTitle: A numerical scheme for computing stable and unstable manifolds in nonautonomous flows
Author: Balasuriya, S.
Abstract: There are many methods for computing stable and unstable manifolds in autonomous flows. When the flow is nonautonomous, however, difficulties arise since the hyperbolic trajectory to which these manifolds are anchored, and the local manifold emanation directions, are changing with time. This article utilizes recent results which approximate the time-variation of both these quantities to design a numerical algorithm which can obtain high resolution in global nonautonomous stable and unstable manifolds. In particular, good numerical approximation is possible locally near the anchor trajectory. Nonautonomous manifolds are computed for two examples: a Rossby wave situation which is highly chaotic, and a nonautonomus (time-aperiodic) Duffing oscillator model in which the manifold emanation directions are rapidly changing. The numerical method is validated and analyzed in these cases using finite-time Lyapunov exponent fields and exactly known nonautonomous manifolds.2016-01-01T00:00:00Z