Emergence of spatio-temporal dynamics from exact coherent solutions in pipe flow

Turbulent-laminar patterns are ubiquitous near transition in wall-bounded shear flows. Despite recent progress in describing their dynamics in analogy to non-equilibrium phase transitions, there is no theory explaining their emergence. Dynamical-system approaches suggest that invariant solutions to the Navier–Stokes equations, such as traveling waves and relative periodic orbits in pipe flow, act as building blocks of the disordered dynamics. While recent studies have shown how transient chaos arises from such solutions, the ensuing dynamics lacks the strong fluctuations in size, shape and speed of the turbulent spots observed in experiments. We here show that chaotic spots with distinct dynamical and kinematic properties merge in phase space and give rise to the enhanced spatio-temporal patterns observed in pipe flow. This paves the way for a dynamical-system foundation to the phenomenology of turbulent-laminar patterns in wall-bounded extended shear flows.Peer ReviewedPostprint (published version

NONLINEAR DYNAMICS OF MODE COMPETITION IN ANNULAR FLOWS

The understanding of the transition to chaotic behavior and turbulence in natural flows has been and continues to be a great scientific challenge. Due to the complexity of this general problem, there has been a need to seek more fundamental laboratory flows from which the important physics can be extracted. The swirling flow between two concentric cylinders, known as Taylor–Couette flow, has been used as canonical example for centrifugal instability and transition to turbulence following a progression of flow instabilities. The aim of the thesis has been to provide a deeper understanding of several experimental observations of spatio-temporally complex flows for which no theoretical picture was available. In order to accomplish this goal, accurate spectral computations of the full Navier–Stokes equations have been combined with equivariant bifurcation and normal form theories. The coupling of these tools not only aids in understanding the nature of the observed flows, but furnishes the setting to compare systems with distinct physical instability mechanisms and geometry. Different configurations of the classical Taylor–Couette apparatus have been considere

Emergence of spatio-temporal dynamics from exact coherent solutions in pipe flow

Turbulent-laminar patterns are ubiquitous near transition in wall-bounded shear flows. Despite recent progress in describing their dynamics in analogy to non-equilibrium phase transitions, there is no theory explaining their emergence. Dynamical-system approaches suggest that invariant solutions to the Navier–Stokes equations, such as traveling waves and relative periodic orbits in pipe flow, act as building blocks of the disordered dynamics. While recent studies have shown how transient chaos arises from such solutions, the ensuing dynamics lacks the strong fluctuations in size, shape and speed of the turbulent spots observed in experiments. We here show that chaotic spots with distinct dynamical and kinematic properties merge in phase space and give rise to the enhanced spatio-temporal patterns observed in pipe flow. This paves the way for a dynamical-system foundation to the phenomenology of turbulent-laminar patterns in wall-bounded extended shear flows.Peer Reviewe

Conductive and convective heat transfer in fluid flows between differentially heated and rotating cylinders

The flow of fluid confined between a heated rotating cylinder and a cooled stationary cylinder is a canonical experiment for the study of heat transfer in engineering. The theoretical treatment of this system is greatly simplified if the cylinders are assumed to be of infinite length or periodic in the axial direction. In these cases heat transfer in the laminar regime occurs only through conduction as in a solid. We here investigate numerically heat transfer and the onset of turbulence in such flows by using both periodic and no-slip boundary conditions in the axial direction. The influence of the geometric parameters is comprehensively studied by varying the radius ratio (0.1 <= eta <= 0.99) and the length-to-gap aspect ratio (5 <= Gamma <= 80). Similarly, a wide range of Prandtl, Rayleigh, and Reynolds numbers is explored (0.01 <= sigma <= 100, Ra <= 30,000, and Re <= 1000, respectively). We obtain a simple criterion, Ra which determines whether the infinite-cylinder assumption can be employed. The coefficient a is well approximated by a cubic fit over the whole n-range. Noteworthy the criterion is independent of the Prandtl number and appears robust with respect to Reynolds number even beyond the laminar regime. (C) 2015 Elsevier Ltd. All rights reserved

Streamwise-localized solutions at the onset of turbulence in pipe flow

Although the equations governing fluid flow are well known, there are no analytical expressions that describe the complexity of turbulent motion. A recent proposition is that in analogy to low dimensional chaotic systems, turbulence is organized around unstable solutions of the governing equations which provide the building blocks of the disordered dynamics. We report the discovery of periodic solutions which just like intermittent turbulence are spatially localized and show that turbulent transients arise from one such solution branch. 2013 American Physical Society

Energy use in the minerals industries of Great Britain

SIGLEAvailable from British Library Document Supply Centre-DSC:3747.5438(70) / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Vector and parallelisation of ODE BVP codes

Paper at VAPP III Conf. Liverpool (GB) 1987SIGLEAvailable from British Library Document Supply Centre- DSC:6184.6725(MU-NAR--145) / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Instability mechanisms and transition scenarios of spiral turbulence in Taylor-Couette flow

Alternating laminar and turbulent helical bands appearing in shear flows between counterrotating cylinders are accurately computed and the near-wall instability phenomena responsible for their generation identified for the first time. The computations show that this intermittent regime can only exist within large domains and that its spiral coherence is not dictated by endwall boundary conditions. A supercritical transition route, consisting of a progressive helical alignment of localised turbulent spots, is carefully studied. Subcritical routes disconnected from secondary laminar flows have also been identified

Shear instabilities in Taylor-Couette flow

Subcritical instabilities in small gap Taylor-Couette (TCF) problem are studied numerically when both cylinders rotate in opposite directions. The computations are carried out for a radius ratio A first exploration is focused on the study of spiral flows originated from subcritical Hopf bifurcations of the basic circular Couette solution. The second exploration addresses the transition from laminar flow to the usually termed as spiral turbulence regime characterized by alternating laminar and turbulent spiral bands which coexist even in regions of the parameter space where the circular Couette flow is linearly stable