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  • 1
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    Instability inside a rotating gas cylinder subject to axial periodic strain (2005)
    American Institute of Physics
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    Publication Date: 2005-11-01
    Print ISSN: 1070-6631
    Electronic ISSN: 1089-7666
    Topics: Physics
    Published by American Institute of Physics
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  • 2
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    Transition in pipe flow: the saddle structure on the boundary of turbulence (2008)
    Cambridge University Press
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    Publication Date: 2008-10-01
    Description: The laminar-turbulent boundary Σ is the set separating initial conditions which relaminarize uneventfully from those which become turbulent. Phase space trajectories on this hypersurface in cylindrical pipe flow appear to be chaotic and show recurring evidence of coherent structures. A general numerical technique is developed for recognizing approaches to these structures and then for identifying the exact coherent solutions themselves. Numerical evidence is presented which suggests that trajectories on Σ are organized around only a few travelling waves and their heteroclinic connections. If the flow is suitably constrained to a subspace with a discrete rotational symmetry, it is possible to find locally attracting travelling waves embedded within Σ. Four new types of travelling waves were found using this approach. © 2008 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 3
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    Lagrangian chaos in confined two-dimensional oscillatory convection (2014)
    Cambridge University Press
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    Publication Date: 2014-10-27
    Description: The chaotic advection of passive tracers in a two-dimensional confined convection flow is addressed numerically near the onset of the oscillatory regime. We investigate here a differentially heated cavity with aspect ratio 2 and Prandtl number 0.71 for Rayleigh numbers around the first Hopf bifurcation. A scattering approach reveals different zones depending on whether the statistics of return times exhibit exponential or algebraic decay. Melnikov functions are computed and predict the appearance of the main mixing regions via the break-up of the homoclinic and heteroclinic orbits. The non-hyperbolic regions are characterised by a larger number of Kolmogorov-Arnold-Moser (KAM) tori. Based on the numerical extraction of many unstable periodic orbits (UPOs) and their stable/unstable manifolds, we suggest a coarse-graining procedure to estimate numerically the spatial fraction of chaos inside the cavity as a function of the Rayleigh number. Mixing is almost complete before the first transition to quasi-periodicity takes place. The algebraic mixing rate is estimated for tracers released from a localised source near the hot wall. © © 2014 Cambridge University PressÂ.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 4
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    Edge states as mediators of bypass transition in boundary-layer flows (2016)
    Cambridge University Press
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    Publication Date: 2016-07-21
    Description: The concept of edge states is investigated in the asymptotic suction boundary layer in relation to the receptivity process to noisy perturbations and the nucleation of turbulent spots. Edge tracking is first performed numerically, without imposing any discrete symmetry, in a large computational domain allowing for full spatial localisation of the perturbation velocity. The edge state is a three-dimensional localised structure recurrently characterised by a single low-speed streak that experiences erratic bursts and planar shifts. This recurrent streaky structure is then compared with predecessors of individual spot nucleation events, triggered by non-localised initial noise. The present results suggest a nonlinear picture, rooted in dynamical systems theory, of the nucleation process of turbulent spots in boundary-layer flows, in which the localised edge state plays the role of state-space mediator. © 2016 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 5
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    Turbulence collapse in a suction boundary layer (2016)
    Cambridge University Press
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    Publication Date: 2016-04-14
    Description: Turbulence in the asymptotic suction boundary layer is investigated numerically at the verge of laminarisation using direct numerical simulation. Following an adiabatic protocol, the Reynolds number Re is decreased in small steps starting from a fully turbulent state until laminarisation is observed. Computations in a large numerical domain allow in principle for the possible coexistence of laminar and turbulent regions. However, contrary to other subcritical shear flows, no laminar-turbulent coexistence is observed, even near the onset of sustained turbulence. High-resolution computations suggest a critical Reynolds number Reg ∼ 270, below which turbulence collapses, based on observation times of O(105) inertial time units. During the laminarisation process, the turbulent flow fragments into a series of transient streamwise-elongated structures, whose interfaces do not display the characteristic obliqueness of classical laminar-turbulent patterns. The law of the wall, i.e. logarithmic scaling of the velocity profile, is retained down to Reg, suggesting a large-scale wall-normal transport absent in internal shear flows close to the onset. In order to test the effect of these large-scale structures on the near-wall region, an artificial volume force is added to damp spanwise and wall-normal fluctuations above y+ = 100, in viscous units. Once the largest eddies have been suppressed by the forcing, and thus turbulence is confined to the near-wall region, oblique laminar-turbulent interfaces do emerge as in other wall-bounded flows, however only transiently. These results suggest that oblique stripes at the onset are a prevalent feature of internal shear flows, but will not occur in canonical boundary layers, including the spatially growing ones. © 2016 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 6
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    Surfing the edge: using feedback control to find nonlinear solutions (2017)
    Cambridge University Press
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    Publication Date: 2017-10-13
    Description: Many transitional wall-bounded shear flows are characterised by the coexistence in state space of laminar and turbulent regimes. Probing the edge boundary between the two attractors has led in the last decade to the numerical discovery of new (unstable) solutions to the incompressible Navier-Stokes equations. However, the iterative bisection method used to compute edge states can become prohibitively costly for large systems. Here we suggest a simple feedback control strategy to stabilise edge states, hence accelerating their numerical identification by several orders of magnitude. The method is illustrated for several configurations of cylindrical pipe flow. Travelling waves solutions are identified as edge states, and can be isolated rapidly in only one short numerical run. A new branch of solutions is also identified. When the edge state is a periodic orbit or chaotic state, the feedback control does not converge precisely to solutions of the uncontrolled system, but nevertheless brings the dynamics very close to the original edge manifold in a single run. We discuss the opportunities offered by the speed and simplicity of this new method to probe the structure of both state space and parameter space. © 2017 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 7
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    Turbulent–laminar coexistence in wall flows with Coriolis, buoyancy or Lorentz forces (2012)
    Cambridge University Press
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    Publication Date: 2012-07-02
    Description: Direct numerical simulations of subcritical rotating, stratified and magneto-hydrodynamic wall-bounded flows are performed in large computational domains, focusing on parameters where laminar and turbulent flow can stably coexist. In most cases, a regime of large-scale oblique laminar-turbulent patterns is identified at the onset of transition, as in the case of pure shear flows. The current study indicates that this oblique regime can be shifted up to large values of the Reynolds number Re by increasing the damping by the Coriolis, buoyancy or Lorentz force. We show evidence for this phenomenon in three distinct flow cases: plane Couette flow with spanwise cyclonic rotation, plane magnetohydrodynamic channel flow with a spanwise or wall-normal magnetic field, and open channel flow under stable stratification. Near-wall turbulence structures inside the turbulent patterns are invariably found to scale in terms of viscous wall units as in the fully turbulent case, while the patterns themselves remain large-scale with a trend towards shorter wavelength for increasing Re. Two distinct regimes are identified: at low Reynolds numbers the patterns extend from one wall to the other, while at large Reynolds number they are confined to the near-wall regions and the patterns on both channel sides are uncorrelated, the core of the flow being highly turbulent without any dominant large-scale structure. © 2012 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 8
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    Slug genesis in cylindrical pipe flow (2010)
    Cambridge University Press
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    Publication Date: 2010-10-05
    Description: Transition to uniform turbulence in cylindrical pipe flow occurs experimentally via the spatial expansion of isolated coherent structures called slugs, triggered by localized finite-amplitude disturbances. We study this process numerically by examining the preferred route in phase space through which a critical disturbance initiates a slug. This entails first identifying the relative attractor - edge state - on the laminar-turbulent boundary in a long pipe and then studying the dynamics along its low-dimensional unstable manifold, leading to the turbulent state. Even though the fully turbulent state delocalizes at Re ≈ 2300, the edge state is found to be localized over the range Re = 2000-6000, and progressively reduces in both energy and spatial extent as Re is increased. A key process in the genesis of a slug is found to be vortex shedding via a Kelvin-Helmholtz mechanism from wall-attached shear layers quickly formed at the edge state's upstream boundary. Whether these shedded vortices travel on average faster or slower downstream than the developing turbulence determines whether a puff or a slug (respectively) is formed. This observation suggests that slugs are out-of-equilibrium puffs which therefore do not co-exist with stable puffs. © 2010 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 9
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    Localized edge states in the asymptotic suction boundary layer (2013)
    Cambridge University Press
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    Publication Date: 2013-02-07
    Description: The dynamics on the laminar-turbulent separatrix is investigated numerically for boundary-layer flows in the subcritical regime. Constant homogeneous suction is applied at the wall, resulting in a parallel asymptotic suction boundary layer (ASBL). When the numerical domain is sufficiently extended in the spanwise direction, the coherent structures found by edge tracking are invariably localized and their dynamics shows bursts that drive a remarkable regular or irregular spanwise dynamics. Depending on the parameters, the asymptotic dynamics on the edge can be either periodic in time or chaotic. A clear mechanism for the regeneration of streaks and streamwise vortices emerges in all cases and is investigated in detail. © 2013 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 10
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    Formation of turbulent patterns near the onset of transition in plane Couette flow (2010)
    Cambridge University Press
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    Publication Date: 2010-03-22
    Description: The formation of turbulent patterns in plane Couette flow is investigated near the onset of transition, using numerical simulation in a very large domain of size 800 h 2 h 356 h. Based on a maximum observation time of 20 000 inertial units, the threshold for the appearance of sustained turbulent motion is Rec = 324 1. For Rec 〈 Re 380, turbulent-banded patterns form, irrespective of whether the initial perturbation is a noise or localized disturbance. Measurements of the turbulent fraction versus Re show evidence for a discontinuous phase transition scenario where turbulent spots play the role of the nuclei. Using a smaller computational box, the angle selection of the turbulent bands in the early stages of their development is shown to be related to the amplitude of the initial perturbation. Copyright © Cambridge University Press 2010.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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