Metric for attractor overlap

We present the first general metric for attractor overlap (MAO) facilitating an unsupervised comparison of flow data sets. The starting point is two or more attractors, i.e., ensembles of states representing different operating conditions. The proposed metric generalizes the standard Hilbert-space distance between two snapshots to snapshot ensembles of two attractors. A reduced-order analysis for big data and many attractors is enabled by coarse-graining the snapshots into representative clusters with corresponding centroids and population probabilities. For a large number of attractors, MAO is augmented by proximity maps for the snapshots, the centroids, and the attractors, giving scientifically interpretable visual access to the closeness of the states. The coherent structures belonging to the overlap and disjoint states between these attractors are distilled by few representative centroids. We employ MAO for two quite different actuated flow configurations: (1) a two-dimensional wake of the fluidic pinball with vortices in a narrow frequency range and (2) three-dimensional wall turbulence with broadband frequency spectrum manipulated by spanwise traveling transversal surface waves. MAO compares and classifies these actuated flows in agreement with physical intuition. For instance, the first feature coordinate of the attractor proximity map correlates with drag for the fluidic pinball and for the turbulent boundary layer. MAO has a large spectrum of potential applications ranging from a quantitative comparison between numerical simulations and experimental particle-image velocimetry data to the analysis of simulations representing a myriad of different operating conditions.Comment: 33 pages, 20 figure

Oscillatory and turbulent flows of liquid metals in differentially heated systems with horizontal and non-horizontal walls

Non isothermal flows of liquid metals induced by buoyancy are central to many advanced technological applications in materials science, often at the cutting-edge of modern engineering. They have indeed a significant impact on the production of many materials obtained via the solidification of a melt. The quality and mechanical or electrical properties of the resulting solids and crystals are adversely affected by thermogravitational convection as it can induce defects in their atomic or molecular structure (this is the case, e.g., of typical crystal-growth techniques such as the horizontal Bridgman (HB), the Floating zone (FZ) or the Czochralski (CZ) methods). The present chapter aims to present a focused review of landmark (past) and very recent contributions on the nature, structure and hierarchy of instabilities of this type of convection. In particular, starting from simple situations corresponding to steady and laminar flows and moving towards fully developed turbulence, we present the typical hydrodynamic and hydrothermal disturbances emerging in differentially heated liquid metals and clarify the relationship among their properties and general influential factors such as: the degree of confinement (aspect ratio), morphology (wall orientation in space) and spatial degrees of freedom (number of active dimensions) of the domain hosting the melt. Manifestations of these modes of convection (including, but not limited to, transverse waves travelling in the downstream or in the upstream direction, standing waves, modulated pulso-traveling disturbances, longitudinal waves and multi-wave patterns) are discussed in detail. More complex situations are placed in the context of existing theories on turbulence in fluids and treated using concepts, methods and tools typical of the chaotic systems analysis

Astrophysical turbulence modeling

The role of turbulence in various astrophysical settings is reviewed. Among the differences to laboratory and atmospheric turbulence we highlight the ubiquitous presence of magnetic fields that are generally produced and maintained by dynamo action. The extreme temperature and density contrasts and stratifications are emphasized in connection with turbulence in the interstellar medium and in stars with outer convection zones, respectively. In many cases turbulence plays an essential role in facilitating enhanced transport of mass, momentum, energy, and magnetic fields in terms of the corresponding coarse-grained mean fields. Those transport properties are usually strongly modified by anisotropies and often completely new effects emerge in such a description that have no correspondence in terms of the original (non coarse-grained) fields.Comment: 88 pages, 26 figures, published in Reports on Progress in Physic

Damping of quasi-2D internal wave attractors by rigid-wall friction

The reflection of internal gravity waves at sloping boundaries leads to focusing or defocusing. In closed domains, focusing typically dominates and projects the wave energy onto 'wave attractors'. For small-amplitude internal waves, the projection of energy onto higher wave numbers by geometric focusing can be balanced by viscous dissipation at high wave numbers. Contrary to what was previously suggested, viscous dissipation in interior shear layers may not be sufficient to explain the experiments on wave attractors in the classical quasi-2D trapezoidal laboratory set-ups. Applying standard boundary layer theory, we provide an elaborate description of the viscous dissipation in the interior shear layer, as well as at the rigid boundaries. Our analysis shows that even if the thin lateral Stokes boundary layers consist of no more than 1% of the wall-to-wall distance, dissipation by lateral walls dominates at intermediate wave numbers. Our extended model for the spectrum of 3D wave attractors in equilibrium closes the gap between observations and theory by Hazewinkel et al. (2008)

A review of turbulent skin-friction drag reduction by near-wall transverse forcing

The quest for reductions in fuel consumption and CO2 emissions in transport has been a powerful driving force for scientific research into methods that might underpin drag-reducing technologies for a variety of vehicular transport on roads, by rail, in the air, and on or in the water. In civil aviation, skin-friction drag accounts for around 50% of the total drag in cruise conditions, thus being a preferential target for research. With laminar conditions excluded, skin friction is intimately linked to the turbulence physics in the fluid layer closest to the skin. Hence, research into drag reduction has focused on methods to depress the turbulence activity near the surface. The most effective method of doing so is to exercise active control on the near-wall layer by subjecting the drag-producing ow in this layer to an unsteady and/or spatially varying cross-ow component, either by the action of transverse wall oscillations, by embedding rotating discs into the surface or by plasma-producing electrodes that accelerate the near-wall fluid in the transverse direction. In ideal conditions, drag-reduction margins of order of 50% can thereby be achieved. The present article provides a near-exhaustive review of research into the response of turbulent near-wall layers to the imposition of unsteady and wavy transverse motion. The review encompasses experiments, simulation, analysis and modelling, mainly in channel flows and boundary layers. It covers issues such as the drag-reduction margin in a variety of actuation scenarios and for a wide range of actuation parameters, the underlying physical phenomena that contribute to the interpretation of the origin of the drag reduction, the dependence of the drag reduction on the Reynolds number, passive control methods that are inspired by active control, and a forward look towards possible future research and practical realizations. The authors hope that this review, by far the most extensive of its kind for this subject, will be judged as a useful foundation for future research targeting friction-drag reduction

Numerical study of transonic buffet on supercritical airfoil with different boundary layer states

Accurate numerical simulations of flow over airfoils play an increasingly important role in the design of aircraft major components such as wings and turbo- machinery blades. These lifting devices often operate in demanding aerodynamic conditions for optimum performances, and may experience the presence of shock waves in operating conditions. Shocks may become unsteady under specific conditions, undergoing a large-scale, low-frequency periodic motion, which affects the entire flow-field. This unsteady phenomenon, named transonic buffet, is the subject of the present numerical investigation, with an oscillating shock over the suction side of the airfoil. In this study, a range of transonic Mach numbers and angles of incidence are considered, but the bulk of the analysis is carried out for flow conditions at free- stream Mach number M∞ = 0.7 and angle of incidence α = 7°, which show well established buffet. Large-eddy simulations (LES) with natural and forced transition carried out at chord Reynolds number Re = 3000000 clearly highlight the effects of the incoming boundary-layer state on the shock oscillations. While a laminar upstream boundary layer yields weak oscillations of the shock, a turbulent incoming boundary layer yields significant buffet. The LES database has been used to establish veracity (or not) of suggested buffet pathways, mainly based on the alleged existence of an acoustic feedback loop. This mechanism is actually found to consist of two separate patterns: coherent pressure disturbances convected from the shock to the trailing edge, and acoustic waves scattered at the trailing edge, feeding the shock motion. Additional exploration of the pressure side role in the unsteadiness reveals that is has but marginal effect on the phenomenon. Direct numerical simulations (DNS) at lower Reynolds number (Re = 300000) suggest a reversal in the previously observed trend. In this case, a laminar incoming boundary layer yields stronger buffet as compared to its turbulent counterpart, highlighting strong dependence of the buffet phenomenon on the Reynolds number when natural transition is considered. In order to passively control buffet, we consider devices whose design is similar to large-eddy break-up devices (LEBU), consisting of a thin circular-arc airfoil placed between shock and trailing edge, with the main goal of: i) breaking the eddies originating at the shock, responsible for the acoustic scattering at the trailing edge; ii) manipulating the acoustic field in the aft part of the airfoil. RANS simulations show potential for this kind of device for complete stabilization of buffet. On the other hand, DNS shows that the device is able to curtail the buffet, but not to eliminate it. Additional tests are needed in order to assess the effectiveness of the control device, whose practical impact might be very larg

Mechanisms of turbulent mixing in the Continental Shelf bottom boundary layer

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 1999The bottom boundary layer is an important dynamical region of shallow water flows. In this thesis, the problem of turbulent mixing in the coastal bottom boundary layer is investigated with a unique set of field measurements of velocity and sound speed that span a significant fraction of the boundary layer obtained over a six-week long period in the late summer of 1996 on the New England shelf. The energetics of the turbulent fluctuations are investigated by testing simplified budgets for turbulent kinetic energy and scalar variance. The turbulent kinetic energy budget is locally balanced while the scalar variance budget is not, probably due to turbulent diffusion. The direct effects of stratification are consistently significant only in the outer part of the boundary layer, where the flux Richardson number is approximately equal to a critical value of 0.2. Turbulence closure is investigated in terms of non-dimensional profiles of velocity and sound speed. Close to the bottom, the results are consistent with Monin-Obukhov similarity theory, while in the outer part of the boundary layer other scales including the height of the boundary layer are important for setting the turbulent length scale.My doctoral work was supported by the Office of Naval Research under grants N000149S10373 and N0001496109S3

Effects of the actuation on the boundary layer of an airfoil at Reynolds Number Re = 60000

Synthetic (zero net mass flux) jets are an active flow control technique to manipulate the flow field in wall-bounded and free-shear flows. The present paper focuses on the role of the periodic actuation mechanisms on the boundary layer of a SD7003 airfoil at Re=U∞C/ν=6×104. Here, Reynolds number is defined in terms of the free-stream velocity U∞ and the airfoil chord C. The actuation is applied near the leading edge of the airfoil and is periodic in time and in the spanwise direction. The actuation successfully eliminates the laminar bubble at AoA=4∘, however, it does not produce an increase in the airfoil aerodynamic efficiency. At angles of attack larger than the point of maximum lift, the actuation eliminates the massive flow separation, the flow being attached to the airfoil surface in a significant part of the airfoil chord. As a consequence, airfoil aerodynamic efficiency increases by a 124% with a reduction of the drag coefficient about 46%. This kind of technique seems to be promising at delaying flow separation and its associated losses when the angle of attack increases beyond the maximum lift for the baseline case.This work has been partially fnancially supported by the Ministerio de Economía y Competitividad, Secretaría de Estado de Investigación, Desarrollo e Innovación, Spain (Ref. TRA2017-88508-R) and by European Union’s Horizon 2020 research and innovation programme (INFRAEDI-02-2018, EXCELLERAT—The European Centre Of Excellence For Engineering Applications H2020.). We also acknowledge Red Española de Surpercomputación (RES) for awarding us access to the MareNostrum IV machine based in Barcelona, Spain (Ref. FI-2018-2-0015 and FI-2018-3-0021).This work is also funded in part by the Coturb program of the European Research Council.Peer ReviewedPostprint (author's final draft

The near-wall region of highly turbulent Taylor-Couette flow

Direct numerical simulations of the Taylor-Couette (TC) problem, the flow between two coaxial and independently rotating cylinders, have been performed. The study focuses on TC flow with mild curvature (small gap) with a radius ratio of $\eta=r_i/r_o=0.909$, an aspect ratio of $\Gamma=L/d=2\pi/3$, and a stationary outer cylinder. Three inner cylinder Reynolds of $1\cdot10^5$, $2\cdot10^5$ and $3\cdot 10^5$ were simulated, corresponding to frictional Reynolds numbers between $Re_\tau\approx 1400$ and $Re_\tau \approx 4000$. An additional case with a large gap, $\eta=0.5$ and driving of $Re=2\cdot10^5$ was also performed. Small-gap TC was found to be dominated by spatially-fixed large-scale structures, known as Taylor rolls (TRs). TRs are attached to the boundary layer, and are active, i.e. they transport angular velocity through Reynolds stresses. An additional simulation with inner cylinder Reynolds number of $Re=1\cdot10^5$ and fixed outer cylinder with an externally imposed axial flow of comparable strength as the wind of the TRs was also conducted. The axial flow was found to convect the TRs without any weakening effect. For small-gap TC, evidence for the existence of logarithmic velocity fluctuations, and of an overlap layer, in which the velocity fluctuations collapse in outer units, was found. Profiles consistent with a logarithmic dependence were also found for the angular velocity in large-gap TC, albeit in a very reduced range of scales. Finally, the behaviour of both small- and large-gap TC was compared to other canonical flows. Small-gap TC has similar behaviour in the near-wall region to other canonical flows, while large-gap TC displays very different behaviour