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Jacques Magnaudet - One of the best experts on this subject based on the ideXlab platform.
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high Reynolds Number turbulence in a shear free boundary layer revisiting the hunt graham theory
Journal of Fluid Mechanics, 2003Co-Authors: Jacques MagnaudetAbstract:The capability of rapid distortion theory to predict the long-time evolution of shearless turbulence close to an impermeable surface has been seriously questioned in recent years. However, experiments and Large-eddy simulations performed at high Reynolds Number show that second-order turbulence statistics follow closely the predictions of the theory elaborated by Hunt & Graham. To clarify this issue, a theoretical analysis is carried out in order to determine the relative magnitude of the vortical corrections which were not taken into account in the original theory. By evaluating the various terms of the enstrophy balance in the near-surface region, it is shown that this relative magnitude is a decreasing function of the turbulent Reynolds Number, an argument reconciling most existing results. Hence the Hunt & Graham theory appears to be a leading-order approximation capable of describing short- and long-time evolutions of shear-free boundary layers in the limit of Large Reynolds Number. The expression for the pressure fluctuation corresponding to this approximation is then derived and approximate Reynolds stress budgets are obtained
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high Reynolds Number turbulence in a shear free boundary layer revisiting the hunt graham theory
Journal of Fluid Mechanics, 2003Co-Authors: Jacques MagnaudetAbstract:The capability of rapid distortion theory to predict the long-time evolution of shearless turbulence close to an impermeable surface has been seriously questioned in recent years. However, experiments and Large-eddy simulations performed at high Reynolds Number show that second-order turbulence statistics follow closely the predictions of the theory elaborated by Hunt & Graham (1978). To clarify this issue, a theoretical analysis is carried out in order to determine the relative magnitude of the vortical corrections which were not taken into account in the original theory. By evaluating the various terms of the enstrophy balance in the near-surface region, it is shown that this relative magnitude is a decreasing function of the turbulent Reynolds Number, an argument reconciling most existing results. Hence the Hunt & Graham theory appears to be a leading-order approximation capable of describing short- and long-time evolutions of shear-free boundary layers in the limit of Large Reynolds Number. The expression for the pressure fluctuation corresponding to this approximation is then derived and approximate Reynolds stress budgets are obtained. These budgets are used to predict and discuss the characteristics of the intercomponent energy transfer near a flat surface in both time-decaying and spatially decaying turbulence. In agreement with available results, predictions reveal that tangential velocity components transfer energy towards the normal component in the former case, while they generally receive energy from this component in the latter case.
Andrew G Walton - One of the best experts on this subject based on the ideXlab platform.
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self sustaining dual critical layer states in plane poiseuillecouette flow at Large Reynolds Number
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2019Co-Authors: Rishi Kumar, Andrew G WaltonAbstract:The nonlinear stability of plane PoiseuilleCouette flow subjected to three-dimensional disturbances is studied asymptotically at Large Reynolds Number R. By analysing the nature of the instability ...
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axisymmetric travelling waves in annular sliding couette flow at finite and asymptotically Large Reynolds Number
Journal of Fluid Mechanics, 2013Co-Authors: Kengo Deguchi, Andrew G WaltonAbstract:The relationship between numerical finite-amplitude equilibrium solutions of the full Navier–Stokes equations and nonlinear solutions arising from a high-Reynolds-Number asymptotic analysis is discussed for a Tollmien–Schlichting wave-type two-dimensional vortical flow structure. The specific flow chosen for this purpose is that which arises from the mutual axial sliding of co-axial cylinders for which nonlinear axisymmetric travelling-wave solutions have been discovered recently by Deguchi & Nagata (J. Fluid Mech., vol. 678, 2011, pp. 156–178). We continue this solution branch to a Reynolds Number and confirm that the behaviour of its so-called lower branch solutions, which typically produce a smaller modification to the laminar state than the other solution branches, quantitatively agrees with the axisymmetric asymptotic theory developed in this paper. We further find that this asymptotic structure breaks down when the disturbance wavelength is comparable with . The new structure which replaces it is investigated and the governing equations are derived and solved. The flow visualization of the resultant solutions reveals that they possess a streamwise localized structure, with the trend agreeing qualitatively with full Navier–Stokes solutions for relatively long-wavelength disturbances.
Hassan M Nagib - One of the best experts on this subject based on the ideXlab platform.
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Large Reynolds Number asymptotics of the streamwise normal stress in zero pressure gradient turbulent boundary layers
Journal of Fluid Mechanics, 2015Co-Authors: Peter A Monkewitz, Hassan M NagibAbstract:A more poetic long title could be 'A voyage from the shifting grounds of existing data on zero-pressure-gradient (abbreviated ZPG) turbulent boundary layers (abbreviated TBLs) to infinite Reynolds Number'. Aided by the requirement of consistency with the Reynolds-averaged momentum equation, the 'shifting grounds' are sufficiently consolidated to allow some firm conclusions on the asymptotic expansion of the streamwise normal stress (+), where the + indicates normalization with the friction velocity u(tau) squared. A detailed analysis of direct numerical simulation data very close to the wall reveals that its inner near-wall asymptotic expansion must be of the form f(0)(y(+)) - f(1)(y(+))/U-infinity(+) + O(U-infinity(+))(-2), where U-infinity(+) = U-infinity/u(tau), y(+) = yu(tau)/v and f(0), f(1) are O(1) functions fitted to data in this paper. This means, in particular, that the inner peak of (+) does not increase indefinitely as the logarithm of the Reynolds Number but reaches a finite limit. The outer expansion of (+), on the other hand, is constructed by fitting a Large Number of data from various sources. This exercise, aided by estimates of turbulence production and dissipation, reveals that the overlap region between inner and outer expansions of (+) is its plateau or second maximum, extending to y(break)(+) = O(U-infinity(+)), where the outer logarithmic decrease towards the boundary layer edge starts. The common part of the two expansions of (+), i.e. the height of the plateau or second maximum, is of the form A infinity - B-infinity/U-infinity(+) + . . . with A(infinity) and B infinity. constant. As a consequence, the logarithmic slope of the outer (+) cannot be independent of the Reynolds Number as suggested by 'attached eddy' models but must slowly decrease as (1/U-infinity(+)). A speculative explanation is proposed for the puzzling finding that the overlap region of (+) is centred near the lower edge of the mean velocity overlap, itself centred at y(+) = O(Re-delta*(1/2)) with Re-delta* the Reynolds Number based on free stream velocity and displacement thickness. Finally, similarities and differences between (+) in ZPG TBLs and in pipe flow are briefly discussed.
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correcting hot wire measurements of stream wise turbulence intensity in boundary layers
Physics of Fluids, 2010Co-Authors: Peter A Monkewitz, R D Duncan, Hassan M NagibAbstract:The current experimental activity aimed at resolving the scaling of stream-wise turbulence intensity profiles uu¯+(y+) with Reynolds Number in turbulent flat plate boundary layers has brought the Largely unresolved issue of correcting systematic errors in hot-wire measurements of uu¯+(y+) into focus. Here, a heuristic scheme is proposed to generate unique uu¯+(y+;Reδ∗) profiles from data obtained with single hot wires of widely different length, aspect ratio and construction over a Large Reynolds Number range of 4000≲Reδ∗≲50 000. A comparison with LDA data and other checks suggest that the present correction scheme produces uu¯+(y+;Reδ∗) profiles close to the (unknown) true profiles.
Joseph Klewicki - One of the best experts on this subject based on the ideXlab platform.
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prospectus towards the development of high fidelity models of wall turbulence at Large Reynolds Number
Philosophical Transactions of the Royal Society A, 2017Co-Authors: Joseph Klewicki, Gregory P Chini, John GibsonAbstract:Recent and on-going advances in mathematical methods and analysis techniques, coupled with the experimental and computational capacity to capture detailed flow structure at increasingly Large Reynolds Numbers, afford an unprecedented opportunity to develop realistic models of high Reynolds Number turbulent wall-flow dynamics. A distinctive attribute of this new generation of models is their grounding in the Navier-Stokes equations. By adhering to this challenging constraint, high-fidelity models ultimately can be developed that not only predict flow properties at high Reynolds Numbers, but that possess a mathematical structure that faithfully captures the underlying flow physics. These first-principles models are needed, for example, to reliably manipulate flow behaviours at extreme Reynolds Numbers. This theme issue of Philosophical Transactions of the Royal Society A provides a selection of contributions from the community of researchers who are working towards the development of such models. Broadly speaking, the research topics represented herein report on dynamical structure, mechanisms and transport; scale interactions and self-similarity; model reductions that restrict nonlinear interactions; and modern asymptotic theories. In this prospectus, the challenges associated with modelling turbulent wall-flows at Large Reynolds Numbers are briefly outlined, and the connections between the contributing papers are highlighted.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at Large Reynolds Number'.
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an invariant representation of mean inertia theoretical basis for a log law in turbulent boundary layers
Journal of Fluid Mechanics, 2017Co-Authors: Caleb Morrillwinter, Jimmy Philip, Joseph KlewickiAbstract:A refined scaling analysis of the two-dimensional mean momentum balance (MMB) for the zero-pressure-gradient turbulent boundary layer (TBL) is presented and experimentally investigated up to high friction Reynolds Numbers, . For canonical boundary layers, the mean inertia, which is a function of the wall-normal distance, appears instead of the constant mean pressure gradient force in the MMB for pipes and channels. The constancy of the pressure gradient has led to theoretical treatments for pipes/channels, that are more precise than for the TBL. Elements of these analyses include the logarithmic behaviour of the mean velocity, specification of the Reynolds shear stress peak location, the square-root Reynolds Number scaling for the log layer onset and a well-defined layer structure based on the balance of terms in the MMB. The present analyses evidence that similarly well-founded results also hold for turbulent boundary layers. This follows from transforming the mean inertia term in the MMB into a form that resembles that in pipes/channels, and is constant across the outer inertial region of the TBL. The physical reasoning is that the mean inertia is primarily a Large-scale outer layer contribution, the ‘shape’ of which becomes invariant of with increasing , and with a ‘magnitude’ that is inversely proportional to . The present analyses are enabled and corroborated using recent high resolution, Large Reynolds Number hot-wire measurements of all the terms in the TBL MMB.
A Kluwick - One of the best experts on this subject based on the ideXlab platform.
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break away separation for high turbulence intensity and Large Reynolds Number
Journal of Fluid Mechanics, 2011Co-Authors: Bernhard Scheichl, A Kluwick, F T SmithAbstract:Massive flow separation from the surface of a plane bluff obstacle in an incompressible uniform stream is addressed theoretically for Large values of the global Reynolds Number Re. The analysis is motivated by a conclusion drawn from recent theoretical results which is corroborated by experimental findings but apparently contrasts with common reasoning: the attached boundary layer extending from the front stagnation point to the position of separation never attains a fully developed turbulent state, even for arbitrarily Large Re. Consequently, the boundary layer exhibits a certain level of turbulence intensity that is linked with the separation process, governed by local viscous-inviscid interaction. Eventually, the latter mechanism is expected to be associated with rapid change of the separating shear layer towards a fully developed turbulent one. A self-consistent flow description in the vicinity of separation is derived, where the present study includes the predominantly turbulent region. We establish a criterion that acts to select the position of separation. The basic analysis here, which appears physically feasible and rational, is carried out without needing to resort to a specific turbulence closure.
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the effect of three dimensional obstacles on marginally separated laminar boundary layer flows
Journal of Fluid Mechanics, 2002Co-Authors: Stefan Braun, A KluwickAbstract:We consider the steady viscous/inviscid interaction of a two-dimensional, nearly separated, boundary layer with an isolated three-dimensional surface-mounted obstacle, for example in the Large Reynolds Number flow around the leading edge of a slender airfoil at a small angle of attack. An integro-differential equation describing the effect of the obstacle on the wall shear stress valid within the interaction regime is derived and solved numerically by means of a spectral method, which is outlined in detail. Typical solutions of this equation are presented for different values of the spanwise width B of the obstacle including the limiting cases B → 0 and B → ∞. Special emphasis is placed on the occurrence of non-uniqueness. On the main (upper) solution branch the disturbances to the flow field caused by the obstacle decay in the lateral direction. Conversely a periodic flow pattern, having no decay in the spanwise direction, was found to form on the lower solution branch. These branches are connected by a bifurcation point, which characterizes the maximum (critical) angle of attack for which a solution of the strictly plane interaction problem exists. An asymptotic investigation of the interaction equation, in the absence of any obstacle, for small deviations of this critical angle clearly reflects the observed behaviour of the numerical results corresponding to the different branches. As a result we can conclude that the primarily local interaction process breaks down in a non-local manner even in the limit of vanishing (three-dimensional local) disturbances of the flow field.
