scholarly journals The relationship between free-stream coherent structures and near-wall streaks at high Reynolds numbers

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160078 ◽  
Author(s):  
K. Deguchi ◽  
P. Hall
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Coherent Structures ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Approach ◽  
Wall Turbulence ◽  
Large Reynolds Number ◽  
Equilibrium Solutions ◽  
New Family

The present work is based on our recent discovery of a new class of exact coherent structures generated near the edge of quite general boundary layer flows. The structures are referred to as free-stream coherent structures and were found using a large Reynolds number asymptotic approach to describe equilibrium solutions of the Navier–Stokes equations. In this paper, first we present results for a new family of free-stream coherent structures existing at relatively large wavenumbers. The new results are consistent with our earlier theoretical result that such structures can generate larger amplitude wall streaks if and only if the local spanwise wavenumber is sufficiently small. In a Blasius boundary layer, the local wavenumber increases in the streamwise direction so the wall streaks can typically exist only over a finite interval. However, here it is shown that they can interact with wall curvature to produce exponentially growing Görtler vortices through the receptivity process by a novel nonparallel mechanism. The theoretical predictions found are confirmed by a hybrid numerical approach. In contrast with previous receptivity investigations, it is shown that the amplitude of the induced vortex is larger than the structures in the free-stream which generate it. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

Free-stream coherent structures in parallel boundary-layer flows

2014 ◽  
Vol 752 ◽  
pp. 602-625 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Coherent Structures ◽  
Free Stream ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Homotopy Continuation ◽  
Boundary Layer Flows ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractOur concern in this paper is with high-Reynolds-number nonlinear equilibrium solutions of the Navier–Stokes equations for boundary-layer flows. Here we consider the asymptotic suction boundary layer (ASBL) which we take as a prototype parallel boundary layer. Solutions of the equations of motion are obtained using a homotopy continuation from two known types of solutions for plane Couette flow. At high Reynolds numbers, it is shown that the first type of solution takes the form of a vortex–wave interaction (VWI) state, see Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666), and is located in the main part of the boundary layer. On the other hand, here the second type is found to support an equilibrium solution of the unit-Reynolds-number Navier–Stokes equations in a layer located a distance of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}O(\ln \mathit{Re})$ from the wall. Here $\mathit{Re}$ is the Reynolds number based on the free-stream speed and the unperturbed boundary-layer thickness. The streaky field produced by the interaction grows exponentially below the layer and takes its maximum size within the unperturbed boundary layer. The results suggest the possibility of two distinct types of streaky coherent structures existing, possibly simultaneously, in disturbed boundary layers.

scholarly journals Free-stream coherent structures in the unsteady Rayleigh boundary layer

2020 ◽  
Vol 85 (6) ◽  
pp. 1021-1040
Author(s):  
Eleanor C Johnstone ◽  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Coherent Structures ◽  
Free Stream ◽  
Stokes Equations ◽  
Boundary Region ◽  
Navier Stokes ◽  
Equilibrium Solutions ◽  
Nonlinear Equilibrium ◽  
Set Up

Abstract Results are presented for nonlinear equilibrium solutions of the Navier–Stokes equations in the boundary layer set up by a flat plate started impulsively from rest. The solutions take the form of a wave–roll–streak interaction, which takes place in a layer located at the edge of the boundary layer. This extends previous results for similar nonlinear equilibrium solutions in steady 2D boundary layers. The results are derived asymptotically and then compared to numerical results obtained by marching the reduced boundary-region disturbance equations forward in time. It is concluded that the previously found canonical free-stream coherent structures in steady boundary layers can be embedded in unbounded, unsteady shear flows.

Free-stream coherent structures in growing boundary layers: a link to near-wall streaks

2015 ◽  
Vol 778 ◽  
pp. 451-484 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Coherent Structures ◽  
Free Stream ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Base Flow ◽  
Interaction Problem ◽  
Near Wall

In a recent paper, Deguchi & Hall (J. Fluid Mech., vol. 752, 2014a, pp. 602–625) described a new kind of exact coherent structure which sits at the edge of an asymptotic suction boundary layer at high values of the Reynolds number $Re$. At a distance $\ln Re$ from the wall, the structure is driven by the fully nonlinear interaction of tiny rolls, waves and streaks convected downstream at almost the free-stream speed. The interaction problem satisfies the unit-Reynolds-number three-dimensional Navier–Stokes equations and is localized in a layer of the same depth as the unperturbed boundary layer. Here, we show that the interaction problem is generic to any boundary layer that approaches its free-stream form through an exponentially small correction. It is shown that away from the layer where it is generated the induced roll–streak flow is dominated by non-parallel effects which now play a major role in the streamwise evolution of the structure. The similarity with the parallel boundary layer case is restricted only to the layer where it is generated. It is shown that non-parallel effects cause the structure to persist only over intervals of finite length in any growing boundary layer and lead to a flow structure reminiscent of turbulent boundary layer simulations. The results found shed light on a possible mechanism to couple near-wall streaks with coherent structures located towards the edge of a turbulent boundary layer. Some discussion of how the mechanism adapts to a three-dimensional base flow is given.

Direct numerical simulation of high-speed transition due to an isolated roughness element

2014 ◽  
Vol 748 ◽  
pp. 848-878 ◽  
Author(s):  
Pramod K. Subbareddy ◽  
Matthew D. Bartkowicz ◽  
Graham V. Candler
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Speed ◽  
Large Scale ◽  
Stokes Equations ◽  
Roughness Element ◽  
Dynamic Mode Decomposition ◽  
Large Reynolds Number ◽  
Dynamic Mode ◽  
Low Dissipation

AbstractWe study the transition of a Mach 6 laminar boundary layer due to an isolated cylindrical roughness element using large-scale direct numerical simulations (DNS). Three flow conditions, corresponding to experiments conducted at the Purdue Mach 6 quiet wind tunnel are simulated. Solutions are obtained using a high-order, low-dissipation scheme for the convection terms in the Navier–Stokes equations. The lowest Reynolds number ($Re$) case is steady, whereas the two higher $Re$ cases break down to a quasi-turbulent state. Statistics from the highest $Re$ case show the presence of a wedge of fully developed turbulent flow towards the end of the domain. The simulations do not employ forcing of any kind, apart from the roughness element itself, and the results suggest a self-sustaining mechanism that causes the flow to transition at a sufficiently large Reynolds number. Statistics, including spectra, are compared with available experimental data. Visualizations of the flow explore the dominant and dynamically significant flow structures: the upstream shock system, the horseshoe vortices formed in the upstream separated boundary layer and the shear layer that separates from the top and sides of the cylindrical roughness element. Streamwise and spanwise planes of data were used to perform a dynamic mode decomposition (DMD) (Rowley et al., J. Fluid Mech., vol. 641, 2009, pp. 115–127; Schmid, J. Fluid Mech., vol. 656, 2010, pp. 5–28).

scholarly journals On the uniqueness of steady flow past a rotating cylinder with suction

2000 ◽  
Vol 411 ◽  
pp. 213-232 ◽  
Author(s):  
E. V. BULDAKOV ◽  
S. I. CHERNYSHENKO ◽  
A. I. RUBAN
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Cross Flow ◽  
Rotation Velocity ◽  
Rotating Cylinder ◽  
Large Reynolds Number ◽  
Order Unity ◽  
Flow Past ◽  
Exponentially Small

The subject of this study is a steady two-dimensional incompressible flow past a rapidly rotating cylinder with suction. The rotation velocity is assumed to be large enough compared with the cross-flow velocity at infinity to ensure that there is no separation. High-Reynolds-number asymptotic analysis of incompressible Navier–Stokes equations is performed. Prandtl's classical approach of subdividing the flow field into two regions, the outer inviscid region and the boundary layer, was used earlier by Glauert (1957) for analysis of a similar flow without suction. Glauert found that the periodicity of the boundary layer allows the velocity circulation around the cylinder to be found uniquely. In the present study it is shown that the periodicity condition does not give a unique solution for suction velocity much greater than 1/Re. It is found that these non-unique solutions correspond to different exponentially small upstream vorticity levels, which cannot be distinguished from zero when considering terms of only a few powers in a large Reynolds number asymptotic expansion. Unique solutions are constructed for suction of order unity, 1/Re, and 1/√Re. In the last case an explicit analysis of the distribution of exponentially small vorticity outside the boundary layer was carried out.

scholarly journals Exact coherent structures at extreme Reynolds number

2016 ◽  
Vol 794 ◽  
pp. 1-4 ◽  
Author(s):  
G. P. Chini
Keyword(s):  
Reynolds Number ◽  
Coherent Structures ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Large Reynolds Number ◽  
Navier Stokes Equations ◽  
Wall Flows ◽  
Tollmien Schlichting ◽  
Turbulent Wall

Exact coherent structures (ECS), unstable three-dimensional solutions of the Navier–Stokes equations, play a fundamental role in transitional and turbulent wall flows. Dempsey et al. (J. Fluid Mech., vol. 791, 2016, pp. 97–121) demonstrate that at large Reynolds number reduced equations can be derived that simplify the computation and facilitate mechanistic understanding of these solutions. Their analysis shows that ECS in plane Poiseuille flow can be sustained by a novel inner–outer interaction between oblique near-wall Tollmien–Schlichting waves and interior streamwise vortices.

scholarly journals Reynolds stress scaling in pipe flow turbulence—first results from CICLoPE

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160187 ◽  
Author(s):  
R. Örlü ◽  
T. Fiorini ◽  
A. Segalini ◽  
G. Bellani ◽  
A. Talamelli ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Reynolds Stress ◽  
Large Scale ◽  
Strong Support ◽  
Wall Turbulence ◽  
Large Reynolds Number ◽  
Normal Distance ◽  
First Results ◽  
Variance Profile

This paper reports the first turbulence measurements performed in the Long Pipe Facility at the Center for International Cooperation in Long Pipe Experiments (CICLoPE). In particular, the Reynolds stress components obtained from a number of straight and boundary-layer-type single-wire and X-wire probes up to a friction Reynolds number of 3.8×10 4 are reported. In agreement with turbulent boundary-layer experiments as well as with results from the Superpipe, the present measurements show a clear logarithmic region in the streamwise variance profile, with a Townsend–Perry constant of A 2 ≈1.26. The wall-normal variance profile exhibits a Reynolds-number-independent plateau, while the spanwise component was found to obey a logarithmic scaling over a much wider wall-normal distance than the other two components, with a slope that is nearly half of that of the Townsend–Perry constant, i.e. A 2, w ≈ A 2 /2. The present results therefore provide strong support for the scaling of the Reynolds stress tensor based on the attached-eddy hypothesis. Intriguingly, the wall-normal and spanwise components exhibit higher amplitudes than in previous studies, and therefore call for follow-up studies in CICLoPE, as well as other large-scale facilities. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

scholarly journals Prospectus: towards the development of high-fidelity models of wall turbulence at large Reynolds number

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160092 ◽  
Author(s):  
J. C. Klewicki ◽  
G. P. Chini ◽  
J. F. Gibson
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Wall Turbulence ◽  
Large Reynolds Number ◽  
High Fidelity ◽  
Dynamical Structure ◽  
Mathematical Methods ◽  
High Reynolds ◽  
Turbulent Wall

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’.

scholarly journals Effect of free-stream turbulence and other vortical disturbances on a laminar boundary layer

1999 ◽  
Vol 380 ◽  
pp. 169-203 ◽  
Author(s):  
S. J. LEIB ◽  
DAVID W. WUNDROW ◽  
M. E. GOLDSTEIN
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Free Stream ◽  
Stokes Equations ◽  
Plate Boundary ◽  
Streamwise Velocity ◽  
Boundary Region ◽  
Quantitative Agreement ◽  
Free Stream Turbulence ◽  
Turbulent Reynolds Number

This paper is concerned with the effect of free-stream turbulence on the pretransitional flat-plate boundary layer. It is assumed that either the turbulent Reynolds number or the downstream distance (or both) is small enough that the flow can be linearized. The dominant disturbances in the boundary layer, which are of the Klebanoff type, are governed by the linearized unsteady boundary-region equations, i.e. the linearized Navier–Stokes equations with the streamwise derivatives neglected in the viscous and pressure-gradient terms. The turbulence is represented as a superposition of vortical free-stream Fourier modes and the corresponding Fourier component solutions to the boundary-region equations are obtained numerically. The results are then superposed to compute the root mean square of the fluctuating streamwise velocity in the boundary layer produced by the actual free-stream turbulence. It is found that the disturbances computed with isotropic free-stream turbulence do not reach the levels measured in experiments. However, good quantitative agreement is obtained with the relatively low turbulent Reynolds number data of Kendall when the measured strong anisotropy of the low-frequency portion of his spectrum is accounted for. Data at higher turbulent Reynolds numbers are affected by nonlinearity, which manifests itself through the generation of small spanwise length scales. We attempt to model this within the context of the linear theory by choosing a free-stream spectrum whose energy is concentrated at larger transverse wavenumbers and achieve very good agreement with the data. The results suggest that even small deviations from pure isotropy can be an important factor in explaining the large amplitudes of the Klebanoff modes in the pre-transitional boundary layer, and also point to the importance of nonlinear effects. We discuss some additional effects that may need to be accounted for in order to obtain a complete description of the Klebanoff modes.

scholarly journals Axisymmetric travelling waves in annular sliding Couette flow at finite and asymptotically large Reynolds number

2013 ◽  
Vol 720 ◽  
pp. 582-617 ◽  
Author(s):  
K. Deguchi ◽  
A. G. Walton
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Travelling Waves ◽  
Travelling Wave ◽  
Finite Amplitude ◽  
Vortical Flow ◽  
Navier Stokes ◽  
Large Reynolds Number ◽  
Equilibrium Solutions ◽  
Specific Flow

AbstractThe 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 $R= 1{0}^{8} $ 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 $R$. 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.

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