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.

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.

Direct simulation of a turbulent boundary layer up to Rθ = 1410

1988 ◽  
Vol 187 ◽  
pp. 61-98 ◽  
Author(s):  
Philippe R. Spalart
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Multiple Scale ◽  
Theoretical Models ◽  
Point Of View ◽  
Navier Stokes ◽  
Statistical Point

The turbulent boundary layer on a flat plate, with zero pressure gradient, is simulated numerically at four stations between Rθ = 225 and Rθ = 1410. The three-dimensional time-dependent Navier-Stokes equations are solved using a spectral method with up to about 107 grid points. Periodic spanwise and streamwise conditions are applied, and a multiple-scale procedure is applied to approximate the slow streamwise growth of the boundary layer. The flow is studied, primarily, from a statistical point of view. The solutions are compared with experimental results. The scaling of the mean and turbulent quantities with Reynolds number is compared with accepted laws, and the significant deviations are documented. The turbulence at the highest Reynolds number is studied in detail. The spectra are compared with various theoretical models. Reynolds-stress budget data are provided for turbulence-model testing.

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’.

scholarly journals Three-dimensional vortex organization in a high-Reynolds-number supersonic turbulent boundary layer

2010 ◽  
Vol 644 ◽  
pp. 35-60 ◽  
Author(s):  
G. E. ELSINGA ◽  
R. J. ADRIAN ◽  
B. W. VAN OUDHEUSDEN ◽  
F. SCARANO
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Velocity Field ◽  
Turbulent Boundary Layer ◽  
Coherent Structures ◽  
Large Scale ◽  
Three Dimensional ◽  
Velocity Fields ◽  
Hairpin Structure ◽  
Streamwise Direction

Tomographic particle image velocimetry was used to quantitatively visualize the three-dimensional coherent structures in a supersonic (Mach 2) turbulent boundary layer in the region between y/δ = 0.15 and 0.89. The Reynolds number based on momentum thickness Reθ = 34000. The instantaneous velocity fields give evidence of hairpin vortices aligned in the streamwise direction forming very long zones of low-speed fluid, consistent with Tomkins & Adrian (J. Fluid Mech., vol. 490, 2003, p. 37). The observed hairpin structure is also a statistically relevant structure as is shown by the conditional average flow field associated to spanwise swirling motion. Spatial low-pass filtering of the velocity field reveals streamwise vortices and signatures of large-scale hairpins (height > 0.5δ), which are weaker than the smaller scale hairpins in the unfiltered velocity field. The large-scale hairpin structures in the instantaneous velocity fields are observed to be aligned in the streamwise direction and spanwise organized along diagonal lines. Additionally the autocorrelation function of the wall-normal swirling motion representing the large-scale hairpin structure returns positive correlation peaks in the streamwise direction (at 1.5δ distance from the DC peak) and along the 45° diagonals, which also suggest a periodic arrangement in those directions. This is evidence for the existence of a spanwise–streamwise organization of the coherent structures in a fully turbulent boundary layer.

The Three-Dimensional Turbulent Boundary Layer on an Infinite Yawed Wing

1971 ◽  
Vol 22 (4) ◽  
pp. 346-362 ◽  
Author(s):  
J. F. Nash ◽  
R. R. Tseng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Lift Coefficient ◽  
Three Dimensional ◽  
Numerical Representation ◽  
Two Dimensional ◽  
Incompressible Turbulent Boundary Layer ◽  
Displacement Thickness ◽  
Attachment Line

SummaryThis paper presents the results of some calculations of the incompressible turbulent boundary layer on an infinite yawed wing. A discussion is made of the effects of increasing lift coefficient, and increasing Reynolds number, on the displacement thickness, and on the magnitude and direction of the skin friction. The effects of the state of the boundary layer (laminar or turbulent) along the attachment line are also considered.A study is made to determine whether the behaviour of the boundary layer can adequately be predicted by a two-dimensional calculation. It is concluded that there is no simple way to do this (as is provided, in the laminar case, by the principle of independence). However, with some modification, a two-dimensional calculation can be made to give an acceptable numerical representation of the chordwise components of the flow.

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.

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