Numerical and experimental investigations of 
oblique boundary layer transition

Berlin, Stellan; Wiegel, M.; Henningson, Dan S.

doi:10.1017/s002211209900511x

Cited by 82 publications

(62 citation statements)

References 41 publications

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“…These spikes are associated to ring-like vortices that separate from the tips of the large -vortices. Similar structures have also been found in the late stages of transition in boundary layers, either in the K-, N-or O-regimes of breakdown (see Berlin, Wiegel & Henningson 1999). These observations indicate that a considerable degree of similarity exists in the late stage of transition in a pipe and in a boundary layer.…”

Section: Introductionsupporting

confidence: 75%

The initial stage of transition in pipe flow: role of optimal base-flow distortions

2004

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We explore the spatial growth of disturbances developing on top of a base flow given by the Hagen-Poiseuille profile, which has been modified by a small axisymmetric and axially invariant distortion. Such deviations from the ideal parabolic profile may, for instance, occur in experiments as a result of experimental uncertainties. The optimal distortion (i.e. the distortion with a prescribed norm that induces the maximum growth rate) is computed by a variational technique. Unstable modes are found to exist for very small values of the norm of the deviation at low Reynolds numbers, and the instability is governed by an inviscid mechanism. The growth of these modes and the ensuing transition to turbulence is then studied by means of direct numerical simulations. Two possible paths of transition are found, one based on the exponential amplification of axisymmetric disturbances and the subsequent formation of -vortices and the other based on the growth and breakdown of streamwise streaks.

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Section: Introductionsupporting

confidence: 75%

The initial stage of transition in pipe flow: role of optimal base-flow distortions

2004

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“…The validation of the DNS results for both K-and H-type transitions is corroborated by recovering the aligned arrangement of the Λ vortices for the K-type transition (see figure 15a) and the staggered arrangement for the H-type transition (see figure 15b), as experimentally observed by Berlin, Wiegel & Henningson (1999) for the flat plate boundary layer. Figure 16 shows the evolution of the skin-friction coefficient versus Re δ * for two different normalized height scales.…”

Section: Effect Of Smooth Forward-facing Steps On K-and H-type Transisupporting

confidence: 74%

“…We label these modes using the notation (ω, β) (Berlin et al 1999), where ω and β are, respectively, the frequency and spanwise wavenumber, each normalized by the corresponding fundamental frequency/wavenumber. It has been observed that the K-type transition scenario has its main initial energy in the (1, 0) mode.…”

Section: Effect Of Smooth Forward-facing Steps On K-and H-type Transimentioning

confidence: 99%

Influence of localised smooth steps on the instability of a boundary layer

Lombard

Sherwin

2017

J. Fluid Mech.

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We consider a smooth, spanwise-uniform forward-facing step defined by a Gauss error function of height 4 %-30 % and four times the width of the local boundary layer thickness δ 99 . The boundary layer flow over a smooth forward-facing stepped plate is studied with particular emphasis on stabilisation and destabilisation of the twodimensional Tollmien-Schlichting (TS) waves and subsequently on three-dimensional disturbances at transition. The interaction between TS waves at a range of frequencies and a base flow over a single or two forward-facing smooth steps is conducted by linear analysis. The results indicate that for a TS wave with a frequency F ∈ [140, 160] (F = ων/U 2 ∞ × 10 6 , where ω and U ∞ denote the perturbation angle frequency and free-stream velocity magnitude, respectively, and ν denotes kinematic viscosity), the amplitude of the TS wave is attenuated in the unstable regime of the neutral stability curve corresponding to a flat plate boundary layer. Furthermore, it is observed that two smooth forward-facing steps lead to a more acute reduction of the amplitude of the TS wave. When the height of a step is increased to more than 20 % of the local boundary layer thickness for a fixed width parameter, the TS wave is amplified, and thereby a destabilisation effect is introduced. Therefore, the stabilisation or destabilisation effect of a smooth step is typically dependent on its shape parameters. To validate the results of the linear stability analysis, where a TS wave is damped by the forward-facing smooth steps direct numerical simulation (DNS) is performed. The results of the DNS correlate favourably with the linear analysis and show that for the investigated frequency of the TS wave, the K-type transition process is altered whereas the onset of the H-type transition is delayed. The results of the DNS suggest that for the perturbation with the non-dimensional frequency parameter F = 150 and in the absence of other external perturbations, two forward-facing smooth steps of height 5 % and 12 % of the boundary layer thickness delayed the H-type transition scenario and completely suppressed for the K-type transition. By considering Gaussian white noise with both fixed and random phase shifts, it is demonstrated by DNS that transition is postponed in time and space by two forward-facing smooth steps.

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“…For example, the development of structures and hairpin vortices was also observed in the late stage of oblique transition (Berlin, Wiegel & Henningson 1999). In this scenario, transition is induced by exciting oblique modes at the inflow, which grow and generate new modes through triad interactions.…”

Section: Comparison With Other Transition Scenariosmentioning

confidence: 99%

The minimal seed of turbulent transition in the boundary layer

et al. 2011

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. This paper describes a scenario of transition from laminar to turbulent flow in a spatially developing boundary layer over a flat plate. The base flow is the Blasius non-parallel flow solution; it is perturbed by optimal disturbances yielding the largest energy growth over a short time interval. Such perturbations are computed by a nonlinear global optimization approach based on a Lagrange multiplier technique. The results show that nonlinear optimal perturbations are characterized by a localized basic building block, called the minimal seed, defined as the smallest flow structure which maximizes the energy growth over short times. It is formed by vortices inclined in the streamwise direction surrounding a region of intense streamwise disturbance velocity. Such a basic structure appears to be a robust feature of the base flow since it is practically invariant with respect to the initial energy of the perturbation, the target time, the Reynolds number and the dimensions of the computational domain. The minimal seed grows very rapidly in time while spreading, and it triggers nonlinear effects which bring the flow to turbulence in a very efficient manner, through the formation of a turbulence spot. This evolution of the initial optimal disturbance has been studied in detail by direct numerical simulations. Using a perturbative formulation of the Navier-Stokes equations, each linear and nonlinear convective term of the equations has been analysed. The results show the fundamental role of the streamwise inclination of the vortices in the process. The nonlinear coupling of the finite amplitude disturbances is crucial to sustain such streamwise inclination, as well as to generate dislocations within the flow structures, and local inflectional velocity distributions. The analysis provides a picture of the transition process characterized by a sequence of structures appearing successively in the flow, namely, vortices, hairpin vortices and streamwise streaks. Finally, a disturbance regeneration cycle is conceived, initiated by the fast nonlinear amplification of the minimal seed, providing a possible scenario for the continuous regeneration of the same fundamental flow structures at smaller space and time scales.

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Numerical and experimental investigations of oblique boundary layer transition

Cited by 82 publications

References 41 publications

The initial stage of transition in pipe flow: role of optimal base-flow distortions

The initial stage of transition in pipe flow: role of optimal base-flow distortions

Influence of localised smooth steps on the instability of a boundary layer

The minimal seed of turbulent transition in the boundary layer

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