Spatially convective global modes in a boundary layer

Alizard, Frédéric; Robinet, Jean-Christophe

doi:10.1063/1.2804958

Cited by 65 publications

(55 citation statements)

References 38 publications

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“…In contrast, stable eigenvalues along an eigenvalue branch can in many situations be very sensitive with respect to numerical parameters e.g. eigenvalue shifts or domain sizes (Ehrenstein & Gallaire 2005;Alizard & Robinet 2007;Garnaud et al 2013;Cerqueira & Sipp 2014). For such flows, a resolvent or impulse-response analysis may be more appropriate.…”

Section: Introductionmentioning

confidence: 99%

Stability and sensitivity of a cross-flow-dominated Falkner–Skan–Cooke boundary layer with discrete surface roughness

et al. 2017

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Stability and sensitivity of a crossflow-dominated Falkner-Skan-Cooke boundary layer with discrete surface roughness. Journal of Fluid MechanicsAccess to the published version may require subscription. N.B. When citing this work, cite the original published paper. With the motivation of determining the critical roughness size, a global stability and sensitivity analysis of a three-dimensional Falkner-Skan-Cooke (FSC) boundary layer with a cylindrical surface roughness is performed. The roughness size is chosen such that breakdown to turbulence is initiated by a global version of traditional secondary instabilities of the crossflow (CF) vortices, instead of an immediate flow tripping at the roughness. The resulting global eigenvalue spectra of the systems are found to be very sensitive to numerical parameters and domain size. This sensitivity to numerical parameters is quantified using the "-pseudospectrum, and the dependency on the domain is analysed through an impulse response and an energy budget. It is shown that the growth rates increase with domain size, which originates from the inclusion of stronger CF vortices in the baseflow. This is reflected in a change in the rate of advective energy transport by the baseflow. It is concluded that the onset of global instability in a FSC boundary layer as the roughness height is increased does not correspond to an immediate flow tripping behind the roughness, but occurs for lower roughness heights if su ciently long domains are considered. However, the great sensitivity results in an inability to accurately pinpoint the exact parameter values for the bifurcation, and the large spatial growth of the disturbances in the long domains eventually becomes larger than what can be resolved using finite precision arithmetics.

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Section: Introductionmentioning

confidence: 99%

Stability and sensitivity of a cross-flow-dominated Falkner–Skan–Cooke boundary layer with discrete surface roughness

et al. 2017

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“…Fluids 22, 014102 ͑2010͒ stable modes, labeled 1 and 2 in Fig. 4 [19][20][21] and for a cavity-induced separated boundarylayer flow. 28 However, although the modes have been found asymptotically stable, they are likely to interact leading to a transient amplification of the perturbations due to the nonorthogonality of the corresponding eigenvectors.…”

Section: -3mentioning

confidence: 99%

“…At the upper and inlet boundaries, a zero perturbation condition is imposed, whereas at the outflow, the flow being locally unstable, a Robin condition based on the approximation of the local dispersion relation is prescribed. 20,21 Concerning the subcritical flow computations, the modes are discretized using N x = 250 collocation points in the x-direction and N y = 48 collocation points in the y-direction. The Appendix provides a numerical study for the grid sensitivity of the solution.…”

Section: Global Eigenvalue Analysismentioning

confidence: 99%

“…In fact, recently, several authors have demonstrated the suitability of the global eigenvalue analysis for studying the transient growth behavior by decomposing flow perturbations as a superposition of global modes. 18 Such a technique has been applied to the study of several flows such as the boundarylayer flow over a flat plate, [19][20][21] the separated boundary-layer flow induced by a bump, [8][9][10] and the flow over a rounded backward-facing step. 16 Indeed, the global analysis is capable of capturing the effects of the non-normality of the linearized NS operator and the consequent interactions among its nonorthogonal global modes.…”

Section: Introductionmentioning

confidence: 99%

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The effects of non-normality and nonlinearity of the Navier–Stokes operator on the dynamics of a large laminar separation bubble

2010

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. The effects of non-normality and nonlinearity of the Navier-Stokes operator on the dynamics of a large laminar separation bubble. The effects of non-normality and nonlinearity of the Navier-Stokes operator on the dynamics of a large laminar separation bubble, 2010, 22 (014102), pp.15. <10.1063/1.3276903>. The effects of non-normality and nonlinearity of the Navier-Stokes operator on the dynamics of a large laminar separation bubble The effects of non-normality and nonlinearity of the two-dimensional Navier-Stokes differential operator on the dynamics of a large laminar separation bubble over a flat plate have been studied in both subcritical and slightly supercritical conditions. The global eigenvalue analysis and direct numerical simulations have been employed in order to investigate the linear and nonlinear stability of the flow. The steady-state solutions of the Navier-Stokes equations at supercritical and slightly subcritical Reynolds numbers have been computed by means of a continuation procedure. Topological flow changes on the base flow have been found to occur close to transition, supporting the hypothesis of some authors that unsteadiness of separated flows could be due to structural changes within the bubble. The global eigenvalue analysis and numerical simulations initialized with small amplitude perturbations have shown that the non-normality of convective modes allows the bubble to act as a strong amplifier of small disturbances. For subcritical conditions, nonlinear effects have been found to induce saturation of such an amplification, originating a wave-packet cycle similar to the one established in supercritical conditions, but which is eventually damped. A transient amplification of finite amplitude perturbations has been observed even in the attached region due to the high sensitivity of the flow to external forcing, as assessed by a linear sensitivity analysis. For supercritical conditions, the non-normality of the modes has been found to generate low-frequency oscillations ͑flapping͒ at large times. The dependence of such frequencies on the Reynolds number has been investigated and a scaling law based on a physical interpretation of the phenomenon has been provided, which is able to explain the onset of a secondary flapping frequency close to transition.

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“…The optimization is also carried out by the global model described in Alizard & Robinet (2007), the perturbation being characterized by only one spanwise wavenumber β, so that q(x, y, z, t) =q(x, y, t)exp (iβz). The shape function is decomposed in temporal modes as 8) where N is the total number of modes,q k are the eigenvectors, ω k are the (complex) eigenvalues and κ 0 k represents the initial energy of each mode.…”

Section: Global Eigenvalue Analysismentioning

confidence: 99%

Optimal wave packets in a boundary layer and initial phases of a turbulent spot

et al. 2010

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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. The three-dimensional global optimal dynamics of a flat-plate boundary layer is studied by means of an adjoint-based optimization in a spatial domain of longbut finite -streamwise dimension. The localized optimal initial perturbation is characterized by a pair of streamwise-modulated counter-rotating vortices, tilted upstream, yielding at the optimal time elongated streaks of alternating sign in the streamwise direction. This indicates that perturbations with non-zero streamwise wavenumber have a role in the transient dynamics of a boundary layer. A scaling law is provided, describing the variation of the streamwise modulation of the optimal initial perturbation with respect to the streamwise domain length and to the Reynolds number. For spanwise-extended domains, a near-optimal three-dimensional perturbation is extracted during the optimization process; it is localized also in the spanwise direction, resulting in a wave packet of elongated disturbances modulated in the spanwise and streamwise directions. The nonlinear evolution of the optimal and near-optimal perturbations is investigated by means of direct numerical simulations. Both perturbations are found to induce transition at lower levels of the initial energy than local optimal and suboptimal perturbations. Moreover, it is observed that transition occurs in a well-defined region of the convected wave packet, close to its centre, via a mechanism including at the same time oscillations of the streaks of both quasi-sinuous and quasi-varicose nature. Hairpin vortices are observed before transition; they have an active role in the breakdown of the streaks and result in a turbulent spot which spreads out in the boundary layer.

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Spatially convective global modes in a boundary layer

Cited by 65 publications

References 38 publications

Stability and sensitivity of a cross-flow-dominated Falkner–Skan–Cooke boundary layer with discrete surface roughness

Stability and sensitivity of a cross-flow-dominated Falkner–Skan–Cooke boundary layer with discrete surface roughness

The effects of non-normality and nonlinearity of the Navier–Stokes operator on the dynamics of a large laminar separation bubble

Optimal wave packets in a boundary layer and initial phases of a turbulent spot

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