Rapid path to transition via nonlinear localized optimal perturbations in a boundary-layer flow

Cherubini, Stefania; Palma, P. De; Robinet, Jean-Christophe; Bottaro, Alessandro

doi:10.1103/physreve.82.066302

Cited by 75 publications

(110 citation statements)

References 22 publications

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“…In particular, the energy gain grows in time following a quasi-exponential curve, unlike the linear case which shows an initial growth phase followed by a decay. The trend of the energy gain curve obtained for Re = 300 is similar to that obtained for Re = 610 (see figure 2 in Cherubini et al 2010a). However, a higher increase of the gain is obtained for Re = 610 with respect to Re = 300.…”

Section: Nonlinear Optimal Perturbationssupporting

confidence: 81%

“…A more generic approach for identifying a purely nonlinear route to transition has been used by Pringle & Kerswell (2010) for the pipe flow, and by Cherubini et al (2010a) for the boundary-layer flow. For the case of the laminar boundary layer developing over a flat plate of interest here, the latter authors have used a global approach extending the linear transient growth analysis of Cherubini et al (2010b) to the nonlinear framework.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Nonlinear Optimal Perturbationssupporting

confidence: 81%

Section: Introductionmentioning

confidence: 99%

The minimal seed of turbulent transition in the boundary layer

et al. 2011

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“…This quest has brought to the discovery of nonlinear optimal perturbations, which are characterized by a very different structure with respect to the linear optimal ones and largely outgrow them in energy due to nonlinear mechanisms. The nonlinear optimal perturbation of minimal energy capable of bringing the flow to transition (i.e., the minimal seed of turbulent transition), has been recently found for a pipe flow (Pringle & Kerswell (2010); Pringle et al (2012)); a boundary layer flow (Cherubini et al (2010a(Cherubini et al ( , 2011b); and a Couette flow (Monokrousos et al (2011);Rabin et al (2012); Cherubini & De Palma (2012)). For the boundary-layer and the Couette flow, the minimal seed is characterized by a fundamental invariant structure, composed of a localized array of vortices and low-momentum regions of typical length scale, capable of maximizing the energy growth most rapidly.…”

Section: Introductionmentioning

confidence: 97%

Nonlinear control of unsteady finite-amplitude perturbations in the Blasius boundary-layer flow

2013

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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. 1Nonlinear control of unsteady finite-amplitude perturbations in the Blasius boundary-layer flow The present work provides an optimal control strategy, based on the nonlinear NavierStokes equations, aiming at hampering the rapid growth of unsteady finite-amplitude perturbations in a Blasius boundary-layer flow. A variational procedure is used to find the blowing and suction control law at the wall providing the maximum damping of the energy of a given perturbation at a given target time, with the final aim of leading the flow back to the laminar state. Two optimally-growing finite-amplitude initial perturbations capable of leading very rapidly to transition have been used to initialize the flow. The nonlinear control procedure has been found able to drive such perturbations back to the laminar state, provided that the target time of the minimisation and the region in which the blowing and suction is applied have been suitably chosen. On the other hand, an equivalent control procedure based on the linearized Navier-Stokes equations has been found much less effective, being not able to lead the flow to the laminar state when finite-amplitude disturbances are considered. Regions of strong sensitivity to blowing and suction have been also identified for the given initial perturbations: when the control is actuated in such regions, laminarization is observed also for a shorter extent of the actuation region. The nonlinear optimal blowing and suction law consists of alternated wall-normal velocity perturbations, which appear to modify the core flow structures by means of two distinct mechanisms: i) a wall-normal velocity-compensation at small times; ii) a rotationcounterbalancing effect al larger times. Similar control laws have been observed for different target times, values of the cost parameter, and streamwise extents of the blowing and suction zone, meaning that these two mechanisms are robust features of the optimal control strategy, provided that the nonlinear effects are taken into account.

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“…Phase-space trajectories closely approximating the edge are computed initializing the flow using the linear and non-linear optimal perturbations provided in Ref. 18 (see Figs. 3 and 4 therein), the perturbation vector u ¼ ðu; v; wÞ T being defined with respect to the spatially developing Blasius flow.…”

mentioning

confidence: 99%