@conference{
	11589_77098,
	author = { Cherubini  Stefania  and  De Palma  Pietro  and  Robinet  Jean-Christophe },
	title = {Non-linear Optimal Perturbations in the Asymptotic Suction Boundary-layer},
	year = {2015},
	publisher = {Elsevier},
	journal = {PROCEDIA IUTAM},
	volume = {14},
	booktitle = {Procedia IUTAM},
	keywords = {hairpin vortices; minimal seeds; non-linear coherent structures; Transition to turbulence; Mechanical Engineering},
	url = {http://www.sciencedirect.com/science/journal/22109838/1},
	doi = {10.1016/j.piutam.2015.03.047},	
	pages = {246--255}
}
@conference{
	11589_77097,
	author = { Cherubini  S  and  Robinet  J -C  and  De Palma  P },
	title = {A nonlinear control strategy for finite-amplitude perturbations in a boundary-layer flow},
	year = {2015},
	publisher = {Elsevier Ltd},
	journal = {ENERGY PROCEDIA},
	volume = {81},
	booktitle = {Energy Procedia},
	keywords = {Blowing and suction; Optimal perturbations; Transition; Energy (all)},
	url = {http://www.sciencedirect.com/science/journal/18766102},
	doi = {10.1016/j.egypro.2015.12.139},	
	pages = {1143--1150}
}
@article{
	11589_5729,
	author = { Farano M  and  Cherubini S  and  Robinet J-C  and  De Palma P },
	title = {Hairpin-like optimal perturbations in plane Poiseuille flow},
	year = {2015},
	journal = {JOURNAL OF FLUID MECHANICS},
	volume = {775},
	abstract = {In this work it is shown that hairpin vortex structures can be the outcome of a nonlinear optimal growth process, in a similar way as streaky structures can be the result of a linear optimal growth mechanism. With this purpose, nonlinear optimizations based on a Lagrange multiplier technique coupled with a direct-adjoint iterative procedure are performed in a plane Poiseuille flow at subcritical values of the Reynolds number, aiming at quickly triggering nonlinear effects. Choosing a suitable time scale for such an optimization process, it is found that the initial optimal perturbation is composed of sweeps and ejections resulting in a hairpin vortex structure at the target time. These alternating sweeps and ejections create an inflectional instability occurring in a localized region away from the wall, generating the head of the primary and secondary hairpin structures, quickly inducing transition to turbulent flow. This result could explain why transitional and turbulent shear flows are characterized by a high density of hairpin vortices. © Cambridge University Press 2015.},
	doi = {10.1017/jfm.2015.320},	
}
@conference{
	11589_25180,
	author = { Loiseau J-C  and  Cherubini S  and  De Palma P  and  Robinet J-C },
	title = {Investigation of the roughness-induced transition: linear and
non-linear optimal perturbations},
	year = {2015},
	booktitle = {86th Annual Meeting
of the International Association
of Applied Mathematics and Mechanics, Book of Abstracts 2015},
	pages = {413--413}
}
@conference{
	11589_25113,
	author = { Farano M  and  Cherubini S  and  Robinet J-C  and  De Palma P },
	title = {P-norm optimal 3D perturbations in the Poiseuille flow},
	year = {2015},
	booktitle = {86th Annual Meeting
of the International Association
of Applied Mathematics and Mechanics, Book of Abstracts 2015},
	pages = {411--411}
}
@conference{
	11589_25121,
	author = { Farano M  and  Cherubini S  and  Robinet J-C  and  De Palma P },
	title = {A hairpin-shaped optimal perturbation in a plane Poiseuille flow},
	year = {2015},
	booktitle = {Sixth International Symposium on Bifurcation and Instabilities in fluid Dynamics},
	pages = {332--332}
}
@article{
	11589_5603,
	author = { Cherubini S  and  De Palma P },
	title = {Minimal-energy perturbations rapidly approaching the edge state in Couette flow},
	year = {2015},
	journal = {JOURNAL OF FLUID MECHANICS},
	volume = {764},
	abstract = {Transition to turbulence in shear flows is often subcritical, thus the dynamics of the flow strongly depends on the shape and amplitude of the perturbation of the laminar state. In the state space, initial perturbations which directly relaminarize are separated from those that go through a chaotic trajectory by a hypersurface having a very small number of unstable dimensions, known as the edge of chaos. Even for the simple case of plane Couette flow in a small domain, the edge of chaos is characterized by a fractal, folded structure. Thus, the problem of determining the threshold energy to trigger subcritical transition consists in finding the states on this complex hypersurface with minimal distance (in the energy norm) from the laminar state. In this work we have investigated the minimal-energy regions of the edge of chaos, by developing a minimization method looking for the minimal-energy perturbations capable of approaching the edge state (within a prescribed tolerance) in a finite target time T. For sufficiently small target times, the value of the minimal energy has been found to vary with T following a power law, whose best fit is given by E T-1.75. For large values of T, the minimal energy achieves a constant value which corresponds to the energy of the minimal seed, namely the perturbation of minimal energy asymptotically approaching the edge state (Rabin et al., J. Fluid Mech., vol. 738, 2012, R1). For T\geqslant 40, all of the symmetries of the edge state are broken and the minimal perturbation appears to be localized in space with a basic structure composed of scattered patches of streamwise velocity with inclined streamwise vortices on their flanks. Finally, we have found that minimal perturbations originate in a small low-energy zone of the state space and follow very fast similar trajectories towards the edge state. Such trajectories are very different from those of linear optimal disturbances, which need much higher initial amplitudes to approach the edge state. The time evolution of these minimal perturbations represents the most efficient path to subcritical transition for Couette flow. © 2015 Cambridge University Press.},
	doi = {10.1017/jfm.2014.716},	
	pages = {572--598}
}
@article{
	11589_3275,
	author = { Cherubini S  and  De Palma P  and  Robinet J-C },
	title = {Nonlinear optimals in the asymptotic suction boundary layer: Transition thresholds and symmetry breaking},
	year = {2015},
	journal = {PHYSICS OF FLUIDS},
	volume = {27},
	abstract = {The effect of a constant homogeneous wall suction on the nonlinear transient growth of localized finite amplitude perturbations in a boundary-layer flow is investigated. Using a variational technique, nonlinear optimal disturbances are computed for the asymptotic suction boundary layer (ASBL) flow, defined as those finite amplitude disturbances yielding the largest energy growth at a given target time T. It is found that homogeneous wall suction remarkably reduces the optimal energy gain in the nonlinear case. Furthermore, mirror-symmetry breaking of the shape of the optimal perturbation appears when decreasing the Reynolds number from 10?000 to 5000, whereas spanwise mirror-symmetry was a robust feature of the nonlinear optimal perturbations found in the Blasius boundary-layer flow. Direct numerical simulations show that the different evolutions of the symmetric and of the non-symmetric initial perturbations are linked to different mechanisms of transport and tilting of the vortices by the mean flow. By bisecting the initial energy of the nonlinear optimal perturbations, minimal energy thresholds for subcritical transition to turbulence have been obtained. These energy thresholds are found to be 1-4 orders of magnitude smaller than those provided in the literature for other transition scenarios. For low to moderate Reynolds numbers, the energy thresholds are found to scale with Re-2, suggesting a new scaling law for transition in the ASBL. © 2015 AIP Publishing LLC.},
	doi = {10.1063/1.4916017},	
}
@article{
	11589_83895,
	author = { Wedin  Håkan  and  Cherubini  Stefania  and  Bottaro  Alessandro },
	title = {Effect of plate permeability on nonlinear stability of the asymptotic suction boundary layer},
	year = {2015},
	journal = {PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS},
	volume = {92},
	keywords = {Condensed Matter Physics; Statistical and Nonlinear Physics; Statistics and Probability},
	url = {http://harvest.aps.org/bagit/articles/10.1103/PhysRevE.92.013022/apsxml},
	doi = {10.1103/PhysRevE.92.013022},	
}
@conference{
	11589_83940,
	author = { Loiseau  J -Ch  and  Robinet  J -Ch  and  Cherubini  S  and  Leriche  E },
	title = {Global Stability Analyses Unraveling Roughness-induced Transition Mechanisms},
	year = {2015},
	publisher = {Elsevier},
	journal = {PROCEDIA IUTAM},
	volume = {14},
	booktitle = {Procedia IUTAM},
	keywords = {boundary layer; global stability; Roughness-induced transition; Mechanical Engineering},
	url = {http://www.sciencedirect.com/science/journal/22109838/1},
	doi = {10.1016/j.piutam.2015.03.039},	
	pages = {182--191}
}
@inbook{
	11589_83927,
	author = { Loiseau  J -Ch  and  Cherubini  S  and  Robinet  J -Ch  and  Leriche  E },
	title = {Influence of the shape on the roughness-induced transition},
	year = {2015},
	volume = {107},
	booktitle = {Instability and Control of Massively Separated Flows},
	keywords = {Mechanical Engineering; Mechanics of Materials; Fluid Flow and Transfer Processes},
	url = {http://www.springerlink.com/content/0926-5112},
	doi = {10.1007/978-3-319-06260-0_18},	
	pages = {123--128}
}
@article{
	11589_83903,
	author = { Pralits  Jan O  and  Bottaro  Alessandro  and  Cherubini  Stefania },
	title = {Weakly nonlinear optimal perturbations},
	year = {2015},
	journal = {JOURNAL OF FLUID MECHANICS},
	volume = {785},
	doi = {10.1017/jfm.2015.622},	
	pages = {135--151}
}
@article{
	11589_519,
	author = { Cherubini S  and  De Palma P },
	title = {Minimal perturbations approaching the edge of chaos in a Couette flow},
	year = {2014},
	journal = {FLUID DYNAMICS RESEARCH},
	volume = {46},
	abstract = {This paper provides an investigation of the structure of the stable manifold of the lower branch steady state for the plane Couette flow. Minimal energy perturbations to the laminar state are computed, which approach within a prescribed tolerance the lower branch steady state in a finite time. For small times, such minimal-energy perturbations maintain at least one of the symmetries characterizing the lower branch state. For a sufficiently large time horizon, such symmetries are broken and the minimal-energy perturbations on the stable manifold are formed by localized asymmetrical vortical structures. These minimal-energy perturbations could be employed to develop a control procedure aiming at stabilizing the low-dissipation lower branch state. © 2014 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.},
	doi = {10.1088/0169-5983/46/4/041403},	
}
@article{
	11589_3591,
	author = { Cherubini S  and  Robinet J-C  and  De Palma P },
	title = {Numerical study of the effect of freestream turbulence on by-pass transition in a boundary layer},
	year = {2014},
	journal = {ENERGY PROCEDIA},
	volume = {45},
	abstract = {We use direct numerical simulations in the presence of free-stream turbulence having different values of intensity, Tu, and integral length scale, L, in order to determine which kind of structures are involved in the path to transition of a boundary-layer flow. The main aim is to determine under which conditions the path to transition involves structures similar to the linear or non-linear optimal perturbations. For high values of Tu and L, we observe a large-amplitude path to transition characterized by localized vortical structures and patches of high- and low-momentum fluctuations. Such a scenario is found to correlate well with the Λ and hairpin structures resulting from the time evolution of non-linear optimal perturbations, whereas, for lower Tu and L, a larger correlation is found with respect to linear optimal disturbances. This indicates that a large-amplitude path to transition exists, different from the one characterized by elongated streaks undergoing secondary instability. To distinguish between the two transition scenarios, a simple parameter linked to the streamwise localisation of high- and low-momentum zones is introduced. Finally, an accurate law to predict the transition location is provided, taking into account both Tu and L, valid for both the transition scenarios.},
	keywords = {Boundary-layer flows; Optimal perturbations; Transition to turbulence},
	doi = {10.1016/j.egypro.2014.01.062},	
	pages = {578--587}
}
@article{
	11589_83915,
	author = { Loiseau  Jean-Christophe  and  Robinet  Jean-Christophe  and  Cherubini  Stefania  and  Leriche  Emmanuel },
	title = {Investigation of the roughness-induced transition: Global stability analyses and direct numerical simulations},
	year = {2014},
	journal = {JOURNAL OF FLUID MECHANICS},
	volume = {760},
	keywords = {Boundary layers; Instability; Transition to turbulence; Mechanical Engineering; Mechanics of Materials; Condensed Matter Physics},
	url = {http://journals.cambridge.org/action/displayJournal?jid=FLM},
	doi = {10.1017/jfm.2014.589},	
	pages = {175--211}
}
@article{
	11589_52116,
	author = { Cherubini S  and  Robinet J-C  and  De Palma P },
	title = {Nonlinear control of unsteady finite-amplitude perturbations in the Blasius boundary-layer flow},
	year = {2013},
	journal = {JOURNAL OF FLUID MECHANICS},
	volume = {737},
	abstract = {"The present work provides an optimal control strategy, based on the nonlinear Navier–Stokes equations, aimed 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 minimization 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 also observed for a shorter extent of the actuation region. The nonlinear optimal blowing and suction law consists of alternating 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 rotation-counterbalancing 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."},
	keywords = {boundary layer control; instability control; nonlinear instability},
	doi = {10.1017/jfm.2013.576},	
	pages = {440--465}
}
@conference{
	11589_25225,
	author = { Cherubini S  and  De Palma P },
	title = {Minimal perturbations targeting the edge in a Couette flow},
	year = {2013},
	booktitle = {BIFURCATIONS AND INSTABILITIES IN FLUID DYNAMICS - Fifth International Symposium}
}
@article{
	11589_8263,
	author = { Cherubini S  and  De Palma P },
	title = {Nonlinear optimal perturbations in a Couette flow: Bursting and transition},
	year = {2013},
	journal = {JOURNAL OF FLUID MECHANICS},
	volume = {716},
	abstract = {This paper provides the analysis of bursting and transition to turbulence in a Couette flow, based on the growth of nonlinear optimal disturbances. We use a global variational procedure to identify such optimal disturbances, defined as those initial perturbations yielding the largest energy growth at a given target time, for given Reynolds number and initial energy. The nonlinear optimal disturbances are found to be characterized by a basic structure, composed of inclined streamwise vortices along localized regions of low and high momentum. This basic structure closely recalls that found in boundary-layer flow (Cherubini et al., J. Fluid Mech., vol. 689, 2011, pp. 221-253), indicating that this structure may be considered the most 'energetic' one at short target times. However, small differences in the shape of these optimal perturbations, due to different levels of the initial energy or target time assigned in the optimization process, may produce remarkable differences in their evolution towards turbulence. In particular, direct numerical simulations have shown that optimal disturbances obtained for large initial energies and target times induce bursting events, whereas for lower values of these parameters the flow is directly attracted towards the turbulent state. For this reason, the optimal disturbances have been classified into two classes, the highly dissipative and the short-path perturbations. Both classes lead the flow to turbulence, skipping the phases of streak formation and secondary instability which are typical of the classical transition scenario for shear flows. The dynamics of this transition scenario exploits three main features of the nonlinear optimal disturbances: (i) the large initial value of the streamwise velocity component; (ii) the streamwise dependence of the disturbance; (iii) the presence of initial inclined streamwise vortices. The short-path perturbations are found to spend a considerable amount of time in the vicinity of the edge state (Schneider et al., Phys. Rev. E, vol. 78, 2008, 037301), whereas the highly dissipative optimal disturbances pass closer to the edge, but they are rapidly repelled away from it, leading the flow to high values of the dissipation rate. After this dissipation peak, the trajectories do not lead towards the turbulent attractor, but they spend some time in the vicinity of an unstable periodic orbit (UPO). This behaviour led us to conjecture that bursting events can be obtained not only as homoclinic orbits approaching the UPO, as recently found by van Veen & Kawahara (Phys. Rev. Lett., vol. 107, 2011, p. 114501), but also as heteroclinic orbits between the equilibrium solution on the edge and the UPO.},
	keywords = {nonlinear dynamical systems; nonlinear instability; transition to turbulence},
	doi = {10.1017/jfm.2012.544},	
	pages = {251--279}
}
@article{
	11589_52352,
	author = { Cherubini S  and  de Tullio M D  and  De Palma P  and  Pascazio G },
	title = {Transient growth in the flow past a three-dimensional smooth roughness element},
	year = {2013},
	journal = {JOURNAL OF FLUID MECHANICS},
	volume = {724},
	abstract = {This work provides a global optimization analysis, looking for perturbations inducing the largest energy growth at a finite time in a boundary-layer flow in the presence of smooth three-dimensional roughness elements. Amplification mechanisms are described which can bypass the asymptotical growth of Tollmien-Schlichting waves. Smooth axisymmetric roughness elements of different height have been studied, at different Reynolds numbers. The results show that even very small roughness elements, inducing only a weak deformation of the base flow, can localize the optimal disturbance characterizing the Blasius boundary-layer flow. Moreover, for large enough bump heights and Reynolds numbers, a strong amplification mechanism has been recovered, inducing an increase of several orders of magnitude of the energy gain with respect to the Blasius case. In particular, the highest value of the energy gain is obtained for an initial varicose perturbation, differently to what found for a streaky parallel flow. Optimal varicose perturbations grow very rapidly by transporting the strong wall-normal shear of the base flow, which is localized in the wake of the bump. Such optimal disturbances are found to lead to transition for initial energies and amplitudes considerably smaller than sinuous optimal ones, inducing hairpin vortices downstream of the roughness element.},
	keywords = {boundary layer stability, boundary layers, transition to turbulence},
	doi = {10.1017/jfm.2013.177},	
	pages = {642--670}
}
@article{
	11589_52329,
	author = { Cherubini S  and  de Tullio M D  and  De Palma P  and  Pascazio G },
	title = {Optimal perturbations in boundary-layer flows over rough surfaces},
	year = {2013},
	journal = {JOURNAL OF FLUIDS ENGINEERING},
	volume = {135},
	booktitle = {ASME 2012 Fluids Engineering Summer Meeting FEDSM2012
July 8–12, 2012, Puerto Rico, USA},
	abstract = {This work provides a three-dimensional energy optimization analysis, looking for perturbations inducing the largest energy growth at a finite time in a boundary-layer flow in the presence of roughness elements. The immersed boundary technique has been coupled with a Lagrangian optimization in a three-dimensional framework. Four roughness elements with different heights have been studied, inducing amplification mechanisms that bypass the asymptotical growth of Tollmien-Schlichting waves. The results show that even very small roughness elements, inducing only a weak deformation of the base flow, can strongly localize the optimal disturbance. Moreover, the highest value of the energy gain is obtained for a varicose perturbation. This result demonstrates the relevance of varicose instabilities for such a flow and shows a different behavior with respect to the secondary instability theory of boundary layer streaks.},
	doi = {10.1115/1.4025028},	
}