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http://hdl.handle.net/10985/6863
Nonlinear optimal perturbations in a Couette flow: bursting and transition
CHERUBINI, Stefania; DE PALMA, Pietro
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.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/68632013-01-01T00:00:00ZCHERUBINI, StefaniaDE PALMA, PietroThis 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.A purely nonlinear route to transition approaching the edge of chaos in a boundary layer
http://hdl.handle.net/10985/6864
A purely nonlinear route to transition approaching the edge of chaos in a boundary layer
CHERUBINI, Stefania; DE PALMA, Pietro; ROBINET, Jean-Christophe; BOTTARO, Alessandro
The understanding of transition in shear flows has recently progressed along new paradigms based on the central role of coherent flow structures and their nonlinear interactions. We follow such paradigms to identify, by means of a nonlinear optimization of the energy growth at short time, the initial perturbation which most easily induces transition in a boundary layer. Moreover, a bisection procedure has been used to identify localized flow structures living on the edge of chaos, found to be populated by hairpin vortices and streaks. Such an edge structure appears to act as a relative attractor for the trajectory of the laminar base state perturbed by the initial finite-amplitude disturbances, mediating the route to turbulence of the flow, via the triggering of a regeneration cycle of Lambda and hairpin structures at different space and time scales. These findings introduce a new, purely nonlinear scenario of transition in a boundary-layer flow.
Publisher version : http://iopscience.iop.org/1873-7005/44/3/031404
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/68642012-01-01T00:00:00ZCHERUBINI, StefaniaDE PALMA, PietroROBINET, Jean-ChristopheBOTTARO, AlessandroThe understanding of transition in shear flows has recently progressed along new paradigms based on the central role of coherent flow structures and their nonlinear interactions. We follow such paradigms to identify, by means of a nonlinear optimization of the energy growth at short time, the initial perturbation which most easily induces transition in a boundary layer. Moreover, a bisection procedure has been used to identify localized flow structures living on the edge of chaos, found to be populated by hairpin vortices and streaks. Such an edge structure appears to act as a relative attractor for the trajectory of the laminar base state perturbed by the initial finite-amplitude disturbances, mediating the route to turbulence of the flow, via the triggering of a regeneration cycle of Lambda and hairpin structures at different space and time scales. These findings introduce a new, purely nonlinear scenario of transition in a boundary-layer flow.Edge states in a boundary layer
http://hdl.handle.net/10985/6868
Edge states in a boundary layer
CHERUBINI, Stefania; DE PALMA, Pietro; ROBINET, Jean-Christophe; BOTTARO, Alessandro
The understanding of laminar-turbulent transition in shear flows has recently progressed along new paradigms based on the central role of nonlinear exact coherent states. We follow such paradigms to identify, for the first time in a spatially developing flow, localized flow structures living on the edge of chaos, which are the precursors of turbulence. These coherent structures are constituted by hairpin vortices and streamwise streaks. The results reported here extend the dynamical systems description of transition to spatially developing flows.
Publisher version : http://pof.aip.org/resource/1/phfle6/v23/i5/p051705_s1?isAuthorized=no
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/68682011-01-01T00:00:00ZCHERUBINI, StefaniaDE PALMA, PietroROBINET, Jean-ChristopheBOTTARO, AlessandroThe understanding of laminar-turbulent transition in shear flows has recently progressed along new paradigms based on the central role of nonlinear exact coherent states. We follow such paradigms to identify, for the first time in a spatially developing flow, localized flow structures living on the edge of chaos, which are the precursors of turbulence. These coherent structures are constituted by hairpin vortices and streamwise streaks. The results reported here extend the dynamical systems description of transition to spatially developing flows.Successive bifurcations in a fully three-dimensional open cavity flow
http://hdl.handle.net/10985/13014
Successive bifurcations in a fully three-dimensional open cavity flow
PICELLA, Francesco; LOISEAU, Jean-Christophe; LUSSEYRAN, F; ROBINET, Jean-Christophe; CHERUBINI, Stefania; PASTUR, L
The transition to unsteadiness of a three-dimensional open cavity flow is investigated using the joint application of direct numerical simulations and fully three-dimensional linear stability analyses, providing a clear understanding of the first two bifurcations occurring in the flow. The first bifurcation is characterized by the emergence of Taylor–Görtler-like vortices resulting from a centrifugal instability of the primary vortex core. Further increasing the Reynolds number eventually triggers self-sustained periodic oscillations of the flow in the vicinity of the spanwise end walls of the cavity. This secondary instability causes the emergence of a new set of Taylor–Görtler vortices experiencing a spanwise drift directed toward the spanwise end walls of the cavity. While a two-dimensional stability analysis would fail to capture this secondary instability due to the neglect of the lateral walls, it is the first time to our knowledge that this drifting of the vortices can be entirely characterized by a three-dimensional linear stability analysis of the flow. Good agreements with experimental observations and measurements strongly support our claim that the initial stages of the transition to turbulence of three-dimensional open cavity flows are solely governed by modal instabilities.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/130142018-01-01T00:00:00ZPICELLA, FrancescoLOISEAU, Jean-ChristopheLUSSEYRAN, FROBINET, Jean-ChristopheCHERUBINI, StefaniaPASTUR, LThe transition to unsteadiness of a three-dimensional open cavity flow is investigated using the joint application of direct numerical simulations and fully three-dimensional linear stability analyses, providing a clear understanding of the first two bifurcations occurring in the flow. The first bifurcation is characterized by the emergence of Taylor–Görtler-like vortices resulting from a centrifugal instability of the primary vortex core. Further increasing the Reynolds number eventually triggers self-sustained periodic oscillations of the flow in the vicinity of the spanwise end walls of the cavity. This secondary instability causes the emergence of a new set of Taylor–Görtler vortices experiencing a spanwise drift directed toward the spanwise end walls of the cavity. While a two-dimensional stability analysis would fail to capture this secondary instability due to the neglect of the lateral walls, it is the first time to our knowledge that this drifting of the vortices can be entirely characterized by a three-dimensional linear stability analysis of the flow. Good agreements with experimental observations and measurements strongly support our claim that the initial stages of the transition to turbulence of three-dimensional open cavity flows are solely governed by modal instabilities.Hairpin-like optimal perturbations in plane Poiseuille flow
http://hdl.handle.net/10985/10316
Hairpin-like optimal perturbations in plane Poiseuille flow
FARANO, Mirko; CHERUBINI, Stefania; ROBINET, Jean-Christophe; DE PALMA, Pietro
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.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/103162015-01-01T00:00:00ZFARANO, MirkoCHERUBINI, StefaniaROBINET, Jean-ChristopheDE PALMA, PietroIn 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.Nonlinear control of unsteady finite-amplitude perturbations in the Blasius boundary-layer flow
http://hdl.handle.net/10985/9012
Nonlinear control of unsteady finite-amplitude perturbations in the Blasius boundary-layer flow
CHERUBINI, Stefania; ROBINET, Jean-Christophe; DE PALMA, Pietro
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.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/90122013-01-01T00:00:00ZCHERUBINI, StefaniaROBINET, Jean-ChristopheDE PALMA, PietroThe 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.Nonlinear optimals in the asymptotic suction boundary layer: Transition thresholds and symmetry breaking
http://hdl.handle.net/10985/10320
Nonlinear optimals in the asymptotic suction boundary layer: Transition thresholds and symmetry breaking
CHERUBINI, Stefania; DE PALMA, Pietro; ROBINET, Jean-Christophe
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.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/103202015-01-01T00:00:00ZCHERUBINI, StefaniaDE PALMA, PietroROBINET, Jean-ChristopheThe 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.Minimal perturbations approaching the edge of chaos in a Couette flow
http://hdl.handle.net/10985/8971
Minimal perturbations approaching the edge of chaos in a Couette flow
CHERUBINI, Stefania; DE PALMA, Pietro
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.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/89712014-01-01T00:00:00ZCHERUBINI, StefaniaDE PALMA, PietroThis 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.Optimal perturbations in boundary layer flows over rough surfaces
http://hdl.handle.net/10985/9013
Optimal perturbations in boundary layer flows over rough surfaces
CHERUBINI, Stefania; DE TULLIO, Marco; DE PALMA, Pietro; PASCAZIO, Giuseppe
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.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/90132013-01-01T00:00:00ZCHERUBINI, StefaniaDE TULLIO, MarcoDE PALMA, PietroPASCAZIO, GiuseppeThis 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.Sensitivity and optimal forcing response in separated boundary layer flows
http://hdl.handle.net/10985/6862
Sensitivity and optimal forcing response in separated boundary layer flows
ALIZARD, Frédéric; CHERUBINI, Stefania; ROBINET, Jean-Christophe
The optimal asymptotic response to time harmonic forcing of a convectively unstable two-dimensional separated boundary layer on a flat plate is numerically revisited from a global point of view. By expanding the flow disturbance variables and the forcing term as a summation of temporal modes, the linear convective instability mechanism associated with the response leading to the maximum gain in energy is theoretically investigated. Such a response is driven by a pseudoresonance of temporal modes due to the non-normality of the underlying linearized evolution operator. In particular, the considered expansion on a limited number of modes is found able to accurately simulate the linear instability mechanism, as suggested by a comparison between the global linear stability analysis and a linearized direct numerical simulation. Furthermore, the dependence of such a mechanism on the Reynolds number and the adverse pressure gradient is investigated, outlining a physical description of the destabilization of the flow induced by the rolling up of the shear layer. Therefore, the convective character of the problem suggests that the considered flat plate separated flows may act as a selective noise amplifier. In order to verfy such a possibility, the responses of the flow to the optimal forcing and to a small level of noise are compared, and their connection to the onset of self-excited vortices observed in literature is investigated. For that purpose, a nonlinear direct numerical simulation is performed, which is initialized by a random noise superposed to the base flow at the inflow boundary points. The band of excited frequencies as well as the associated peak match with the ones computed by the asymptotic global analysis. Finally, the connection between the onset of unsteadiness and the optimal response is further supported by a comparison between the optimal circular frequency and a typical Strouhal number predicted by numerical simulations of previous authors in similar cases.
Publisher version : http://pof.aip.org/resource/1/phfle6/v21/i6/p064108_s1?isAuthorized=no
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10985/68622009-01-01T00:00:00ZALIZARD, FrédéricCHERUBINI, StefaniaROBINET, Jean-ChristopheThe optimal asymptotic response to time harmonic forcing of a convectively unstable two-dimensional separated boundary layer on a flat plate is numerically revisited from a global point of view. By expanding the flow disturbance variables and the forcing term as a summation of temporal modes, the linear convective instability mechanism associated with the response leading to the maximum gain in energy is theoretically investigated. Such a response is driven by a pseudoresonance of temporal modes due to the non-normality of the underlying linearized evolution operator. In particular, the considered expansion on a limited number of modes is found able to accurately simulate the linear instability mechanism, as suggested by a comparison between the global linear stability analysis and a linearized direct numerical simulation. Furthermore, the dependence of such a mechanism on the Reynolds number and the adverse pressure gradient is investigated, outlining a physical description of the destabilization of the flow induced by the rolling up of the shear layer. Therefore, the convective character of the problem suggests that the considered flat plate separated flows may act as a selective noise amplifier. In order to verfy such a possibility, the responses of the flow to the optimal forcing and to a small level of noise are compared, and their connection to the onset of self-excited vortices observed in literature is investigated. For that purpose, a nonlinear direct numerical simulation is performed, which is initialized by a random noise superposed to the base flow at the inflow boundary points. The band of excited frequencies as well as the associated peak match with the ones computed by the asymptotic global analysis. Finally, the connection between the onset of unsteadiness and the optimal response is further supported by a comparison between the optimal circular frequency and a typical Strouhal number predicted by numerical simulations of previous authors in similar cases.