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http://hdl.handle.net/10985/17848
Global Stability Analyses Unraveling Roughness-induced Transition Mechanisms
LOISEAU, Jean-Christophe; ROBINET, Jean-Christophe; CHERUBINI, Stefania; LERICHE, Emmanuel
The linear global instability and resulting transition to turbulence induced by a cylindrical roughness element of heighth and diameter d=3h immersed within an incompressible boundary layer flow along a flat plate is investigated using the joint application of direct numerical simulations and three-dimensional stability analyses. The configuration investigated is the same as the one investigated experimentally by Fransson et al. Base flow computations show that the roughness element induces a wake composed of a central low-speed region surrounded by a three-dimensional shear layer and a pair of low- and high-speed streaks on each side. Results from the global stability analyses highlight the unstable nature of the central low-speed region and its crucial importance in the laminar-turbulent transition process. For the set of parameters considered, it is able to sustain a varicose global instability for which the predicted critical Reynolds number is only 6% larger than the one reported in Ref. 10. A kinetic energy budget and wavemaker analysis revealed that this mode finds its root in the reversed flow region right downstream the roughness element and extracts most of its energy from the central low-speed region and streaks further downstream. Direct numerical simulations of the flow past this roughness element puts in the limelight the ability for this linear instability to give birth to hairpin vortices and thus trigger transition to turbulence.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/178482015-01-01T00:00:00ZLOISEAU, Jean-ChristopheROBINET, Jean-ChristopheCHERUBINI, StefaniaLERICHE, EmmanuelThe linear global instability and resulting transition to turbulence induced by a cylindrical roughness element of heighth and diameter d=3h immersed within an incompressible boundary layer flow along a flat plate is investigated using the joint application of direct numerical simulations and three-dimensional stability analyses. The configuration investigated is the same as the one investigated experimentally by Fransson et al. Base flow computations show that the roughness element induces a wake composed of a central low-speed region surrounded by a three-dimensional shear layer and a pair of low- and high-speed streaks on each side. Results from the global stability analyses highlight the unstable nature of the central low-speed region and its crucial importance in the laminar-turbulent transition process. For the set of parameters considered, it is able to sustain a varicose global instability for which the predicted critical Reynolds number is only 6% larger than the one reported in Ref. 10. A kinetic energy budget and wavemaker analysis revealed that this mode finds its root in the reversed flow region right downstream the roughness element and extracts most of its energy from the central low-speed region and streaks further downstream. Direct numerical simulations of the flow past this roughness element puts in the limelight the ability for this linear instability to give birth to hairpin vortices and thus trigger transition to turbulence.Influence of the Shape on the Roughness-Induced Transition
http://hdl.handle.net/10985/17803
Influence of the Shape on the Roughness-Induced Transition
LOISEAU, Jean-Christophe; CHERUBINI, Stefania; ROBINET, Jean-Christophe; LERICHE, Emmanuel
lobal instability analysis of the three-dimensional flow past two rough- ness elements of different shape, namely a cylinder and a bump, is presented. In both cases, the eigenspectrum is made of modes characterised by a varicose symmetry and localised mostly in the zones of large base flow shear. The primary instabil- ity exhibited is the same in both cases and consists in an isolated unstable mode closely related to streaks local instability. For the cylinder however, a whole branch of modes is in addition destabilised as the Reynolds number is further increased.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/178032015-01-01T00:00:00ZLOISEAU, Jean-ChristopheCHERUBINI, StefaniaROBINET, Jean-ChristopheLERICHE, Emmanuellobal instability analysis of the three-dimensional flow past two rough- ness elements of different shape, namely a cylinder and a bump, is presented. In both cases, the eigenspectrum is made of modes characterised by a varicose symmetry and localised mostly in the zones of large base flow shear. The primary instabil- ity exhibited is the same in both cases and consists in an isolated unstable mode closely related to streaks local instability. For the cylinder however, a whole branch of modes is in addition destabilised as the Reynolds number is further increased.Bifurcation analysis and frequency prediction in shear-driven cavity flow
http://hdl.handle.net/10985/18039
Bifurcation analysis and frequency prediction in shear-driven cavity flow
BENGANA, Y.; LOISEAU, Jean-Christophe; ROBINET, Jean-Christophe; TUCKERMAN, L. S.
A comprehensive study of the two-dimensional incompressible shear-driven flow in an open square cavity is carried out. Two successive bifurcations lead to two limit cycles with different frequencies and different numbers of structures which propagate along the top of the cavity and circulate in its interior. A branch of quasi-periodic states produced by secondary Hopf bifurcations transfers the stability from one limit cycle to the other. A full analysis of this scenario is obtained by means of nonlinear simulations, linear stability analysis and Floquet analysis. We characterize the temporal behaviour of the limit cycles and quasi-periodic state via Fourier transforms and their spatial behaviour via the Hilbert transform. We address the relevance of linearization about the mean flow. Although here the nonlinear frequencies are not very far from those obtained by linearization about the base flow, the difference is substantially reduced when eigenvalues are obtained instead from linearization about the mean and in addition, the corresponding growth rate is small, a combination of properties called RZIF (real zero imaginary frequency). Moreover growth rates obtained by linearization about the mean of one limit cycle are correlated with relative stability to the other limit cycle. Finally, we show that the frequencies of the successive modes are separated by a constant increment.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/180392019-01-01T00:00:00ZBENGANA, Y.LOISEAU, Jean-ChristopheROBINET, Jean-ChristopheTUCKERMAN, L. S.A comprehensive study of the two-dimensional incompressible shear-driven flow in an open square cavity is carried out. Two successive bifurcations lead to two limit cycles with different frequencies and different numbers of structures which propagate along the top of the cavity and circulate in its interior. A branch of quasi-periodic states produced by secondary Hopf bifurcations transfers the stability from one limit cycle to the other. A full analysis of this scenario is obtained by means of nonlinear simulations, linear stability analysis and Floquet analysis. We characterize the temporal behaviour of the limit cycles and quasi-periodic state via Fourier transforms and their spatial behaviour via the Hilbert transform. We address the relevance of linearization about the mean flow. Although here the nonlinear frequencies are not very far from those obtained by linearization about the base flow, the difference is substantially reduced when eigenvalues are obtained instead from linearization about the mean and in addition, the corresponding growth rate is small, a combination of properties called RZIF (real zero imaginary frequency). Moreover growth rates obtained by linearization about the mean of one limit cycle are correlated with relative stability to the other limit cycle. Finally, we show that the frequencies of the successive modes are separated by a constant increment.Numerical investigation of the interaction between laminar to turbulent transition and the wake of an airfoil
http://hdl.handle.net/10985/17835
Numerical investigation of the interaction between laminar to turbulent transition and the wake of an airfoil
DUCOIN, A.; LOISEAU, Jean-Christophe; ROBINET, Jean-Christophe
The objective of this work is to investigate numerically the different physical mechanisms of the transition to turbulence of a separated boundary-layer flow over an airfoil at low angle of attack. In this study, the spectral elements code Nek5000 is used to simulate the flow over a SD7003 wing section at an angle of attack of α = 4 ◦ . Several laminar cases are first studied from Re = 2000 to Re = 10000, and a gradual increase of the Reynolds number is then performed in order to investigate one transitional case at Re = 20000. Computations are compared with measurements where the instability mechanisms in the separated zone and near wake zone have been analyzed. The mechanism of transition is investigated, where the DMD (Dynamic Mode Decomposition) is used in order to extract the main physical modes of the flow and to highlight the interaction between the transition and the wake flow. The results suggest that the transition process appears to be physically independent of the wake flow, while the LSB shedding process is locked-in with the von Kármán instability and acts as a sub-harmonic.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/178352016-01-01T00:00:00ZDUCOIN, A.LOISEAU, Jean-ChristopheROBINET, Jean-ChristopheThe objective of this work is to investigate numerically the different physical mechanisms of the transition to turbulence of a separated boundary-layer flow over an airfoil at low angle of attack. In this study, the spectral elements code Nek5000 is used to simulate the flow over a SD7003 wing section at an angle of attack of α = 4 ◦ . Several laminar cases are first studied from Re = 2000 to Re = 10000, and a gradual increase of the Reynolds number is then performed in order to investigate one transitional case at Re = 20000. Computations are compared with measurements where the instability mechanisms in the separated zone and near wake zone have been analyzed. The mechanism of transition is investigated, where the DMD (Dynamic Mode Decomposition) is used in order to extract the main physical modes of the flow and to highlight the interaction between the transition and the wake flow. The results suggest that the transition process appears to be physically independent of the wake flow, while the LSB shedding process is locked-in with the von Kármán instability and acts as a sub-harmonic.Time-Stepping and Krylov Method for large scale instability problems
http://hdl.handle.net/10985/17840
Time-Stepping and Krylov Method for large scale instability problems
LOISEAU, Jean-Christophe; BUCCI, Michele Alessandro; CHERUBINI, Stefania; ROBINET, Jean-Christophe
With the ever increasing computational power available and the development of high-performances computing, investigating the properties of realistic very large-scale nonlinear dynamical systems has become reachable. It must be noted however that the memory capabilities of computers increase at a slower rate than their computational capabilities. Consequently, the traditional matrix-forming approaches wherein the Jacobian matrix of the system considered is explicitly assembled become rapidly intractable. Over the past two decades, so-called matrix-free approaches have emerged as an efficient alternative. The aim of this chapter is thus to provide an overview of well-grounded matrix-free methods for fixed points computations and linear stability analyses of very large-scale nonlinear dynamical systems.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/178402018-01-01T00:00:00ZLOISEAU, Jean-ChristopheBUCCI, Michele AlessandroCHERUBINI, StefaniaROBINET, Jean-ChristopheWith the ever increasing computational power available and the development of high-performances computing, investigating the properties of realistic very large-scale nonlinear dynamical systems has become reachable. It must be noted however that the memory capabilities of computers increase at a slower rate than their computational capabilities. Consequently, the traditional matrix-forming approaches wherein the Jacobian matrix of the system considered is explicitly assembled become rapidly intractable. Over the past two decades, so-called matrix-free approaches have emerged as an efficient alternative. The aim of this chapter is thus to provide an overview of well-grounded matrix-free methods for fixed points computations and linear stability analyses of very large-scale nonlinear dynamical systems.From the POD-Galerkin method to sparse manifold models
http://hdl.handle.net/10985/23061
From the POD-Galerkin method to sparse manifold models
BRUNTON, Steven; NOACK, Bernd; LOISEAU, Jean-Christophe
Reduced-order models are essential for the accurate and efficient prediction, estimation, and control of complex systems. This is especially true in fluid dynamics, where the fully resolved state space may easily contain millions or billions of degrees of freedom. Because these systems typically evolve on a low-dimensional attractor, model reduction is defined by two essential steps: (1) identify a good state space for the attractor and (2) identifying the dynamics on this attractor. The leading method for model reduction in fluids is Galerkin projection of the Navier–Stokes equations onto a linear subspace of modes obtained via proper orthogonal decomposition (POD). However, there are serious challenges in this approach, including truncation errors, stability issues, difficulty handling transients, and mode deformation with changing boundaries and operating conditions. Many of these challenges result from the choice of a linear POD subspace in which to represent the dynamics. In this chapter, we describe an alternative approach, feature-based manifold modeling (FeMM), in which the low-dimensional attractor and nonlinear dynamics are characterized from typical experimental data: time-resolved sensor data and optional nontime-resolved particle image velocimetry (PIV) snapshots. FeMM consists of three steps: First, the sensor signals are lifted to a dynamic feature space. Second, we identify a sparse human-interpretable nonlinear dynamical system for the feature state based on the sparse identification of nonlinear dynamics (SINDy). Third, if PIV snapshots are available, a local linear mapping from the feature state to the velocity field is performed to reconstruct the full state of the system. We demonstrate this approach, and compare with POD-Galerkin modeling, on the incompressible two-dimensional flow around a circular cylinder. Best practices and perspectives for future research are also included, along with open-source code for this example.
Tue, 01 Jun 2021 00:00:00 GMThttp://hdl.handle.net/10985/230612021-06-01T00:00:00ZBRUNTON, StevenNOACK, BerndLOISEAU, Jean-ChristopheReduced-order models are essential for the accurate and efficient prediction, estimation, and control of complex systems. This is especially true in fluid dynamics, where the fully resolved state space may easily contain millions or billions of degrees of freedom. Because these systems typically evolve on a low-dimensional attractor, model reduction is defined by two essential steps: (1) identify a good state space for the attractor and (2) identifying the dynamics on this attractor. The leading method for model reduction in fluids is Galerkin projection of the Navier–Stokes equations onto a linear subspace of modes obtained via proper orthogonal decomposition (POD). However, there are serious challenges in this approach, including truncation errors, stability issues, difficulty handling transients, and mode deformation with changing boundaries and operating conditions. Many of these challenges result from the choice of a linear POD subspace in which to represent the dynamics. In this chapter, we describe an alternative approach, feature-based manifold modeling (FeMM), in which the low-dimensional attractor and nonlinear dynamics are characterized from typical experimental data: time-resolved sensor data and optional nontime-resolved particle image velocimetry (PIV) snapshots. FeMM consists of three steps: First, the sensor signals are lifted to a dynamic feature space. Second, we identify a sparse human-interpretable nonlinear dynamical system for the feature state based on the sparse identification of nonlinear dynamics (SINDy). Third, if PIV snapshots are available, a local linear mapping from the feature state to the velocity field is performed to reconstruct the full state of the system. We demonstrate this approach, and compare with POD-Galerkin modeling, on the incompressible two-dimensional flow around a circular cylinder. Best practices and perspectives for future research are also included, along with open-source code for this example.Nonlinear stochastic modelling with Langevin regression
http://hdl.handle.net/10985/23069
Nonlinear stochastic modelling with Langevin regression
CALLAHAM, J. L.; RIGAS, G.; BRUNTON, S. L.; LOISEAU, Jean-Christophe
Many physical systems characterized by nonlinear multiscale interactions can be modelled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative macroscopic behaviour are known, it is often difficult to derive a stochastic model that is consistent with observations. This is especially true for systems such as turbulence where the perturbations do not behave like Gaussian white noise, introducing non-Markovian behaviour to the dynamics. We address these challenges with a framework for identifying interpretable stochastic nonlinear dynamics from experimental data, using forward and adjoint Fokker–Planck equations to enforce statistical consistency. If the form of the Langevin equation is unknown, a simple sparsifying procedure can provide an appropriate functional form. We demonstrate that this method can learn stochastic models in two artificial examples: recovering a nonlinear Langevin equation forced by coloured noise and approximating the second-order dynamics of a particle in a double-well potential with the corresponding first-order bifurcation normal form. Finally, we apply Langevin regression to experimental measurements of a turbulent bluff body wake and show that the statistical behaviour of the centre of pressure can be described by the dynamics of the corresponding laminar flow driven by nonlinear state-dependent noise.
Tue, 01 Jun 2021 00:00:00 GMThttp://hdl.handle.net/10985/230692021-06-01T00:00:00ZCALLAHAM, J. L.RIGAS, G.BRUNTON, S. L.LOISEAU, Jean-ChristopheMany physical systems characterized by nonlinear multiscale interactions can be modelled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative macroscopic behaviour are known, it is often difficult to derive a stochastic model that is consistent with observations. This is especially true for systems such as turbulence where the perturbations do not behave like Gaussian white noise, introducing non-Markovian behaviour to the dynamics. We address these challenges with a framework for identifying interpretable stochastic nonlinear dynamics from experimental data, using forward and adjoint Fokker–Planck equations to enforce statistical consistency. If the form of the Langevin equation is unknown, a simple sparsifying procedure can provide an appropriate functional form. We demonstrate that this method can learn stochastic models in two artificial examples: recovering a nonlinear Langevin equation forced by coloured noise and approximating the second-order dynamics of a particle in a double-well potential with the corresponding first-order bifurcation normal form. Finally, we apply Langevin regression to experimental measurements of a turbulent bluff body wake and show that the statistical behaviour of the centre of pressure can be described by the dynamics of the corresponding laminar flow driven by nonlinear state-dependent noise.Deep Recurrent Encoder: an end-to-end network to model magnetoencephalography at scale
http://hdl.handle.net/10985/23068
Deep Recurrent Encoder: an end-to-end network to model magnetoencephalography at scale
CHEHAB, Omar; DEFOSSEZ, Alexandre; GRAMFORT, Alexandre; KING, Jean-Remi; LOISEAU, Jean-Christophe
Understanding how the brain responds to sensory inputs from non-invasive brain recordings like magnetoencephalography (MEG) can be particularly challenging: (i) the high-dimensional dynamics of mass neuronal activity are notoriously difficult to model, (ii) signals can greatly vary across subjects and trials and (iii) the relationship between these brain responses and the stimulus features is non-trivial. These challenges have led the community to develop a variety of preprocessing and analytical (almost exclusively linear) methods, each designed to tackle one of these issues. Instead, we propose to address these challenges through a specific end-to-end deep learning architecture, trained to predict the MEG responses of multiple subjects at once. We successfully test this approach on a large cohort of MEG recordings acquired during a one-hour reading task. Our Deep Recurrent Encoder (DRE) reliably predicts MEG responses to words with a three-fold improvement over classic linear methods. We further describe a simple variable importance analysis to investigate the MEG representations learnt by our model and recover the expected evoked responses to word length and word frequency. Last, we show that, contrary to linear encoders, our model captures modulations of the brain response in relation to baseline fluctuations in the alpha frequency band. The quantitative improvement of the present deep learning approach paves the way to a better characterization of the complex dynamics of brain activity from large MEG datasets.
Sat, 01 Oct 2022 00:00:00 GMThttp://hdl.handle.net/10985/230682022-10-01T00:00:00ZCHEHAB, OmarDEFOSSEZ, AlexandreGRAMFORT, AlexandreKING, Jean-RemiLOISEAU, Jean-ChristopheUnderstanding how the brain responds to sensory inputs from non-invasive brain recordings like magnetoencephalography (MEG) can be particularly challenging: (i) the high-dimensional dynamics of mass neuronal activity are notoriously difficult to model, (ii) signals can greatly vary across subjects and trials and (iii) the relationship between these brain responses and the stimulus features is non-trivial. These challenges have led the community to develop a variety of preprocessing and analytical (almost exclusively linear) methods, each designed to tackle one of these issues. Instead, we propose to address these challenges through a specific end-to-end deep learning architecture, trained to predict the MEG responses of multiple subjects at once. We successfully test this approach on a large cohort of MEG recordings acquired during a one-hour reading task. Our Deep Recurrent Encoder (DRE) reliably predicts MEG responses to words with a three-fold improvement over classic linear methods. We further describe a simple variable importance analysis to investigate the MEG representations learnt by our model and recover the expected evoked responses to word length and word frequency. Last, we show that, contrary to linear encoders, our model captures modulations of the brain response in relation to baseline fluctuations in the alpha frequency band. The quantitative improvement of the present deep learning approach paves the way to a better characterization of the complex dynamics of brain activity from large MEG datasets.On the role of nonlinear correlations in reduced-order modelling
http://hdl.handle.net/10985/23072
On the role of nonlinear correlations in reduced-order modelling
CALLAHAM, Jared L.; BRUNTON, Steven L.; LOISEAU, Jean-Christophe
This work investigates nonlinear dimensionality reduction as a means of improving the accuracy and stability of reduced-order models of advection-dominated flows. Nonlinear correlations between temporal proper orthogonal decomposition (POD) coefficients can be exploited to identify latent low-dimensional structure, approximating the attractor with a minimal set of driving modes and a manifold equation for the remaining modes. By viewing these nonlinear correlations as an invariant manifold reduction, this least-order representation can be used to stabilize POD–Galerkin models or as a state space for data-driven model identification. In the latter case, we use sparse polynomial regression to learn a compact, interpretable dynamical system model from the time series of the active modal coefficients. We demonstrate this perspective on a quasiperiodic shear-driven cavity flow and show that the dynamics evolves on a torus generated by two independent Stuart–Landau oscillators. The specific approach to nonlinear correlations analysis used in this work is applicable to periodic and quasiperiodic flows, and cannot be applied to chaotic or turbulent flows. However, the results illustrate the limitations of linear modal representations of advection-dominated flows and motivate the use of nonlinear dimensionality reduction more broadly for exploiting underlying structure in reduced-order models.
Tue, 01 Mar 2022 00:00:00 GMThttp://hdl.handle.net/10985/230722022-03-01T00:00:00ZCALLAHAM, Jared L.BRUNTON, Steven L.LOISEAU, Jean-ChristopheThis work investigates nonlinear dimensionality reduction as a means of improving the accuracy and stability of reduced-order models of advection-dominated flows. Nonlinear correlations between temporal proper orthogonal decomposition (POD) coefficients can be exploited to identify latent low-dimensional structure, approximating the attractor with a minimal set of driving modes and a manifold equation for the remaining modes. By viewing these nonlinear correlations as an invariant manifold reduction, this least-order representation can be used to stabilize POD–Galerkin models or as a state space for data-driven model identification. In the latter case, we use sparse polynomial regression to learn a compact, interpretable dynamical system model from the time series of the active modal coefficients. We demonstrate this perspective on a quasiperiodic shear-driven cavity flow and show that the dynamics evolves on a torus generated by two independent Stuart–Landau oscillators. The specific approach to nonlinear correlations analysis used in this work is applicable to periodic and quasiperiodic flows, and cannot be applied to chaotic or turbulent flows. However, the results illustrate the limitations of linear modal representations of advection-dominated flows and motivate the use of nonlinear dimensionality reduction more broadly for exploiting underlying structure in reduced-order models.Influence of freestream turbulence on the flow over a wall roughness
http://hdl.handle.net/10985/20464
Influence of freestream turbulence on the flow over a wall roughness
BUCCI, Michele Alessandro; CHERUBINI, Stefania; LOISEAU, Jean-Christophe; ROBINET, Jean-Christophe
The effect of freestream turbulence on the dynamics of an incompressible flow past a cylindrical roughness element in subcritical conditions (i.e., for Reynolds numbers below the onset of linear instability) has been investigated by the joint application of direct numerical simulations, linear modal and nonmodal stability analyses, and dynamic mode decomposition. At first, the influence of the Reynolds number and the ratio of the boundary layer’s thickness to roughness height on the three-dimensional spatiotemporal (global) stability of the flow has been investigated. Depending on the operating conditions, the leading instability can either be varicose (symmetric) or sinuous (antisymmetric). In both cases, when the flow is excited by broadband frequency forcing, dynamic mode decomposition extracts only varicose coherent structures even though optimal response analysis predicts a strong amplification of sinuous disturbances having frequency close to that of the marginally stable sinuous eigenmode. This apparent discrepancy is attributed to the fact that the sinuous instability is sensitive to a very limited range of frequencies barely excited by freestream turbulence while varicose disturbances are associated with high amplification in a much wider frequency range. Hence, in this case the flow behaves as an amplifier of varicose perturbations rather than a resonator. Consequences on the subsequent transition to turbulence have been studied, highlighting that varicose perturbations extract energy from the near-wake region, get continuously amplified due to the excitation provided by freestream turbulence, and eventually give rise to a shedding of hairpin vortices.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/204642021-01-01T00:00:00ZBUCCI, Michele AlessandroCHERUBINI, StefaniaLOISEAU, Jean-ChristopheROBINET, Jean-ChristopheThe effect of freestream turbulence on the dynamics of an incompressible flow past a cylindrical roughness element in subcritical conditions (i.e., for Reynolds numbers below the onset of linear instability) has been investigated by the joint application of direct numerical simulations, linear modal and nonmodal stability analyses, and dynamic mode decomposition. At first, the influence of the Reynolds number and the ratio of the boundary layer’s thickness to roughness height on the three-dimensional spatiotemporal (global) stability of the flow has been investigated. Depending on the operating conditions, the leading instability can either be varicose (symmetric) or sinuous (antisymmetric). In both cases, when the flow is excited by broadband frequency forcing, dynamic mode decomposition extracts only varicose coherent structures even though optimal response analysis predicts a strong amplification of sinuous disturbances having frequency close to that of the marginally stable sinuous eigenmode. This apparent discrepancy is attributed to the fact that the sinuous instability is sensitive to a very limited range of frequencies barely excited by freestream turbulence while varicose disturbances are associated with high amplification in a much wider frequency range. Hence, in this case the flow behaves as an amplifier of varicose perturbations rather than a resonator. Consequences on the subsequent transition to turbulence have been studied, highlighting that varicose perturbations extract energy from the near-wake region, get continuously amplified due to the excitation provided by freestream turbulence, and eventually give rise to a shedding of hairpin vortices.