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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.Nonlinear optimal perturbations in a Couette flow: bursting and transition
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.Minimal-energy perturbations rapidly approaching the edge state in Couette flow
http://hdl.handle.net/10985/10319
Minimal-energy perturbations rapidly approaching the edge state in Couette flow
CHERUBINI, Stefania; DE PALMA, Pietro
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 etÂ 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.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/103192015-01-01T00:00:00ZCHERUBINI, StefaniaDE PALMA, PietroTransition 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 etÂ 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.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.Transient growth in the flow past a three-dimensional smooth roughness element
http://hdl.handle.net/10985/8973
Transient growth in the flow past a three-dimensional smooth roughness element
CHERUBINI, Stefania; DE TULLIO, Marco; DE PALMA, Pietro; PASCAZIO, Giuseppe
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.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/89732013-01-01T00:00:00ZCHERUBINI, StefaniaDE TULLIO, MarcoDE PALMA, PietroPASCAZIO, GiuseppeThis 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.Optimal bursts in turbulent channel flow
http://hdl.handle.net/10985/11634
Optimal bursts in turbulent channel flow
FARANO, Mirko; CHERUBINI, Stefania; DE PALMA, Pietro; ROBINET, Jean-Christophe
Bursts are recurrent, transient, highly energetic events characterized by localized variations of velocity and vorticity in turbulent wall-bounded ﬂows. In this work, a nonlinear energy optimization strategy is employed to investigate whether the origin of such bursting events in a turbulent channel ﬂow can be related to the presence of high-amplitude coherent structures. The results show that bursting events correspond to optimal energy ﬂow structures embedded in the fully turbulent ﬂow. In particular, optimal structures inducing energy peaks at short time are initially composed of highly oscillating vortices and streaks near the wall. At moderate friction Reynolds numbers, through the bursts, energy is exchanged between the streaks and packets of hairpin vortices of different sizes reaching the outer scale. Such an optimal ﬂow conﬁguration reproduces well the spatial spectra as well as the probability density function typical of turbulent ﬂows, recovering the mechanism of direct-inverse energy cascade. These results represent an important step towards understanding the dynamics of turbulence at moderate Reynolds numbers and pave the way to new nonlinear techniques to manipulate and control the self-sustained turbulence dynamics.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/116342017-01-01T00:00:00ZFARANO, MirkoCHERUBINI, StefaniaDE PALMA, PietroROBINET, Jean-ChristopheBursts are recurrent, transient, highly energetic events characterized by localized variations of velocity and vorticity in turbulent wall-bounded ﬂows. In this work, a nonlinear energy optimization strategy is employed to investigate whether the origin of such bursting events in a turbulent channel ﬂow can be related to the presence of high-amplitude coherent structures. The results show that bursting events correspond to optimal energy ﬂow structures embedded in the fully turbulent ﬂow. In particular, optimal structures inducing energy peaks at short time are initially composed of highly oscillating vortices and streaks near the wall. At moderate friction Reynolds numbers, through the bursts, energy is exchanged between the streaks and packets of hairpin vortices of different sizes reaching the outer scale. Such an optimal ﬂow conﬁguration reproduces well the spatial spectra as well as the probability density function typical of turbulent ﬂows, recovering the mechanism of direct-inverse energy cascade. These results represent an important step towards understanding the dynamics of turbulence at moderate Reynolds numbers and pave the way to new nonlinear techniques to manipulate and control the self-sustained turbulence dynamics.Linear and nonlinear optimal growth mechanisms for generating turbulent bands
http://hdl.handle.net/10985/21696
Linear and nonlinear optimal growth mechanisms for generating turbulent bands
PARENTE, ENZA; DE PALMA, Pietro; CHERUBINI, Stefania; ROBINET, Jean-Christophe
Recently, many authors have investigated the origin and growth of turbulent bands in shear flows, highlighting the role of streaks and their inflectional instability in the process of band generation and sustainment. Recalling that streaks are created by an optimal transient growth mechanism, and motivated by the observation of a strong increase of the disturbance kinetic energy corresponding to the creation of turbulent bands, we use linear and nonlinear energy optimisations in a tilted domain to unveil the main mechanisms allowing the creation of a turbulent band in a channel flow. Linear transient growth analysis shows an optimal growth for wavenumbers having an angle of approximately 35◦, close to the peak values of the premultiplied energy spectra of direct numerical simulations. This linear optimal perturbation generates oblique streaks, which, for a sufficiently large initial energy, induce turbulence in the whole domain, due to the lack of spatial localisation. However, spatially localised perturbations obtained by adding nonlinear effects to the optimisation or by artificially confining the linear optimal to a localised region in the transverse direction are characterised by a large-scale flow and lead to the generation of a localised turbulent band. These results suggest that two main elements are needed for inducing turbulent bands in a tilted domain: (i) a linear energy growth mechanism, such as the lift-up, for generating large-amplitude flow structures, which produce inflection points; (ii) spatial localisation, linked to the presence or generation of large-scale vortices. We show that these elements alone generate isolated turbulent bands also in large non-tilted domains.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10985/216962022-01-01T00:00:00ZPARENTE, ENZADE PALMA, PietroCHERUBINI, StefaniaROBINET, Jean-ChristopheRecently, many authors have investigated the origin and growth of turbulent bands in shear flows, highlighting the role of streaks and their inflectional instability in the process of band generation and sustainment. Recalling that streaks are created by an optimal transient growth mechanism, and motivated by the observation of a strong increase of the disturbance kinetic energy corresponding to the creation of turbulent bands, we use linear and nonlinear energy optimisations in a tilted domain to unveil the main mechanisms allowing the creation of a turbulent band in a channel flow. Linear transient growth analysis shows an optimal growth for wavenumbers having an angle of approximately 35◦, close to the peak values of the premultiplied energy spectra of direct numerical simulations. This linear optimal perturbation generates oblique streaks, which, for a sufficiently large initial energy, induce turbulence in the whole domain, due to the lack of spatial localisation. However, spatially localised perturbations obtained by adding nonlinear effects to the optimisation or by artificially confining the linear optimal to a localised region in the transverse direction are characterised by a large-scale flow and lead to the generation of a localised turbulent band. These results suggest that two main elements are needed for inducing turbulent bands in a tilted domain: (i) a linear energy growth mechanism, such as the lift-up, for generating large-amplitude flow structures, which produce inflection points; (ii) spatial localisation, linked to the presence or generation of large-scale vortices. We show that these elements alone generate isolated turbulent bands also in large non-tilted domains.Numerical Study of the Effect of Freestream Turbulence on by-pass Transition in a Boundary Layer
http://hdl.handle.net/10985/9011
Numerical Study of the Effect of Freestream Turbulence on by-pass Transition in a Boundary Layer
CHERUBINI, Stefania; DE PALMA, Pietro; ROBINET, Jean-Christophe
We use direct numerical simulations in the presence of free-stream turbulence having different values of intensity, T u, 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 T u 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 L and hairpin structures resulting from the time evolution of non-linear optimal perturbations, whereas, for lower T u 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 T u and L, valid for both the transition scenarios.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/90112014-01-01T00:00:00ZCHERUBINI, StefaniaDE PALMA, PietroROBINET, Jean-ChristopheWe use direct numerical simulations in the presence of free-stream turbulence having different values of intensity, T u, 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 T u 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 L and hairpin structures resulting from the time evolution of non-linear optimal perturbations, whereas, for lower T u 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 T u and L, valid for both the transition scenarios.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; BOTTARO, Alessandro; ROBINET, Jean-Christophe
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, PietroBOTTARO, AlessandroROBINET, Jean-ChristopheThe 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.Rapid path to transition via nonlinear localized optimal perturbations in a boundary-layer flow
http://hdl.handle.net/10985/6861
Rapid path to transition via nonlinear localized optimal perturbations in a boundary-layer flow
CHERUBINI, Stefania; DE PALMA, Pietro; BOTTARO, Alessandro; ROBINET, Jean-Christophe
Recent studies have suggested that in some cases transition can be triggered by some purely nonlinear mechanisms. Here we aim at verifying such an hypothesis, looking for a localized perturbation able to lead a boundary-layer flow to a chaotic state, following a nonlinear route. Nonlinear optimal localized perturbations have been computed by means of an energy optimization which includes the nonlinear terms of the Navier- Stokes equations. Such perturbations lie on the turbulent side of the laminar-turbulent boundary, whereas, for the same value of the initial energy, their linear counterparts do not. The evolution of these perturbations toward a turbulent flow involves the presence of streamwise-inclined vortices at short times and of hairpin structures prior to breakdown.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10985/68612010-01-01T00:00:00ZCHERUBINI, StefaniaDE PALMA, PietroBOTTARO, AlessandroROBINET, Jean-ChristopheRecent studies have suggested that in some cases transition can be triggered by some purely nonlinear mechanisms. Here we aim at verifying such an hypothesis, looking for a localized perturbation able to lead a boundary-layer flow to a chaotic state, following a nonlinear route. Nonlinear optimal localized perturbations have been computed by means of an energy optimization which includes the nonlinear terms of the Navier- Stokes equations. Such perturbations lie on the turbulent side of the laminar-turbulent boundary, whereas, for the same value of the initial energy, their linear counterparts do not. The evolution of these perturbations toward a turbulent flow involves the presence of streamwise-inclined vortices at short times and of hairpin structures prior to breakdown.