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http://hdl.handle.net/10985/18608
Weakly nonlinear optimal perturbations
PRALITS, Jan O.; BOTTARO, Alessandro; CHERUBINI, Stefania
A simple approach is described for computing spatially extended, weakly nonlinear optimal disturbances, suitable for maintaining a disturbance-regeneration cycle in a simple shear flow. Weakly nonlinear optimals, computed over a short time interval for the expansion used to remain tenable, are oblique waves which display a shorter streamwise and a longer spanwise wavelength than their linear counterparts. Threshold values of the initial excitation energy, separating the region of damped waves from that where disturbances grow without bounds, are found. Weakly nonlinear optimal solutions of varying initial amplitudes are then fed as initial conditions into direct numerical simulations of the Navier–Stokes equations and it is shown that the weakly nonlinear model permits the identification of flow states which cause rapid breakdown to turbulence.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/186082015-01-01T00:00:00ZPRALITS, Jan O.BOTTARO, AlessandroCHERUBINI, StefaniaA simple approach is described for computing spatially extended, weakly nonlinear optimal disturbances, suitable for maintaining a disturbance-regeneration cycle in a simple shear flow. Weakly nonlinear optimals, computed over a short time interval for the expansion used to remain tenable, are oblique waves which display a shorter streamwise and a longer spanwise wavelength than their linear counterparts. Threshold values of the initial excitation energy, separating the region of damped waves from that where disturbances grow without bounds, are found. Weakly nonlinear optimal solutions of varying initial amplitudes are then fed as initial conditions into direct numerical simulations of the Navier–Stokes equations and it is shown that the weakly nonlinear model permits the identification of flow states which cause rapid breakdown to turbulence.Effect of plate permeability on nonlinear stability of the asymptotic suction boundary layer
http://hdl.handle.net/10985/10314
Effect of plate permeability on nonlinear stability of the asymptotic suction boundary layer
WEDIN, Hakan; CHERUBINI, Stefania; BOTTARO, Alessandro
The nonlinear stability of the asymptotic suction boundary layer is studied numerically, searching for finite-amplitude solutions that bifurcate from the laminar flow state. By changing the boundary conditions for disturbances at the plate from the classical no-slip condition to more physically sound ones, the stability characteristics of the flow may change radically, both for the linearized as well as the nonlinear problem. The wall boundary condition takes into account the permeability K of the plate; for very low permeability, it is acceptable to impose the classical boundary condition (K=0). This leads to a Reynolds number of approximately Rec=54400 for the onset of linearly unstable waves, and close to Reg=3200 for the emergence of nonlinear solutions [F. A. Milinazzo and P. G. Saffman, J. Fluid Mech. 160, 281 (1985)JFLSA70022-112010.1017/S0022112085003482; J. H. M. Fransson, Ph.D. thesis, Royal Institute of Technology, KTH, Sweden, 2003]. However, for larger values of the plate's permeability, the lower limit for the existence of linear and nonlinear solutions shifts to significantly lower Reynolds numbers. For the largest permeability studied here, the limit values of the Reynolds numbers reduce down to Rec=796 and Reg=294. For all cases studied, the solutions bifurcate subcritically toward lower Re, and this leads to the conjecture that they may be involved in the very first stages of a transition scenario similar to the classical route of the Blasius boundary layer initiated by Tollmien-Schlichting (TS) waves. The stability of these nonlinear solutions is also investigated, showing a low-frequency main unstable mode whose growth rate decreases with increasing permeability and with the Reynolds number, following a power law Re-ρ, where the value of ρ depends on the permeability coefficient K. The nonlinear dynamics of the flow in the vicinity of the computed finite-amplitude solutions is finally investigated by direct numerical simulations, providing a viable scenario for subcritical transition due to TS waves
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/103142015-01-01T00:00:00ZWEDIN, HakanCHERUBINI, StefaniaBOTTARO, AlessandroThe nonlinear stability of the asymptotic suction boundary layer is studied numerically, searching for finite-amplitude solutions that bifurcate from the laminar flow state. By changing the boundary conditions for disturbances at the plate from the classical no-slip condition to more physically sound ones, the stability characteristics of the flow may change radically, both for the linearized as well as the nonlinear problem. The wall boundary condition takes into account the permeability K of the plate; for very low permeability, it is acceptable to impose the classical boundary condition (K=0). This leads to a Reynolds number of approximately Rec=54400 for the onset of linearly unstable waves, and close to Reg=3200 for the emergence of nonlinear solutions [F. A. Milinazzo and P. G. Saffman, J. Fluid Mech. 160, 281 (1985)JFLSA70022-112010.1017/S0022112085003482; J. H. M. Fransson, Ph.D. thesis, Royal Institute of Technology, KTH, Sweden, 2003]. However, for larger values of the plate's permeability, the lower limit for the existence of linear and nonlinear solutions shifts to significantly lower Reynolds numbers. For the largest permeability studied here, the limit values of the Reynolds numbers reduce down to Rec=796 and Reg=294. For all cases studied, the solutions bifurcate subcritically toward lower Re, and this leads to the conjecture that they may be involved in the very first stages of a transition scenario similar to the classical route of the Blasius boundary layer initiated by Tollmien-Schlichting (TS) waves. The stability of these nonlinear solutions is also investigated, showing a low-frequency main unstable mode whose growth rate decreases with increasing permeability and with the Reynolds number, following a power law Re-ρ, where the value of ρ depends on the permeability coefficient K. The nonlinear dynamics of the flow in the vicinity of the computed finite-amplitude solutions is finally investigated by direct numerical simulations, providing a viable scenario for subcritical transition due to TS wavesA 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.The minimal seed of turbulent transition in the boundary layer
http://hdl.handle.net/10985/6718
The minimal seed of turbulent transition in the boundary layer
CHERUBINI, Stefania; DE PALMA, Pietro; BOTTARO, Alessandro; ROBINET, Jean-Christophe
This paper describes a scenario of transition from laminar to turbulent flow in a spatially developing boundary layer over a flat plate. The base flow is the Blasius non-parallel flow solution; it is perturbed by optimal disturbances yielding the largest energy growth over a short time interval. Such perturbations are computed by a nonlinear global optimization approach based on a Lagrange multiplier technique. The results show that nonlinear optimal perturbations are characterized by a localized basic building block, called the minimal seed, defined as the smallest flow structure which maximizes the energy growth over short times. It is formed by vortices inclined in the streamwise direction surrounding a region of intense streamwise disturbance velocity. Such a basic structure appears to be a robust feature of the base flow since it is practically invariant with respect to the initial energy of the perturbation, the target time, the Reynolds number and the dimensions of the computational domain. The minimal seed grows very rapidly in time while spreading, and it triggers nonlinear effects which bring the flow to turbulence in a very efficient manner, through the formation of a turbulence spot. This evolution of the initial optimal disturbance has been studied in detail by direct numerical simulations. Using a perturbative formulation of the Navier–Stokes equations, each linear and nonlinear convective term of the equations has been analysed. The results show the fundamental role of the streamwise inclination of the vortices in the process. The nonlinear coupling of the finite amplitude disturbances is crucial to sustain such streamwise inclination, as well as to generate dislocations within the flow structures, and local inflectional velocity distributions. The analysis provides a picture of the transition process characterized by a sequence of structures appearing successively in the flow, namely, 3 vortices, hairpin vortices and streamwise streaks. Finally, a disturbance regeneration cycle is conceived, initiated by the fast nonlinear amplification of the minimal seed, providing a possible scenario for the continuous regeneration of the same fundamental flow structures at smaller space and time scales.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10985/67182011-01-01T00:00:00ZCHERUBINI, StefaniaDE PALMA, PietroBOTTARO, AlessandroROBINET, Jean-ChristopheThis paper describes a scenario of transition from laminar to turbulent flow in a spatially developing boundary layer over a flat plate. The base flow is the Blasius non-parallel flow solution; it is perturbed by optimal disturbances yielding the largest energy growth over a short time interval. Such perturbations are computed by a nonlinear global optimization approach based on a Lagrange multiplier technique. The results show that nonlinear optimal perturbations are characterized by a localized basic building block, called the minimal seed, defined as the smallest flow structure which maximizes the energy growth over short times. It is formed by vortices inclined in the streamwise direction surrounding a region of intense streamwise disturbance velocity. Such a basic structure appears to be a robust feature of the base flow since it is practically invariant with respect to the initial energy of the perturbation, the target time, the Reynolds number and the dimensions of the computational domain. The minimal seed grows very rapidly in time while spreading, and it triggers nonlinear effects which bring the flow to turbulence in a very efficient manner, through the formation of a turbulence spot. This evolution of the initial optimal disturbance has been studied in detail by direct numerical simulations. Using a perturbative formulation of the Navier–Stokes equations, each linear and nonlinear convective term of the equations has been analysed. The results show the fundamental role of the streamwise inclination of the vortices in the process. The nonlinear coupling of the finite amplitude disturbances is crucial to sustain such streamwise inclination, as well as to generate dislocations within the flow structures, and local inflectional velocity distributions. The analysis provides a picture of the transition process characterized by a sequence of structures appearing successively in the flow, namely, 3 vortices, hairpin vortices and streamwise streaks. Finally, a disturbance regeneration cycle is conceived, initiated by the fast nonlinear amplification of the minimal seed, providing a possible scenario for the continuous regeneration of the same fundamental flow structures at smaller space and time scales.Edge states in a boundary layer
http://hdl.handle.net/10985/6868
Edge states in a boundary layer
CHERUBINI, Stefania; DE PALMA, Pietro; BOTTARO, Alessandro; ROBINET, Jean-Christophe
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, PietroBOTTARO, AlessandroROBINET, Jean-ChristopheThe 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.Optimal wave packets in a boundary layer and initial phases of a turbulent spot
http://hdl.handle.net/10985/6717
Optimal wave packets in a boundary layer and initial phases of a turbulent spot
CHERUBINI, Stefania; BOTTARO, Alessandro; DE PALMA, Pietro; ROBINET, Jean-Christophe
The three-dimensional global optimal dynamics of a flat-plate boundary layer is studied by means of an adjoint-based optimization in a spatial domain of long – but finite – streamwise dimension. The localized optimal initial perturbation is characterized by a pair of streamwise-modulated counter-rotating vortices, tilted upstream, yielding at the optimal time elongated streaks of alternating sign in the streamwise direction. This indicates that perturbations with non-zero streamwise wavenumber have a role in the transient dynamics of a boundary layer. A scaling law is provided, describing the variation of the streamwise modulation of the optimal initial perturbation with respect to the streamwise domain length and to the Reynolds number. For spanwise-extended domains, a near-optimal three-dimensional perturbation is extracted during the optimization process; it is localized also in the spanwise direction, resulting in a wave packet of elongated disturbances modulated in the spanwise and streamwise directions. The nonlinear evolution of the optimal and near-optimal perturbations is investigated by means of direct numerical simulations. Both perturbations are found to induce transition at lower levels of the initial energy than local optimal and suboptimal perturbations. Moreover, it is observed that transition occurs in a well-defined region of the convected wave packet, close to its centre, via a mechanism including at the same time oscillations of the streaks of both quasi-sinuous and quasi-varicose nature. Hairpin vortices are observed before transition; they have an active role in the breakdown of the streaks and result in a turbulent spot which spreads out in the boundary layer.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10985/67172010-01-01T00:00:00ZCHERUBINI, StefaniaBOTTARO, AlessandroDE PALMA, PietroROBINET, Jean-ChristopheThe three-dimensional global optimal dynamics of a flat-plate boundary layer is studied by means of an adjoint-based optimization in a spatial domain of long – but finite – streamwise dimension. The localized optimal initial perturbation is characterized by a pair of streamwise-modulated counter-rotating vortices, tilted upstream, yielding at the optimal time elongated streaks of alternating sign in the streamwise direction. This indicates that perturbations with non-zero streamwise wavenumber have a role in the transient dynamics of a boundary layer. A scaling law is provided, describing the variation of the streamwise modulation of the optimal initial perturbation with respect to the streamwise domain length and to the Reynolds number. For spanwise-extended domains, a near-optimal three-dimensional perturbation is extracted during the optimization process; it is localized also in the spanwise direction, resulting in a wave packet of elongated disturbances modulated in the spanwise and streamwise directions. The nonlinear evolution of the optimal and near-optimal perturbations is investigated by means of direct numerical simulations. Both perturbations are found to induce transition at lower levels of the initial energy than local optimal and suboptimal perturbations. Moreover, it is observed that transition occurs in a well-defined region of the convected wave packet, close to its centre, via a mechanism including at the same time oscillations of the streaks of both quasi-sinuous and quasi-varicose nature. Hairpin vortices are observed before transition; they have an active role in the breakdown of the streaks and result in a turbulent spot which spreads out in the boundary layer.