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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.Investigation of the roughness-induced transition: global stability analyses and direct numerical simulations
http://hdl.handle.net/10985/8974
Investigation of the roughness-induced transition: global stability analyses and direct numerical simulations
LOISEAU, Jean-Christophe; ROBINET, Jean-Christophe; CHERUBINI, Stefania; LERICHE, Emmanuel
The linear global instability and resulting transition to turbulence induced by an isolated cylindrical roughness element of height h and diameter d immersed within an incompressible boundary layer flow along a flat plate is investigated using the joint application of direct numerical simulations and fully three-dimensional global stability analyses. For the range of parameters investigated, 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 of its sides. 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. It is able to sustain two different global instabilities: a sinuous and a varicose one. Each of these globally unstable modes is related to a different physical mechanism. While the varicose mode has its root in the instability of the whole three-dimensional shear layer surrounding the central low-speed region, the sinuous instability turns out to be similar to the von Kármán instability in the two-dimensional cylinder wake and has its root in the lateral shear layers of the separated zone. The aspect ratio of the roughness element plays a key role on the selection of the dominant instability: whereas the flow over thin cylindrical roughness elements transitions due to a sinuous instability of the near-wake region, for larger roughness elements the varicose instability of the central low-speed region turns out to be the dominant one. Direct numerical simulations of the flow past an aspect ratio 1 roughness element sustaining only the sinuous instability have revealed that the bifurcation occurring in this particular case is supercritical. Finally, comparison of the transition thresholds predicted by global linear stability analyses with the von Doenhoff–Braslow transition diagram provides qualitatively good agreement
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/89742014-01-01T00:00:00ZLOISEAU, Jean-ChristopheROBINET, Jean-ChristopheCHERUBINI, StefaniaLERICHE, EmmanuelThe linear global instability and resulting transition to turbulence induced by an isolated cylindrical roughness element of height h and diameter d immersed within an incompressible boundary layer flow along a flat plate is investigated using the joint application of direct numerical simulations and fully three-dimensional global stability analyses. For the range of parameters investigated, 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 of its sides. 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. It is able to sustain two different global instabilities: a sinuous and a varicose one. Each of these globally unstable modes is related to a different physical mechanism. While the varicose mode has its root in the instability of the whole three-dimensional shear layer surrounding the central low-speed region, the sinuous instability turns out to be similar to the von Kármán instability in the two-dimensional cylinder wake and has its root in the lateral shear layers of the separated zone. The aspect ratio of the roughness element plays a key role on the selection of the dominant instability: whereas the flow over thin cylindrical roughness elements transitions due to a sinuous instability of the near-wake region, for larger roughness elements the varicose instability of the central low-speed region turns out to be the dominant one. Direct numerical simulations of the flow past an aspect ratio 1 roughness element sustaining only the sinuous instability have revealed that the bifurcation occurring in this particular case is supercritical. Finally, comparison of the transition thresholds predicted by global linear stability analyses with the von Doenhoff–Braslow transition diagram provides qualitatively good agreementRoughness-induced transition by quasi-resonance of a varicose global mode
http://hdl.handle.net/10985/17804
Roughness-induced transition by quasi-resonance of a varicose global mode
BUCCI, Michele Alessandro; PUCKERT, D. K.; ANDRIANO, C.; LOISEAU, Jean-Christophe; CHERUBINI, Stefania; ROBINET, Jean-Christophe; RIST, U.
The onset of unsteadiness in a boundary-layer flow past a cylindrical roughness element is investigated for three flow configurations at subcritical Reynolds numbers, both experimentally and numerically. On the one hand, a quasi-periodic shedding of hairpin vortices is observed for all configurations in the experiment. On the other hand, global stability analyses have revealed the existence of a varicose isolated mode, as well as of a sinuous one, both being linearly stable. Nonetheless, the isolated stable varicose modes are highly sensitive, as ascertained by pseudospectrum analysis. To investigate how these modes might influence the dynamics of the flow, an optimal forcing analysis is performed. The optimal response consists of a varicose perturbation closely related to the least stable varicose isolated eigenmode and induces dynamics similar to that observed experimentally. The quasi-resonance of such a global mode to external forcing might thus be responsible for the onset of unsteadiness at subcritical Reynolds numbers, hence providing a simple explanation for the experimental observations.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/178042017-01-01T00:00:00ZBUCCI, Michele AlessandroPUCKERT, D. K.ANDRIANO, C.LOISEAU, Jean-ChristopheCHERUBINI, StefaniaROBINET, Jean-ChristopheRIST, U.The onset of unsteadiness in a boundary-layer flow past a cylindrical roughness element is investigated for three flow configurations at subcritical Reynolds numbers, both experimentally and numerically. On the one hand, a quasi-periodic shedding of hairpin vortices is observed for all configurations in the experiment. On the other hand, global stability analyses have revealed the existence of a varicose isolated mode, as well as of a sinuous one, both being linearly stable. Nonetheless, the isolated stable varicose modes are highly sensitive, as ascertained by pseudospectrum analysis. To investigate how these modes might influence the dynamics of the flow, an optimal forcing analysis is performed. The optimal response consists of a varicose perturbation closely related to the least stable varicose isolated eigenmode and induces dynamics similar to that observed experimentally. The quasi-resonance of such a global mode to external forcing might thus be responsible for the onset of unsteadiness at subcritical Reynolds numbers, hence providing a simple explanation for the experimental observations.Constrained sparse Galerkin regression
http://hdl.handle.net/10985/17796
Constrained sparse Galerkin regression
LOISEAU, Jean-Christophe; BRUNTON, Steven L.
The sparse identification of nonlinear dynamics (SINDy) is a recently proposed data-driven modelling framework that uses sparse regression techniques to identify nonlinear low-order models. With the goal of low-order models of a fluid flow, we combine this approach with dimensionality reduction techniques (e.g. proper orthogonal decomposition) and extend it to enforce physical constraints in the regression, e.g. energy-preserving quadratic nonlinearities. The resulting models, hereafter referred to as Galerkin regression models, incorporate many beneficial aspects of Galerkin projection, but without the need for a high-fidelity solver to project the Navier–Stokes equations. Instead, the most parsimonious nonlinear model is determined that is consistent with observed measurement data and satisfies necessary constraints. Galerkin regression models also readily generalize to include higher-order nonlinear terms that model the effect of truncated modes. The effectiveness of such an approach is demonstrated on two canonical flow configurations: the two-dimensional flow past a circular cylinder and the shear-driven cavity flow. For both cases, the accuracy of the identified models compare favourably against reduced-order models obtained from a standard Galerkin projection procedure. Finally, the entire code base for our constrained sparse Galerkin regression algorithm is freely available online.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/177962018-01-01T00:00:00ZLOISEAU, Jean-ChristopheBRUNTON, Steven L.The sparse identification of nonlinear dynamics (SINDy) is a recently proposed data-driven modelling framework that uses sparse regression techniques to identify nonlinear low-order models. With the goal of low-order models of a fluid flow, we combine this approach with dimensionality reduction techniques (e.g. proper orthogonal decomposition) and extend it to enforce physical constraints in the regression, e.g. energy-preserving quadratic nonlinearities. The resulting models, hereafter referred to as Galerkin regression models, incorporate many beneficial aspects of Galerkin projection, but without the need for a high-fidelity solver to project the Navier–Stokes equations. Instead, the most parsimonious nonlinear model is determined that is consistent with observed measurement data and satisfies necessary constraints. Galerkin regression models also readily generalize to include higher-order nonlinear terms that model the effect of truncated modes. The effectiveness of such an approach is demonstrated on two canonical flow configurations: the two-dimensional flow past a circular cylinder and the shear-driven cavity flow. For both cases, the accuracy of the identified models compare favourably against reduced-order models obtained from a standard Galerkin projection procedure. Finally, the entire code base for our constrained sparse Galerkin regression algorithm is freely available online.Intermittency and transition to chaos in the cubical lid-driven cavity flow
http://hdl.handle.net/10985/17838
Intermittency and transition to chaos in the cubical lid-driven cavity flow
LOISEAU, Jean-Christophe; ROBINET, Jean-Christophe; LERICHE, Emmanuel
Transition from steady state to intermittent chaos in the cubical lid-driven flow is investigated numerically. Fully three-dimensional stability analyses have revealed that the flow experiences an Andronov-Poincaré-Hopf bifurcation at a critical Reynolds number Rec = 1914. As for the 2D-periodic lid-driven cavity flows, the unstable mode originates from a centrifugal instability of the primary vortex core. A Reynolds-Orr analysis reveals that the unstable perturbation relies on a combination of the lift-up and anti lift-up mechanisms to extract its energy from the base flow. Once linearly unstable, direct numerical simulations show that the flow is driven toward a primary limit cycle before eventually exhibiting intermittent chaotic dynamics. Though only one eigenpair of the linearized Navier-Stokes operator is unstable, the dynamics during the intermittencies are surprisingly well characterized by one of the stable eigenpairs.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/178382016-01-01T00:00:00ZLOISEAU, Jean-ChristopheROBINET, Jean-ChristopheLERICHE, EmmanuelTransition from steady state to intermittent chaos in the cubical lid-driven flow is investigated numerically. Fully three-dimensional stability analyses have revealed that the flow experiences an Andronov-Poincaré-Hopf bifurcation at a critical Reynolds number Rec = 1914. As for the 2D-periodic lid-driven cavity flows, the unstable mode originates from a centrifugal instability of the primary vortex core. A Reynolds-Orr analysis reveals that the unstable perturbation relies on a combination of the lift-up and anti lift-up mechanisms to extract its energy from the base flow. Once linearly unstable, direct numerical simulations show that the flow is driven toward a primary limit cycle before eventually exhibiting intermittent chaotic dynamics. Though only one eigenpair of the linearized Navier-Stokes operator is unstable, the dynamics during the intermittencies are surprisingly well characterized by one of the stable eigenpairs.Bifurcation analysis and frequency prediction in shear-driven cavity flow
http://hdl.handle.net/10985/17998
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/10985/179982019-01-01T00:00:00ZBENGANA, 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.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.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.Global Stability Analyses Unraveling Roughness-induced Transition Mechanisms
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.