SAM
https://sam.ensam.eu:443
The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 05 Mar 2023 00:24:23 GMT2023-03-05T00:24:23ZSpace–time dynamics of optimal wavepackets for streaks in a channel entrance flow
http://hdl.handle.net/10985/18898
Space–time dynamics of optimal wavepackets for streaks in a channel entrance flow
ALIZARD, Frédéric; CADIOU, A.; LE PENVEN, L.; DI PIERRO, B.; BUFFAT, M.
The laminar–turbulent transition of a plane channel entrance flow is revisited using global linear optimization analyses and direct numerical simulations. The investigated case corresponds to uniform upstream velocity conditions and a moderate value of Reynolds number so that the two-dimensional developing flow is linearly stable under the parallel flow assumption. However, the boundary layers in the entry zone are capable of supporting the development of streaks, which may experience secondary instability and evolve to turbulence. In this study, global optimal linear perturbations are computed and studied in the nonlinear regime for different values of streak amplitude and optimization time. These optimal perturbations take the form of wavepackets having either varicose or sinuous symmetry. It is shown that, for short optimization times, varicose wavepackets grow through a combination of Orr and lift-up effects, whereas for longer target times, both sinuous and varicose wavepackets exhibit an instability mechanism driven by the presence of inflection points in the streaky flow. In addition, while the optimal varicose modes obtained for short optimization times are localized near the inlet, where the base flow is strongly three-dimensional, when the target time is increased, the sinuous and varicose optimal modes are displaced farther downstream, in the nearly parallel streaky flow. Finally, the optimal wavepackets are found to lead to turbulence for sufficiently high initial amplitudes. It is noticed that the resulting turbulent flows have the same wall-shear stress, whether the wavepackets have been obtained for short or for long time optimization.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/188982018-01-01T00:00:00ZALIZARD, FrédéricCADIOU, A.LE PENVEN, L.DI PIERRO, B.BUFFAT, M.The laminar–turbulent transition of a plane channel entrance flow is revisited using global linear optimization analyses and direct numerical simulations. The investigated case corresponds to uniform upstream velocity conditions and a moderate value of Reynolds number so that the two-dimensional developing flow is linearly stable under the parallel flow assumption. However, the boundary layers in the entry zone are capable of supporting the development of streaks, which may experience secondary instability and evolve to turbulence. In this study, global optimal linear perturbations are computed and studied in the nonlinear regime for different values of streak amplitude and optimization time. These optimal perturbations take the form of wavepackets having either varicose or sinuous symmetry. It is shown that, for short optimization times, varicose wavepackets grow through a combination of Orr and lift-up effects, whereas for longer target times, both sinuous and varicose wavepackets exhibit an instability mechanism driven by the presence of inflection points in the streaky flow. In addition, while the optimal varicose modes obtained for short optimization times are localized near the inlet, where the base flow is strongly three-dimensional, when the target time is increased, the sinuous and varicose optimal modes are displaced farther downstream, in the nearly parallel streaky flow. Finally, the optimal wavepackets are found to lead to turbulence for sufficiently high initial amplitudes. It is noticed that the resulting turbulent flows have the same wall-shear stress, whether the wavepackets have been obtained for short or for long time optimization.Restricted nonlinear model for high- and low-drag events in plane channel flow
http://hdl.handle.net/10985/18049
Restricted nonlinear model for high- and low-drag events in plane channel flow
ALIZARD, Frédéric; BIAU, Damien
A restricted nonlinear (RNL) model, obtained by partitioning the state variables into streamwise-averaged quantities and superimposed perturbations, is used in order to track the exact coherent state in plane channel flow investigated by Toh & Itano (J. Fluid Mech., vol. 481, 2003, pp. 67–76). When restricting nonlinearities to quadratic interaction of the fluctuating part into the streamwise-averaged component, it is shown that the coherent structure and its dynamics closely match results from direct numerical simulation (DNS), even if only a single streamwise Fourier mode is retained. In particular, both solutions exhibit long quiescent phases, spanwise shifts and bursting events. It is also shown that the dynamical trajectory passes close to equilibria that exhibit either low- or high-drag states. When statistics are collected at times where the friction velocity peaks, the mean flow and root-mean-square profiles show the essential features of wall turbulence obtained by DNS for the same friction Reynolds number. For low-drag events, the mean flow profiles are related to a universal asymptotic state called maximum drag reduction (Xi & Graham, Phys. Rev. Lett., vol. 108, 2012, 028301). Hence, the intermittent nature of self-sustaining processes in the buffer layer is contained in the dynamics of the RNL model, organized in two exact coherent states plus an asymptotic turbulent-like attractor. We also address how closely turbulent dynamics approaches these equilibria by exploiting a DNS database associated with a larger domain.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/180492019-01-01T00:00:00ZALIZARD, FrédéricBIAU, DamienA restricted nonlinear (RNL) model, obtained by partitioning the state variables into streamwise-averaged quantities and superimposed perturbations, is used in order to track the exact coherent state in plane channel flow investigated by Toh & Itano (J. Fluid Mech., vol. 481, 2003, pp. 67–76). When restricting nonlinearities to quadratic interaction of the fluctuating part into the streamwise-averaged component, it is shown that the coherent structure and its dynamics closely match results from direct numerical simulation (DNS), even if only a single streamwise Fourier mode is retained. In particular, both solutions exhibit long quiescent phases, spanwise shifts and bursting events. It is also shown that the dynamical trajectory passes close to equilibria that exhibit either low- or high-drag states. When statistics are collected at times where the friction velocity peaks, the mean flow and root-mean-square profiles show the essential features of wall turbulence obtained by DNS for the same friction Reynolds number. For low-drag events, the mean flow profiles are related to a universal asymptotic state called maximum drag reduction (Xi & Graham, Phys. Rev. Lett., vol. 108, 2012, 028301). Hence, the intermittent nature of self-sustaining processes in the buffer layer is contained in the dynamics of the RNL model, organized in two exact coherent states plus an asymptotic turbulent-like attractor. We also address how closely turbulent dynamics approaches these equilibria by exploiting a DNS database associated with a larger domain.Invariant solutions in a channel flow using a minimal restricted nonlinear model
http://hdl.handle.net/10985/18606
Invariant solutions in a channel flow using a minimal restricted nonlinear model
ALIZARD, Frédéric
Simulations using a Restricted Nonlinear (RNL) system, where mean flow distortion resulting from Reynolds stress feedback regenerates rolls, is applied in a channel flow under subcritical conditions. This quasi-linear restriction of the dynamics is used to study invariant solutions located in the bulk of the flow found recently by Rawat et al. (2016) [14]. It is shown that the RNL system truncated to a single streamwise mode for the perturbation supports invariant solutions that are found to bifurcate from a relative periodic orbit into a travelling wave solution when the spanwise size is increasing. In particular, the travelling wave solution exhibits a spanwise localized structure that remains unchanged for large values of the spanwise extent as the invariant solution lying on the lower branch found by Rawat et al. (2016) [14]. In addition, travelling wave solutions provided by this minimal RNL system are self-similar with respect to the Reynolds number based on the centreline velocity, and the half-channel height varying from 2000 to 5000.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/186062017-01-01T00:00:00ZALIZARD, FrédéricSimulations using a Restricted Nonlinear (RNL) system, where mean flow distortion resulting from Reynolds stress feedback regenerates rolls, is applied in a channel flow under subcritical conditions. This quasi-linear restriction of the dynamics is used to study invariant solutions located in the bulk of the flow found recently by Rawat et al. (2016) [14]. It is shown that the RNL system truncated to a single streamwise mode for the perturbation supports invariant solutions that are found to bifurcate from a relative periodic orbit into a travelling wave solution when the spanwise size is increasing. In particular, the travelling wave solution exhibits a spanwise localized structure that remains unchanged for large values of the spanwise extent as the invariant solution lying on the lower branch found by Rawat et al. (2016) [14]. In addition, travelling wave solutions provided by this minimal RNL system are self-similar with respect to the Reynolds number based on the centreline velocity, and the half-channel height varying from 2000 to 5000.Three-dimensional instability of a ow past a sphere: Mach evolution of the regular and Hopf bifurcations
http://hdl.handle.net/10985/14215
Three-dimensional instability of a ow past a sphere: Mach evolution of the regular and Hopf bifurcations
SANSICA, Andrea; ROBINET, Jean-Christophe; ALIZARD, Frédéric; GONCALVES, Eric
A fully three-dimensional linear stability analysis is carried out to investigate the unstable bifurcations of a compressible viscous fluid past a sphere. A time-stepper technique is used to compute both equilibrium states and leading eigenmodes. In agreement with previous studies, the numerical results reveal a regular bifurcation under the action of a steady mode and a supercritical Hopf bifurcation that causes the onset of unsteadiness but also illustrate the limitations of previous linear approaches, based on parallel and axisymmetric base flow assumptions, or weakly nonlinear theories. The evolution of the unstable bifurcations is investigated up to low-supersonic speeds. For increasing Mach numbers, the thresholds move towards higher Reynolds numbers. The unsteady fluctuations are weakened and an axisymmetrization of the base flow occurs. For a sufficiently high Reynolds number, the regular bifurcation disappears and the flow directly passes from an unsteady planar-symmetric solution to a stationary axisymmetric stable one when the Mach number is increased. A stability map is drawn by tracking the bifurcation boundaries for different Reynolds and Mach numbers. When supersonic conditions are reached, the flow becomes globally stable and switches to a noise-amplifier system. A continuous Gaussian white noise forcing is applied in front of the shock to examine the convective nature of the flow. A Fourier analysis and a dynamic mode decomposition show a modal response that recalls that of the incompressible unsteady cases. Although transition in the wake does not occur for the chosen Reynolds number and forcing amplitude, this suggests a link between subsonic and supersonic dynamics.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/142152018-01-01T00:00:00ZSANSICA, AndreaROBINET, Jean-ChristopheALIZARD, FrédéricGONCALVES, EricA fully three-dimensional linear stability analysis is carried out to investigate the unstable bifurcations of a compressible viscous fluid past a sphere. A time-stepper technique is used to compute both equilibrium states and leading eigenmodes. In agreement with previous studies, the numerical results reveal a regular bifurcation under the action of a steady mode and a supercritical Hopf bifurcation that causes the onset of unsteadiness but also illustrate the limitations of previous linear approaches, based on parallel and axisymmetric base flow assumptions, or weakly nonlinear theories. The evolution of the unstable bifurcations is investigated up to low-supersonic speeds. For increasing Mach numbers, the thresholds move towards higher Reynolds numbers. The unsteady fluctuations are weakened and an axisymmetrization of the base flow occurs. For a sufficiently high Reynolds number, the regular bifurcation disappears and the flow directly passes from an unsteady planar-symmetric solution to a stationary axisymmetric stable one when the Mach number is increased. A stability map is drawn by tracking the bifurcation boundaries for different Reynolds and Mach numbers. When supersonic conditions are reached, the flow becomes globally stable and switches to a noise-amplifier system. A continuous Gaussian white noise forcing is applied in front of the shock to examine the convective nature of the flow. A Fourier analysis and a dynamic mode decomposition show a modal response that recalls that of the incompressible unsteady cases. Although transition in the wake does not occur for the chosen Reynolds number and forcing amplitude, this suggests a link between subsonic and supersonic dynamics.Investigation of the dynamics in separated turbulent flow
http://hdl.handle.net/10985/18000
Investigation of the dynamics in separated turbulent flow
FADLA, Fawzi; ALIZARD, Frédéric; KEIRSBULCK, Laurent; ROBINET, Jean-Christophe; LAVAL, Jean-Philippe; FOUCAUT, Jean-Marc; CHOVET, Camila; LIPPERT, Marc
Dynamical behavior of the turbulent channel flow separation induced by a wall-mounted two-dimensional bump is studied, with an emphasis on unsteadiness characteristics of vortical motions evolving in the separated flow. The present investigations are based on an experimental approach and Direct Numerical Simulation (Dns). The main interests are devoted to give further insight on mean flow properties, characteristic scales and physical mechanisms of low-frequencies unsteadiness. The study also aims to clarify the Reynolds number effects. Results are presented for turbulent flows at moderate Reynolds-number ranging from 125 to 730 where is based on friction velocity and channel half-height. A large database of time-resolved two-dimensional Piv measurements is used to obtain the velocity distributions in a region covering the entire shear layer and the flow surrounding the bump. An examination of both high resolved velocity and wall-shear stress measurements showed that for moderate Reynolds numbers, a separated region exists until a critical value. Under this conditions, a thin region of reverse flow is formed above the bump and a large-scale vortical activity is clearly observed and analyzed. Three distinct self-sustained oscillations are identified in the separated zone. The investigation showed that the flow exhibits the shear-layer instability and vortex-shedding type instability of the bubble. A low-frequency self-sustained oscillation associated with a flapping phenomenon is also identified. The experimental results are further emphasized using post-processed data from Direct Numerical Simulations, such as flow statistics and Dynamic Mode Decomposition. Physical mechanisms associated with observed self-sustained oscillations are then suggested and results are discussed in the light of instabilities observed in a laminar regime for the same flow configuration.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/180002019-01-01T00:00:00ZFADLA, FawziALIZARD, FrédéricKEIRSBULCK, LaurentROBINET, Jean-ChristopheLAVAL, Jean-PhilippeFOUCAUT, Jean-MarcCHOVET, CamilaLIPPERT, MarcDynamical behavior of the turbulent channel flow separation induced by a wall-mounted two-dimensional bump is studied, with an emphasis on unsteadiness characteristics of vortical motions evolving in the separated flow. The present investigations are based on an experimental approach and Direct Numerical Simulation (Dns). The main interests are devoted to give further insight on mean flow properties, characteristic scales and physical mechanisms of low-frequencies unsteadiness. The study also aims to clarify the Reynolds number effects. Results are presented for turbulent flows at moderate Reynolds-number ranging from 125 to 730 where is based on friction velocity and channel half-height. A large database of time-resolved two-dimensional Piv measurements is used to obtain the velocity distributions in a region covering the entire shear layer and the flow surrounding the bump. An examination of both high resolved velocity and wall-shear stress measurements showed that for moderate Reynolds numbers, a separated region exists until a critical value. Under this conditions, a thin region of reverse flow is formed above the bump and a large-scale vortical activity is clearly observed and analyzed. Three distinct self-sustained oscillations are identified in the separated zone. The investigation showed that the flow exhibits the shear-layer instability and vortex-shedding type instability of the bubble. A low-frequency self-sustained oscillation associated with a flapping phenomenon is also identified. The experimental results are further emphasized using post-processed data from Direct Numerical Simulations, such as flow statistics and Dynamic Mode Decomposition. Physical mechanisms associated with observed self-sustained oscillations are then suggested and results are discussed in the light of instabilities observed in a laminar regime for the same flow configuration.Global Instability in Shock Wave Laminar Boundary-Layer Interaction
http://hdl.handle.net/10985/18613
Global Instability in Shock Wave Laminar Boundary-Layer Interaction
GUIHO, F.; ALIZARD, Frédéric; ROBINET, Jean-Christophe
The linear global stability of an interaction between an oblique shock wave and a laminar boundary layer is carried out for various oblique shock angles. It is illustrated that such a flow acts as a noise amplifier. The least temporally damped global modes are classified into three main categories, low, medium and high frequencies. The high frequencies are localized into the attached boundary layer, the medium frequencies are associated with Kelvin–Helmholtz like structures along the shear layer and convective waves in the separated flow downstream whereas the low frequencies are driven by the interaction zone. In particular, a low frequency mode emerges which is scaled by the interaction length and the freestream velocity.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/186132015-01-01T00:00:00ZGUIHO, F.ALIZARD, FrédéricROBINET, Jean-ChristopheThe linear global stability of an interaction between an oblique shock wave and a laminar boundary layer is carried out for various oblique shock angles. It is illustrated that such a flow acts as a noise amplifier. The least temporally damped global modes are classified into three main categories, low, medium and high frequencies. The high frequencies are localized into the attached boundary layer, the medium frequencies are associated with Kelvin–Helmholtz like structures along the shear layer and convective waves in the separated flow downstream whereas the low frequencies are driven by the interaction zone. In particular, a low frequency mode emerges which is scaled by the interaction length and the freestream velocity.Optimal transient growth in compressible turbulent boundary layers
http://hdl.handle.net/10985/18612
Optimal transient growth in compressible turbulent boundary layers
ALIZARD, Frédéric; PIROZZOLI, Sergio; BERNARDINI, Matteo; GRASSO, Francesco
The structure of zero-pressure-gradient compressible turbulent boundary layers is analysed using the tools of optimal transient growth theory. The approach relies on the extension to compressible flows of the theoretical framework originally developed by Reynolds & Hussain (J. Fluid Mech., vol. 52, 1972, pp. 263–288) for incompressible flows. The model is based on a density-weighted triple decomposition of the instantaneous field into the contributions of the mean flow, the organized (coherent) motions and the disorganized background turbulent fluctuations. The mean field and the eddy viscosity characterizing the incoherent fluctuations are here obtained from a direct numerical simulation database. Most temporally amplified modes (optimal modes) are found to be consistent with scaling laws of turbulent boundary layers for both inner and outer layers, as well as in the logarithmic region, where they exhibit a self-similar spreading. Four free-stream Mach numbers are considered: $\mathit{Ma}_{\infty }=0.2$, 2, 3 and 4. Weak effects of compressibility on the characteristics length and the orientation angles are observed for both the inner- and the outer-layer modes. Furthermore, taking into account the effects of mean density variations, a universal behaviour is suggested for the optimal modes that populate the log layer, regardless of the Mach number. The relevance of the optimal modes in describing the near-wall layer dynamics and the eddies that populate the outer region is discussed.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/186122015-01-01T00:00:00ZALIZARD, FrédéricPIROZZOLI, SergioBERNARDINI, MatteoGRASSO, FrancescoThe structure of zero-pressure-gradient compressible turbulent boundary layers is analysed using the tools of optimal transient growth theory. The approach relies on the extension to compressible flows of the theoretical framework originally developed by Reynolds & Hussain (J. Fluid Mech., vol. 52, 1972, pp. 263–288) for incompressible flows. The model is based on a density-weighted triple decomposition of the instantaneous field into the contributions of the mean flow, the organized (coherent) motions and the disorganized background turbulent fluctuations. The mean field and the eddy viscosity characterizing the incoherent fluctuations are here obtained from a direct numerical simulation database. Most temporally amplified modes (optimal modes) are found to be consistent with scaling laws of turbulent boundary layers for both inner and outer layers, as well as in the logarithmic region, where they exhibit a self-similar spreading. Four free-stream Mach numbers are considered: $\mathit{Ma}_{\infty }=0.2$, 2, 3 and 4. Weak effects of compressibility on the characteristics length and the orientation angles are observed for both the inner- and the outer-layer modes. Furthermore, taking into account the effects of mean density variations, a universal behaviour is suggested for the optimal modes that populate the log layer, regardless of the Mach number. The relevance of the optimal modes in describing the near-wall layer dynamics and the eddies that populate the outer region is discussed.Sensitivity analysis of optimal transient growth for turbulent boundary layers
http://hdl.handle.net/10985/18609
Sensitivity analysis of optimal transient growth for turbulent boundary layers
ALIZARD, Frédéric; ROBINET, Jean-Christophe; FILLIARD, Guillaume
Structural approaches based on modal decomposition of the flow dynamics have gained acceptance for a wide variety of turbulent shear flows. In this context, a singular value decomposition associated with a governing operator, aiming to model the linear amplification of coherent structures, is used to reproduce some fundamental motions in a turbulent boundary layer. In particular, as already found by Cossu et al. (2009), elongated streaky structures scaled in inner and outer units are identified. The sensitivity of these singular values to a mean flow modification is analysed. It is illustrated that the linear amplification of very large-scales which populate the outer motion is not affected when the leading singular value associated with the inner layer is damped. Moreover, we notice that the resulting optimal mean flow deviation is consistent with findings of Xu et al. (2007) in which the active control of a turbulent boundary layer is studied through direct numerical simulations.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/186092015-01-01T00:00:00ZALIZARD, FrédéricROBINET, Jean-ChristopheFILLIARD, GuillaumeStructural approaches based on modal decomposition of the flow dynamics have gained acceptance for a wide variety of turbulent shear flows. In this context, a singular value decomposition associated with a governing operator, aiming to model the linear amplification of coherent structures, is used to reproduce some fundamental motions in a turbulent boundary layer. In particular, as already found by Cossu et al. (2009), elongated streaky structures scaled in inner and outer units are identified. The sensitivity of these singular values to a mean flow modification is analysed. It is illustrated that the linear amplification of very large-scales which populate the outer motion is not affected when the leading singular value associated with the inner layer is damped. Moreover, we notice that the resulting optimal mean flow deviation is consistent with findings of Xu et al. (2007) in which the active control of a turbulent boundary layer is studied through direct numerical simulations.Linear stability of optimal streaks in the log-layer of turbulent channel flows
http://hdl.handle.net/10985/18611
Linear stability of optimal streaks in the log-layer of turbulent channel flows
ALIZARD, Frédéric
The importance of secondary instability of streaks for the generation of vortical struc-tures attached to the wall in the logarithmic region of turbulent channels is studied. Thestreaks and their linear instability are computed by solving equations associated withthe organized motion that include an eddy-viscosity modeling the effect of incoherentfluctuations. Three friction Reynolds numbers,Reτ=2000,3000, and 5000, areinvestigated. For all flow cases, optimal streamwise vortices (i.e., having the highestpotential for linear transient energy amplification) are used as initial conditions. Dueto the lift-up mechanism, these optimal perturbations lead to the nonlinear growthof streaks. Based on a Floquet theory along the spanwise direction, we observe theonset of streak secondary instability for a wide range of spanwise wavelengths whenthe streak amplitude exceeds a critical value. Under neutral conditions, it is shown thatstreak instability modes have their energy mainly concentrated in the overlap layer andpropagate with a phase velocity equal to the mean streamwise velocity of the log-layer.These neutral log-layer modes exhibit a sinuous pattern and have characteristic sizesthat are proportional to the wall distance in both streamwise and spanwise directions, inagreement with the Townsend’s attached eddy hypothesis (A. Townsend, the structureof turbulent shear flow, Cambridge university press, 1976 2nd edition). In particular,for a distance from the wall varying fromy+≈100 (in wall units) toy≈0.3h, wherehis half the height of the channel, the neutral log-layer modes are self-similar with aspanwise width ofλz≈y/0.3 and a streamwise length ofλx≈3λz, independently ofthe Reynolds number. Based on this observation, it is suggested that compact vorticalstructures attached to the wall can be ascribed to streak secondary instabilities. Inaddition, spatial distributions of fluctuating vorticity components show that the onsetof secondary instability is associated with the roll-up of the shear layer at the edgeof the low-speed streak, similarly to a three-dimensional mixing layer.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/186112015-01-01T00:00:00ZALIZARD, FrédéricThe importance of secondary instability of streaks for the generation of vortical struc-tures attached to the wall in the logarithmic region of turbulent channels is studied. Thestreaks and their linear instability are computed by solving equations associated withthe organized motion that include an eddy-viscosity modeling the effect of incoherentfluctuations. Three friction Reynolds numbers,Reτ=2000,3000, and 5000, areinvestigated. For all flow cases, optimal streamwise vortices (i.e., having the highestpotential for linear transient energy amplification) are used as initial conditions. Dueto the lift-up mechanism, these optimal perturbations lead to the nonlinear growthof streaks. Based on a Floquet theory along the spanwise direction, we observe theonset of streak secondary instability for a wide range of spanwise wavelengths whenthe streak amplitude exceeds a critical value. Under neutral conditions, it is shown thatstreak instability modes have their energy mainly concentrated in the overlap layer andpropagate with a phase velocity equal to the mean streamwise velocity of the log-layer.These neutral log-layer modes exhibit a sinuous pattern and have characteristic sizesthat are proportional to the wall distance in both streamwise and spanwise directions, inagreement with the Townsend’s attached eddy hypothesis (A. Townsend, the structureof turbulent shear flow, Cambridge university press, 1976 2nd edition). In particular,for a distance from the wall varying fromy+≈100 (in wall units) toy≈0.3h, wherehis half the height of the channel, the neutral log-layer modes are self-similar with aspanwise width ofλz≈y/0.3 and a streamwise length ofλx≈3λz, independently ofthe Reynolds number. Based on this observation, it is suggested that compact vorticalstructures attached to the wall can be ascribed to streak secondary instabilities. Inaddition, spatial distributions of fluctuating vorticity components show that the onsetof secondary instability is associated with the roll-up of the shear layer at the edgeof the low-speed streak, similarly to a three-dimensional mixing layer.A domain decomposition matrix-free method for global linear stability
http://hdl.handle.net/10985/8644
A domain decomposition matrix-free method for global linear stability
ALIZARD, Frédéric; ROBINET, Jean-Christophe; GLOERFELT, Xavier
This work is dedicated to the presentation of a matrix-free method for global linear stability analysis in geometries composed of multi-connected rectangular subdomains. An Arnoldi technique using snapshots in subdomains of the entire geometry combined with a multidomain linearized Direct Numerical Finite difference simulations based on an influence matrix for partitioning are adopted. The method is illustrated by three benchmark problems: the lid-driven cavity, the square cylinder and the open cavity flow. The efficiency of the method to extract large-scale structures in a multidomain framework is emphasized. The possibility to use subset of the full domain to recover the perturbation associated with the entire flow field is also highlighted. Such a method appears thus a promising tool to deal with large computational domains and three-dimensionality within a parallel architecture.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/86442012-01-01T00:00:00ZALIZARD, FrédéricROBINET, Jean-ChristopheGLOERFELT, XavierThis work is dedicated to the presentation of a matrix-free method for global linear stability analysis in geometries composed of multi-connected rectangular subdomains. An Arnoldi technique using snapshots in subdomains of the entire geometry combined with a multidomain linearized Direct Numerical Finite difference simulations based on an influence matrix for partitioning are adopted. The method is illustrated by three benchmark problems: the lid-driven cavity, the square cylinder and the open cavity flow. The efficiency of the method to extract large-scale structures in a multidomain framework is emphasized. The possibility to use subset of the full domain to recover the perturbation associated with the entire flow field is also highlighted. Such a method appears thus a promising tool to deal with large computational domains and three-dimensionality within a parallel architecture.