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http://hdl.handle.net/10985/17848
Global Stability Analyses Unraveling Roughness-induced Transition Mechanisms
LOISEAU, Jean-Christophe; ROBINET, Jean-Christophe; CHERUBINI, Stefania; LERICHE, Emmanuel
The linear global instability and resulting transition to turbulence induced by a cylindrical roughness element of heighth and diameter d=3h immersed within an incompressible boundary layer flow along a flat plate is investigated using the joint application of direct numerical simulations and three-dimensional stability analyses. The configuration investigated is the same as the one investigated experimentally by Fransson et al. Base flow computations show that the roughness element induces a wake composed of a central low-speed region surrounded by a three-dimensional shear layer and a pair of low- and high-speed streaks on each side. Results from the global stability analyses highlight the unstable nature of the central low-speed region and its crucial importance in the laminar-turbulent transition process. For the set of parameters considered, it is able to sustain a varicose global instability for which the predicted critical Reynolds number is only 6% larger than the one reported in Ref. 10. A kinetic energy budget and wavemaker analysis revealed that this mode finds its root in the reversed flow region right downstream the roughness element and extracts most of its energy from the central low-speed region and streaks further downstream. Direct numerical simulations of the flow past this roughness element puts in the limelight the ability for this linear instability to give birth to hairpin vortices and thus trigger transition to turbulence.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/178482015-01-01T00:00:00ZLOISEAU, Jean-ChristopheROBINET, Jean-ChristopheCHERUBINI, StefaniaLERICHE, EmmanuelThe linear global instability and resulting transition to turbulence induced by a cylindrical roughness element of heighth and diameter d=3h immersed within an incompressible boundary layer flow along a flat plate is investigated using the joint application of direct numerical simulations and three-dimensional stability analyses. The configuration investigated is the same as the one investigated experimentally by Fransson et al. Base flow computations show that the roughness element induces a wake composed of a central low-speed region surrounded by a three-dimensional shear layer and a pair of low- and high-speed streaks on each side. Results from the global stability analyses highlight the unstable nature of the central low-speed region and its crucial importance in the laminar-turbulent transition process. For the set of parameters considered, it is able to sustain a varicose global instability for which the predicted critical Reynolds number is only 6% larger than the one reported in Ref. 10. A kinetic energy budget and wavemaker analysis revealed that this mode finds its root in the reversed flow region right downstream the roughness element and extracts most of its energy from the central low-speed region and streaks further downstream. Direct numerical simulations of the flow past this roughness element puts in the limelight the ability for this linear instability to give birth to hairpin vortices and thus trigger transition to turbulence.Influence of the Shape on the Roughness-Induced Transition
http://hdl.handle.net/10985/17803
Influence of the Shape on the Roughness-Induced Transition
LOISEAU, Jean-Christophe; CHERUBINI, Stefania; ROBINET, Jean-Christophe; LERICHE, Emmanuel
lobal instability analysis of the three-dimensional flow past two rough- ness elements of different shape, namely a cylinder and a bump, is presented. In both cases, the eigenspectrum is made of modes characterised by a varicose symmetry and localised mostly in the zones of large base flow shear. The primary instabil- ity exhibited is the same in both cases and consists in an isolated unstable mode closely related to streaks local instability. For the cylinder however, a whole branch of modes is in addition destabilised as the Reynolds number is further increased.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/178032015-01-01T00:00:00ZLOISEAU, Jean-ChristopheCHERUBINI, StefaniaROBINET, Jean-ChristopheLERICHE, Emmanuellobal instability analysis of the three-dimensional flow past two rough- ness elements of different shape, namely a cylinder and a bump, is presented. In both cases, the eigenspectrum is made of modes characterised by a varicose symmetry and localised mostly in the zones of large base flow shear. The primary instabil- ity exhibited is the same in both cases and consists in an isolated unstable mode closely related to streaks local instability. For the cylinder however, a whole branch of modes is in addition destabilised as the Reynolds number is further increased.Computing heteroclinic orbits using adjoint-based methods
http://hdl.handle.net/10985/17881
Computing heteroclinic orbits using adjoint-based methods
FARANO, Mirko; CHERUBINI, Stefania; ROBINET, Jean-Christophe; DE PALMA, Pietro; SCHNEIDER, T. M.
Transitional turbulence in shear flows is supported by a network of unstable exact invariant solutions of the Navier–Stokes equations. The network is interconnected by heteroclinic connections along which the turbulent trajectories evolve between invariant solutions. While many invariant solutions in the form of equilibria, travelling waves and periodic orbits have been identified, computing heteroclinic connections remains a challenge. We propose a variational method for computing orbits dynamically connecting small neighbourhoods around equilibrium solutions. Using local information on the dynamics linearized around these equilibria, we demonstrate that we can choose neighbourhoods such that the connecting orbits shadow heteroclinic connections. The proposed method allows one to approximate heteroclinic connections originating from states with multi-dimensional unstable manifold and thereby provides access to heteroclinic connections that cannot easily be identified using alternative shooting methods. For plane Couette flow, we demonstrate the method by recomputing three known connections and identifying six additional previously unknown orbits.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/178812018-01-01T00:00:00ZFARANO, MirkoCHERUBINI, StefaniaROBINET, Jean-ChristopheDE PALMA, PietroSCHNEIDER, T. M.Transitional turbulence in shear flows is supported by a network of unstable exact invariant solutions of the Navier–Stokes equations. The network is interconnected by heteroclinic connections along which the turbulent trajectories evolve between invariant solutions. While many invariant solutions in the form of equilibria, travelling waves and periodic orbits have been identified, computing heteroclinic connections remains a challenge. We propose a variational method for computing orbits dynamically connecting small neighbourhoods around equilibrium solutions. Using local information on the dynamics linearized around these equilibria, we demonstrate that we can choose neighbourhoods such that the connecting orbits shadow heteroclinic connections. The proposed method allows one to approximate heteroclinic connections originating from states with multi-dimensional unstable manifold and thereby provides access to heteroclinic connections that cannot easily be identified using alternative shooting methods. For plane Couette flow, we demonstrate the method by recomputing three known connections and identifying six additional previously unknown orbits.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.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; ROBINET, Jean-Christophe; DE PALMA, Pietro; CHERUBINI, Stefania
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, ENZAROBINET, Jean-ChristopheDE PALMA, PietroCHERUBINI, StefaniaRecently, 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.Continuing invariant solutions towards the turbulent flow
http://hdl.handle.net/10985/21936
Continuing invariant solutions towards the turbulent flow
PARENTE, Enza; FARANO, Mirko; ROBINET, Jean-Christophe; DE PALMA, Pietro; CHERUBINI, Stefania
A new mathematical framework is proposed for characterizing the coherent motion of fluctuations around a mean turbulent channel flow. We search for statistically invariant coherent solutions of the unsteady Reynolds-averaged Navier–Stokes
equations written in a perturbative form with respect to the turbulent mean flow, using a suitable approximation of the Reynolds stress tensor. This is achieved by setting up a continuation procedure of known solutions of the perturbative Navier–Stokes
equations, based on the continuous increase of the turbulent eddy viscosity towards its turbulent value. The recovered solutions, being sustained only in the presence of the Reynolds stress tensor, are representative of the statistically coherent motion of
turbulent flows. For small friction Reynolds number and/or domain size, the statistically invariant motion is almost identical to the corresponding invariant solution of the Navier–Stokes equations. Whereas, for sufficiently large friction number and/or domain size, it considerably departs from the starting invariant solution of the Navier–Stokes equations, presenting spatial structures, main wavelengths and scaling very close to those characterizing both large- and small-scale motion of turbulent channel flows.
This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 2)’.
Sun, 01 May 2022 00:00:00 GMThttp://hdl.handle.net/10985/219362022-05-01T00:00:00ZPARENTE, EnzaFARANO, MirkoROBINET, Jean-ChristopheDE PALMA, PietroCHERUBINI, StefaniaA new mathematical framework is proposed for characterizing the coherent motion of fluctuations around a mean turbulent channel flow. We search for statistically invariant coherent solutions of the unsteady Reynolds-averaged Navier–Stokes
equations written in a perturbative form with respect to the turbulent mean flow, using a suitable approximation of the Reynolds stress tensor. This is achieved by setting up a continuation procedure of known solutions of the perturbative Navier–Stokes
equations, based on the continuous increase of the turbulent eddy viscosity towards its turbulent value. The recovered solutions, being sustained only in the presence of the Reynolds stress tensor, are representative of the statistically coherent motion of
turbulent flows. For small friction Reynolds number and/or domain size, the statistically invariant motion is almost identical to the corresponding invariant solution of the Navier–Stokes equations. Whereas, for sufficiently large friction number and/or domain size, it considerably departs from the starting invariant solution of the Navier–Stokes equations, presenting spatial structures, main wavelengths and scaling very close to those characterizing both large- and small-scale motion of turbulent channel flows.
This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 2)’.Influence of freestream turbulence on the flow over a wall roughness
http://hdl.handle.net/10985/20464
Influence of freestream turbulence on the flow over a wall roughness
BUCCI, Michele Alessandro; CHERUBINI, Stefania; LOISEAU, Jean-Christophe; ROBINET, Jean-Christophe
The effect of freestream turbulence on the dynamics of an incompressible flow past a cylindrical roughness element in subcritical conditions (i.e., for Reynolds numbers below the onset of linear instability) has been investigated by the joint application of direct numerical simulations, linear modal and nonmodal stability analyses, and dynamic mode decomposition. At first, the influence of the Reynolds number and the ratio of the boundary layer’s thickness to roughness height on the three-dimensional spatiotemporal (global) stability of the flow has been investigated. Depending on the operating conditions, the leading instability can either be varicose (symmetric) or sinuous (antisymmetric). In both cases, when the flow is excited by broadband frequency forcing, dynamic mode decomposition extracts only varicose coherent structures even though optimal response analysis predicts a strong amplification of sinuous disturbances having frequency close to that of the marginally stable sinuous eigenmode. This apparent discrepancy is attributed to the fact that the sinuous instability is sensitive to a very limited range of frequencies barely excited by freestream turbulence while varicose disturbances are associated with high amplification in a much wider frequency range. Hence, in this case the flow behaves as an amplifier of varicose perturbations rather than a resonator. Consequences on the subsequent transition to turbulence have been studied, highlighting that varicose perturbations extract energy from the near-wake region, get continuously amplified due to the excitation provided by freestream turbulence, and eventually give rise to a shedding of hairpin vortices.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/204642021-01-01T00:00:00ZBUCCI, Michele AlessandroCHERUBINI, StefaniaLOISEAU, Jean-ChristopheROBINET, Jean-ChristopheThe effect of freestream turbulence on the dynamics of an incompressible flow past a cylindrical roughness element in subcritical conditions (i.e., for Reynolds numbers below the onset of linear instability) has been investigated by the joint application of direct numerical simulations, linear modal and nonmodal stability analyses, and dynamic mode decomposition. At first, the influence of the Reynolds number and the ratio of the boundary layer’s thickness to roughness height on the three-dimensional spatiotemporal (global) stability of the flow has been investigated. Depending on the operating conditions, the leading instability can either be varicose (symmetric) or sinuous (antisymmetric). In both cases, when the flow is excited by broadband frequency forcing, dynamic mode decomposition extracts only varicose coherent structures even though optimal response analysis predicts a strong amplification of sinuous disturbances having frequency close to that of the marginally stable sinuous eigenmode. This apparent discrepancy is attributed to the fact that the sinuous instability is sensitive to a very limited range of frequencies barely excited by freestream turbulence while varicose disturbances are associated with high amplification in a much wider frequency range. Hence, in this case the flow behaves as an amplifier of varicose perturbations rather than a resonator. Consequences on the subsequent transition to turbulence have been studied, highlighting that varicose perturbations extract energy from the near-wake region, get continuously amplified due to the excitation provided by freestream turbulence, and eventually give rise to a shedding of hairpin vortices.Weakly nonlinear optimal perturbations
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.Modal and nonmodal stability of a stably stratified boundary layer flow
http://hdl.handle.net/10985/19638
Modal and nonmodal stability of a stably stratified boundary layer flow
PARENTE, Enza; ROBINET, Jean-Christophe; DE PALMA, Pietro; CHERUBINI, Stefania
The modal and nonmodal linear stability of a stably stratified Blasius boundary layer flow, composed of a velocity and a thermal boundary layer, is investigated. The temporal and spatial linear stability of such flow is investigated for several Richardson, Reynolds, and Prandtl numbers. While increasing the Richardson number stabilizes the flow, a more complex behavior is found when changing the Prandtl number, leading to a stabilization of the flow up to Pr = 7, followed by a destabilization. The nonmodal linear stability of the same flow is then investigated using a direct-adjoint procedure optimizing four different approximations of the energy norm based on a weighted sum of the kinetic and the potential energies. No matter the norm approximation, for short target times an increase of the Richardson number induces a decrease of the optimal energy gain and time at which it is obtained and an increase of the optimal streamwise wave number, which considerably departs from zero. Moreover, the dependence of the energy growth on the Reynolds number transitions from quadratic to linear, whereas the optimal time, which varies linearly with Re in the nonstratified case, remains constant. This suggests that the optimal energy growth mechanism arises from the joint effect of the lift-up and the Orr mechanism, that simultaneously act to increase the shear production term on a rather short timescale, counterbalancing the stabilizing effect of the buoyancy production term. Although these short-time mechanisms are found to be robust with respect to the chosen norm, a different amplification mechanism is observed for long target times for three of the proposed norms. This strong energy growth, due to the coupling between velocity and temperature perturbations in the free stream, disappears when the variation of the stratification strength with height is accurately taken into account in the definition of the norm.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10985/196382020-01-01T00:00:00ZPARENTE, EnzaROBINET, Jean-ChristopheDE PALMA, PietroCHERUBINI, StefaniaThe modal and nonmodal linear stability of a stably stratified Blasius boundary layer flow, composed of a velocity and a thermal boundary layer, is investigated. The temporal and spatial linear stability of such flow is investigated for several Richardson, Reynolds, and Prandtl numbers. While increasing the Richardson number stabilizes the flow, a more complex behavior is found when changing the Prandtl number, leading to a stabilization of the flow up to Pr = 7, followed by a destabilization. The nonmodal linear stability of the same flow is then investigated using a direct-adjoint procedure optimizing four different approximations of the energy norm based on a weighted sum of the kinetic and the potential energies. No matter the norm approximation, for short target times an increase of the Richardson number induces a decrease of the optimal energy gain and time at which it is obtained and an increase of the optimal streamwise wave number, which considerably departs from zero. Moreover, the dependence of the energy growth on the Reynolds number transitions from quadratic to linear, whereas the optimal time, which varies linearly with Re in the nonstratified case, remains constant. This suggests that the optimal energy growth mechanism arises from the joint effect of the lift-up and the Orr mechanism, that simultaneously act to increase the shear production term on a rather short timescale, counterbalancing the stabilizing effect of the buoyancy production term. Although these short-time mechanisms are found to be robust with respect to the chosen norm, a different amplification mechanism is observed for long target times for three of the proposed norms. This strong energy growth, due to the coupling between velocity and temperature perturbations in the free stream, disappears when the variation of the stratification strength with height is accurately taken into account in the definition of the norm.Permeability models affecting nonlinear stability in the asymptotic suction boundary layer: the Forchheimer versus the Darcy model
http://hdl.handle.net/10985/18610
Permeability models affecting nonlinear stability in the asymptotic suction boundary layer: the Forchheimer versus the Darcy model
WEDIN, Håkan; CHERUBINI, Stefania
The asymptotic suction boundary layer (ASBL) is used for studying two permeability models, namely the Darcy and the Forchheimer model, the latter being more physically correct according to the literature. The term that defines the two apart is a function of the non-Darcian wall permeability ${\hat{K}}_{2}$ and of the wall suction ${\hat{V}}_{0}$, whereas the Darcian wall permeability ${\hat{K}}_{1}$ is common to the two models. The underlying interest of the study lies in the field of transition to turbulence where focus is put on two-dimensional nonlinear traveling waves (TWs) and their three-dimensional linear stability. Following a previous study by Wedin et al (2015 Phys. Rev. E 92 013022), where only the Darcy model was considered, the present work aims at comparing the two models, assessing where in the parameter space they cease to produce the same results. For low values of ${\hat{K}}_{1}$ both models produce almost identical TW solutions. However, when both increasing the suction ${\hat{V}}_{0}$ to sufficiently high amplitudes (i.e. lowering the Reynolds number Re, based on the displacement thickness) and using large values of the wall porosity, differences are observed. In terms of the non-dimensional Darcian wall permeability parameter, a, strong differences in the overall shape of the bifurcation curves are observed for $a\gtrsim 0.70$, with the emergence of a new family of solutions at Re lower than 100. For these large values of a, a Forchheimer number ${{Fo}}_{\max }\gtrsim 0.5$ is found, where Fo expresses the ratio between the kinetic and viscous forces acting on the porous wall. Moreover, the minimum Reynolds number, ${{Re}}_{g}$, for which the Navier–Stokes equations allow for nonlinear solutions, decreases for increasing values of a. Fixing the streamwise wavenumber to α = 0.154, as used in the study by Wedin et al referenced above, we find that ${{Re}}_{g}$ is lowered from Re ≈ 3000 for zero permeability, to below 50 for a = 0.80 for both permeability models. Finally, the stability of the TW solutions is assessed using a three-dimensional linearized direct numerical simulation (DNS). Low-frequency unstable modes are found for both permeability models; however, the Darcy model is found to overpredict the growth rate, and underpredict the streamwise extension of the most unstable mode. These results indicate that a careful choice of the underlying permeability model is crucial for accurately studying the transition to turbulence of boundary-layer flows over porous walls.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/186102016-01-01T00:00:00ZWEDIN, HåkanCHERUBINI, StefaniaThe asymptotic suction boundary layer (ASBL) is used for studying two permeability models, namely the Darcy and the Forchheimer model, the latter being more physically correct according to the literature. The term that defines the two apart is a function of the non-Darcian wall permeability ${\hat{K}}_{2}$ and of the wall suction ${\hat{V}}_{0}$, whereas the Darcian wall permeability ${\hat{K}}_{1}$ is common to the two models. The underlying interest of the study lies in the field of transition to turbulence where focus is put on two-dimensional nonlinear traveling waves (TWs) and their three-dimensional linear stability. Following a previous study by Wedin et al (2015 Phys. Rev. E 92 013022), where only the Darcy model was considered, the present work aims at comparing the two models, assessing where in the parameter space they cease to produce the same results. For low values of ${\hat{K}}_{1}$ both models produce almost identical TW solutions. However, when both increasing the suction ${\hat{V}}_{0}$ to sufficiently high amplitudes (i.e. lowering the Reynolds number Re, based on the displacement thickness) and using large values of the wall porosity, differences are observed. In terms of the non-dimensional Darcian wall permeability parameter, a, strong differences in the overall shape of the bifurcation curves are observed for $a\gtrsim 0.70$, with the emergence of a new family of solutions at Re lower than 100. For these large values of a, a Forchheimer number ${{Fo}}_{\max }\gtrsim 0.5$ is found, where Fo expresses the ratio between the kinetic and viscous forces acting on the porous wall. Moreover, the minimum Reynolds number, ${{Re}}_{g}$, for which the Navier–Stokes equations allow for nonlinear solutions, decreases for increasing values of a. Fixing the streamwise wavenumber to α = 0.154, as used in the study by Wedin et al referenced above, we find that ${{Re}}_{g}$ is lowered from Re ≈ 3000 for zero permeability, to below 50 for a = 0.80 for both permeability models. Finally, the stability of the TW solutions is assessed using a three-dimensional linearized direct numerical simulation (DNS). Low-frequency unstable modes are found for both permeability models; however, the Darcy model is found to overpredict the growth rate, and underpredict the streamwise extension of the most unstable mode. These results indicate that a careful choice of the underlying permeability model is crucial for accurately studying the transition to turbulence of boundary-layer flows over porous walls.