Jacob Page, Joe Holey, Michael P. Brenner, Rich R. Kerswell
Convolutional autoencoders are used to deconstruct the changing dynamics of two-dimensional Kolmogorov flow as <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005524_inline1.png"/> <jats:tex-math>$Re$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is increased from weakly chaotic flow at <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005524_inline2.png"/> <jats:tex-math>$Re=40$</jats:tex-math> </jats:alternatives> </jats:inline-formula> to a chaotic state dominated by a domain-filling vortex pair at <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005524_inline3.png"/> <jats:tex-math>$Re=400$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. ‘Latent Fourier analysis’ (Page <jats:italic>et al.</jats:italic>, <jats:italic>Phys. Rev. Fluids</jats:italic>6, 2021, p. 034402) reveals a detached class of bursting dynamics at <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005524_inline4.png"/> <jats:tex-math>$Re=40$</jats:tex-math> </jats:alternatives> </jats:inline-formula> which merge with the low-dissipation dynamics as <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005524_inline5.png"/> <jats:tex-math>$Re$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is increased to <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005524_inline6.png"/> <jats:tex-math>$100$</jats:tex-math> </jats:alternatives> </jats:inline-formula> and provides an efficient representation within which to find unstable periodic orbits (UPOs) using recurrent flow analysis. Focusing on initial guesses with energy in higher latent Fourier wavenumbers allows a significant number of high-dissipation-rate UPOs associated with the bursting events to be found for the first time. At <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005524_inline7.png"/> <jats:tex-math>$Re=400$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, the UPOs discovered at lower <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005524_inline8.png"/> <jats:tex-math>$Re$</jats:tex-math> </jats:alternatives> </jats:inline-formula> move away from the attractor, and an entirely different embedding structure is formed within the network devoid of small-scale vortices. Here latent Fourier proje
{"title":"Exact coherent structures in two-dimensional turbulence identified with convolutional autoencoders","authors":"Jacob Page, Joe Holey, Michael P. Brenner, Rich R. Kerswell","doi":"10.1017/jfm.2024.552","DOIUrl":"https://doi.org/10.1017/jfm.2024.552","url":null,"abstract":"Convolutional autoencoders are used to deconstruct the changing dynamics of two-dimensional Kolmogorov flow as <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005524_inline1.png\"/> <jats:tex-math>$Re$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is increased from weakly chaotic flow at <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005524_inline2.png\"/> <jats:tex-math>$Re=40$</jats:tex-math> </jats:alternatives> </jats:inline-formula> to a chaotic state dominated by a domain-filling vortex pair at <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005524_inline3.png\"/> <jats:tex-math>$Re=400$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. ‘Latent Fourier analysis’ (Page <jats:italic>et al.</jats:italic>, <jats:italic>Phys. Rev. Fluids</jats:italic>6, 2021, p. 034402) reveals a detached class of bursting dynamics at <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005524_inline4.png\"/> <jats:tex-math>$Re=40$</jats:tex-math> </jats:alternatives> </jats:inline-formula> which merge with the low-dissipation dynamics as <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005524_inline5.png\"/> <jats:tex-math>$Re$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is increased to <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005524_inline6.png\"/> <jats:tex-math>$100$</jats:tex-math> </jats:alternatives> </jats:inline-formula> and provides an efficient representation within which to find unstable periodic orbits (UPOs) using recurrent flow analysis. Focusing on initial guesses with energy in higher latent Fourier wavenumbers allows a significant number of high-dissipation-rate UPOs associated with the bursting events to be found for the first time. At <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005524_inline7.png\"/> <jats:tex-math>$Re=400$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, the UPOs discovered at lower <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005524_inline8.png\"/> <jats:tex-math>$Re$</jats:tex-math> </jats:alternatives> </jats:inline-formula> move away from the attractor, and an entirely different embedding structure is formed within the network devoid of small-scale vortices. Here latent Fourier proje","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"19 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Motivated by the recent numerical results of Khalid <jats:italic>et al.</jats:italic> (<jats:italic>Phys. Rev. Lett.</jats:italic>, vol. 127, 2021, 134502), we consider the large-Weissenberg-number (<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005007_inline1.png"/> <jats:tex-math>$W$</jats:tex-math> </jats:alternatives> </jats:inline-formula>) asymptotics of the centre mode instability in inertialess viscoelastic channel flow. The instability is of the critical layer type in the distinguished ultra-dilute limit where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005007_inline2.png"/> <jats:tex-math>$W(1-beta )=O(1)$</jats:tex-math> </jats:alternatives> </jats:inline-formula> as <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005007_inline3.png"/> <jats:tex-math>$W rightarrow infty$</jats:tex-math> </jats:alternatives> </jats:inline-formula> (<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005007_inline4.png"/> <jats:tex-math>$beta$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the ratio of solvent-to-total viscosity). In contrast to centre modes in the Orr–Sommerfeld equation, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005007_inline5.png"/> <jats:tex-math>$1-c=O(1)$</jats:tex-math> </jats:alternatives> </jats:inline-formula> as <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005007_inline6.png"/> <jats:tex-math>$W rightarrow infty$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005007_inline7.png"/> <jats:tex-math>$c$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the phase speed normalised by the centreline speed as a central ‘outer’ region is always needed to adjust the non-zero cross-stream velocity at the critical layer down to zero at the centreline. The critical layer acts as a pair of intense ‘bellows’ which blows the flow streamlines apart locally and then sucks them back together again. This compression/rarefaction amplifies the streamwise-normal polymer stress which in turn drives the streamwise flow through local polymer stresses at the critical layer. The streamwise flow energises the cross-stream flow via continuity which in turn intensifies the critical layer to close the cycle. We also treat the large-Reynolds-number (<jats:inline-formu
{"title":"Asymptotics of the centre-mode instability in viscoelastic channel flow: with and without inertia","authors":"Rich R. Kerswell, Jacob Page","doi":"10.1017/jfm.2024.500","DOIUrl":"https://doi.org/10.1017/jfm.2024.500","url":null,"abstract":"Motivated by the recent numerical results of Khalid <jats:italic>et al.</jats:italic> (<jats:italic>Phys. Rev. Lett.</jats:italic>, vol. 127, 2021, 134502), we consider the large-Weissenberg-number (<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005007_inline1.png\"/> <jats:tex-math>$W$</jats:tex-math> </jats:alternatives> </jats:inline-formula>) asymptotics of the centre mode instability in inertialess viscoelastic channel flow. The instability is of the critical layer type in the distinguished ultra-dilute limit where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005007_inline2.png\"/> <jats:tex-math>$W(1-beta )=O(1)$</jats:tex-math> </jats:alternatives> </jats:inline-formula> as <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005007_inline3.png\"/> <jats:tex-math>$W rightarrow infty$</jats:tex-math> </jats:alternatives> </jats:inline-formula> (<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005007_inline4.png\"/> <jats:tex-math>$beta$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the ratio of solvent-to-total viscosity). In contrast to centre modes in the Orr–Sommerfeld equation, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005007_inline5.png\"/> <jats:tex-math>$1-c=O(1)$</jats:tex-math> </jats:alternatives> </jats:inline-formula> as <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005007_inline6.png\"/> <jats:tex-math>$W rightarrow infty$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005007_inline7.png\"/> <jats:tex-math>$c$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the phase speed normalised by the centreline speed as a central ‘outer’ region is always needed to adjust the non-zero cross-stream velocity at the critical layer down to zero at the centreline. The critical layer acts as a pair of intense ‘bellows’ which blows the flow streamlines apart locally and then sucks them back together again. This compression/rarefaction amplifies the streamwise-normal polymer stress which in turn drives the streamwise flow through local polymer stresses at the critical layer. The streamwise flow energises the cross-stream flow via continuity which in turn intensifies the critical layer to close the cycle. We also treat the large-Reynolds-number (<jats:inline-formu","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"57 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We employ the methods of statistical mechanics to obtain closures for the balance equations of momentum and fluctuation kinetic energy that govern the ballistic motion of grains rebounding at a rigid, bumpy bed that are driven by turbulent or non-turbulent shearing fluids, in the absence of mid-trajectory collisions and fluid velocity fluctuations. We obtain semi-analytical solutions for steady and fully developed saltation over horizontal beds for the vertical profiles of particle concentration and stresses and fluid and particle velocities. These compare favourably with measurements in discrete-element numerical simulations in the wide range of conditions of Earth and other planetary environments. The predictions of the particle horizontal mass flux and its scaling with the amount of particles in the system, the properties of the carrier fluid and the intensity of the shearing also agree with numerical simulations and wind-tunnel experiments.
{"title":"Collisionless kinetic theory for saltation over a rigid, bumpy bed","authors":"Diego Berzi, Alexandre Valance, James T. Jenkins","doi":"10.1017/jfm.2024.520","DOIUrl":"https://doi.org/10.1017/jfm.2024.520","url":null,"abstract":"We employ the methods of statistical mechanics to obtain closures for the balance equations of momentum and fluctuation kinetic energy that govern the ballistic motion of grains rebounding at a rigid, bumpy bed that are driven by turbulent or non-turbulent shearing fluids, in the absence of mid-trajectory collisions and fluid velocity fluctuations. We obtain semi-analytical solutions for steady and fully developed saltation over horizontal beds for the vertical profiles of particle concentration and stresses and fluid and particle velocities. These compare favourably with measurements in discrete-element numerical simulations in the wide range of conditions of Earth and other planetary environments. The predictions of the particle horizontal mass flux and its scaling with the amount of particles in the system, the properties of the carrier fluid and the intensity of the shearing also agree with numerical simulations and wind-tunnel experiments.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"32 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The linear stability of plane Couette–Poiseuille flow (CPF) is studied with the physical effects of stratification, rotation and viscosity all included for the first time together. With no stratification, two instability mechanisms are present due to the shear and rotation which, for the most part, do not interact as they favour different forms of two-dimensionality. However, there are some small parts of parameter space where new three-dimensional instability appears indicating that Rayleigh's criterion is also violated in parameter space beyond where shear instability is expected. No fully localised centrifugal instabilities can be found for CPF, but they are shown to exist if the base flow shear has a maximum in the domain (the base flow needs to be at least cubic in the cross-stream variable rather than just quadratic as in CPF). With stable stratification present, new instabilities are found due to the combined effects of stratification and rotation, but only some appear to be of the resonance-type associated with the strato-rotational instability. The other unstable branches are more accurately interpreted as a stratification-modified centrifugal instability. Three-dimensional versions of this violate Rayleigh's criterion even when this is extended to include stratification. When stratification is stronger than rotation, the resonance-type instabilities are only dominant for cyclonic flows.
{"title":"Linear stability of stratified, rotating, viscous plane Couette–Poiseuille flow","authors":"William Oxley, Rich R. Kerswell","doi":"10.1017/jfm.2024.549","DOIUrl":"https://doi.org/10.1017/jfm.2024.549","url":null,"abstract":"The linear stability of plane Couette–Poiseuille flow (CPF) is studied with the physical effects of stratification, rotation and viscosity all included for the first time together. With no stratification, two instability mechanisms are present due to the shear and rotation which, for the most part, do not interact as they favour different forms of two-dimensionality. However, there are some small parts of parameter space where new three-dimensional instability appears indicating that Rayleigh's criterion is also violated in parameter space beyond where shear instability is expected. No fully localised centrifugal instabilities can be found for CPF, but they are shown to exist if the base flow shear has a maximum in the domain (the base flow needs to be at least cubic in the cross-stream variable rather than just quadratic as in CPF). With stable stratification present, new instabilities are found due to the combined effects of stratification and rotation, but only some appear to be of the resonance-type associated with the strato-rotational instability. The other unstable branches are more accurately interpreted as a stratification-modified centrifugal instability. Three-dimensional versions of this violate Rayleigh's criterion even when this is extended to include stratification. When stratification is stronger than rotation, the resonance-type instabilities are only dominant for cyclonic flows.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"7 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mamta Jotkar, Pietro de Anna, Marco Dentz, Luis Cueto-Felgueroso
It is known that the dispersion of colloidal particles in porous media is determined by medium structure, pore-scale flow variability and diffusion. However, much less is known about how diffusiophoresis, that is, the motion of colloidal particles along salt gradients, impacts large-scale particle dispersion in porous media. To shed light on this question, we perform detailed pore-scale simulations of fluid flow, solute transport and diffusiophoretic particle transport in a two-dimensional hyper-uniform porous medium. Particles and solute are initially uniformly distributed throughout the medium. The medium is flushed at constant flow rate, and particle breakthrough curves are recorded at the outlet to assess the macroscopic effects of diffusiophoresis. Particle breakthrough curves show non-Fickian behaviour manifested by strong tailing that is controlled by the diffusiophoretic mobility. Although diffusiophoresis is a short-time, microscopic phenomenon owing to the fast attenuation of salt gradients, it governs macroscopic colloid dispersion through the partitioning of particles into transmitting and dead-end pores. We quantify these behaviours by an upscaled analytical model that describes both the retention and release of colloids in dead-end pores and the observed long-time tailings. Our results suggest that diffusiophoresis is an efficient tool to control particle dispersion and filtration through porous media.
{"title":"The impact of diffusiophoresis on hydrodynamic dispersion and filtration in porous media","authors":"Mamta Jotkar, Pietro de Anna, Marco Dentz, Luis Cueto-Felgueroso","doi":"10.1017/jfm.2024.546","DOIUrl":"https://doi.org/10.1017/jfm.2024.546","url":null,"abstract":"It is known that the dispersion of colloidal particles in porous media is determined by medium structure, pore-scale flow variability and diffusion. However, much less is known about how diffusiophoresis, that is, the motion of colloidal particles along salt gradients, impacts large-scale particle dispersion in porous media. To shed light on this question, we perform detailed pore-scale simulations of fluid flow, solute transport and diffusiophoretic particle transport in a two-dimensional hyper-uniform porous medium. Particles and solute are initially uniformly distributed throughout the medium. The medium is flushed at constant flow rate, and particle breakthrough curves are recorded at the outlet to assess the macroscopic effects of diffusiophoresis. Particle breakthrough curves show non-Fickian behaviour manifested by strong tailing that is controlled by the diffusiophoretic mobility. Although diffusiophoresis is a short-time, microscopic phenomenon owing to the fast attenuation of salt gradients, it governs macroscopic colloid dispersion through the partitioning of particles into transmitting and dead-end pores. We quantify these behaviours by an upscaled analytical model that describes both the retention and release of colloids in dead-end pores and the observed long-time tailings. Our results suggest that diffusiophoresis is an efficient tool to control particle dispersion and filtration through porous media.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"34 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jiaxiang Zhong, Feng Qu, Di Sun, Qingsong Liu, Qing Wang, Junqiang Bai
The unsteady mechanism of unstart flow for an inlet with rectangular-to-elliptical shape transition (REST) under the off-design condition at a Mach of 4 is investigated using the delay detached eddy simulation method. With the help of numerical simulations, the unsteady dynamics, especially the low-frequency characteristics of the REST inlet unstart flow, as well as the self-sustaining mechanism, is investigated. The instantaneous flow illustrates the unsteady phenomena of the REST unstart flow, including the interaction between the cowl-closure leading edge (CLE) shock and the shear layer, breathing of the separation bubble, flapping of the separation shock, instability of the shear layer and vortex shedding along the shear layer. The spectral analysis reveals that the lower frequency dynamics is associated with the breathing of the separation bubble and the flapping motion of the separation shock wave, while the higher frequency is related to the instability of the shear layer affected by cowl-closure leading edge shock and the formation of shedding vortices. Further, coherence analysis shows that the contribution of these flow structures dominating the low-frequency dynamics couple with each other. Based on the dynamic mode decomposition results, the characteristics that contribute to the unsteady behaviour of unstart flow are summarized. The streamwise vortices downstream of the separation and the shedding vortices are believed to be the main driving force of the global low-frequency unsteadiness of the REST inlet unstart flow under the off-design condition. Moreover, the CLE shock plays an important role in the process during the dominant flow structure conversion from the backflow within the separation bubble into elongated streamwise structures.
{"title":"Low-frequency unsteadiness mechanisms of unstart flow in an inlet with rectangular-to-elliptical shape transition under off-design condition at a Mach number of 4","authors":"Jiaxiang Zhong, Feng Qu, Di Sun, Qingsong Liu, Qing Wang, Junqiang Bai","doi":"10.1017/jfm.2024.504","DOIUrl":"https://doi.org/10.1017/jfm.2024.504","url":null,"abstract":"The unsteady mechanism of unstart flow for an inlet with rectangular-to-elliptical shape transition (REST) under the off-design condition at a Mach of 4 is investigated using the delay detached eddy simulation method. With the help of numerical simulations, the unsteady dynamics, especially the low-frequency characteristics of the REST inlet unstart flow, as well as the self-sustaining mechanism, is investigated. The instantaneous flow illustrates the unsteady phenomena of the REST unstart flow, including the interaction between the cowl-closure leading edge (CLE) shock and the shear layer, breathing of the separation bubble, flapping of the separation shock, instability of the shear layer and vortex shedding along the shear layer. The spectral analysis reveals that the lower frequency dynamics is associated with the breathing of the separation bubble and the flapping motion of the separation shock wave, while the higher frequency is related to the instability of the shear layer affected by cowl-closure leading edge shock and the formation of shedding vortices. Further, coherence analysis shows that the contribution of these flow structures dominating the low-frequency dynamics couple with each other. Based on the dynamic mode decomposition results, the characteristics that contribute to the unsteady behaviour of unstart flow are summarized. The streamwise vortices downstream of the separation and the shedding vortices are believed to be the main driving force of the global low-frequency unsteadiness of the REST inlet unstart flow under the off-design condition. Moreover, the CLE shock plays an important role in the process during the dominant flow structure conversion from the backflow within the separation bubble into elongated streamwise structures.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"46 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The low-frequency modal and non-modal linear dynamics of an incompressible, pressure-gradient-induced turbulent separation bubble (TSB) are investigated, with the objective of studying the mechanism responsible for the low-frequency contraction and expansion (breathing) commonly observed in experimental studies. The configuration of interest is a TSB generated on a flat test surface by a succession of adverse and favourable pressure gradients. The base flow selected for the analysis is the average TSB from the direct numerical simulation of Coleman et al. (J. Fluid Mech., vol. 847, 2018, pp. 28–70). Global mode analysis reveals that the eigenmodes of the linear operator are damped for all frequencies and wavenumbers. Furthermore, the least damped eigenmode appears to occur at zero frequency and low, non-zero spanwise wavenumber when scaled with the separation length. Resolvent analysis is then employed to examine the forced dynamics of the flow. At low frequency, a region of low, non-zero spanwise wavenumber is also discernible, where the receptivity appears to be driven by the identified weakly damped global mode. The corresponding optimal energy gain is shown to have the shape of a first-order, low-pass filter with a cut-off frequency consistent with the low-frequency unsteadiness in TSBs. The results from resolvent analysis are compared to the unsteady experimental database of Le Floc'h et al. (J. Fluid Mech., vol. 902, 2020, A13) in a similar TSB flow. The alignment between the optimal response and the first spectral proper orthogonal decomposition mode computed from the experiments is shown to be close to $95,%$, while the spanwise wavenumber of the optimal response is consistent with that of the low-frequency breathing motion captured experimentally. This indicates that the fluctuations observed experimentally at low frequency closely match the response computed from resolvent analysis. Based on these results, we propose that the forced dynamics of the flow, driven by the weakly damped global mode, serve as a plausible mechanism for the origin of the low-frequency breathing motion commonly observed in experimental studies of TSBs.
{"title":"On the low-frequency dynamics of turbulent separation bubbles","authors":"C. Cura, A. Hanifi, A.V.G. Cavalieri, J. Weiss","doi":"10.1017/jfm.2024.532","DOIUrl":"https://doi.org/10.1017/jfm.2024.532","url":null,"abstract":"The low-frequency modal and non-modal linear dynamics of an incompressible, pressure-gradient-induced turbulent separation bubble (TSB) are investigated, with the objective of studying the mechanism responsible for the low-frequency contraction and expansion (breathing) commonly observed in experimental studies. The configuration of interest is a TSB generated on a flat test surface by a succession of adverse and favourable pressure gradients. The base flow selected for the analysis is the average TSB from the direct numerical simulation of Coleman <jats:italic>et al.</jats:italic> (<jats:italic>J. Fluid Mech.</jats:italic>, vol. 847, 2018, pp. 28–70). Global mode analysis reveals that the eigenmodes of the linear operator are damped for all frequencies and wavenumbers. Furthermore, the least damped eigenmode appears to occur at zero frequency and low, non-zero spanwise wavenumber when scaled with the separation length. Resolvent analysis is then employed to examine the forced dynamics of the flow. At low frequency, a region of low, non-zero spanwise wavenumber is also discernible, where the receptivity appears to be driven by the identified weakly damped global mode. The corresponding optimal energy gain is shown to have the shape of a first-order, low-pass filter with a cut-off frequency consistent with the low-frequency unsteadiness in TSBs. The results from resolvent analysis are compared to the unsteady experimental database of Le Floc'h <jats:italic>et al.</jats:italic> (<jats:italic>J. Fluid Mech.</jats:italic>, vol. 902, 2020, A13) in a similar TSB flow. The alignment between the optimal response and the first spectral proper orthogonal decomposition mode computed from the experiments is shown to be close to <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005329_inline1.png\"/> <jats:tex-math>$95,%$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, while the spanwise wavenumber of the optimal response is consistent with that of the low-frequency breathing motion captured experimentally. This indicates that the fluctuations observed experimentally at low frequency closely match the response computed from resolvent analysis. Based on these results, we propose that the forced dynamics of the flow, driven by the weakly damped global mode, serve as a plausible mechanism for the origin of the low-frequency breathing motion commonly observed in experimental studies of TSBs.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"242 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A high-resolution simulation of a thermal vortex ring is analysed from the point of view of the vortex dynamics. A power-spectrum analysis of vortex-ring sections suggests that the simulated flows are overall ‘two dimensional’ in the large-scale limit, being dominated by axisymmetric components, but with a substantial contribution from the non-axisymmetric component at small scales. Contribution of the non-axisymmetric components is negligible in budgets of volume integrals of the vorticity and potential vorticity as well as the impulse (moments of the vorticity weighted by $s^n$ with $n=-1$, 0, 1, where $s$ is the distance from the vertical axis of the vortex ring). A concise description of the dynamics is obtained as a function of geometrical factors together with these three integral variables. Analysis shows that the geometrical factors are fairly close to constant with time, and thus, a redundant closed description of the system is obtained in the similarity regime after spin up of the vortex ring. This redundancy leads to a constraint on the geometrical factors, which is reasonably satisfied by the simulation. A closed description is also obtained over the initial spin-up period of the vortex ring by adding a phenomenologically derived prognostic equation for the source for the volume integral of the potential vorticity (with $n=-1$). Analysis of the budget supports this description.
{"title":"Thermal vortex ring: vortex-dynamics analysis of a high-resolution simulation","authors":"Jun-Ichi Yano, Hugh Morrison","doi":"10.1017/jfm.2024.485","DOIUrl":"https://doi.org/10.1017/jfm.2024.485","url":null,"abstract":"A high-resolution simulation of a thermal vortex ring is analysed from the point of view of the vortex dynamics. A power-spectrum analysis of vortex-ring sections suggests that the simulated flows are overall ‘two dimensional’ in the large-scale limit, being dominated by axisymmetric components, but with a substantial contribution from the non-axisymmetric component at small scales. Contribution of the non-axisymmetric components is negligible in budgets of volume integrals of the vorticity and potential vorticity as well as the impulse (moments of the vorticity weighted by <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024004853_inline1.png\"/> <jats:tex-math>$s^n$</jats:tex-math> </jats:alternatives> </jats:inline-formula> with <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024004853_inline2.png\"/> <jats:tex-math>$n=-1$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, 0, 1, where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024004853_inline3.png\"/> <jats:tex-math>$s$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the distance from the vertical axis of the vortex ring). A concise description of the dynamics is obtained as a function of geometrical factors together with these three integral variables. Analysis shows that the geometrical factors are fairly close to constant with time, and thus, a redundant closed description of the system is obtained in the similarity regime after spin up of the vortex ring. This redundancy leads to a constraint on the geometrical factors, which is reasonably satisfied by the simulation. A closed description is also obtained over the initial spin-up period of the vortex ring by adding a phenomenologically derived prognostic equation for the source for the volume integral of the potential vorticity (with <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024004853_inline4.png\"/> <jats:tex-math>$n=-1$</jats:tex-math> </jats:alternatives> </jats:inline-formula>). Analysis of the budget supports this description.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"3 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hiroyuki Miyoshi, Toby L. Kirk, Marc Hodes, Darren G. Crowdy
{"title":"Fully developed flow through shrouded-fin arrays: exact and asymptotic solutions","authors":"Hiroyuki Miyoshi, Toby L. Kirk, Marc Hodes, Darren G. Crowdy","doi":"10.1017/jfm.2024.505","DOIUrl":"https://doi.org/10.1017/jfm.2024.505","url":null,"abstract":"<p><img href=\"S0022112024005056_figAb.png\" mimesubtype=\"png\" mimetype=\"image\" orientation=\"\" position=\"\" src=\"https://static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0022112024005056/resource/name/S0022112024005056_figAb.png?pub-status=live\" type=\"\"/></p>","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"32 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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