Journal of Fluid Mechanics最新文献_第8页

On the coupling instability of a gas jet impinging on a liquid film 关于撞击液膜的气体射流的耦合不稳定性

IF 3.7 2区工程技术

Journal of Fluid Mechanics Pub Date : 2024-08-27 DOI: 10.1017/jfm.2024.553

David Barreiro-Villaverde, Anne Gosset, Marcos Lema, Miguel A. Mendez

{"title":"On the coupling instability of a gas jet impinging on a liquid film","authors":"David Barreiro-Villaverde, Anne Gosset, Marcos Lema, Miguel A. Mendez","doi":"10.1017/jfm.2024.553","DOIUrl":"https://doi.org/10.1017/jfm.2024.553","url":null,"abstract":"We investigate the dynamics of a gas jet impinging perpendicular to a thin liquid film dragged by a rising vertical substrate. This configuration is relevant to the jet-wiping process in hot-dip galvanization and it is unstable. Previous studies analysed the dynamics of the instability in the case of liquids with low Kapitza numbers (highly viscous liquids), more amenable to experimental and numerical investigations. This work extends the previous investigations by focusing on the wiping at much higher Kapitza numbers, which are more relevant to the galvanizing process. The simulations are carried out by combining volume of fluid and large-eddy simulations, and the dynamics of the gas–liquid interaction is analysed using extended multiscale proper orthogonal decomposition. The simulations allowed for analysing the jet-wiping instability in new flow conditions. Despite the largely different conditions, the results show that the interaction between the gas jet and the liquid film is qualitatively similar, featuring two-dimensional waves in the liquid correlated with oscillations and deflections of the gas jet in all cases. The wave characteristics (e.g. frequency and propagation speed) scale remarkably well using the Shkadov-like scaling based on the liquid, suggesting a dominant role of the liquid film in the coupling, and potentially enabling extrapolation of the results to a broader range of wiping conditions. Finally, we use the numerical results to discuss the limitations of liquid-film models, which constitute currently the only possible approach to study the jet-wiping process in industrial conditions.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"16 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207464","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}

引用次数: 0

Thin-film flow due to an asymmetric distribution of surface tension and applications to surfactant deposition 表面张力不对称分布导致的薄膜流动及其在表面活性剂沉积中的应用

IF 3.7 2区工程技术

Journal of Fluid Mechanics Pub Date : 2024-08-27 DOI: 10.1017/jfm.2024.501

Jun Eshima, Luc Deike, Howard A. Stone

{"title":"Thin-film flow due to an asymmetric distribution of surface tension and applications to surfactant deposition","authors":"Jun Eshima, Luc Deike, Howard A. Stone","doi":"10.1017/jfm.2024.501","DOIUrl":"https://doi.org/10.1017/jfm.2024.501","url":null,"abstract":"Thin-film equations are utilised in many different areas of fluid dynamics when there exists a direction in which the aspect ratio can be considered small. We consider thin free films with Marangoni effects in the extensional flow regime, where velocity gradients occur predominantly along the film. In practice, because of the local deposition of surfactants or input of energy, asymmetric distributions of surfactants or surface tension more generally, are possible. Such examples include the surface of bubbles and the rupture of thin films. In this study, we consider the asymmetric thin-film equations for extensional flow with Marangoni effects. Concentrating on the case of small Reynolds number $ Re $ , we study the deposition of insoluble surfactants on one side of a liquid sheet otherwise at rest and the resulting thinning and rupture of the sheet. The analogous problem with a uniformly thinning liquid sheet is also considered. In addition, the centreline deformation is discussed. In particular, we show analytically that if the surface tension isotherm $sigma = sigma (varGamma )$ is nonlinear (surface tension $sigma$ varies with surfactant concentration $varGamma$ ), then accounting for top–bottom asymmetry leads to slower (faster) thinning and pinching if $sigma = sigma (varGamma )$ is convex (concave). The analytical progress reported in this paper allows us to discuss the production of satellite drops from rupture via Marangoni effects, which, if relevant to surface bubbles, would be an aerosol production mechanism that is distinct from jet drops and film drops.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"63 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226604","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}

引用次数: 0

Dewetting of a corner film wrapping a wall-mounted cylinder 壁挂式圆筒角膜的脱水处理

IF 3.7 2区工程技术

Journal of Fluid Mechanics Pub Date : 2024-08-27 DOI: 10.1017/jfm.2024.416

Si Suo, Seyed Morteza Habibi Khorasani, Shervin Bagheri

{"title":"Dewetting of a corner film wrapping a wall-mounted cylinder","authors":"Si Suo, Seyed Morteza Habibi Khorasani, Shervin Bagheri","doi":"10.1017/jfm.2024.416","DOIUrl":"https://doi.org/10.1017/jfm.2024.416","url":null,"abstract":"In this study, we investigate the stability of a film that is attached to a corner between a cylinder and a substrate, using a combination of theoretical and numerical approaches. Notably, we place our focus on flat and thin films where the contact line is almost perpendicular to the cylinder wall whereas a small angle forms between the contact line and the substrate, and the film size is smaller than the cylinder radius. The film stability, which depends on the film size and the wall wettability, is first predicted by a standard linear stability analysis (LSA) within the long-wave theoretical framework. We find that the film size plays the most important role in controlling the film stability. Specifically, the thicker the film is, the less sensitive it becomes to the large-wavenumber perturbation. The wall wettability mainly impacts the growth rates of perturbations and slightly influences the marginal stability and postinstability patterns of wrapping films. We compare the LSA predictions with numerical results obtained from a disjoining pressure model (DPM) and volume-of-fluid (VOF) simulations, which provide more insights into the film breakup process. At the early stage there is a strong agreement between the LSA predictions and the DPM results. Notably, as the perturbation grows, thin film regions connecting two neighbouring satellite droplets form which may eventually lead to a stable or temporary secondary droplet, an aspect which the LSA is incapable of capturing. In addition, the VOF simulations suggest that beyond a critical film size, merging between two neighbouring drops becomes involved during the breakup stage. Therefore, the LSA predictions are able to provide only an upper limit on the final number of satellite droplets.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"9 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207460","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}

引用次数: 0

Understanding the effect of Prandtl number on momentum and scalar mixing rates in neutral and stably stratified flows using gradient field dynamics 利用梯度场动力学理解普朗特尔数对中性和稳定分层流中动量和标量混合率的影响

IF 3.7 2区工程技术

Journal of Fluid Mechanics Pub Date : 2024-08-27 DOI: 10.1017/jfm.2024.548

Andrew D. Bragg, Stephen M. de Bruyn Kops

{"title":"Understanding the effect of Prandtl number on momentum and scalar mixing rates in neutral and stably stratified flows using gradient field dynamics","authors":"Andrew D. Bragg, Stephen M. de Bruyn Kops","doi":"10.1017/jfm.2024.548","DOIUrl":"https://doi.org/10.1017/jfm.2024.548","url":null,"abstract":"Recently, direct numerical simulations (DNS) of stably stratified turbulence have shown that as the Prandtl number ( $Pr$ ) is increased from 1 to 7, the mean turbulent potential energy dissipation rate (TPE-DR) drops dramatically, while the mean turbulent kinetic energy dissipation rate (TKE-DR) increases significantly. Through an analysis of the equations governing the fluctuating velocity and density gradients we provide a mechanistic explanation for this surprising behaviour and test the predictions using DNS. We show that the mean density gradient gives rise to a mechanism that opposes the production of fluctuating density gradients, and this is connected to the emergence of ramp cliffs. The same term appears in the velocity gradient equation but with the opposite sign, and is the contribution from buoyancy. This term is ultimately the reason why the TPE-DR reduces while the TKE-DR increases with increasing $Pr$ . Our analysis also predicts that the effects of buoyancy on the smallest scales of the flow become stronger as $Pr$ is increased, and this is confirmed by our DNS data. A consequence of this is that the standard buoyancy Reynolds number does not correctly estimate the impact of buoyancy at the smallest scales when $Pr$ deviates from 1, and we derive a suitable alternative parameter. Finally, an analysis of the filtered gradient equations reveals that the mean density gradient term changes sign at sufficiently large scales, such that buoyancy acts as a source for velocity gradients at small scales, but as a sink at large scales.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"46 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207466","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}

引用次数: 0

One-winged butterflies: mode selection for azimuthal magnetorotational instability by thermal convection 单翼蝴蝶：热对流方位磁定向不稳定性的模式选择

IF 3.7 2区工程技术

Journal of Fluid Mechanics Pub Date : 2024-08-27 DOI: 10.1017/jfm.2024.517

Ashish Mishra, George Mamatsashvili, Martin Seilmayer, Frank Stefani

{"title":"One-winged butterflies: mode selection for azimuthal magnetorotational instability by thermal convection","authors":"Ashish Mishra, George Mamatsashvili, Martin Seilmayer, Frank Stefani","doi":"10.1017/jfm.2024.517","DOIUrl":"https://doi.org/10.1017/jfm.2024.517","url":null,"abstract":"The effects of thermal convection on turbulence in accretion discs, and particularly its interplay with the magnetorotational instability (MRI), are of significant astrophysical interest. Despite extensive theoretical and numerical studies, such an interplay has not been explored experimentally. We conduct linear analysis of the azimuthal version of MRI (AMRI) in the presence of thermal convection and compare the results with our experimental data published before. We show that the critical Hartmann number ( $Ha$ ) for the onset of AMRI is reduced by convection. Importantly, convection breaks symmetry between $m = pm 1$ instability modes ( $m$ is the azimuthal wavenumber). This preference for one mode over the other makes the AMRI wave appear as a ‘one-winged butterfly’.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"11 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207469","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}

引用次数: 0

Turbulent jet theory via Lie symmetry analysis: the free plane jet 通过李对称分析的湍流射流理论：自由平面射流

IF 3.7 2区工程技术

Journal of Fluid Mechanics Pub Date : 2024-08-22 DOI: 10.1017/jfm.2024.527

Nadeem A. Malik, Fazle Hussain

{"title":"Turbulent jet theory via Lie symmetry analysis: the free plane jet","authors":"Nadeem A. Malik, Fazle Hussain","doi":"10.1017/jfm.2024.527","DOIUrl":"https://doi.org/10.1017/jfm.2024.527","url":null,"abstract":"A theory of incompressible turbulent plane jets (TPJs) is proposed by advancing an improved boundary layer approximation over the limiting classical – retaining more terms in the momentum balance equations. A pressure deficit inside the jet (with respect to the ambient) must exist due to transverse turbulence (Miller & Comings, <jats:italic>J. Fluid Mech.</jats:italic>, vol. 3, 1957, pp. 1–16; Hussain & Clarke, <jats:italic>Phys. Fluids</jats:italic>, vol. 20, 1977, pp. 1416–1426). Contrary to the universally accepted invariance of the total momentum flux <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005275_inline1.png\"/> <jats:tex-math>$J_T(x)$</jats:tex-math> </jats:alternatives> </jats:inline-formula> (non-dimensionalized by its inlet value) as a function of the streamwise distance <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005275_inline2.png\"/> <jats:tex-math>$x$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, we prove that <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005275_inline3.png\"/> <jats:tex-math>$J_T(x) >1$</jats:tex-math> </jats:alternatives> </jats:inline-formula> – a condition that all TPJs must satisfy; surprisingly, prior theories and most experiments do not satisfy this condition. This motivated us to apply Lie symmetry analysis with translational and dilatational transformations of the modified equations (incorporating <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005275_inline4.png\"/> <jats:tex-math>$J_T>1$</jats:tex-math> </jats:alternatives> </jats:inline-formula>), which yields scaling laws for key jet measures: the mean streamwise and transverse velocities <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005275_inline5.png\"/> <jats:tex-math>$U(x,y)$</jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005275_inline6.png\"/> <jats:tex-math>$V(x,y)$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, the turbulence intensities, the Reynolds shear stress <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005275_inline8.png\"/> <jats:tex-math>$-rho ,overline {u'v'}(x,y)$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, the mean pressure <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org","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":"142226606","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}

引用次数: 0

Prandtl number dependence of flow topology in quasi-two-dimensional turbulent Rayleigh–Bénard convection 准二维湍流雷利-贝纳德对流中流动拓扑的普朗特数依赖性

IF 3.7 2区工程技术

Journal of Fluid Mechanics Pub Date : 2024-08-22 DOI: 10.1017/jfm.2024.550

Ze-Hao Wang, Xin Chen, Ao Xu, Heng-Dong Xi

引用次数: 0

On the flow dynamics around a surface-mounted cube and boundary layer effects 表面安装立方体周围的流动动力学和边界层效应

IF 3.7 2区工程技术

Journal of Fluid Mechanics Pub Date : 2024-08-22 DOI: 10.1017/jfm.2024.551

Barbara L. da Silva, David Sumner, Donald J. Bergstrom

{"title":"On the flow dynamics around a surface-mounted cube and boundary layer effects","authors":"Barbara L. da Silva, David Sumner, Donald J. Bergstrom","doi":"10.1017/jfm.2024.551","DOIUrl":"https://doi.org/10.1017/jfm.2024.551","url":null,"abstract":"Motivated by contradicting or insufficient information regarding the large-scale flow dynamics around surface-mounted finite-height square prisms of small aspect ratio, the present study investigates the dominant vortex shedding and low-frequency dynamics around a surface-mounted cube. These flow modes were obtained from the spectral proper orthogonal decomposition of large-eddy simulation results, at a Reynolds number of $textit {Re}=1times 10^4$ and two different types of boundary layer: a thin and laminar boundary layer with thickness $delta /D=0.2$ and a thick and turbulent boundary layer with $delta /D=0.8$ . The main antisymmetric mode pair revealed a new flow pattern with the alternate shedding of streamwise flow structures, indicating a transition from the half-loops of taller prisms to only streamwise strands (i.e. no vertical core) for smaller aspect ratio. The formation process of the streamwise structures is due to a reorientation of the vorticity of the arch vortex in the streamwise direction characteristic of the shed structures. The low-frequency drift mode affected the length of the recirculation region, the strength of vortex shedding, and the near-wall flow field and pressure distribution on the cube's faces, leading to low-frequency variations in the fluctuating drag and normal force coefficients. These large-scale flow dynamics were similar for both boundary layers, but minor differences were identified, related mostly to the occurrence of flow attachment and the formation of a headband vortex for the thicker boundary layer.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"78 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207626","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}

引用次数: 0

Exact coherent structures in two-dimensional turbulence identified with convolutional autoencoders 用卷积自动编码器识别二维湍流中的精确相干结构

IF 3.7 2区工程技术

Journal of Fluid Mechanics Pub Date : 2024-08-22 DOI: 10.1017/jfm.2024.552

Jacob Page, Joe Holey, Michael P. Brenner, Rich R. Kerswell

{"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}

引用次数: 0

Asymptotics of the centre-mode instability in viscoelastic channel flow: with and without inertia 粘弹性通道流中心模式不稳定性的渐近学：有惯性和无惯性

IF 3.7 2区工程技术

Journal of Fluid Mechanics Pub Date : 2024-08-22 DOI: 10.1017/jfm.2024.500

Rich R. Kerswell, Jacob Page

{"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}

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