This study proposes a new mechanism that can lead to layering or convection from the finite amplitude perturbation acting on the double diffusive convection with uniform background shear. We focus on the double diffusive convection in the diffusive regime with the cold fresh water laying above the warm salty water. We demonstrate that, although the unperturbed system is linearly stable, the finite amplitude perturbation can trigger the initial flow motions which subsequently obtain energy from the gravitational potential energy and from the uniform background shear, and evolve to layering or convection. By using the linear stability analysis for the initial growth stage and the energy analysis for the following transitional stage, the critical Richardson number can be predicted theoretically. Here the Richardson number measures the relative strength of stratification to the background shear. The dominant wavenumbers and the growth rates of the corresponding modes given by linear theory agree well with the two-dimensional direct numerical simulations, and so does the critical Richardson number predicted by the theoretical model. The layering state is dominated by the double diffusion process, while the convection state at smaller Richardson number exhibits stronger influences from shear and generates smaller heat and salinity fluxes. The theoretical model is further applied to the parameter range which is relevant to the real oceanic environments and reveals that for the typical density ratio observed in the staircase regions in the Arctic Ocean, the current mechanism can lead to layering for relatively weak shear.
{"title":"Double diffusive convection in the diffusive regime with a uniform background shear","authors":"Junyi Li, Yantao Yang","doi":"10.1017/jfm.2024.672","DOIUrl":"https://doi.org/10.1017/jfm.2024.672","url":null,"abstract":"This study proposes a new mechanism that can lead to layering or convection from the finite amplitude perturbation acting on the double diffusive convection with uniform background shear. We focus on the double diffusive convection in the diffusive regime with the cold fresh water laying above the warm salty water. We demonstrate that, although the unperturbed system is linearly stable, the finite amplitude perturbation can trigger the initial flow motions which subsequently obtain energy from the gravitational potential energy and from the uniform background shear, and evolve to layering or convection. By using the linear stability analysis for the initial growth stage and the energy analysis for the following transitional stage, the critical Richardson number can be predicted theoretically. Here the Richardson number measures the relative strength of stratification to the background shear. The dominant wavenumbers and the growth rates of the corresponding modes given by linear theory agree well with the two-dimensional direct numerical simulations, and so does the critical Richardson number predicted by the theoretical model. The layering state is dominated by the double diffusion process, while the convection state at smaller Richardson number exhibits stronger influences from shear and generates smaller heat and salinity fluxes. The theoretical model is further applied to the parameter range which is relevant to the real oceanic environments and reveals that for the typical density ratio observed in the staircase regions in the Arctic Ocean, the current mechanism can lead to layering for relatively weak shear.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"18 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256258","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 perform linear stability analysis and direct numerical simulations to study the effect of the radius ratio on the instability and flow characteristics of the sheared annular centrifugal Rayleigh–Bénard convection, where the cold inner cylinder and the hot outer cylinder rotate with a small angular velocity difference. With the shear enhancement, the thermal convection is suppressed and finally becomes stable for different radius ratios ${eta in mathbb {R}|0.2leqslant eta le 0.95}$. Considering the inhomogeneous distribution of shear stresses in the base flow, a new global Richardson number $Ri_g$ is defined and the marginal-state curves for different radius ratios are successfully unified in the parameter domain of $Ri_g$ and the Rayleigh number $Ra$. The results are consistent with the marginal-state curve of the wall-sheared classical Rayleigh–Bénard convection in the streamwise direction, demonstrating that the basic stabilization mechanisms are identical. Moreover, systems with small radius ratios exhibit greater geometric asymmetry. On the one hand, this results in a smaller equivalent aspect ratio for the system, accommodating fewer convection roll pairs; fewer roll pairs are more likely to cause a transition in the flow structure during shear enhancement. On the other hand, the shear distribution is more inhomogeneous, allowing for an outward shift of the convection region and the elevation of bulk temperature under strong shear.
我们通过线性稳定性分析和直接数值模拟研究了半径比对剪切环形离心雷利-贝纳德对流的不稳定性和流动特性的影响，其中冷内圆筒和热外圆筒以较小的角速度差旋转。随着剪切力的增强，热对流被抑制，并最终在不同半径比 ${eta in mathbb {R}|0.2leqslant eta le 0.95}$ 下变得稳定。考虑到基底流中剪应力的不均匀分布，定义了一个新的全局理查森数 $Ri_g$，并成功地将不同半径比的边际状态曲线统一在参数域 $Ri_g$ 和瑞利数 $Ra$ 中。结果与流向壁剪切经典瑞利-贝纳德对流的边际状态曲线一致，表明基本稳定机制是相同的。此外，半径比小的系统表现出更大的几何不对称性。一方面，这导致系统的等效长宽比更小，可容纳的对流辊对更少；辊对更少更容易在剪切增强过程中导致流动结构的转变。另一方面，剪切力分布更不均匀，使得对流区域外移，在强剪切力作用下体积温度升高。
{"title":"Effect of radius ratio on the sheared annular centrifugal turbulent convection","authors":"Jun Zhong, Junyi Li, Chao Sun","doi":"10.1017/jfm.2024.543","DOIUrl":"https://doi.org/10.1017/jfm.2024.543","url":null,"abstract":"We perform linear stability analysis and direct numerical simulations to study the effect of the radius ratio on the instability and flow characteristics of the sheared annular centrifugal Rayleigh–Bénard convection, where the cold inner cylinder and the hot outer cylinder rotate with a small angular velocity difference. With the shear enhancement, the thermal convection is suppressed and finally becomes stable for different radius ratios <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005433_inline1.png\"/> <jats:tex-math>${eta in mathbb {R}|0.2leqslant eta le 0.95}$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. Considering the inhomogeneous distribution of shear stresses in the base flow, a new global Richardson number <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005433_inline2.png\"/> <jats:tex-math>$Ri_g$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is defined and the marginal-state curves for different radius ratios are successfully unified in the parameter domain of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005433_inline3.png\"/> <jats:tex-math>$Ri_g$</jats:tex-math> </jats:alternatives> </jats:inline-formula> and the Rayleigh number <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005433_inline4.png\"/> <jats:tex-math>$Ra$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. The results are consistent with the marginal-state curve of the wall-sheared classical Rayleigh–Bénard convection in the streamwise direction, demonstrating that the basic stabilization mechanisms are identical. Moreover, systems with small radius ratios exhibit greater geometric asymmetry. On the one hand, this results in a smaller equivalent aspect ratio for the system, accommodating fewer convection roll pairs; fewer roll pairs are more likely to cause a transition in the flow structure during shear enhancement. On the other hand, the shear distribution is more inhomogeneous, allowing for an outward shift of the convection region and the elevation of bulk temperature under strong shear.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"23 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256262","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}
This study conducts particle-resolved direct numerical simulations to analyse how finite-size spherical particles affect the decay rate of turbulent kinetic energy in non-sustained homogeneous isotropic turbulence. The decaying particle-laden homogeneous isotropic turbulence is generated with two set-ups, i.e. (1) releasing particles into a single-phase decaying homogeneous isotropic turbulence and (2) switching off the driving force of a sustained particle-laden homogeneous isotropic turbulence. With both set-ups, the decay of turbulent kinetic energy follows a power-law when the flow is fully relaxed, similar to their single-phase counterparts. The dependence of the power-law decay exponent $n$ on the particle-to-fluid density ratio, particle size and volume fraction is also investigated, and a predictive model is developed. We find that the presence of heavier particles slows down the long-time power-law decay exponent.
{"title":"Decay rate of homogeneous isotropic turbulence laden with finite-size particles","authors":"Qichao Sun, Cheng Peng, Lian-Ping Wang, Songying Chen, Zuchao Zhu","doi":"10.1017/jfm.2024.698","DOIUrl":"https://doi.org/10.1017/jfm.2024.698","url":null,"abstract":"This study conducts particle-resolved direct numerical simulations to analyse how finite-size spherical particles affect the decay rate of turbulent kinetic energy in non-sustained homogeneous isotropic turbulence. The decaying particle-laden homogeneous isotropic turbulence is generated with two set-ups, i.e. (1) releasing particles into a single-phase decaying homogeneous isotropic turbulence and (2) switching off the driving force of a sustained particle-laden homogeneous isotropic turbulence. With both set-ups, the decay of turbulent kinetic energy follows a power-law when the flow is fully relaxed, similar to their single-phase counterparts. The dependence of the power-law decay exponent <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024006980_inline1.png\"/> <jats:tex-math>$n$</jats:tex-math> </jats:alternatives> </jats:inline-formula> on the particle-to-fluid density ratio, particle size and volume fraction is also investigated, and a predictive model is developed. We find that the presence of heavier particles slows down the long-time power-law decay exponent.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"203 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256278","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}
Liquid metal buoyant flow around two differentially heated horizontal cylinders in the presence of a uniform vertical magnetic field is investigated experimentally. While magneto-convection in pipes or ducts has been studied theoretically and experimentally in recent years, data for heat transfer at immersed obstacles are rare and, to our knowledge, detailed experimental investigations on this fundamental magnetohydrodynamic problem do not exist. In the present work, two horizontal cylinders inserted into an adiabatic rectangular cavity filled with gallium–indium–tin are kept at constant temperatures to establish a driving temperature gradient in the surrounding liquid metal. The buoyancy-driven flow, quantified by the Grashof number $Gr$, is varied in the range ${10^{6} leq Gr leq ~5times 10^{7}}$. With increasing magnetic field, expressed via the Hartmann number $Ha$, different flow regimes are identified from measurements for $0 leq Ha leq ~3000$. The effect of the electromagnetic force primarily consists in suppressing turbulence and damping the convective flow. The heat transfer is quantified in terms of the non-dimensional Nusselt number $Nu$, and its dependence on $Gr/{Ha}^{2}$, which is identified as the important group governing the flow, is discussed.
{"title":"Experimental investigation on magneto-convective flows around two differentially heated horizontal cylinders","authors":"Cyril Courtessole, H.-J. Brinkmann, L. Bühler","doi":"10.1017/jfm.2024.591","DOIUrl":"https://doi.org/10.1017/jfm.2024.591","url":null,"abstract":"Liquid metal buoyant flow around two differentially heated horizontal cylinders in the presence of a uniform vertical magnetic field is investigated experimentally. While magneto-convection in pipes or ducts has been studied theoretically and experimentally in recent years, data for heat transfer at immersed obstacles are rare and, to our knowledge, detailed experimental investigations on this fundamental magnetohydrodynamic problem do not exist. In the present work, two horizontal cylinders inserted into an adiabatic rectangular cavity filled with gallium–indium–tin are kept at constant temperatures to establish a driving temperature gradient in the surrounding liquid metal. The buoyancy-driven flow, quantified by the Grashof number <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005913_inline1.png\"/> <jats:tex-math>$Gr$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, is varied in the range <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005913_inline2.png\"/> <jats:tex-math>${10^{6} leq Gr leq ~5times 10^{7}}$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. With increasing magnetic field, expressed via the Hartmann number <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005913_inline3.png\"/> <jats:tex-math>$Ha$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, different flow regimes are identified from measurements for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005913_inline4.png\"/> <jats:tex-math>$0 leq Ha leq ~3000$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. The effect of the electromagnetic force primarily consists in suppressing turbulence and damping the convective flow. The heat transfer is quantified in terms of the non-dimensional Nusselt number <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005913_inline5.png\"/> <jats:tex-math>$Nu$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, and its dependence on <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005913_inline6.png\"/> <jats:tex-math>$Gr/{Ha}^{2}$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, which is identified as the important group governing the flow, is discussed.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"13 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256279","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}
Consider the motion of a thin layer of electrically conducting fluid, between two closely spaced parallel plates, in a classical Hele-Shaw geometry. Furthermore, let the system be immersed in a uniform external magnetic field (normal to the plates) and let electrical current be driven between conducting probes immersed in the fluid layer. In the present paper, we analyse the ensuing fluid flow at low Hartmann numbers. Physically, the system is particularly interesting because it allows for circulation in the flow, which is not possible in the standard pressure-driven Hele-Shaw cell. We first elucidate the mechanism of flow generation both physically and mathematically. After formulating the problem using complex variables, we present mathematical solutions for a class of canonical multiply connected geometries in terms of the prime function framework developed by Crowdy (Solving Problems in Multiply Connected Domains, SIAM, 2020). We then demonstrate how recently developed fast numerical methods may be applied to accurately determine the flow field in arbitrary geometries.
{"title":"Magnetohydrodynamic flow control in Hele-Shaw cells","authors":"Kyle I. McKee","doi":"10.1017/jfm.2024.618","DOIUrl":"https://doi.org/10.1017/jfm.2024.618","url":null,"abstract":"Consider the motion of a thin layer of electrically conducting fluid, between two closely spaced parallel plates, in a classical Hele-Shaw geometry. Furthermore, let the system be immersed in a uniform external magnetic field (normal to the plates) and let electrical current be driven between conducting probes immersed in the fluid layer. In the present paper, we analyse the ensuing fluid flow at low Hartmann numbers. Physically, the system is particularly interesting because it allows for circulation in the flow, which is not possible in the standard pressure-driven Hele-Shaw cell. We first elucidate the mechanism of flow generation both physically and mathematically. After formulating the problem using complex variables, we present mathematical solutions for a class of canonical multiply connected geometries in terms of the prime function framework developed by Crowdy (<jats:italic>Solving Problems in Multiply Connected Domains</jats:italic>, SIAM, 2020). We then demonstrate how recently developed fast numerical methods may be applied to accurately determine the flow field in arbitrary geometries.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"54 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256256","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 report on an experimental study in which Lagrangian tracking is applied to millions of microscopic particles floating on the free surface of turbulent water. We leverage a large jet-stirred zero-mean-flow apparatus, where the Reynolds number is sufficiently high for an inertial range to emerge while the surface deformation remains minimal. Two-point statistics reveal specific features of the flow, deviating from the classic description derived for incompressible turbulence. The magnitude of the relative velocity is strongly intermittent, especially at small separations, leading to anomalous scaling of the second-order structure functions in the dissipative range. This is driven by the divergent component of the flow, leading to fast approaching/separation rates of nearby particles. The Lagrangian relative velocity shows strong persistence of the initial state, such that the ballistic pair separation extends to the inertial range of time delays. Based on these observations, we propose a classification of particle pairs based on their initial separation rate. When this is much smaller than the relative velocity prescribed by inertial scaling (which is the case for the majority of the observed particle pairs), the relative velocity transitions to a diffusive growth and the Richardson–Obukhov super-diffusive dispersion is recovered.
{"title":"Relative dispersion in free-surface turbulence","authors":"Yaxing Li, Yifan Wang, Yinghe Qi, Filippo Coletti","doi":"10.1017/jfm.2024.637","DOIUrl":"https://doi.org/10.1017/jfm.2024.637","url":null,"abstract":"We report on an experimental study in which Lagrangian tracking is applied to millions of microscopic particles floating on the free surface of turbulent water. We leverage a large jet-stirred zero-mean-flow apparatus, where the Reynolds number is sufficiently high for an inertial range to emerge while the surface deformation remains minimal. Two-point statistics reveal specific features of the flow, deviating from the classic description derived for incompressible turbulence. The magnitude of the relative velocity is strongly intermittent, especially at small separations, leading to anomalous scaling of the second-order structure functions in the dissipative range. This is driven by the divergent component of the flow, leading to fast approaching/separation rates of nearby particles. The Lagrangian relative velocity shows strong persistence of the initial state, such that the ballistic pair separation extends to the inertial range of time delays. Based on these observations, we propose a classification of particle pairs based on their initial separation rate. When this is much smaller than the relative velocity prescribed by inertial scaling (which is the case for the majority of the observed particle pairs), the relative velocity transitions to a diffusive growth and the Richardson–Obukhov super-diffusive dispersion is recovered.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"16 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256261","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}
Single-flagellated bacteria are ubiquitous in nature. They exhibit various swimming modes using their flagella to explore complex surroundings such as soil and porous polymer networks. Some single-flagellated bacteria swim with two distinct modes, one with the flagellum extended away from its body and another with the flagellum wrapped around it. The wrapped mode has been observed when bacteria swim under tight confinements or in highly viscous polymeric melts. In this study we investigate the hydrodynamics of these two modes inside a circular pipe. We find that the wrapped mode is slower than the extended mode in bulk but more efficient under strong confinement due to a hydrodynamic increase of its flagellum translation–rotation coupling and an Archimedes’ screw-like configuration that helps to move the fluid along the pipe.
{"title":"Swimming efficiently by wrapping","authors":"H. Gidituri, M. Ellero, F. Balboa Usabiaga","doi":"10.1017/jfm.2024.594","DOIUrl":"https://doi.org/10.1017/jfm.2024.594","url":null,"abstract":"Single-flagellated bacteria are ubiquitous in nature. They exhibit various swimming modes using their flagella to explore complex surroundings such as soil and porous polymer networks. Some single-flagellated bacteria swim with two distinct modes, one with the flagellum extended away from its body and another with the flagellum wrapped around it. The wrapped mode has been observed when bacteria swim under tight confinements or in highly viscous polymeric melts. In this study we investigate the hydrodynamics of these two modes inside a circular pipe. We find that the wrapped mode is slower than the extended mode in bulk but more efficient under strong confinement due to a hydrodynamic increase of its flagellum translation–rotation coupling and an Archimedes’ screw-like configuration that helps to move the fluid along the pipe.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"31 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256282","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}
Lei Ren, Xin Tao, Lu Zhang, Ke-Qing Xia, Yi-Chao Xie
We present a systematic study on the effects of small aspect ratios <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S002211202400630X_inline1.png"/> <jats:tex-math>$varGamma$</jats:tex-math> </jats:alternatives> </jats:inline-formula> on heat transport in liquid metal convection with a Prandtl number of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S002211202400630X_inline2.png"/> <jats:tex-math>$Pr=0.029$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. The study covers <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S002211202400630X_inline3.png"/> <jats:tex-math>$1/20le varGamma le 1$</jats:tex-math> </jats:alternatives> </jats:inline-formula> experimentally and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S002211202400630X_inline4.png"/> <jats:tex-math>$1/50le varGamma le 1$</jats:tex-math> </jats:alternatives> </jats:inline-formula> numerically, and a Rayleigh number <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S002211202400630X_inline5.png"/> <jats:tex-math>$Ra$</jats:tex-math> </jats:alternatives> </jats:inline-formula> range of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S002211202400630X_inline6.png"/> <jats:tex-math>$4times 10^3 le Ra le 7times 10^{9}$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. It is found experimentally that the local effective heat transport scaling exponent <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S002211202400630X_inline7.png"/> <jats:tex-math>$gamma$</jats:tex-math> </jats:alternatives> </jats:inline-formula> changes with both <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S002211202400630X_inline8.png"/> <jats:tex-math>$Ra$</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="S002211202400630X_inline9.png"/> <jats:tex-math>$varGamma$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, attaining a <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S002211202400630X_inline10.png"/> <jats:tex-math>$varGamma$</jats:tex-math> </jats:alternatives> </jats:inline-formula>-dependent maximum value before transition-to-turbulence and appro
{"title":"Heat transport in liquid metal convection from onset to turbulence: the effect of small aspect ratio","authors":"Lei Ren, Xin Tao, Lu Zhang, Ke-Qing Xia, Yi-Chao Xie","doi":"10.1017/jfm.2024.630","DOIUrl":"https://doi.org/10.1017/jfm.2024.630","url":null,"abstract":"We present a systematic study on the effects of small aspect ratios <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002211202400630X_inline1.png\"/> <jats:tex-math>$varGamma$</jats:tex-math> </jats:alternatives> </jats:inline-formula> on heat transport in liquid metal convection with a Prandtl number of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002211202400630X_inline2.png\"/> <jats:tex-math>$Pr=0.029$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. The study covers <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002211202400630X_inline3.png\"/> <jats:tex-math>$1/20le varGamma le 1$</jats:tex-math> </jats:alternatives> </jats:inline-formula> experimentally and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002211202400630X_inline4.png\"/> <jats:tex-math>$1/50le varGamma le 1$</jats:tex-math> </jats:alternatives> </jats:inline-formula> numerically, and a Rayleigh number <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002211202400630X_inline5.png\"/> <jats:tex-math>$Ra$</jats:tex-math> </jats:alternatives> </jats:inline-formula> range of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002211202400630X_inline6.png\"/> <jats:tex-math>$4times 10^3 le Ra le 7times 10^{9}$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. It is found experimentally that the local effective heat transport scaling exponent <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002211202400630X_inline7.png\"/> <jats:tex-math>$gamma$</jats:tex-math> </jats:alternatives> </jats:inline-formula> changes with both <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002211202400630X_inline8.png\"/> <jats:tex-math>$Ra$</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=\"S002211202400630X_inline9.png\"/> <jats:tex-math>$varGamma$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, attaining a <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002211202400630X_inline10.png\"/> <jats:tex-math>$varGamma$</jats:tex-math> </jats:alternatives> </jats:inline-formula>-dependent maximum value before transition-to-turbulence and appro","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"75 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256255","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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