Bluff-body wakes generally become three-dimensional (3-D) and then turbulent when the Reynolds number exceeds a few hundred. Other than an alternate shedding of the spanwise vortices behind the body and a gradual decay and annihilation of the vortices with distance downstream, whether a secondary vortex street would develop in the relatively far wake has been a long-standing argument in the literature. This argument is addressed in the present study. Specifically, direct numerical simulations and transient growth analysis are performed to examine the two-dimensional and 3-D wakes of different bluff bodies, including circular cylinder, square cylinder, diamond cylinder and rectangular cylinders with different cross-sectional aspect ratios. We found that a secondary vortex street is absent for most 3-D and turbulent wakes. The root cause is the weakening of spanwise vortices by 3-D wake instability modes and streamwise circulation/vorticity. The weakened spanwise vortices induce reduced mean shear in the intermediate wake, which then induces much smaller perturbation energy growth that is below the threshold for the emergence of a secondary vortex street. This finding suggests that the 3-D and turbulence characteristics, and the momentum, mass and heat transport in the relatively far wake of bluff bodies, would not be influenced by extra anisotropy or inhomogeneity caused by a secondary vortex street.
{"title":"On the absence of a secondary vortex street in three-dimensional and turbulent cylinder wakes","authors":"Hongyi Jiang","doi":"10.1017/jfm.2024.615","DOIUrl":"https://doi.org/10.1017/jfm.2024.615","url":null,"abstract":"Bluff-body wakes generally become three-dimensional (3-D) and then turbulent when the Reynolds number exceeds a few hundred. Other than an alternate shedding of the spanwise vortices behind the body and a gradual decay and annihilation of the vortices with distance downstream, whether a secondary vortex street would develop in the relatively far wake has been a long-standing argument in the literature. This argument is addressed in the present study. Specifically, direct numerical simulations and transient growth analysis are performed to examine the two-dimensional and 3-D wakes of different bluff bodies, including circular cylinder, square cylinder, diamond cylinder and rectangular cylinders with different cross-sectional aspect ratios. We found that a secondary vortex street is absent for most 3-D and turbulent wakes. The root cause is the weakening of spanwise vortices by 3-D wake instability modes and streamwise circulation/vorticity. The weakened spanwise vortices induce reduced mean shear in the intermediate wake, which then induces much smaller perturbation energy growth that is below the threshold for the emergence of a secondary vortex street. This finding suggests that the 3-D and turbulence characteristics, and the momentum, mass and heat transport in the relatively far wake of bluff bodies, would not be influenced by extra anisotropy or inhomogeneity caused by a secondary vortex street.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"19 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256263","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}
Peng-Jun-Yi Zhang, Zhen-Hua Wan, De-Jun Sun, Xi-Yun Lu
The scaling relations mapping the turbulence statistics in compressible turbulent boundary layers (TBLs) onto their incompressible counterparts are of fundamental significance for turbulence modelling, such as the Morkovin scaling for velocity fields, while for pressure fluctuation fields, a corresponding scaling relation is currently absent. In this work, the underlying scaling relations of pressure fluctuations about Mach number ($M$) contained in their generation mechanisms are explored by analysing a series of direct numerical simulation data of compressible TBLs over a wide Mach number range $(0.5leq M leq 8.0)$. Based on the governing equation of pressure fluctuations, they are decomposed into components according to the properties of source terms. It is notable that the intensity of the compressible component, predominantly originating from the acoustic mode, obeys a monotonic distribution about the Mach number and wall distance; further, the intensity of the rest of the pressure components, which are mainly generated by the vorticity mode, demonstrates a uniform distribution consistent with its incompressible counterpart. Moreover, the coupling between the two components is negligibly weak. Based on the scaling relations, semiempirical models for the fluctuation intensity of both pressure and its components are constructed. Hence, a mapping relation is obtained that the profiles of pressure fluctuation intensities in compressible TBLs can be mapped onto their incompressible counterparts by removing the contribution from the acoustic mode, which can be provided by the model. The intrinsic scaling relation can provide some basic insight for pressure fluctuation modelling.
将可压缩湍流边界层（TBLs）中的湍流统计量映射到不可压缩湍流边界层中的湍流统计量的比例关系对于湍流建模具有重要意义，例如速度场的莫尔科文比例关系，而对于压力波动场，目前还没有相应的比例关系。在这项工作中，通过分析一系列马赫数范围为（0.5leq M leq8.0）的可压缩湍流层的直接数值模拟数据，探索了压力波动关于马赫数（$M$）的基本缩放关系及其产生机制。基于压力波动的支配方程，根据源项的特性将其分解为若干部分。值得注意的是，主要由声波模式产生的可压缩分量的强度服从于马赫数和壁距的单调分布；此外，主要由涡度模式产生的其余压力分量的强度表现出与其不可压缩分量一致的均匀分布。此外，这两个分量之间的耦合微弱到可以忽略不计。根据比例关系，构建了压力及其分量波动强度的半经验模型。因此，可压缩 TBL 中的压力波动强度剖面可以通过去除声学模式的贡献映射到不可压缩的对应剖面上，这种映射关系可以由模型提供。这种内在的比例关系可以为压力波动建模提供一些基本启示。
{"title":"The intrinsic scaling relation between pressure fluctuations and Mach number in compressible turbulent boundary layers","authors":"Peng-Jun-Yi Zhang, Zhen-Hua Wan, De-Jun Sun, Xi-Yun Lu","doi":"10.1017/jfm.2024.566","DOIUrl":"https://doi.org/10.1017/jfm.2024.566","url":null,"abstract":"The scaling relations mapping the turbulence statistics in compressible turbulent boundary layers (TBLs) onto their incompressible counterparts are of fundamental significance for turbulence modelling, such as the Morkovin scaling for velocity fields, while for pressure fluctuation fields, a corresponding scaling relation is currently absent. In this work, the underlying scaling relations of pressure fluctuations about Mach number (<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005664_inline1.png\"/> <jats:tex-math>$M$</jats:tex-math> </jats:alternatives> </jats:inline-formula>) contained in their generation mechanisms are explored by analysing a series of direct numerical simulation data of compressible TBLs over a wide Mach number range <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005664_inline2.png\"/> <jats:tex-math>$(0.5leq M leq 8.0)$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. Based on the governing equation of pressure fluctuations, they are decomposed into components according to the properties of source terms. It is notable that the intensity of the compressible component, predominantly originating from the acoustic mode, obeys a monotonic distribution about the Mach number and wall distance; further, the intensity of the rest of the pressure components, which are mainly generated by the vorticity mode, demonstrates a uniform distribution consistent with its incompressible counterpart. Moreover, the coupling between the two components is negligibly weak. Based on the scaling relations, semiempirical models for the fluctuation intensity of both pressure and its components are constructed. Hence, a mapping relation is obtained that the profiles of pressure fluctuation intensities in compressible TBLs can be mapped onto their incompressible counterparts by removing the contribution from the acoustic mode, which can be provided by the model. The intrinsic scaling relation can provide some basic insight for pressure fluctuation modelling.","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":"142256254","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 introduce a low-order dynamical system to describe thermal convection in an annular domain. The model derives systematically from a Fourier–Laurent truncation of the governing Navier–Stokes Boussinesq equations and accounts for spatial dependence of the flow and temperature fields. Comparison with fully resolved direct numerical simulations (DNS) shows that the model captures parameter bifurcations and reversals of the large-scale circulation (LSC), including states of (i) steady circulating flow, (ii) chaotic LSC reversals and (iii) periodic LSC reversals. Casting the system in terms of the fluid's angular momentum and centre of mass (CoM) reveals equivalence to a damped pendulum with forcing that raises the CoM above the fulcrum. This formulation offers a transparent mechanism for LSC reversals, namely the inertial overshoot of a forced pendulum, and it yields an explicit formula for the frequency $f^*$ of regular LSC reversals in the high-Rayleigh-number (Ra) limit. This formula is shown to be in excellent agreement with DNS and produces the scaling law $f^* sim {Ra}^{0.5}$.
{"title":"Large-scale circulation reversals explained by pendulum correspondence","authors":"Nicholas J. Moore, Jinzi Mac Huang","doi":"10.1017/jfm.2024.584","DOIUrl":"https://doi.org/10.1017/jfm.2024.584","url":null,"abstract":"We introduce a low-order dynamical system to describe thermal convection in an annular domain. The model derives systematically from a Fourier–Laurent truncation of the governing Navier–Stokes Boussinesq equations and accounts for spatial dependence of the flow and temperature fields. Comparison with fully resolved direct numerical simulations (DNS) shows that the model captures parameter bifurcations and reversals of the large-scale circulation (LSC), including states of (i) steady circulating flow, (ii) chaotic LSC reversals and (iii) periodic LSC reversals. Casting the system in terms of the fluid's angular momentum and centre of mass (CoM) reveals equivalence to a damped pendulum with forcing that raises the CoM above the fulcrum. This formulation offers a transparent mechanism for LSC reversals, namely the inertial overshoot of a forced pendulum, and it yields an explicit formula for the frequency <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005846_inline1.png\"/> <jats:tex-math>$f^*$</jats:tex-math> </jats:alternatives> </jats:inline-formula> of regular LSC reversals in the high-Rayleigh-number (<jats:italic>Ra</jats:italic>) limit. This formula is shown to be in excellent agreement with DNS and produces the scaling law <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005846_inline2.png\"/> <jats:tex-math>$f^* sim {Ra}^{0.5}$</jats:tex-math> </jats:alternatives> </jats:inline-formula>.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"6 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256257","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 practical implementation of machine learning in flow control is limited due to its significant training expenses. In the present study the convolutional neural network (CNN) trained with the data of the restricted nonlinear (RNL) model is used to predict the normal velocity on a detection plane at $y^+=10$ in a turbulent channel flow, and the predicted velocity is used as wall blowing and suction for drag reduction. An active control test is carried out by using the well-trained CNN in direct numerical simulation (DNS). Substantial drag reduction rates up to 19 % and 16 % are obtained based on the spanwise and streamwise wall shear stresses, respectively. Furthermore, we explore the online control of wall turbulence by combining the RNL model with reinforcement learning (RL). The RL is constructed to determine the optimal wall blowing and suction based on its observation of the wall shear stresses without using the label data on the detection plane for training. The controlling and training processes are conducted synchronously in a RNL flow field. The control strategy discovered by RL has similar drag reduction rates with those obtained previously by the established method. Also, the training cost decreases by over thirty times at $Re_{tau }=950$ compared with the DNS-RL model. The present results provide a perspective that combining the RNL model with machine learning control for drag reduction in wall turbulence can be effective and computationally economical. Also, this approach can be easily extended to flows at higher Reynolds numbers.
{"title":"A combined active control method of restricted nonlinear model and machine learning technology for drag reduction in turbulent channel flow","authors":"Bing-Zheng Han, Wei-Xi Huang, Chun-Xiao Xu","doi":"10.1017/jfm.2024.558","DOIUrl":"https://doi.org/10.1017/jfm.2024.558","url":null,"abstract":"The practical implementation of machine learning in flow control is limited due to its significant training expenses. In the present study the convolutional neural network (CNN) trained with the data of the restricted nonlinear (RNL) model is used to predict the normal velocity on a detection plane at <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005585_inline1.png\"/> <jats:tex-math>$y^+=10$</jats:tex-math> </jats:alternatives> </jats:inline-formula> in a turbulent channel flow, and the predicted velocity is used as wall blowing and suction for drag reduction. An active control test is carried out by using the well-trained CNN in direct numerical simulation (DNS). Substantial drag reduction rates up to 19 % and 16 % are obtained based on the spanwise and streamwise wall shear stresses, respectively. Furthermore, we explore the online control of wall turbulence by combining the RNL model with reinforcement learning (RL). The RL is constructed to determine the optimal wall blowing and suction based on its observation of the wall shear stresses without using the label data on the detection plane for training. The controlling and training processes are conducted synchronously in a RNL flow field. The control strategy discovered by RL has similar drag reduction rates with those obtained previously by the established method. Also, the training cost decreases by over thirty times at <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005585_inline2.png\"/> <jats:tex-math>$Re_{tau }=950$</jats:tex-math> </jats:alternatives> </jats:inline-formula> compared with the DNS-RL model. The present results provide a perspective that combining the RNL model with machine learning control for drag reduction in wall turbulence can be effective and computationally economical. Also, this approach can be easily extended to flows at higher Reynolds numbers.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"52 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256223","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}
Many biological fluids are composed of suspended polymers immersed in a viscous fluid. A prime example is mucus, where the polymers are also known to form a network. While the presence of this microstructure is linked with an overall non-Newtonian response of the fluid, swimming cells and microorganisms similar in size to the network pores and polymer filaments instead experience the heterogeneous nature of the environment, interacting directly with the polymers as obstacles as they swim. To characterise and understand locomotion in these heterogeneous environments, we simulate the motion of an undulatory swimmer through three-dimensional suspensions and networks of elastic filaments, exploring the effects of filament and link compliance and filament concentration up to 20 % volume fraction. For compliant environments, the swimming speed increases with filament concentration to values approximately 10 % higher than in a viscous fluid. In stiffer environments, a non-monotonic dependence is observed, with an initial increase in speed to values 5 % greater than in a viscous fluid, followed by a dramatic reduction to speeds just a fraction of its value in a viscous fluid. Velocity fluctuations are also more pronounced in stiffer environments. We demonstrate that speed enhancements are linked to hydrodynamic interactions with the microstructure, while reductions are due to the filaments restricting the amplitude of the swimmer's propulsive wave. Unlike previous studies where interactions with obstacles allowed for significant enhancements in swimming speeds, the modest enhancements seen here are more comparable to those given by models where the environment is treated as a continuous viscoelastic fluid.
{"title":"Undulatory swimming in suspensions and networks of flexible filaments","authors":"Adam K. Townsend, Eric E. Keaveny","doi":"10.1017/jfm.2024.603","DOIUrl":"https://doi.org/10.1017/jfm.2024.603","url":null,"abstract":"Many biological fluids are composed of suspended polymers immersed in a viscous fluid. A prime example is mucus, where the polymers are also known to form a network. While the presence of this microstructure is linked with an overall non-Newtonian response of the fluid, swimming cells and microorganisms similar in size to the network pores and polymer filaments instead experience the heterogeneous nature of the environment, interacting directly with the polymers as obstacles as they swim. To characterise and understand locomotion in these heterogeneous environments, we simulate the motion of an undulatory swimmer through three-dimensional suspensions and networks of elastic filaments, exploring the effects of filament and link compliance and filament concentration up to 20 % volume fraction. For compliant environments, the swimming speed increases with filament concentration to values approximately 10 % higher than in a viscous fluid. In stiffer environments, a non-monotonic dependence is observed, with an initial increase in speed to values 5 % greater than in a viscous fluid, followed by a dramatic reduction to speeds just a fraction of its value in a viscous fluid. Velocity fluctuations are also more pronounced in stiffer environments. We demonstrate that speed enhancements are linked to hydrodynamic interactions with the microstructure, while reductions are due to the filaments restricting the amplitude of the swimmer's propulsive wave. Unlike previous studies where interactions with obstacles allowed for significant enhancements in swimming speeds, the modest enhancements seen here are more comparable to those given by models where the environment is treated as a continuous viscoelastic fluid.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"28 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256145","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}
Diffuse interface models are an important class of models used to describe multi-phase flows. In the case of incompressible viscous fluids there are a number of different diffuse interface models which have been known for many years. Nevertheless, a model based on mixture theory with a full set of conservation laws for the conservation of linear momentum of each constituent was not yet available. This gap was filled by ten Eikelder et al. (J. Fluid Mech., in press) recently and a first comparison with known models of Navier–Stokes/Cahn–Hilliard type is given. A detailed understanding of the relations between these models remains an important question.
{"title":"Mixture theory for diffuse interface models of two-phase flows","authors":"Helmut Abels","doi":"10.1017/jfm.2024.638","DOIUrl":"https://doi.org/10.1017/jfm.2024.638","url":null,"abstract":"Diffuse interface models are an important class of models used to describe multi-phase flows. In the case of incompressible viscous fluids there are a number of different diffuse interface models which have been known for many years. Nevertheless, a model based on mixture theory with a full set of conservation laws for the conservation of linear momentum of each constituent was not yet available. This gap was filled by ten Eikelder <jats:italic>et al.</jats:italic> (<jats:italic>J. Fluid Mech.</jats:italic>, in press) recently and a first comparison with known models of Navier–Stokes/Cahn–Hilliard type is given. A detailed understanding of the relations between these models remains an important question.","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":"142256291","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}
Xiang I.A. Yang, Peng E.S. Chen, Wen Zhang, Robert Kunz
The mean flow in a turbulent boundary layer (TBL) deviates from the canonical law of the wall (LoW) when influenced by a pressure gradient. Consequently, LoW-based near-wall treatments are inadequate for such flows. Chen et al. (J. Fluid Mech., vol. 970, 2023, A3) derived a Navier–Stokes-based velocity transformation that accurately describes the mean flow in TBLs with arbitrary pressure gradients. However, this transformation requires information on total shear stress, which is not always readily available, limiting its predictive power. In this work, we invert the transformation and develop a predictive near-wall model. Our model includes an additional transport equation that tracks the Lagrangian integration of the total shear stress. Particularly noteworthy is that the model introduces no new parameters and requires no calibration. We validate the developed model against experimental and computational data in the literature, and the results are favourable. Furthermore, we compare our model with equilibrium models. These equilibrium models inevitably fail when there are strong pressure gradients, but they prove to be sufficient for boundary layers subjected to weak, moderate and even moderately high pressure gradients. These results compel us to conclude that history effects in mean flow, which negatively impact the validity of equilibrium models, can largely be accounted for by the material time derivative term and the pressure gradient term, both of which require no additional modelling.
{"title":"Predictive near-wall modelling for turbulent boundary layers with arbitrary pressure gradients","authors":"Xiang I.A. Yang, Peng E.S. Chen, Wen Zhang, Robert Kunz","doi":"10.1017/jfm.2024.565","DOIUrl":"https://doi.org/10.1017/jfm.2024.565","url":null,"abstract":"The mean flow in a turbulent boundary layer (TBL) deviates from the canonical law of the wall (LoW) when influenced by a pressure gradient. Consequently, LoW-based near-wall treatments are inadequate for such flows. Chen <jats:italic>et al.</jats:italic> (<jats:italic>J. Fluid Mech.</jats:italic>, vol. 970, 2023, A3) derived a Navier–Stokes-based velocity transformation that accurately describes the mean flow in TBLs with arbitrary pressure gradients. However, this transformation requires information on total shear stress, which is not always readily available, limiting its predictive power. In this work, we invert the transformation and develop a predictive near-wall model. Our model includes an additional transport equation that tracks the Lagrangian integration of the total shear stress. Particularly noteworthy is that the model introduces no new parameters and requires no calibration. We validate the developed model against experimental and computational data in the literature, and the results are favourable. Furthermore, we compare our model with equilibrium models. These equilibrium models inevitably fail when there are strong pressure gradients, but they prove to be sufficient for boundary layers subjected to weak, moderate and even moderately high pressure gradients. These results compel us to conclude that history effects in mean flow, which negatively impact the validity of equilibrium models, can largely be accounted for by the material time derivative term and the pressure gradient term, both of which require no additional modelling.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"17 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256252","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 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}
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