Modons, or dipolar vortices, are common and long-lived features of the upper ocean, consisting of a pair of counter-rotating monopolar vortices moving through self-advection. Such structures remain stable over long times and may be important for fluid transport over large distances. Here, we present a semi-analytical method for finding fully nonlinear modon solutions in a multi-layer quasi-geostrophic model with arbitrarily many layers. Our approach is to reduce the problem to a multi-parameter linear eigenvalue problem which can be solved using numerical techniques from linear algebra. The method is shown to replicate previous results for one- and two-layer models and is applied to a three-layer model to find a solution describing a mid-depth propagating, topographic vortex.
{"title":"Modon solutions in an N-layer quasi-geostrophic model","authors":"Matthew N. Crowe, Edward R. Johnson","doi":"10.1017/jfm.2024.619","DOIUrl":"https://doi.org/10.1017/jfm.2024.619","url":null,"abstract":"Modons, or dipolar vortices, are common and long-lived features of the upper ocean, consisting of a pair of counter-rotating monopolar vortices moving through self-advection. Such structures remain stable over long times and may be important for fluid transport over large distances. Here, we present a semi-analytical method for finding fully nonlinear modon solutions in a multi-layer quasi-geostrophic model with arbitrarily many layers. Our approach is to reduce the problem to a multi-parameter linear eigenvalue problem which can be solved using numerical techniques from linear algebra. The method is shown to replicate previous results for one- and two-layer models and is applied to a three-layer model to find a solution describing a mid-depth propagating, topographic vortex.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"15 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256218","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 stimulation of instability and transport in the bottom boundary layer by internal solitary waves has been documented for over twenty years. However, the challenge of shallow slopes and a disparity of scales between the large-scale wave and the small-scale boundary layer has proven challenging for simulations. We present laboratory scale simulations that resolve the three-dimensionalisation in the boundary layer during the entire shoaling process. We find that the late stage, in which the incoming wave fissions into boluses, provides the most consistent source of three-dimensionalisation. In the early stage of shoaling, three-dimensionalisation occurs not so much due to separation bubble instability, but due to the interaction of vortices shed from the separation bubble with the overlying pycnocline. This interaction overturns the pycnocline, and creates bursts in kinetic energy and viscous dissipation, suggesting that the shed vortices induce turbulent motion and sediment resuspension in the water column above and behind the separation bubble.
{"title":"On the three-dimensional structure of instabilities beneath shallow-shoaling internal waves","authors":"Nicolas Castro-Folker, Marek Stastna","doi":"10.1017/jfm.2024.703","DOIUrl":"https://doi.org/10.1017/jfm.2024.703","url":null,"abstract":"The stimulation of instability and transport in the bottom boundary layer by internal solitary waves has been documented for over twenty years. However, the challenge of shallow slopes and a disparity of scales between the large-scale wave and the small-scale boundary layer has proven challenging for simulations. We present laboratory scale simulations that resolve the three-dimensionalisation in the boundary layer during the entire shoaling process. We find that the late stage, in which the incoming wave fissions into boluses, provides the most consistent source of three-dimensionalisation. In the early stage of shoaling, three-dimensionalisation occurs not so much due to separation bubble instability, but due to the interaction of vortices shed from the separation bubble with the overlying pycnocline. This interaction overturns the pycnocline, and creates bursts in kinetic energy and viscous dissipation, suggesting that the shed vortices induce turbulent motion and sediment resuspension in the water column above and behind the separation bubble.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"19 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256222","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}
An interesting resurrection phenomenon (including the initial complete submersion, subsequent resurfacing and final rebounding) of a superhydrophobic sphere impacting onto a liquid bath was observed in experiments and direct numerical simulations by Galeano-Rios et al. (J. Fluid Mech., vol. 912, 2021, A17). We investigate the mechanisms of the liquid entry for a superhydrophobic cylinder in this paper. The superhydrophobic cylinder, commonly employed as supporting legs for insects and robots at the liquid surface, can exhibit liquid-entry mechanisms different from those observed with the sphere. The direct numerical simulation method is applied to the impact of a two-dimensional (2-D) superhydrophobic cylinder (modelled as a pseudo-solid) onto a liquid bath. We find that for the impacting cylinder the resurrection phenomenon can also exist, and the cylinder can either rebound (get detached from the liquid surface) or stay afloat after resurfacing. The cylinder impact behaviour is classified into four regimes, i.e. floating, bouncing, resurrecting (resurrecting-floating and resurrecting-bouncing) and sinking, dependent on the Weber number and the density ratio of the cylinder to the liquid. For the regimes of floating and bouncing, the force analysis indicates that the form drag dominates the motion of the cylinder in the very beginning of the impact, while subsequently the surface tension force also plays a role with the contact line pinning on the horizontal midline of the cylinder. For the critical states of the highlighted resurrecting regime, our numerical results show that the rising height for the completely submerged cylinder of different density ratios remains nearly unchanged. Accordingly, a relation between the maximum ascending velocity and the density ratio is derived to predict whether the completely submerged cylinder can resurface.
{"title":"Resurrection of a superhydrophobic cylinder impacting onto liquid bath","authors":"Wanqiu Zhang, Yaochen Mei, Chenyu Fu, Xinping Zhou","doi":"10.1017/jfm.2024.691","DOIUrl":"https://doi.org/10.1017/jfm.2024.691","url":null,"abstract":"An interesting resurrection phenomenon (including the initial complete submersion, subsequent resurfacing and final rebounding) of a superhydrophobic sphere impacting onto a liquid bath was observed in experiments and direct numerical simulations by Galeano-Rios <jats:italic>et al.</jats:italic> (<jats:italic>J. Fluid Mech.</jats:italic>, vol. 912, 2021, A17). We investigate the mechanisms of the liquid entry for a superhydrophobic cylinder in this paper. The superhydrophobic cylinder, commonly employed as supporting legs for insects and robots at the liquid surface, can exhibit liquid-entry mechanisms different from those observed with the sphere. The direct numerical simulation method is applied to the impact of a two-dimensional (2-D) superhydrophobic cylinder (modelled as a pseudo-solid) onto a liquid bath. We find that for the impacting cylinder the resurrection phenomenon can also exist, and the cylinder can either rebound (get detached from the liquid surface) or stay afloat after resurfacing. The cylinder impact behaviour is classified into four regimes, i.e. floating, bouncing, resurrecting (resurrecting-floating and resurrecting-bouncing) and sinking, dependent on the Weber number and the density ratio of the cylinder to the liquid. For the regimes of floating and bouncing, the force analysis indicates that the form drag dominates the motion of the cylinder in the very beginning of the impact, while subsequently the surface tension force also plays a role with the contact line pinning on the horizontal midline of the cylinder. For the critical states of the highlighted resurrecting regime, our numerical results show that the rising height for the completely submerged cylinder of different density ratios remains nearly unchanged. Accordingly, a relation between the maximum ascending velocity and the density ratio is derived to predict whether the completely submerged cylinder can resurface.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"22 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269809","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}
Amanda S.M. Smyth, Takafumi Nishino, Andhini N. Zurman-Nasution
Linear unsteady aerofoil theory, while successfully used for the prediction of unsteady aerofoil lift for many decades, has yet to be proven adequate for predicting the propulsive performance of oscillating aerofoils. In this paper we test the hypothesis that the central shortcoming of linear small-amplitude models, such as the Garrick function, is the failure to account for the flow acceleration caused by aerofoil thrust. A new analytical model is developed by coupling the Garrick function to a cycle-averaged actuator disc model, in a manner analogous to the blade-element momentum theory for wind turbines and propellers. This amounts to assuming the Garrick function to be locally valid and, in combination with a global control volume analysis, enables the prediction of flow acceleration at the aerofoil. The new model is demonstrated to substantially improve the agreement with large-eddy simulations of an aerofoil in combined heave and pitch motion.
{"title":"Coupled unsteady actuator disc and linear theory of an oscillating foil propulsor","authors":"Amanda S.M. Smyth, Takafumi Nishino, Andhini N. Zurman-Nasution","doi":"10.1017/jfm.2024.624","DOIUrl":"https://doi.org/10.1017/jfm.2024.624","url":null,"abstract":"Linear unsteady aerofoil theory, while successfully used for the prediction of unsteady aerofoil lift for many decades, has yet to be proven adequate for predicting the propulsive performance of oscillating aerofoils. In this paper we test the hypothesis that the central shortcoming of linear small-amplitude models, such as the Garrick function, is the failure to account for the flow acceleration caused by aerofoil thrust. A new analytical model is developed by coupling the Garrick function to a cycle-averaged actuator disc model, in a manner analogous to the blade-element momentum theory for wind turbines and propellers. This amounts to assuming the Garrick function to be locally valid and, in combination with a global control volume analysis, enables the prediction of flow acceleration at the aerofoil. The new model is demonstrated to substantially improve the agreement with large-eddy simulations of an aerofoil in combined heave and pitch motion.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"72 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256251","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}
Diego B.S. Audiffred, André V.G. Cavalieri, Igor A. Maia, Eduardo Martini, Peter Jordan
We present an experimental study of reactive control of turbulent jets, in which we target axisymmetric coherent structures, known to play a key role in the generation of sound. We first consider a forced jet, in which coherent structures are amplified above background levels, facilitating their detection, estimation and control. We then consider the more challenging case of an unforced jet. The linear control targets coherent structures in the region just downstream of the nozzle exit plane, where linear models are known to be appropriate for description of the lowest-order azimuthal modes of the turbulence. The control law is constructed in frequency space, based on empirically determined transfer functions. And the Wiener–Hopf formalism is used to enforce causality and to provide an optimal controller, as opposed to the sub-optimal control laws provided by simpler wave-cancellation methods. Significant improvements are demonstrated in the control of both forced and unforced jets. In the former case, order-of-magnitude reductions are achieved; and in the latter, turbulence levels are reduced by up to 60 %. The results open new perspectives for the control of turbulent flow at high Reynolds number.
{"title":"Reactive experimental control of turbulent jets","authors":"Diego B.S. Audiffred, André V.G. Cavalieri, Igor A. Maia, Eduardo Martini, Peter Jordan","doi":"10.1017/jfm.2024.569","DOIUrl":"https://doi.org/10.1017/jfm.2024.569","url":null,"abstract":"We present an experimental study of reactive control of turbulent jets, in which we target axisymmetric coherent structures, known to play a key role in the generation of sound. We first consider a forced jet, in which coherent structures are amplified above background levels, facilitating their detection, estimation and control. We then consider the more challenging case of an unforced jet. The linear control targets coherent structures in the region just downstream of the nozzle exit plane, where linear models are known to be appropriate for description of the lowest-order azimuthal modes of the turbulence. The control law is constructed in frequency space, based on empirically determined transfer functions. And the Wiener–Hopf formalism is used to enforce causality and to provide an optimal controller, as opposed to the sub-optimal control laws provided by simpler wave-cancellation methods. Significant improvements are demonstrated in the control of both forced and unforced jets. In the former case, order-of-magnitude reductions are achieved; and in the latter, turbulence levels are reduced by up to 60 %. The results open new perspectives for the control of turbulent flow at high Reynolds number.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"106 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269427","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}
Tianning Tang, Haoyu Ding, Saishuai Dai, Paul H. Taylor, Jun Zang, Thomas A.A. Adcock
Steep wave breaking on a vertical cylinder (a typical foundation supporting offshore wind turbines) will induce slam loads. Many questions on the important violent wave loading and the associated secondary load cycle remain unanswered. We use laboratory experiments with unidirectional waves to investigate the fluid loading on vertical cylinders. We use a novel three-phase decomposition approach that allows us to separate different types of nonlinearity. Our findings reveal the existence of an additional quasi-impulsive loading component that is associated with the secondary load cycle and occurs in the backwards direction against that of the incoming waves. This quasi-impulsive force occurs at the end of the secondary load cycle and close to the passage of the downward zero-crossing point of the undisturbed wave. Wavelet analysis showed that the impulsive force exhibits superficially similar behaviour to a typical wave-slamming event but in the reverse direction. To monitor the scattered wave field and extract run-up on the cylinder, we installed a four-camera synchronised video system and found a strong temporal correlation between the arrival time of the Type-II scattered wave onto the cylinder and the occurrence of this quasi-impulsive force. The temporal characteristics of this quasi-impulsive force can be approximated by the Goda wave impact model, taking the collision of the Type-II scattered waves at the rear stagnation point as the impact source.
垂直圆柱体（支撑海上风力涡轮机的典型地基）上的陡峭波浪会引起猛烈荷载。关于重要的剧烈波浪载荷和相关的二次载荷循环的许多问题仍未得到解答。我们利用单向波的实验室实验来研究垂直圆柱体上的流体载荷。我们采用了一种新颖的三相分解方法，该方法允许我们分离不同类型的非线性。我们的研究结果表明，存在一个额外的准脉冲加载分量，它与二次加载循环相关，并发生在与入射波相反的反方向上。这种准脉冲力发生在二次加载周期的末端，接近于未扰动波的向下零交叉点。小波分析表明，脉冲力的表现与典型的海浪冲击事件表面相似，但方向相反。为了监测散射波场并提取圆柱体上的上升力，我们安装了一个四摄像头同步视频系统，并发现 II 型散射波到达圆柱体的时间与这种准脉冲力的发生之间具有很强的时间相关性。这种准脉冲力的时间特征可以用 Goda 波撞击模型来近似表示，该模型以 II 型散射波在后停滞点的碰撞为撞击源。
{"title":"An experimental study of a quasi-impulsive backwards wave force associated with the secondary load cycle on a vertical cylinder","authors":"Tianning Tang, Haoyu Ding, Saishuai Dai, Paul H. Taylor, Jun Zang, Thomas A.A. Adcock","doi":"10.1017/jfm.2024.648","DOIUrl":"https://doi.org/10.1017/jfm.2024.648","url":null,"abstract":"Steep wave breaking on a vertical cylinder (a typical foundation supporting offshore wind turbines) will induce slam loads. Many questions on the important violent wave loading and the associated secondary load cycle remain unanswered. We use laboratory experiments with unidirectional waves to investigate the fluid loading on vertical cylinders. We use a novel three-phase decomposition approach that allows us to separate different types of nonlinearity. Our findings reveal the existence of an additional quasi-impulsive loading component that is associated with the secondary load cycle and occurs in the backwards direction against that of the incoming waves. This quasi-impulsive force occurs at the end of the secondary load cycle and close to the passage of the downward zero-crossing point of the undisturbed wave. Wavelet analysis showed that the impulsive force exhibits superficially similar behaviour to a typical wave-slamming event but in the reverse direction. To monitor the scattered wave field and extract run-up on the cylinder, we installed a four-camera synchronised video system and found a strong temporal correlation between the arrival time of the Type-II scattered wave onto the cylinder and the occurrence of this quasi-impulsive force. The temporal characteristics of this quasi-impulsive force can be approximated by the Goda wave impact model, taking the collision of the Type-II scattered waves at the rear stagnation point as the impact source.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"17 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256216","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}
Anna Prati, Michele Larcher, James T. Jenkins, Luigi La Ragione
We study the behaviour of a particle bed immersed in water when a flow generated by an oscillating plate is induced above it. We first consider a rigid plate submerged and oscillated over a particle bed. During upward motion of the plate, a portion of the bed fails, allowing particle displacement, and the bed surface to deform into a heap. We have already determined the flow of the fluid above and within the bed. This work describes the particle motion within the failed region of the bed: when the particles are mobile, they follow the fluid. We depth average the balance of mass and obtain an evolution equation for the displacement of the bed surface. We solve this equation and compare the predictions with the measurements of surface displacement in earlier experiments on rigid square plates. We carry out new experiments to measure the surface displacements under elongated plates. Elongated rigid plates behave similarly to the rigid square ones. Flexible plates produce multiple heaps. We determine that the peaks of these heaps are correlated with the flexural modes of the plates and occur at points along the bed at which the fluid pressure has its extreme values. Different plate flexural modes, resulting in different numbers of heaps, are produced by driving the plate at different frequencies. The particle motion within the bed and heap evolution under a flexible plate can be roughly described by regarding it as two or more rigid plates. We test the predictions of the theory against experiments.
{"title":"Particle motion in a bed under a rigid plate, submerged and oscillated over its surface, and bed morphologies induced by flexible plates","authors":"Anna Prati, Michele Larcher, James T. Jenkins, Luigi La Ragione","doi":"10.1017/jfm.2024.705","DOIUrl":"https://doi.org/10.1017/jfm.2024.705","url":null,"abstract":"We study the behaviour of a particle bed immersed in water when a flow generated by an oscillating plate is induced above it. We first consider a rigid plate submerged and oscillated over a particle bed. During upward motion of the plate, a portion of the bed fails, allowing particle displacement, and the bed surface to deform into a heap. We have already determined the flow of the fluid above and within the bed. This work describes the particle motion within the failed region of the bed: when the particles are mobile, they follow the fluid. We depth average the balance of mass and obtain an evolution equation for the displacement of the bed surface. We solve this equation and compare the predictions with the measurements of surface displacement in earlier experiments on rigid square plates. We carry out new experiments to measure the surface displacements under elongated plates. Elongated rigid plates behave similarly to the rigid square ones. Flexible plates produce multiple heaps. We determine that the peaks of these heaps are correlated with the flexural modes of the plates and occur at points along the bed at which the fluid pressure has its extreme values. Different plate flexural modes, resulting in different numbers of heaps, are produced by driving the plate at different frequencies. The particle motion within the bed and heap evolution under a flexible plate can be roughly described by regarding it as two or more rigid plates. We test the predictions of the theory against experiments.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"4 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A series of recent studies has indicated that the component of the bottom drag caused by irregular small-scale topography in the ocean varies non-monotonically with the flow speed. The roughness-induced forcing increases with the speed of relatively slow abyssal currents but, somewhat counterintuitively, starts to decrease when flows are sufficiently swift. This reduction in drag at high speeds leads to the instability of laterally uniform currents, and the resulting evolutionary patterns are explored using numerical and analytical methods. The drag-law instability manifests in the spontaneous emergence of parallel jets, aligned in the direction of the basic flow and separated by relatively quiescent regions. We hypothesize that the mechanisms identified in this investigation could play a role in the dynamics of zonal striations commonly observed in the ocean.
{"title":"The instability of non-monotonic drag laws","authors":"Timour Radko","doi":"10.1017/jfm.2024.635","DOIUrl":"https://doi.org/10.1017/jfm.2024.635","url":null,"abstract":"A series of recent studies has indicated that the component of the bottom drag caused by irregular small-scale topography in the ocean varies non-monotonically with the flow speed. The roughness-induced forcing increases with the speed of relatively slow abyssal currents but, somewhat counterintuitively, starts to decrease when flows are sufficiently swift. This reduction in drag at high speeds leads to the instability of laterally uniform currents, and the resulting evolutionary patterns are explored using numerical and analytical methods. The drag-law instability manifests in the spontaneous emergence of parallel jets, aligned in the direction of the basic flow and separated by relatively quiescent regions. We hypothesize that the mechanisms identified in this investigation could play a role in the dynamics of zonal striations commonly observed in the ocean.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"44 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256259","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}
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