Pub Date : 2024-09-12DOI: 10.1103/physrevfluids.9.094802
Raphael Stuhlmeier, Conor Heffernan, Alberto Alberello, Emilian Părău
This paper sets out to explore the modulational (or Benjamin-Feir) instability of a monochromatic wave propagating in the presence of damping such as that induced by sea ice on the ocean surface. The fundamental wave motion is modelled using the spatial Zakharov equation, to which either uniform or nonuniform (frequency-dependent) damping is added. By means of mode truncation the spatial analog of the classical Benjamin-Feir instability can be studied analytically using dynamical systems techniques. The formulation readily yields the free surface and its envelope, giving insight into the physical implications of damping on the modulational instability. The evolution of an initially unstable mode is also studied numerically by integrating the damped, spatial Zakharov equation, in order to complement the analytical theory. This sheds light on the effects of damping on spectral broadening arising from this instability.
{"title":"Modulational instability of nonuniformly damped, broad-banded waves: Applications to waves in sea ice","authors":"Raphael Stuhlmeier, Conor Heffernan, Alberto Alberello, Emilian Părău","doi":"10.1103/physrevfluids.9.094802","DOIUrl":"https://doi.org/10.1103/physrevfluids.9.094802","url":null,"abstract":"This paper sets out to explore the modulational (or Benjamin-Feir) instability of a monochromatic wave propagating in the presence of damping such as that induced by sea ice on the ocean surface. The fundamental wave motion is modelled using the spatial Zakharov equation, to which either uniform or nonuniform (frequency-dependent) damping is added. By means of mode truncation the spatial analog of the classical Benjamin-Feir instability can be studied analytically using dynamical systems techniques. The formulation readily yields the free surface and its envelope, giving insight into the physical implications of damping on the modulational instability. The evolution of an initially unstable mode is also studied numerically by integrating the damped, spatial Zakharov equation, in order to complement the analytical theory. This sheds light on the effects of damping on spectral broadening arising from this instability.","PeriodicalId":20160,"journal":{"name":"Physical Review Fluids","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-12DOI: 10.1103/physrevfluids.9.093902
Diederik Beckers, Jeff D. Eldredge
This study explores the application of deep reinforcement learning (RL) to design an airfoil pitch controller capable of minimizing lift variations in randomly disturbed flows. The controller, treated as an agent in a partially observable Markov decision process, receives non-Markovian observations from the environment, simulating practical constraints where flow information is limited to force and pressure sensors. Deep RL, particularly the TD3 algorithm, is used to approximate an optimal control policy under such conditions. Testing is conducted for a flat plate airfoil in two environments: a classical unsteady environment with vertical acceleration disturbances (i.e., a Wagner setup) and a viscous flow model with pulsed point force disturbances. In both cases, augmenting observations of the lift, pitch angle, and angular velocity with extra wake information (e.g., from pressure sensors) and retaining memory of past observations enhances RL control performance. Results demonstrate the capability of RL control to match or exceed standard linear controllers in minimizing lift variations. Special attention is given to the choice of training data and the generalization to unseen disturbances.
{"title":"Deep reinforcement learning of airfoil pitch control in a highly disturbed environment using partial observations","authors":"Diederik Beckers, Jeff D. Eldredge","doi":"10.1103/physrevfluids.9.093902","DOIUrl":"https://doi.org/10.1103/physrevfluids.9.093902","url":null,"abstract":"This study explores the application of deep reinforcement learning (RL) to design an airfoil pitch controller capable of minimizing lift variations in randomly disturbed flows. The controller, treated as an agent in a partially observable Markov decision process, receives non-Markovian observations from the environment, simulating practical constraints where flow information is limited to force and pressure sensors. Deep RL, particularly the TD3 algorithm, is used to approximate an optimal control policy under such conditions. Testing is conducted for a flat plate airfoil in two environments: a classical unsteady environment with vertical acceleration disturbances (i.e., a Wagner setup) and a viscous flow model with pulsed point force disturbances. In both cases, augmenting observations of the lift, pitch angle, and angular velocity with extra wake information (e.g., from pressure sensors) and retaining memory of past observations enhances RL control performance. Results demonstrate the capability of RL control to match or exceed standard linear controllers in minimizing lift variations. Special attention is given to the choice of training data and the generalization to unseen disturbances.","PeriodicalId":20160,"journal":{"name":"Physical Review Fluids","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-12DOI: 10.1103/physrevfluids.9.094002
Vincent Gourmandie, Juliette Pierre, Valentin Leroy, Caroline Derec
In this study, we systematically investigate the effect of surface tension on bubble entrapment after drop impact in the pinching regime. Experiments are conducted using three different systems: pure water, aqueous solutions with ethanol, or with surfactant molecules, both at various concentrations. Results are compiled for a large set of values of the surface tension and the drop impact velocity . Across all solutions, the cavity development dynamics exhibit similarity and are effectively characterized by dimensionless gravito-capillary parameters. Whatever the surface tension, our measurements indicate that only of the impact energy is converted into potential energy of the cavity. However, a notable distinction arises when considering bubble entrapment. We have constructed a bubbling diagram in the () plane, and observed that the conditions for bubble entrapment are altered with changing surface tension in water-ethanol mixtures. More intriguingly, these conditions are modified in a distinctly different manner for surfactant solutions. To interpret our experimental findings, we compile a comprehensive set of experimental and numerical results from the literature. We demonstrate the possibility of unifying results across all systems and our water-ethanol mixtures through an empirical law including the influence of surface tension and viscosity. Although no physical justification exists at this stage, this empirical law suggests the significant role of capillary waves traveling along the cavity interface in bubble entrapment. Within this context, the behavior of surfactant-laden solutions aligns with other homogeneous solutions by considering the elastic properties conferred upon the interfaces by surfactant molecules.
{"title":"Bubble entrapment by drop impact: Combined effect of surface tension and viscosity","authors":"Vincent Gourmandie, Juliette Pierre, Valentin Leroy, Caroline Derec","doi":"10.1103/physrevfluids.9.094002","DOIUrl":"https://doi.org/10.1103/physrevfluids.9.094002","url":null,"abstract":"In this study, we systematically investigate the effect of surface tension on bubble entrapment after drop impact in the pinching regime. Experiments are conducted using three different systems: pure water, aqueous solutions with ethanol, or with surfactant molecules, both at various concentrations. Results are compiled for a large set of values of the surface tension <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>γ</mi></math> and the drop impact velocity <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>U</mi></math>. Across all solutions, the cavity development dynamics exhibit similarity and are effectively characterized by dimensionless gravito-capillary parameters. Whatever the surface tension, our measurements indicate that only <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>40</mn><mo>%</mo></mrow></math> of the impact energy is converted into potential energy of the cavity. However, a notable distinction arises when considering bubble entrapment. We have constructed a <i>bubbling diagram</i> in the (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>U</mi><mo>,</mo><mi>γ</mi></math>) plane, and observed that the conditions for bubble entrapment are altered with changing surface tension in water-ethanol mixtures. More intriguingly, these conditions are modified in a distinctly different manner for surfactant solutions. To interpret our experimental findings, we compile a comprehensive set of experimental and numerical results from the literature. We demonstrate the possibility of unifying results across all systems and our water-ethanol mixtures through an empirical law including the influence of surface tension and viscosity. Although no physical justification exists at this stage, this empirical law suggests the significant role of capillary waves traveling along the cavity interface in bubble entrapment. Within this context, the behavior of surfactant-laden solutions aligns with other homogeneous solutions by considering the elastic properties conferred upon the interfaces by surfactant molecules.","PeriodicalId":20160,"journal":{"name":"Physical Review Fluids","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-09DOI: 10.1103/physrevfluids.9.l091601
Kenneth R. Langley, Tariq Alghamdi, Andres A. Aguirre-Pablo, Nathan B. Speirs, S. T. Thoroddsen, Peter Taborek
High-speed videos in an optical cryostat, with frame rates up to fps, are used to study the dynamics of laser-induced cavitation in helium near the critical point and in the supercritical region. The propagation of strong shock waves are observed in both regimes. The time dependence of the cavitation bubble radius as well as the acoustic pressure field outside the bubble are described by standard compressible flow models. In the temperature range , a symmetric cloud of micron-scale bubbles are observed outside the main cavitation bubble as it approaches its maximum radius which is due to homogeneous nucleation and spinodal decomposition in the low-pressure fluid outside the bubble. Nucleation of secondary bubbles is also observed far below the critical point, but this requires large negative pressures that can be generated by shock waves that reflect from the primary bubble.
{"title":"Laser-induced cavitation in liquid He4 near the liquid-vapor critical point","authors":"Kenneth R. Langley, Tariq Alghamdi, Andres A. Aguirre-Pablo, Nathan B. Speirs, S. T. Thoroddsen, Peter Taborek","doi":"10.1103/physrevfluids.9.l091601","DOIUrl":"https://doi.org/10.1103/physrevfluids.9.l091601","url":null,"abstract":"High-speed videos in an optical cryostat, with frame rates up to <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>5</mn><mo>×</mo><msup><mn>10</mn><mn>6</mn></msup></mrow></math> fps, are used to study the dynamics of laser-induced cavitation in helium near the critical point and in the supercritical region. The propagation of strong shock waves are observed in both regimes. The time dependence of the cavitation bubble radius as well as the acoustic pressure field outside the bubble are described by standard compressible flow models. In the temperature range <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>4</mn><mi>K</mi><mo><</mo><mi>T</mi><mo><</mo><mn>5.2</mn><mi>K</mi></mrow></math>, a symmetric cloud of micron-scale bubbles are observed outside the main cavitation bubble as it approaches its maximum radius which is due to homogeneous nucleation and spinodal decomposition in the low-pressure fluid outside the bubble. Nucleation of secondary bubbles is also observed far below the critical point, but this requires large negative pressures that can be generated by shock waves that reflect from the primary bubble.","PeriodicalId":20160,"journal":{"name":"Physical Review Fluids","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the stability of gravity-driven viscous liquid films flowing down a vertical cylinder that is uniformly coated with a thin layer of elastic solids. Combining the gravity-driven viscous flows with the elastic deformation of the coated soft layer, we formulate a long-wave model to describe the evolution of a film flow-soft structure coupled system. Based on the model, we systematically examine the impact of the coating properties, including the elasticity and thickness on the temporal and spatiotemporal stability. Temporal stability analysis shows that the soft layer plays a dual role, namely, the elasticity acts as a destabilizing factor, leading to large deformations of both film interface and soft surface. However, due to the geometrical effect, increasing the layer thickness stabilizes the Rayleigh-Plateau instability. By contrast, the linear phase speed is always enhanced with increasing the elasticity or the thickness of the coated layer. We then analyze the spatiotemporal nature of free-surface instabilities and find that the elasticity can trigger the film flows from being absolutely unstable to convectively unstable. Transient numerical solutions of the full asymptotic model further verify the predictions from linear stability analysis, and more importantly, reveal the nonlinear effect of the softness. Compared to liquid films falling down the cylinder with rigid walls, the soft surface can enhance the coalescence of faster, larger sliding droplets with preceding slower, smaller sliding ones, thus resulting in a more unstable system. Our study highlights the potential of coating a thin layer of soft materials onto the walls of substrate to regulate the dynamics of liquid film systems, and may have implications for the emerging bioinspired applications; for instance, the large-scale collection and transport of water on flexible microfiber arrays.
{"title":"Stability of gravity-driven viscous films flowing down a soft cylinder","authors":"Youchuang Chao, Lailai Zhu, Zijing Ding, Tiantian Kong, Juntao Chang, Ziao Wang","doi":"10.1103/physrevfluids.9.094001","DOIUrl":"https://doi.org/10.1103/physrevfluids.9.094001","url":null,"abstract":"We study the stability of gravity-driven viscous liquid films flowing down a vertical cylinder that is uniformly coated with a thin layer of elastic solids. Combining the gravity-driven viscous flows with the elastic deformation of the coated soft layer, we formulate a long-wave model to describe the evolution of a film flow-soft structure coupled system. Based on the model, we systematically examine the impact of the coating properties, including the elasticity and thickness on the temporal and spatiotemporal stability. Temporal stability analysis shows that the soft layer plays a dual role, namely, the elasticity acts as a destabilizing factor, leading to large deformations of both film interface and soft surface. However, due to the geometrical effect, increasing the layer thickness stabilizes the Rayleigh-Plateau instability. By contrast, the linear phase speed is always enhanced with increasing the elasticity or the thickness of the coated layer. We then analyze the spatiotemporal nature of free-surface instabilities and find that the elasticity can trigger the film flows from being absolutely unstable to convectively unstable. Transient numerical solutions of the full asymptotic model further verify the predictions from linear stability analysis, and more importantly, reveal the nonlinear effect of the softness. Compared to liquid films falling down the cylinder with rigid walls, the soft surface can enhance the coalescence of faster, larger sliding droplets with preceding slower, smaller sliding ones, thus resulting in a more unstable system. Our study highlights the potential of coating a thin layer of soft materials onto the walls of substrate to regulate the dynamics of liquid film systems, and may have implications for the emerging bioinspired applications; for instance, the large-scale collection and transport of water on flexible microfiber arrays.","PeriodicalId":20160,"journal":{"name":"Physical Review Fluids","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-05DOI: 10.1103/physrevfluids.9.094301
Harkirat Singh, David L. Henann
Many dense granular systems are non-monodisperse, consisting of particles of different sizes, and will segregate based on size during flow. This phenomenon is an important aspect of many industrial and geophysical processes, necessitating predictive continuum models. This paper systematically studies a key aspect of the three-dimensional nature of segregation and diffusion in flowing, dense, bidisperse granular mixtures—namely, segregation and diffusion acting along the direction perpendicular to the plane of shearing, which we refer to as the anti-plane modes of segregation and diffusion. To this end, we consider discrete-element method (DEM) simulations of flows of dense, bidisperse mixtures of frictional spheres in an idealized configuration that isolates anti-plane segregation and diffusion. We find that previously developed constitutive equations, calibrated to DEM simulation results from flows in which both the segregation and diffusion processes occur within the plane of shearing, do not capture aspects of the anti-plane segregation dynamics. Accordingly, we utilize DEM simulation results to inform and calibrate constitutive equations for the segregation and diffusion fluxes in their anti-plane modes. Predictions of the resulting continuum model for the anti-plane segregation dynamics are tested against additional DEM simulation results across different cases, while parameters such as the shear strain rate and mixture composition are varied, and we find that the calibrated model predictions match well with the DEM simulation results. Finally, we suggest a strategy for generalizing the constitutive forms for the segregation and diffusion fluxes to obtain three-dimensional constitutive equations that account for both the in-plane and the anti-plane modes of the segregation and diffusion processes.
许多致密颗粒系统都是非单分散的，由不同大小的颗粒组成，在流动过程中会根据大小发生分离。这种现象是许多工业和地球物理过程的一个重要方面，需要建立预测性连续模型。本文系统地研究了流动、致密、双分散粒状混合物中偏析和扩散三维性质的一个关键方面，即沿垂直于剪切平面方向的偏析和扩散作用，我们将其称为偏析和扩散的反平面模式。为此，我们采用离散元素法（DEM）模拟了摩擦球双向分散的致密混合物在理想化配置下的流动，该配置隔离了反平面偏析和扩散。我们发现，根据 DEM 模拟结果校准的先前开发的构成方程无法捕捉到反平面偏析动力学的各个方面，而偏析和扩散过程均发生在剪切平面内。因此，我们利用 DEM 模拟结果，为反面模式的偏析和扩散通量提供信息，并校准其构成方程。在改变剪切应变率和混合物成分等参数的同时，我们还根据不同情况下的其他 DEM 模拟结果，测试了由此产生的反面偏析动力学连续模型的预测结果，结果发现校准后的模型预测结果与 DEM 模拟结果非常吻合。最后，我们提出了一种对偏析和扩散通量的构成形式进行概括的策略，以获得同时考虑偏析和扩散过程的平面内和反面模式的三维构成方程。
{"title":"Anti-plane segregation and diffusion in dense, bidisperse granular shear flow","authors":"Harkirat Singh, David L. Henann","doi":"10.1103/physrevfluids.9.094301","DOIUrl":"https://doi.org/10.1103/physrevfluids.9.094301","url":null,"abstract":"Many dense granular systems are non-monodisperse, consisting of particles of different sizes, and will segregate based on size during flow. This phenomenon is an important aspect of many industrial and geophysical processes, necessitating predictive continuum models. This paper systematically studies a key aspect of the three-dimensional nature of segregation and diffusion in flowing, dense, bidisperse granular mixtures—namely, segregation and diffusion acting along the direction perpendicular to the plane of shearing, which we refer to as the anti-plane modes of segregation and diffusion. To this end, we consider discrete-element method (DEM) simulations of flows of dense, bidisperse mixtures of frictional spheres in an idealized configuration that isolates anti-plane segregation and diffusion. We find that previously developed constitutive equations, calibrated to DEM simulation results from flows in which both the segregation and diffusion processes occur within the plane of shearing, do not capture aspects of the anti-plane segregation dynamics. Accordingly, we utilize DEM simulation results to inform and calibrate constitutive equations for the segregation and diffusion fluxes in their anti-plane modes. Predictions of the resulting continuum model for the anti-plane segregation dynamics are tested against additional DEM simulation results across different cases, while parameters such as the shear strain rate and mixture composition are varied, and we find that the calibrated model predictions match well with the DEM simulation results. Finally, we suggest a strategy for generalizing the constitutive forms for the segregation and diffusion fluxes to obtain three-dimensional constitutive equations that account for both the in-plane and the anti-plane modes of the segregation and diffusion processes.","PeriodicalId":20160,"journal":{"name":"Physical Review Fluids","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-05DOI: 10.1103/physrevfluids.9.093901
Ilya Barmak, Alexander Gelfgat, Neima Brauner
This work deals with the stability of two-phase stratified air-water flows in horizontal circular pipes. For this purpose, we performed a linear stability analysis, which considers all possible three-dimensional infinitesimal disturbances and takes into account deformations of the air-water interface. The main results are presented in the form of stability maps, which compare well with the available experimental data. The neutral stability curves are accompanied by the corresponding wavenumbers and wave speeds of the critical perturbations, as well as by spatial patterns of their velocity components. Accordingly, several modes of the critical perturbation are revealed. Long waves are found to be the critical perturbation over part of the stability boundary, and they are affected by the surface tension due to the confinement effect of the lateral direction. Exploring the effect of pipe diameter on the stability boundary and critical perturbations shows that for small water holdups (i.e., thin water film) the scaling of the critical gas velocity by the gas Froude number is valid for pipe diameters larger than about 0.1 m, where the surface tension effects due to the lateral confinement become negligible. Comparing results obtained in pipe, square-duct, and two-plate geometries, we show that there are cases where the simplified geometry of two parallel plates can be employed to model the realistic geometry reasonably well.
{"title":"Instability of stratified air-water flows in circular pipes","authors":"Ilya Barmak, Alexander Gelfgat, Neima Brauner","doi":"10.1103/physrevfluids.9.093901","DOIUrl":"https://doi.org/10.1103/physrevfluids.9.093901","url":null,"abstract":"This work deals with the stability of two-phase stratified air-water flows in horizontal circular pipes. For this purpose, we performed a linear stability analysis, which considers all possible three-dimensional infinitesimal disturbances and takes into account deformations of the air-water interface. The main results are presented in the form of stability maps, which compare well with the available experimental data. The neutral stability curves are accompanied by the corresponding wavenumbers and wave speeds of the critical perturbations, as well as by spatial patterns of their velocity components. Accordingly, several modes of the critical perturbation are revealed. Long waves are found to be the critical perturbation over part of the stability boundary, and they are affected by the surface tension due to the confinement effect of the lateral direction. Exploring the effect of pipe diameter on the stability boundary and critical perturbations shows that for small water holdups (i.e., thin water film) the scaling of the critical gas velocity by the gas Froude number is valid for pipe diameters larger than about 0.1 m, where the surface tension effects due to the lateral confinement become negligible. Comparing results obtained in pipe, square-duct, and two-plate geometries, we show that there are cases where the simplified geometry of two parallel plates can be employed to model the realistic geometry reasonably well.","PeriodicalId":20160,"journal":{"name":"Physical Review Fluids","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-05DOI: 10.1103/physrevfluids.9.094401
Diego Martínez-Argüello, Sergio Rica
This paper investigates the evolution of the Euler equations near a potential blow-up solution. We employ an approach where this solution exhibits second-type self-similarity, characterized by an undetermined exponent . This exponent can be seen as a nonlinear eigenvalue, determined by the solution of a self-similar partial differential equation with appropriate boundary conditions. Specifically, we demonstrate the existence of an axisymmetric solution of the Euler equations by expanding the axial vorticity using associated Legendre polynomials as a basis. This expansion results in an infinite hierarchy of ordinary differential equations, which, when truncated up to a certain order , allows for the numerical resolution of a finite set of ordinary differential equations. Through this numerical analysis, we obtain a solution that satisfies the appropriate boundary conditions for a specific value of the exponent . By exploring various truncations, we establish a sequence in for the parameter , providing evidence of the convergence of the exponent . Our findings suggest a self-similar exponent , presenting a promising path for a numerical or analytical approach indicating that may indeed be exactly 2.
{"title":"Evidence of a finite-time pointlike singularity solution for the Euler equations for perfect fluids","authors":"Diego Martínez-Argüello, Sergio Rica","doi":"10.1103/physrevfluids.9.094401","DOIUrl":"https://doi.org/10.1103/physrevfluids.9.094401","url":null,"abstract":"This paper investigates the evolution of the Euler equations near a potential blow-up solution. We employ an approach where this solution exhibits second-type self-similarity, characterized by an undetermined exponent <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>ν</mi></math>. This exponent can be seen as a nonlinear eigenvalue, determined by the solution of a self-similar partial differential equation with appropriate boundary conditions. Specifically, we demonstrate the existence of an axisymmetric solution of the Euler equations by expanding the axial vorticity using associated Legendre polynomials as a basis. This expansion results in an infinite hierarchy of ordinary differential equations, which, when truncated up to a certain order <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi>N</mi><mo>*</mo></msup></math>, allows for the numerical resolution of a finite set of ordinary differential equations. Through this numerical analysis, we obtain a solution that satisfies the appropriate boundary conditions for a specific value of the exponent <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>ν</mi></math>. By exploring various truncations, we establish a sequence in <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi>N</mi><mo>*</mo></msup></math> for the parameter <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>ν</mi><msup><mi>N</mi><mo>*</mo></msup></msub></math>, providing evidence of the convergence of the exponent <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>ν</mi></math>. Our findings suggest a self-similar exponent <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>ν</mi><mo>≈</mo><mn>2</mn></mrow></math>, presenting a promising path for a numerical or analytical approach indicating that <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>ν</mi></math> may indeed be exactly 2.","PeriodicalId":20160,"journal":{"name":"Physical Review Fluids","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The dual-channel characteristics of large-scale helicity transfer in compressible turbulent flows, including subgrid-scale (SGS) and viscosity terms, are investigated. After selecting a suitable definition for large-scale helicity, we confirm the existence of the dual channel of SGS and viscosity terms of large-scale helicity governing equations and theoretically prove that no dual pressure term channel exists. The second channel of the SGS and viscosity terms also consists of two terms, which originate from the rotation of the SGS stress and the baroclinic of the velocity and density gradients, respectively. The identical relationship of the ensemble averages of the dual channel of SGS and viscosity terms can be theoretically and numerically confirmed, whereas their second channel which is associated with shocklets is more intermittent. For the SGS term, the compression regions are dominant in contrast to the expansion regions, and the strain regions are dominant in contrast to the rotation regions in the inertial scale range. The viscous dissipation mechanism of large-scale helicity differs from that of large-scale kinetic energy. It is dominated by the first channel on the inside of the vortex structure and by the second channel on the outside. The further decompositions of the second channel of the SGS and viscosity terms provide a possible mechanism for the inverse helicity transfer. This means that expansion motions promote inverse helicity transfer through the second terms of their second channels.
{"title":"Helicity transfer in compressible turbulent flows","authors":"Zheng Yan, Junfeng Wu, Zhu Lei, Jianchun Wang, Lifeng Wang, Xinliang Li, Changping Yu","doi":"10.1103/physrevfluids.9.094603","DOIUrl":"https://doi.org/10.1103/physrevfluids.9.094603","url":null,"abstract":"The dual-channel characteristics of large-scale helicity transfer in compressible turbulent flows, including subgrid-scale (SGS) and viscosity terms, are investigated. After selecting a suitable definition for large-scale helicity, we confirm the existence of the dual channel of SGS and viscosity terms of large-scale helicity governing equations and theoretically prove that no dual pressure term channel exists. The second channel of the SGS and viscosity terms also consists of two terms, which originate from the rotation of the SGS stress and the baroclinic of the velocity and density gradients, respectively. The identical relationship of the ensemble averages of the dual channel of SGS and viscosity terms can be theoretically and numerically confirmed, whereas their second channel which is associated with shocklets is more intermittent. For the SGS term, the compression regions are dominant in contrast to the expansion regions, and the strain regions are dominant in contrast to the rotation regions in the inertial scale range. The viscous dissipation mechanism of large-scale helicity differs from that of large-scale kinetic energy. It is dominated by the first channel on the inside of the vortex structure and by the second channel on the outside. The further decompositions of the second channel of the SGS and viscosity terms provide a possible mechanism for the inverse helicity transfer. This means that expansion motions promote inverse helicity transfer through the second terms of their second channels.","PeriodicalId":20160,"journal":{"name":"Physical Review Fluids","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-03DOI: 10.1103/physrevfluids.9.l092601
Prahladh S. Iyer, Mujeeb R. Malik
It is well known that the scale-similarity class of subgrid models have a high correlation with the actual subgrid stresses in a priori tests. However, these models are typically underdissipative and not robust enough to be practically useful for large-eddy simulation. On the other hand, the dynamic Smagorinsky model (DSM), which is a popular subgrid model, is sufficiently dissipative and robust, but has a lower correlation with actual subgrid stresses in a priori tests. There have been many successful attempts to combine the two models into a “mixed” subgrid model that have typically retained the favorable properties of both. However, most dynamic mixed models require two or more levels of test filtering beyond the (often implicit) grid filtered quantities that are solved, in contrast to a single test filtering operation for the dynamic Smagorinsky model. The additional cost involved in test filtering has likely hindered the widespread use of dynamic mixed models in production codes. We propose an efficient dynamic mixed model that is constrained to have the same subgrid dissipation as the DSM model, and only requires a single level of test filtering. Thus, the additional computational cost is negligible compared to the DSM model. A posteriori simulations of the turbulent channel flow reveal that the proposed mixed model is as robust as the DSM model, and more accurate on coarser grids. Notably, smooth-body turbulent separation is better captured by the new model when combined with a standard wall model.
{"title":"Efficient dynamic mixed subgrid-scale model","authors":"Prahladh S. Iyer, Mujeeb R. Malik","doi":"10.1103/physrevfluids.9.l092601","DOIUrl":"https://doi.org/10.1103/physrevfluids.9.l092601","url":null,"abstract":"It is well known that the scale-similarity class of subgrid models have a high correlation with the actual subgrid stresses in <i>a priori</i> tests. However, these models are typically underdissipative and not robust enough to be practically useful for large-eddy simulation. On the other hand, the dynamic Smagorinsky model (DSM), which is a popular subgrid model, is sufficiently dissipative and robust, but has a lower correlation with actual subgrid stresses in <i>a priori</i> tests. There have been many successful attempts to combine the two models into a “mixed” subgrid model that have typically retained the favorable properties of both. However, most dynamic mixed models require two or more levels of test filtering beyond the (often implicit) grid filtered quantities that are solved, in contrast to a single test filtering operation for the dynamic Smagorinsky model. The additional cost involved in test filtering has likely hindered the widespread use of dynamic mixed models in production codes. We propose an efficient dynamic mixed model that is constrained to have the same subgrid dissipation as the DSM model, and only requires a single level of test filtering. Thus, the additional computational cost is negligible compared to the DSM model. <i>A posteriori</i> simulations of the turbulent channel flow reveal that the proposed mixed model is as robust as the DSM model, and more accurate on coarser grids. Notably, smooth-body turbulent separation is better captured by the new model when combined with a standard wall model.","PeriodicalId":20160,"journal":{"name":"Physical Review Fluids","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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