Pub Date : 2026-03-01Epub Date: 2025-10-28DOI: 10.1016/j.euromechflu.2025.204397
E. Zuccoli, U. Kadri
We investigate the effects of compressibility in the propagation of shallow-water waves and extend the classical shallow-water equations to a compressible regime. Both non-dispersive and weakly-dispersive nonlinear waves are then analysed with the help of the multiple scales method, ultimately leading to the studying of a Burgers and a Korteweg–deVries equation, respectively. A parametric study is conducted in order to investigate the interplay of both nonlinearity and compressibility and assess how compressibility may alter the nonlinear properties of the waves. In particular, parameters varied are the compressibility coefficient , the amplitude of the waves and the width of the initial wave profile . In a non-dispersive regime, shock and rarefaction waves form and interact one another leading to a progressive reduction of the wave amplitude in time. The compressibility of the fluid speeds up the shock formation, with beneficial effects in terms of wave amplitude reduction. In a weakly dispersive regime, on the other hand, higher compressibility values may amplify the initial perturbation, leading to the formation of a discrete number of solitons having amplitudes much greater than the amplitude at the initial stage. The analysis presented in this work aims at improving our predictions on the dynamics of nonlinear compressible shallow-water waves both in terms of wave amplitude variation and propagation time. Among various applications, our enhanced models can notably improve the estimation of tsunami arrival times and contribute to more accurate weather forecasts. Furthermore, the work presented here lays the foundation for future experimental studies and assessments in this field.
{"title":"Compressible effects in the propagation of nonlinear shallow water waves: Models and simulations","authors":"E. Zuccoli, U. Kadri","doi":"10.1016/j.euromechflu.2025.204397","DOIUrl":"10.1016/j.euromechflu.2025.204397","url":null,"abstract":"<div><div>We investigate the effects of compressibility in the propagation of shallow-water waves and extend the classical shallow-water equations to a compressible regime. Both non-dispersive and weakly-dispersive nonlinear waves are then analysed with the help of the multiple scales method, ultimately leading to the studying of a Burgers and a Korteweg–deVries equation, respectively. A parametric study is conducted in order to investigate the interplay of both nonlinearity and compressibility and assess how compressibility may alter the nonlinear properties of the waves. In particular, parameters varied are the compressibility coefficient <span><math><mi>μ</mi></math></span>, the amplitude of the waves <span><math><mi>ϵ</mi></math></span> and the width of the initial wave profile <span><math><mi>σ</mi></math></span>. In a non-dispersive regime, shock and rarefaction waves form and interact one another leading to a progressive reduction of the wave amplitude in time. The compressibility of the fluid <span><math><mi>μ</mi></math></span> speeds up the shock formation, with beneficial effects in terms of wave amplitude reduction. In a weakly dispersive regime, on the other hand, higher compressibility values may amplify the initial perturbation, leading to the formation of a discrete number of solitons having amplitudes much greater than the amplitude at the initial stage. The analysis presented in this work aims at improving our predictions on the dynamics of nonlinear compressible shallow-water waves both in terms of wave amplitude variation and propagation time. Among various applications, our enhanced models can notably improve the estimation of tsunami arrival times and contribute to more accurate weather forecasts. Furthermore, the work presented here lays the foundation for future experimental studies and assessments in this field.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"116 ","pages":"Article 204397"},"PeriodicalIF":2.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145414861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-11-12DOI: 10.1016/j.euromechflu.2025.204416
Jie Li, Li Peng, Yu Hao
Precise regulation of ion transport in nanofluidics demonstrates great application prospects in the field of ion separation and pre-enrichment. Compared with unipolar nanochannels, bipolar nanochannels show superior performance in ion transport control and can achieve higher ion enrichment ratio and ion interception efficiency. Beyond these fundamental advantages, such nanofluidics gain additional relevance from the widespread use of non-Newtonian fluids across biomedical and chemical applications. This research explores a novel approach—converting a unipolar nanochannel into a bipolar configuration by integrating a gated structure at its center and utilizing a positively charged surface. The Navier-Stokes equations model fluid dynamics, while the Poisson-Nernst-Planck formulation depicts electric potential and ion concentration profiles. Through numerical simulations, the electrokinetic transport behavior of power-law fluids within the bipolar nanochannel is analyzed. The findings indicate that for the fluid characterized by a power-law index of n = 0.95, a rise in gate surface charge density from 0 to 25 mC/m2 leads to a roughly 25 % boost in ionic current. However, this increase comes at a cost—the ion selectivity coefficient drops sharply by 46 %. Furthermore, at gate densities of 0 and 40 mC/m2, the power-law index rises from 0.95 to 1.05, with the ionic current climbing about 31 % and 4 % accordingly.
{"title":"Electrokinetic ion transport of non-Newtonian fluids in a bipolar nanochannel","authors":"Jie Li, Li Peng, Yu Hao","doi":"10.1016/j.euromechflu.2025.204416","DOIUrl":"10.1016/j.euromechflu.2025.204416","url":null,"abstract":"<div><div>Precise regulation of ion transport in nanofluidics demonstrates great application prospects in the field of ion separation and pre-enrichment. Compared with unipolar nanochannels, bipolar nanochannels show superior performance in ion transport control and can achieve higher ion enrichment ratio and ion interception efficiency. Beyond these fundamental advantages, such nanofluidics gain additional relevance from the widespread use of non-Newtonian fluids across biomedical and chemical applications. This research explores a novel approach—converting a unipolar nanochannel into a bipolar configuration by integrating a gated structure at its center and utilizing a positively charged surface. The Navier-Stokes equations model fluid dynamics, while the Poisson-Nernst-Planck formulation depicts electric potential and ion concentration profiles. Through numerical simulations, the electrokinetic transport behavior of power-law fluids within the bipolar nanochannel is analyzed. The findings indicate that for the fluid characterized by a power-law index of <em>n</em> = 0.95, a rise in gate surface charge density from 0 to 25 mC/m<sup>2</sup> leads to a roughly 25 % boost in ionic current. However, this increase comes at a cost—the ion selectivity coefficient drops sharply by 46 %. Furthermore, at gate densities of 0 and 40 mC/m<sup>2</sup>, the power-law index rises from 0.95 to 1.05, with the ionic current climbing about 31 % and 4 % accordingly.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"116 ","pages":"Article 204416"},"PeriodicalIF":2.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145517713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-11-03DOI: 10.1016/j.euromechflu.2025.204404
Rohit, Ashish Sonker, Abhishek Raj
This study numerically and experimentally investigates the motion of a shear-thinning liquid droplet on an inclined compliant substrate, highlighting its distinct dynamics compared to Newtonian fluids. Unlike Newtonian liquids with constant viscosity, the shear-thinning droplet exhibits variations in viscosity due to differences in shear rate across its height. These viscosity changes significantly influence its movement, interaction with the substrate, and deformation. Newtonian () and Newtonian , were selected to match the zero- shear viscosity and infinite shear viscosity of the shear-thinning liquid (XG-1) for comparative analysis. The shear-thinning droplet (XG-1) was found to have a velocity 8.76 % lower than the low-viscosity Newtonian () droplet but 528 % higher than the high-viscosity Newtonian () droplet. Consequently, its displacement was found to be 7.5 % lesser than Newtonian () but 171 % greater than Newtonian (). Compared to Newtonian liquids, the shear-thinning droplet exhibits moderate fluctuations in base length and height, as well as an intermediate level of contact angle hysteresis (CAH). The motion of the droplet also affects the deformation in the flexible substrate, leading to 6.5 % greater membrane deflection than Newtonian () but 7.63 % less than Newtonian (). The deformation of the shear-thinning droplet is significant due to rapid viscosity transitions, distinguishing it from the stable shape of a highly viscous Newtonian droplet. Changes in membrane flexural rigidity and droplet size further influence displacement, deformation, and wobbling. Higher flexural rigidity reduces membrane deflection, increases droplet displacement, and reduces droplet CAH, while larger droplets with higher Bond numbers experience greater deformation and instability. These findings provide valuable insights into the role of viscosity variations in droplet dynamics.
{"title":"Sliding dynamics of shear-thinning liquid droplets on inclined compliant hydrophobic substrates","authors":"Rohit, Ashish Sonker, Abhishek Raj","doi":"10.1016/j.euromechflu.2025.204404","DOIUrl":"10.1016/j.euromechflu.2025.204404","url":null,"abstract":"<div><div>This study numerically and experimentally investigates the motion of a shear-thinning liquid droplet on an inclined compliant substrate, highlighting its distinct dynamics compared to Newtonian fluids. Unlike Newtonian liquids with constant viscosity, the shear-thinning droplet exhibits variations in viscosity due to differences in shear rate across its height. These viscosity changes significantly influence its movement, interaction with the substrate, and deformation. Newtonian (<span><math><mrow><mi>μ</mi><mi>₀</mi></mrow></math></span>) and Newtonian <span><math><mrow><mfenced><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mi>∞</mi></mrow></msub></mrow></mfenced></mrow></math></span>, were selected to match the zero- shear viscosity <span><math><mrow><mo>(</mo><mi>μ</mi><mi>₀</mi><mo>)</mo></mrow></math></span> and infinite shear viscosity <span><math><mrow><msub><mrow><mo>(</mo><mi>μ</mi></mrow><mrow><mi>∞</mi></mrow></msub><mo>)</mo></mrow></math></span> of the shear-thinning liquid (XG-1) for comparative analysis. The shear-thinning droplet (XG-1) was found to have a velocity 8.76 % lower than the low-viscosity Newtonian (<span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span>) droplet but 528 % higher than the high-viscosity Newtonian (<span><math><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>) droplet. Consequently, its displacement was found to be 7.5 % lesser than Newtonian (<span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span>) but 171 % greater than Newtonian (<span><math><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>). Compared to Newtonian liquids, the shear-thinning droplet exhibits moderate fluctuations in base length and height, as well as an intermediate level of contact angle hysteresis (CAH). The motion of the droplet also affects the deformation in the flexible substrate, leading to 6.5 % greater membrane deflection than Newtonian (<span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span>) but 7.63 % less than Newtonian (<span><math><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>). The deformation of the shear-thinning droplet is significant due to rapid viscosity transitions, distinguishing it from the stable shape of a highly viscous Newtonian <span><math><mrow><mo>(</mo><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo><mspace></mspace></mrow></math></span>droplet. Changes in membrane flexural rigidity and droplet size further influence displacement, deformation, and wobbling. Higher flexural rigidity reduces membrane deflection, increases droplet displacement, and reduces droplet CAH, while larger droplets with higher Bond numbers experience greater deformation and instability. These findings provide valuable insights into the role of viscosity variations in droplet dynamics.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"116 ","pages":"Article 204404"},"PeriodicalIF":2.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145517714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-11-22DOI: 10.1016/j.euromechflu.2025.204419
Aruna A, Radha S, Swarup Barik
The paper presents a two-dimensional concentration distribution of a solute cloud in a non-Newtonian Casson fluid flowing through a tube with an absorbing wall. A multiscale homogenization method is employed to analyze the dispersion, mean, and transverse concentration distributions in both the plug and shear flow regions, which is developed by the yield-stress-driven flow behavior of the Casson fluid. Although most previous studies have primarily focused on determining the dispersion coefficient and mean concentration distribution for non-Newtonian fluids, our study extends this by deriving analytical expressions for the two-dimensional concentration distribution in Casson fluid flows. Numerical simulations are performed to validate the analytical results. The results show that increasing the radius of the plug reduces the dispersion of the solute as a result of suppressed radial mixing within the uniform velocity region. The mean and transverse concentration distributions are strongly influenced by both the plug flow and wall absorption parameters. Although concentration gradients persist longer in the plug region due to the absence of mixing, shear flow accelerates homogenization in the shear region. Stronger wall absorption further restricts transverse mixing, sustaining cross-sectional nonuniformity in both regions. These insights provide a clearer understanding of nutrient and oxygen transport in capillary flows involving non-Newtonian fluids.
{"title":"Multi-scale analysis of solute dispersion in a Casson fluid flow in a tube with wall absorption","authors":"Aruna A, Radha S, Swarup Barik","doi":"10.1016/j.euromechflu.2025.204419","DOIUrl":"10.1016/j.euromechflu.2025.204419","url":null,"abstract":"<div><div>The paper presents a two-dimensional concentration distribution of a solute cloud in a non-Newtonian Casson fluid flowing through a tube with an absorbing wall. A multiscale homogenization method is employed to analyze the dispersion, mean, and transverse concentration distributions in both the plug and shear flow regions, which is developed by the yield-stress-driven flow behavior of the Casson fluid. Although most previous studies have primarily focused on determining the dispersion coefficient and mean concentration distribution for non-Newtonian fluids, our study extends this by deriving analytical expressions for the two-dimensional concentration distribution in Casson fluid flows. Numerical simulations are performed to validate the analytical results. The results show that increasing the radius of the plug reduces the dispersion of the solute as a result of suppressed radial mixing within the uniform velocity region. The mean and transverse concentration distributions are strongly influenced by both the plug flow and wall absorption parameters. Although concentration gradients persist longer in the plug region due to the absence of mixing, shear flow accelerates homogenization in the shear region. Stronger wall absorption further restricts transverse mixing, sustaining cross-sectional nonuniformity in both regions. These insights provide a clearer understanding of nutrient and oxygen transport in capillary flows involving non-Newtonian fluids.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"116 ","pages":"Article 204419"},"PeriodicalIF":2.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145615188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Modeling Lagrangian turbulence remains a fundamental challenge due to its multiscale, intermittent, and non-Gaussian nature. Recent advances in data-driven diffusion models have enabled the generation of realistic Lagrangian velocity trajectories that accurately reproduce statistical properties across scales and capture rare extreme events. This study investigates three key aspects of diffusion-based modeling for Lagrangian turbulence. First, we assess architectural robustness by comparing a U-Net backbone with a transformer-based alternative, finding strong consistency in generated trajectories, with only minor discrepancies at small scales. Second, leveraging a deterministic variant of diffusion model formulation, namely the deterministic denoising diffusion implicit model (DDIM), we identify structured features in the initial latent noise that align consistently with extreme acceleration events. Third, we explore accelerated generation by reducing the number of diffusion steps, and find that DDIM enables substantial speedups with minimal loss of statistical fidelity. These findings highlight the robustness of diffusion models and their potential for interpretable, scalable modeling of complex turbulent systems.
{"title":"Deterministic diffusion models for Lagrangian turbulence: Robustness and encoding of extreme events","authors":"Tianyi Li , Flavio Tuteri , Michele Buzzicotti , Fabio Bonaccorso , Luca Biferale","doi":"10.1016/j.euromechflu.2025.204402","DOIUrl":"10.1016/j.euromechflu.2025.204402","url":null,"abstract":"<div><div>Modeling Lagrangian turbulence remains a fundamental challenge due to its multiscale, intermittent, and non-Gaussian nature. Recent advances in data-driven diffusion models have enabled the generation of realistic Lagrangian velocity trajectories that accurately reproduce statistical properties across scales and capture rare extreme events. This study investigates three key aspects of diffusion-based modeling for Lagrangian turbulence. First, we assess architectural robustness by comparing a U-Net backbone with a transformer-based alternative, finding strong consistency in generated trajectories, with only minor discrepancies at small scales. Second, leveraging a deterministic variant of diffusion model formulation, namely the deterministic denoising diffusion implicit model (DDIM), we identify structured features in the initial latent noise that align consistently with extreme acceleration events. Third, we explore accelerated generation by reducing the number of diffusion steps, and find that DDIM enables substantial speedups with minimal loss of statistical fidelity. These findings highlight the robustness of diffusion models and their potential for interpretable, scalable modeling of complex turbulent systems.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"116 ","pages":"Article 204402"},"PeriodicalIF":2.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145464114","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-10-30DOI: 10.1016/j.euromechflu.2025.204400
Qingliang Zhan , Zhiyong Wang , Zihan Cao , Xin Liu
Image-based deep learning methods, such as two dimensional convolutional neural networks, have recently played an increasingly important role in the study of fluids. However, the flow decomposition mechanism of these deep learning models remains open. In this work, by extracting and decoupling the spatial features hidden in the snapshots, the physical meaning of the flow decomposition and order reduction model is investigated. The observed snapshot at each time stamp is compressed into a low dimensional latent code with independent component by the encoder, and then the decoder reconstructs the flow spatial feature from the latent space, forming an unsupervised scheme for flow decomposition. Laminar and turbulent flows around circular cylinder at Re= 100 and Re= 3900 are analyzed. The results of the laminar case show that the code parameters represent the magnitude of respective spatial features at each instant, while the decoder output of the unit latent vector is the corresponding flow spatial mode. Furthermore, the turbulence results indicate that the deep learning models are more accurate in reconstructing the turbulence than conventional linear theory-based method, while maintaining the independence of the decomposed features. This study presents the decomposition mechanism and the interpretability of 2-dimensional convolutional autoencoders for flow decomposition and feature decoupling.
{"title":"Interpretability of snapshot-based convolutional autoencoder for flow decomposition and feature decoupling","authors":"Qingliang Zhan , Zhiyong Wang , Zihan Cao , Xin Liu","doi":"10.1016/j.euromechflu.2025.204400","DOIUrl":"10.1016/j.euromechflu.2025.204400","url":null,"abstract":"<div><div>Image-based deep learning methods, such as two dimensional convolutional neural networks, have recently played an increasingly important role in the study of fluids. However, the flow decomposition mechanism of these deep learning models remains open. In this work, by extracting and decoupling the spatial features hidden in the snapshots, the physical meaning of the flow decomposition and order reduction model is investigated. The observed snapshot at each time stamp is compressed into a low dimensional latent code with independent component by the encoder, and then the decoder reconstructs the flow spatial feature from the latent space, forming an unsupervised scheme for flow decomposition. Laminar and turbulent flows around circular cylinder at <em>Re</em>= 100 and <em>Re</em>= 3900 are analyzed. The results of the laminar case show that the code parameters represent the magnitude of respective spatial features at each instant, while the decoder output of the unit latent vector is the corresponding flow spatial mode. Furthermore, the turbulence results indicate that the deep learning models are more accurate in reconstructing the turbulence than conventional linear theory-based method, while maintaining the independence of the decomposed features. This study presents the decomposition mechanism and the interpretability of 2-dimensional convolutional autoencoders for flow decomposition and feature decoupling.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"116 ","pages":"Article 204400"},"PeriodicalIF":2.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145464162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-10-28DOI: 10.1016/j.euromechflu.2025.204398
Shuo Peng, Qian Chen
The turbulent/non-turbulent interface (TNTI) is a thin layer with a steep gradient of vorticity magnitude that separates turbulent from irrotational fluids in turbulent shear flows. The interface plays a crucial role in the exchange of mass, momentum and energy and scalars between the two sides, as the properties of the fluids on either side differ significantly. Consequently, accurately detecting the TNTI is essential for the study of related physical phenomena. Currently, various methods for TNTI detection have been developed. This paper provides a comprehensive review of the primary TNTI detection methods, beginning with three typical methods based on vorticity, passive scalars, and turbulent kinetic energy. These methods are thoroughly analyzed in terms of their detection mechanisms, detection threshold selection criteria, and overall performance in diverse flow environments. Furthermore, the paper explores innovative methods that have been developed in recent years, such as machine learning approaches, the homogeneity criterion, and virtual particle tracking methods. Finally, the paper synthesizes the strengths and limitations of these TNTI detection methods and offers insights into future research on the detection of the TNTI.
{"title":"Turbulent/non-turbulent interface detection methods for turbulent shear flows","authors":"Shuo Peng, Qian Chen","doi":"10.1016/j.euromechflu.2025.204398","DOIUrl":"10.1016/j.euromechflu.2025.204398","url":null,"abstract":"<div><div>The turbulent/non-turbulent interface (TNTI) is a thin layer with a steep gradient of vorticity magnitude that separates turbulent from irrotational fluids in turbulent shear flows. The interface plays a crucial role in the exchange of mass, momentum and energy and scalars between the two sides, as the properties of the fluids on either side differ significantly. Consequently, accurately detecting the TNTI is essential for the study of related physical phenomena. Currently, various methods for TNTI detection have been developed. This paper provides a comprehensive review of the primary TNTI detection methods, beginning with three typical methods based on vorticity, passive scalars, and turbulent kinetic energy. These methods are thoroughly analyzed in terms of their detection mechanisms, detection threshold selection criteria, and overall performance in diverse flow environments. Furthermore, the paper explores innovative methods that have been developed in recent years, such as machine learning approaches, the homogeneity criterion, and virtual particle tracking methods. Finally, the paper synthesizes the strengths and limitations of these TNTI detection methods and offers insights into future research on the detection of the TNTI.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"116 ","pages":"Article 204398"},"PeriodicalIF":2.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145464113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-11-19DOI: 10.1016/j.euromechflu.2025.204421
Dadi Dimple S.S., B. Sri Padmavati
We consider a translating and rotating spherical slip–stick Janus particle of unit radius in an oscillatory Stokes flow. Janus particles are unique microparticles with surfaces that exhibit two or more different physical properties in different regions owing to different surface roughness in these regions. Here we assume that the sphere’s surface consists of two different regions characterized by different slip parameters in each region. We give a method of solution and elucidate it with different configurations of such regions illustrated by a sphere enveloped by (i) a cap, (ii) a horizontal strip, and (iii) a patch. We study the effect of such a heterogeneous nature of the surface on some physical properties, such as drag and torque experienced by the sphere. We also observe the effect of non-uniform surface roughness on the translational and rotational velocity of the particle.
{"title":"Oscillatory Stokes flow past a slip–stick Janus sphere","authors":"Dadi Dimple S.S., B. Sri Padmavati","doi":"10.1016/j.euromechflu.2025.204421","DOIUrl":"10.1016/j.euromechflu.2025.204421","url":null,"abstract":"<div><div>We consider a translating and rotating spherical slip–stick Janus particle of unit radius in an oscillatory Stokes flow. Janus particles are unique microparticles with surfaces that exhibit two or more different physical properties in different regions owing to different surface roughness in these regions. Here we assume that the sphere’s surface consists of two different regions characterized by different slip parameters in each region. We give a method of solution and elucidate it with different configurations of such regions illustrated by a sphere enveloped by (i) a cap, (ii) a horizontal strip, and (iii) a patch. We study the effect of such a heterogeneous nature of the surface on some physical properties, such as drag and torque experienced by the sphere. We also observe the effect of non-uniform surface roughness on the translational and rotational velocity of the particle.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"116 ","pages":"Article 204421"},"PeriodicalIF":2.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145615190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Controlling the flow structure around an airfoil is crucial for increasing lift and reducing drag. Delaying flow separation improves aerodynamic performance, especially in aircraft and wind turbines. In recent years, artificial intelligence and machine learning methods have emerged as fast and cost-effective alternatives to traditional approaches in fluid mechanics. In this study, we aimed to control the flow around the NACA (National Advisory Committee for Aeronautics) 4412 airfoil using vortex generators (VGs) and to develop a machine-learning-based flow simulator that predicts velocity components based on angle of attack, VG yaw angle, and spatial coordinates. Experimental measurements were conducted in an open-surface, closed-loop water channel at a Reynolds number of Re = 1.0 × 10⁴ using a two-dimensional Particle Image Velocimetry (PIV) system. A total of 60,500 data points were collected per velocity component from 20 experimental cases within the range of α = 0°–20° and β = 15°–30°. A Multilayer Perceptron (MLP) model implemented using TensorFlow was trained to predict the ensemble-averaged 〈u〉 and 〈v〉 velocity components. We analyzed the effects of hidden layer neuron count and mini-batch size, achieving the highest accuracy with 41 neurons and a batch size of 4, yielding R² values of 0.978 for 〈u〉 and 0.950 for 〈v〉. The error distributions were symmetric and closely approximated a Gaussian distribution. Experimental results showed that VGs delayed early-stage flow separation at low α but became less effective at higher α. The MLP model successfully reconstructed major flow features, providing a reliable data-driven alternative to CFD-based methods. Future work will extend the model to various airfoils, VG designs, Reynolds numbers, and unsteady flows using time-resolved PIV data.
控制翼型周围的流动结构是增加升力和减少阻力的关键。延迟流动分离可以改善空气动力学性能，特别是在飞机和风力涡轮机中。近年来，人工智能和机器学习方法已经成为流体力学中传统方法的快速和经济的替代品。在这项研究中，我们的目标是使用涡发生器（VG）控制NACA（美国国家航空咨询委员会）4412翼型周围的流动，并开发一个基于机器学习的流动模拟器，该模拟器可以根据迎角、VG偏航角和空间坐标来预测速度分量。实验测量采用二维粒子图像测速（PIV）系统，在雷诺数Re = 1.0 × 10⁴的开表面闭环水道中进行。在α = 0°-20°和β = 15°-30°范围内的20个实验案例中，每个速度分量共收集了60500个数据点。使用TensorFlow实现的多层感知器（MLP）模型被训练来预测集合平均< u >和< v >速度分量。我们分析了隐藏层神经元数量和小批大小的影响，在41个神经元和4个批大小的情况下获得了最高的准确性，< u >和< v >的R²值分别为0.978和0.950。误差分布是对称的，近似于高斯分布。实验结果表明，在低α条件下，VGs延迟了早期的流动分离，而在高α条件下，VGs的作用减弱。MLP模型成功地重建了主要的流体特征，为基于cfd的方法提供了可靠的数据驱动替代方案。未来的工作将扩展模型到各种翼型，VG设计，雷诺数，和非定常流动使用时间分辨PIV数据。
{"title":"Machine learning based flow simulator: Flow around an airfoil with vortex generators","authors":"Muharrem Hilmi Aksoy , Murat Ispir , Mahdi Tabatabaei Malazi , Abdulkerim Okbaz","doi":"10.1016/j.euromechflu.2025.204417","DOIUrl":"10.1016/j.euromechflu.2025.204417","url":null,"abstract":"<div><div>Controlling the flow structure around an airfoil is crucial for increasing lift and reducing drag. Delaying flow separation improves aerodynamic performance, especially in aircraft and wind turbines. In recent years, artificial intelligence and machine learning methods have emerged as fast and cost-effective alternatives to traditional approaches in fluid mechanics. In this study, we aimed to control the flow around the NACA (National Advisory Committee for Aeronautics) 4412 airfoil using vortex generators (VGs) and to develop a machine-learning-based flow simulator that predicts velocity components based on angle of attack, VG yaw angle, and spatial coordinates. Experimental measurements were conducted in an open-surface, closed-loop water channel at a Reynolds number of <em>Re</em> = 1.0 × 10⁴ using a two-dimensional Particle Image Velocimetry (PIV) system. A total of 60,500 data points were collected per velocity component from 20 experimental cases within the range of α = 0°–20° and β = 15°–30°. A Multilayer Perceptron (MLP) model implemented using TensorFlow was trained to predict the ensemble-averaged 〈<em>u</em>〉 and 〈<em>v</em>〉 velocity components. We analyzed the effects of hidden layer neuron count and mini-batch size, achieving the highest accuracy with 41 neurons and a batch size of 4, yielding <em>R</em>² values of 0.978 for 〈<em>u</em>〉 and 0.950 for 〈<em>v</em>〉. The error distributions were symmetric and closely approximated a Gaussian distribution. Experimental results showed that VGs delayed early-stage flow separation at low α but became less effective at higher <em>α</em>. The MLP model successfully reconstructed major flow features, providing a reliable data-driven alternative to CFD-based methods. Future work will extend the model to various airfoils, VG designs, Reynolds numbers, and unsteady flows using time-resolved PIV data.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"116 ","pages":"Article 204417"},"PeriodicalIF":2.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145615189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-10-29DOI: 10.1016/j.euromechflu.2025.204401
Shravan Kumar Rudrabhatla , D. Srinivasacharya
Physics-Informed Neural Networks (PINNs) provide a powerful framework for solving complex engineering problems by integrating governing physical laws with noisy or incomplete data. This study applies PINNs to analyse boundary layer flow and heat transfer in a non-Newtonian Casson fluid over a vertically stretching sheet. By incorporating physical constraints into the network’s loss function, PINNs optimise weights and biases to approximate solutions of governing ordinary differential equations (ODEs), ensuring physics-consistent predictions. Key parameters such as the Casson fluid parameter, chemical reaction parameter, thermal and concentration buoyancy parameters, Eckert number, Prandtl number, and suction/injection parameter are examined. The effects of these parameters on flow, temperature, and concentration fields are analysed using graphical representations. Furthermore, the accuracy of the PINN-based approach is validated through a comparative study with MATLAB’s BVP4C routine (Boundary Value Problem 4th-Order Collocation), demonstrating strong agreement and confirming its effectiveness in solving nonlinear differential equations in heat and mass transfer problems.
{"title":"Deep learning framework for casson fluid flow: A PINN approach to heat and mass transfer with chemical reaction and viscous dissipation","authors":"Shravan Kumar Rudrabhatla , D. Srinivasacharya","doi":"10.1016/j.euromechflu.2025.204401","DOIUrl":"10.1016/j.euromechflu.2025.204401","url":null,"abstract":"<div><div>Physics-Informed Neural Networks (PINNs) provide a powerful framework for solving complex engineering problems by integrating governing physical laws with noisy or incomplete data. This study applies PINNs to analyse boundary layer flow and heat transfer in a non-Newtonian Casson fluid over a vertically stretching sheet. By incorporating physical constraints into the network’s loss function, PINNs optimise weights and biases to approximate solutions of governing ordinary differential equations (ODEs), ensuring physics-consistent predictions. Key parameters such as the Casson fluid parameter, chemical reaction parameter, thermal and concentration buoyancy parameters, Eckert number, Prandtl number, and suction/injection parameter are examined. The effects of these parameters on flow, temperature, and concentration fields are analysed using graphical representations. Furthermore, the accuracy of the PINN-based approach is validated through a comparative study with MATLAB’s BVP4C routine (Boundary Value Problem 4th-Order Collocation), demonstrating strong agreement and confirming its effectiveness in solving nonlinear differential equations in heat and mass transfer problems.</div></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":"116 ","pages":"Article 204401"},"PeriodicalIF":2.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145464115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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