
[Sponsors] 
Largescale circulation of the atmosphere in the Earth's extratropics is dominated by eddies, eastward (westerly) zonal winds, and their interaction. Eddies not only bring about weather variabilities but also help maintain the average state of climate. In recent years, our understanding of how largescale eddies and mean flows interact in the extratropical atmosphere has advanced significantly due to new dynamical constraints on finiteamplitude eddies and the related eddyfree reference state. This article reviews the theoretical foundations for finiteamplitude Rossby wave activity and related concepts. Theory is then applied to atmospheric data to elucidate how angular momentum is redistributed by the generation, transmission, and dissipation of Rossby waves and to reveal how an anomalously large wave event such as atmospheric blocking may arise from regional eddymean flow interaction.
Stephen H. Davis (1939–2021) was an applied mathematician, fluid dynamicist, and materials scientist who lead the field in his contributions to interfacial dynamics, thermal convection, thin films, and solidification for over 50 years. Here, we briefly review his personal and professional life and some of his most significant contributions to the field.
Airtanker firefighting is the most spectacular tool used to fight wildland fires. However, it employs a rudimentary largescale spraying technology operating at a high speed and a long distance from the target. This review gives an overview of the fluid dynamics processes that govern this practice, which are characterized by rich and varied physical phenomena. The liquid column penetration in the air, its largescale fragmentation, and an intense surface atomization give shape to the rainfall produced by the airtanker and the deposition of the final product on the ground. The cloud dynamics is controlled by droplet breakup, evaporation, and wind dispersion. The process of liquid deposition onto the forest canopy is full of open questions of great interest for rainfall retention in vegetation. Of major importance, but still requiring investigation, is the role of the complex nonNewtonian viscoelastic and shearthinning behavior of the retardant dropped to stop the fire propagation. The review describes the need for future research devoted to the subject.
This review highlights major developments and milestones during the early days of numerical simulation of turbulent flows and its use to increase our understanding of turbulence phenomena. The period covered starts with the first simulations of decaying homogeneous isotropic turbulence in 1971–1972 and ends about 25 years later. Some earlier history of the progress in weather prediction is included if relevant. Only direct simulation, in which all scales of turbulence are accounted for explicitly, and largeeddy simulation, in which the effect of the smaller scales is modeled, are discussed. The method by which all scales are modeled, Reynoldsaveraged Navier–Stokes, is not covered.
Understanding and predicting turbulent flow phenomena remain a challenge for both theory and applications. The nonlinear and nonlocal character of smallscale turbulence can be comprehensively described in terms of the velocity gradients, which determine fundamental quantities like dissipation, enstrophy, and the smallscale topology of turbulence. The dynamical equation for the velocity gradient succinctly encapsulates the nonlinear physics of turbulence; it offers an intuitive description of a host of turbulence phenomena and enables establishing connections between turbulent dynamics, statistics, and flow structure. The consideration of filtered velocity gradients enriches this view to express the multiscale aspects of nonlinearity and flow structure in a formulation directly applicable to largeeddy simulations. Driven by theoretical advances together with growing computational and experimental capabilities, recent activities in this area have elucidated key aspects of turbulence physics and advanced modeling capabilities.
Rotatingdisk flows were first considered by von Kármán in a seminal paper in 1921, where boundary layers in general were discussed and, in two of the nine sections, results for the laminar and turbulent boundary layers over a rotating disk were presented. It was not until in 1955 that flow visualization discovered the existence of stationary crossflow vortices on the disk prior to the transition to turbulence. The rotating disk can be seen as a special case of rotating cones, and recent research has shown that broad cones behave similarly to disks, whereas sharp cones are susceptible to a different type of instability. Here, we provide a review of the major developments since von Kármán's work from 100 years ago, regarding instability, transition, and turbulence in the boundary layers, and we include some analysis not previously published.
Bubble plumes are ubiquitous in nature. Instances in the natural world include the release of methane and carbon dioxide from the seabed or the bottom of a lake and from a subsea oil well blowout. This review describes the dynamics of bubble plumes and their various spreading patterns in the surrounding environment. We explore how the motion of the plume is affected by the density stratification in the external environment, as well as by internal processes of dissolution of the bubbles and chemical reaction. We discuss several examples, such as natural disasters, global warming, and fishing techniques used by some whales and dolphins.
We review some fundamentals of turbulent drag reduction and the turbulent drag reduction techniques using streamwise traveling waves of blowing/suction from the wall and wall deformation. For both types of streamwise traveling wave controls, their significant drag reduction capabilities have been well confirmed by direct numerical simulation at relatively low Reynolds numbers. The drag reduction mechanisms by these streamwise traveling waves are considered to be the combination of direct effects due to pumping and indirect effects of the attenuation of velocity fluctuations due to reduced receptivity. Prediction of their drag reduction capabilities at higher Reynolds numbers and attempts at experimental validation are also intensively ongoing toward their practical implementation.
Ventilation is central to human civilization. Without it, the indoor environment rapidly becomes uncomfortable or dangerous, but too much ventilation can be expensive. We spend much of our time indoors, where we are exposed to pollutants and can be infected by airborne diseases. Ventilation removes pollution and bioaerosols from indoor sources but also brings in pollution from outdoors. To determine an appropriate level of ventilation and an appropriate way of providing it, one must understand that the needs for ventilation extend beyond simple thermal comfort; the quality of indoor air is at least as important. An effective ventilation system will remove unwanted contaminants, whether generated within the space by activities or by the simple act of breathing, and ensure that the ventilation system does not itself introduce or spread contaminants from elsewhere. This review explores how ventilation flows in buildings influence personal exposure to indoor pollutants and the spread of airborne diseases.
In the last ten years, advances in experimental techniques have enabled remarkable discoveries of how the dynamics of thin gas films can profoundly influence the behavior of liquid droplets. Drops impacting onto solids can skate on a film of air so that they bounce off solids. For drop–drop collisions, this effect, which prevents coalescence, has been long recognized. Notably, the precise physical mechanisms governing these phenomena have been a topic of intense debate, leading to a synergistic interplay of experimental, theoretical, and computational approaches. This review attempts to synthesize our knowledge of when and how drops bounce, with a focus on (a) the unconventional microscale and nanoscale physics required to predict transitions to/from merging and (b) the development of computational models. This naturally leads to the exploration of an array of other topics, such as the Leidenfrost effect and dynamic wetting, in which gas films also play a prominent role.
Publication date: 30 June 2024
Source: Computers & Fluids, Volume 278
Author(s): Niccolò Tonicello, Andrea Lario, Gianluigi Rozza, Gianmarco Mengaldo
Publication date: 30 June 2024
Source: Computers & Fluids, Volume 278
Author(s): Mathilde Tavares, Christophe Josserand, Alexandre Limare, José M^{a} LopezHerrera, Stéphane Popinet
Publication date: 30 June 2024
Source: Computers & Fluids, Volume 278
Author(s): Shengsheng Xia, Yingjie Wei, Cong Wang
Publication date: 30 June 2024
Source: Computers & Fluids, Volume 278
Author(s): Judith Angel, Jörn Behrens, Sebastian Götschel, Marten Hollm, Daniel Ruprecht, Robert Seifried
Publication date: 30 June 2024
Source: Computers & Fluids, Volume 278
Author(s): Jaehee Chang, Kiyoung Kim, Haecheon Choi
Publication date: 30 June 2024
Source: Computers & Fluids, Volume 278
Author(s): Philip Heger, Daniel Hilger, Markus Full, Norbert Hosters
Publication date: 30 June 2024
Source: Computers & Fluids, Volume 278
Author(s): Nils Hoppe, Nico Fleischmann, Benedikt Biller, Stefan Adami, Nikolaus A. Adams
Publication date: Available online 14 June 2024
Source: Computers & Fluids
Author(s): Giuseppe Sirianni, Alberto Guardone, Barbara Re, Rémi Abgrall
Publication date: Available online 10 June 2024
Source: Computers & Fluids
Author(s): Nandan Sarkar, Siddharth D. Sharma, Suman Chakraborty, Somnath Roy
Publication date: Available online 15 June 2024
Source: Computers & Fluids
Author(s): Luan M. Vieira, Matteo Giacomini, Ruben Sevilla, Antonio Huerta
A fullyexplicit, iterationfree, weaklycompressible method to simulate immiscible incompressible twophase flows is presented. This computationally efficient algorithm combines the general pressure equation (GPE), modified switching technique for advection and capturing of surfaces (MSTACS) which is an algebraic volumeoffluid approach for interface capturing and the operatorsplit (OS) method. It can accurately handle problems involving a range of density and viscosity ratios and surface tension effects. Since it is fullyexplicit, the algorithm is highly scalable for parallel computing.
We present a fullyexplicit, iterationfree, weaklycompressible method to simulate immiscible incompressible twophase flows. To update pressure, we circumvent the computationally expensive Poisson equation and use the general pressure equation which is solved explicitly. In addition, a less diffusive algebraic volumeoffluid approach is used as the interface capturing technique and in order to facilitate improved parallel computing scalability, the technique is discretised temporally using the operatorsplit methodology. Our method is fullyexplicit and stable with simple local spatial discretization, and hence, it is easy to implement. Several two and threedimensional canonical twophase flows are simulated. The qualitative and quantitative results prove that our method is capable of accurately handling problems involving a range of density and viscosity ratios and surface tension effects.
A modified fifthorder WENOZ scheme is developed by modifying the nonnormalized nonlinear weights of a reformulated fifthorder adaptive order WENO scheme. The modified scheme has significantly higher resolution compared with the existing WENOZ+ and WENOZ+M schemes with a little more computational overhead per time step.
A modified fifthorder WENOZ scheme is proposed by analogy with the nonnormalized weights of the reformulated fifthorder adaptive order (AO) WENO scheme. We show that if the original fifthorder WENOAO scheme is rewritten as the form of the conventional WENO combination, the resulting nonnormalized weights can be divided into three parts: a constant one term, a local stencil smoothness measure term and a global stencil smoothness measure term. In order to make use of the latter two terms for constructing a modified WENOZ scheme with enhanced performance, we change the form of the third term and introduce an adaptive scaling factor to adjust the contributions from the second and third terms. Numerical examples show that the modified fifthorder WENOZ scheme has the advantage of high resolution in smooth regions and sharp capturing of discontinuities, and it can obtain evidently better results for shocked flows with smallscale structures compared with the recently developed WENOZ+ and WENOZ+M schemes.
A datadriven turbulence model that solves the Reynolds stress transport equation along with the momentum balance is developed, the model is fueled by a sourceterm that combines the unclosed terms in the Reynolds stress tensor equation. Using neural networks, trained with direct numerical simulations data, we were able to predict this sourceterm and correct the Reynolds averaged Navier–Stokes flow in the squareduct. This is the first time that machine learning corrections of turbulent flows are driven by a coupled transport equation combined with the momentum equations.
The long lasting demand for better turbulence models and the still prohibitively computational cost of highfidelity fluid dynamics simulations, like direct numerical simulations and large eddy simulations, have led to a rising interest in coupling available highfidelity datasets and popular, yet limited, Reynolds averaged Navier–Stokes simulations through machine learning (ML) techniques. Many of the recent advances used the Reynolds stress tensor or, less frequently, the Reynolds force vector as the target for these corrections. In the present work, we considered an unexplored strategy, namely to use the modeled terms of the Reynolds stress transport equation as the target for the ML predictions, employing a neural network approach. After that, we solve the coupled set of governing equations to obtain the mean velocity field. We apply this strategy to solve the flow through a square duct. The obtained results consistently recover the secondary flow, which is not present in the baseline simulations that used the κ−ϵ$$ \kappa \epsilon $$ model. The results were compared with other approaches of the literature, showing a path that can be useful in the seek of more universal models in turbulence.
The auxiliary boundary condition must be specified for the discontinuous finite element methods (e.g., DG, SD, FR/CPR) to evaluate the solution gradients. Since the velocity gradient near the wall is not fully resolved in the WMLES grid, we recommend a looser auxiliary condition than the usual noslip condition. Superior performance of the proposed WMLES framework was confirmed for a benchmarking nonequilibrium periodic hill flow with curvilinear walls compared to the results of an algebraic WMLES and a DDES.
To robustly and accurately simulate wallbounded turbulent flows at high Reynolds numbers, we propose suitable boundary treatments for wallmodeled largeeddy simulation (WMLES) coupled with a highorder flux reconstruction (FR) method. First, we show the need to impose an auxiliary boundary condition on auxiliary variables (solution gradients) that are commonly introduced in highorder discontinuous finite element methods (DFEMs). Auxiliary boundary conditions are introduced in WMLES, where the grid resolution is too coarse to resolve the inner layer of a turbulent boundary layer. Another boundary treatment to further enhance stability with underresolved grids, is the use of a modal filter only in the wallnormal direction of walladjacent cells to remove the oscillations. A grid convergence study of turbulent channel flow with a high Reynolds number (Reτ≈5200$$ R{e}_{\tau}\approx 5200 $$) shows that the present WMLES framework accurately predicts velocity profiles, Reynolds shear stress, and skin friction coefficients at the grid resolutions recommended in the literature. It was confirmed that a small amount of filtering is sufficient to stabilize computation, with negligible influence on prediction accuracy. In addition, nonequilibrium periodic hill flow with a curved wall, including flow separation, reattachment, and acceleration at a high Reynolds number (Reh≈37,000$$ R{e}_h\approx 37,000 $$), is reported. Considering stability and the prediction accuracy, we recommend a loose auxiliary wall boundary conditions with a less steep velocity gradient for WMLES using highorder DFEMs.
This paper develops a three dimensional phase field model, based on a recently improved Allen–Cahn phase field model. The model was discretized using a finite difference method on a halfstaggered grid. More important, interfacial tension was expressed in a potential form. The model was tested against a number of cases and was applied to impacts in various conditions. Besides, the model was parallelized using the shared memory parallelism, OpenMP, to facilitate computation.
The traditional Allen–Cahn phase field model doesn't conserve mass and is mostly used in solidification microstructure formation. However, a recently modified Allen–Cahn phase field model has riveted the attention of the academic community. It was obtained by subtracting the curvaturedriven flow term from the advective Allen–Cahn phase field model, and thus improves the boundedness of the phase field. More recently, the model has been further refined with the recovered signed distance function to compute interface normal vectors. This paper develops a three dimensional phase field model, based on the abovementioned Allen–Cahn phase field model. The model was discretized using a finite difference method on a halfstaggered grid. More important, interfacial tension was expressed in a potential form. The model was tested against a number of cases and was applied to impacts in various conditions. Besides, the model was parallelized using the shared memory parallelism, OpenMP, to facilitate computation.
The boundary data immersion method smears the fluidstructure interface in the smoothing region and incurs deviations. The proposed algorithm switches to lower order difference schemes near the interfaces and applies adaptive mesh refining there to compensate the accuracy loss.
The fluidstructure interaction is simulated using the boundary data immersion method. As the fluidstructure interface is smeared in the smoothing region, deviations are incurred in fluid simulations. For compressible flow, high order difference schemes with more mesh cells for the stencils are usually employed to achieve high overall accuracy, but near interfaces it requires wider smoothing region of several mesh cells for computational stability and hence lowers its accuracy significantly. To address this issue, the proposed algorithm switches to lower order difference schemes near the interfaces and applies adaptive mesh refining there to compensate the accuracy loss. Implemented with Structured Adaptive Mesh Refinement Application Infrastructure (SAMRAI), the algorithm shows notable improvement in the overall accuracy and efficiency in cases such as channel flow and flow past a cylinder. The algorithm is used to simulate the shock wave past a fixed or free cylinder with Ma =2.67$$ =2.67 $$ and Re =1482$$ =1482 $$, which reveals the relaxation process and the temporal evolution of the drag coefficient, it goes through a valley and maintains at relatively high value for the fixed cylinder, while that of the free cylinder tends to decrease in fluctuation which is found to be caused by the interaction between the forward moving cylinder and vortexes in the unsteady wake.
In this article, the implicitexplicit RK time discretization coupled with LDG spatial discretization numerical algorithm for the micropolar fluid equations are presented. Moreover, the stability of the firstorder and secondorder fully discrete method are proved. Finally, the numerical experiments are given to verify the theoretical order and effectiveness of the presented method.
In this article, the spatial local discontinuous Galerkin (LDG) approximation coupled with the temporal implicitexplicit Runge–Kutta (RK) evolution for the micropolar fluid equations are adopted to construct the discretization method. To avoid the incompressibility constraint, the artificial compressibility strategy method is used to convert the micropolar fluid equations into the Cauchy–Kovalevskaja type equations. Then the LDG method based on the modal expansion and the implicitexplicit RK method are properly combined to construct the expected thirdorder method. Theoretically, the unconditionally stable of the fully discrete method are derived in multidimensions for triangular meshs. And the numerical experiments are given to verify the theoretical and effectiveness of the presented methods.
Cascaded collision operator is adapted to multilayer shallow water flows. Two sets of particle distribution function (PDF) are solved separately, with external forces modeling the mutual actions between the two layers. The model is able to reproduce ideal dam break flows and gravity currents.
Many environmental phenomena, such as flows in rivers or in coastal region can be characterised by means of the ‘shallow approach’. A multilayer scheme allows to extend it to density layered shallow water flows (e.g., gravity currents). Although a variety of models allowing numerical investigation of single and multilayer shallow water flows, based on continuum and particle approaches, have been widely discussed, there are still some computational aspects that need further investigation. Focusing on the Lattice Boltzmann models (LBM), available multilayer models generally use the standard linear collision operator (CO). In this work we adopt a multi relaxation time (MRT) cascaded collision operator to develop a twolayered liquid LatticeBoltzmann model (CaLB2). Specifically, the model solves the shallow water equations, taking into account two separate sets of particle distribution function (PDF), one for each layer, solved separately. Layers are connected through coupling terms, defined as external forces that model the mutual actions between the two layers. The model is validated through comparisons with experimental and numerical results from test cases available in literature. First results are very promising, highlighting a good correspondence between simulation results and literature benchmarks.
We report the effect of three nondimensionalization approaches on the solution of the 2D differentially heated cavity problem. The governing equations were discretized using orthogonal collocation and solved via the Newton–Raphson method with LU factorization. Approach II was found to be the most suitable for nondimensionalization.
This work reports a numerical study on the effect of three nondimensionalization approaches that are commonly used to solve the classic problem of the 2D differentially heated cavity. The governing equations were discretized using orthogonal collocation with Legendre polynomials, and the resulting algebraic system was solved via Newton–Raphson method with LU factorization. The simulations were performed for Rayleigh numbers between 10^{3} and 10^{8}, considering the Prandtl number equal to 0.71 and a geometric aspect ratio equal to 1, analyzing the convergence and the computation time on the flow lines, isotherms and the Nusselt number. The mesh size that provides independent results was 51 × 51. Approach II was the most suitable for the nondimensionalization of the differentially heated cavity problem.
Publication date: 1 September 2024
Source: Journal of Computational Physics, Volume 512
Author(s): Bo Lin, Ying Ma, Chushan Wang
Publication date: 1 September 2024
Source: Journal of Computational Physics, Volume 512
Author(s): Zihao Zou, Xiaolin Zhong
Publication date: 1 September 2024
Source: Journal of Computational Physics, Volume 512
Author(s): Jan Nordström
Publication date: 1 September 2024
Source: Journal of Computational Physics, Volume 512
Author(s): Stefano Piccardo, Matteo Giacomini, Antonio Huerta
Publication date: 1 September 2024
Source: Journal of Computational Physics, Volume 512
Author(s): Haoyu Tang, Louis J. Durlofsky
Publication date: 1 September 2024
Source: Journal of Computational Physics, Volume 512
Author(s): Natan Hoffmann, Amareshwara Sainadh Chamarthi, Steven H. Frankel
Publication date: 1 September 2024
Source: Journal of Computational Physics, Volume 512
Author(s): Emmanuel Franck, Victor MichelDansac, Laurent Navoret
Publication date: 1 September 2024
Source: Journal of Computational Physics, Volume 512
Author(s): Tuan Anh Dao, Murtazo Nazarov
Publication date: 15 September 2024
Source: Journal of Computational Physics, Volume 513
Author(s): Sakthi Kumar Arul Prakash, Conrad Tucker
Publication date: 1 September 2024
Source: Journal of Computational Physics, Volume 512
Author(s): Qingzhou Shu, Qinglin Tang, Shaobo Zhang, Yong Zhang
This study explores coherent structures in a swirling turbulent jet. Stationary axisymmetric solutions of the Reynolds–Averaged Navier–Stokes equations at \(Re=200,000\) were obtained using an open source computational fluid dynamics code and the Spalart–Allmaras eddy viscosity model. Then, resolvent analysis with the same eddy viscosity field provided coherent structures of the turbulent fluctuations on the base flow. As in many earlier studies, a large gain separation is identified between the optimal and suboptimal resolvent modes, permitting a focus on the most amplified response mode and its corresponding optimal forcing. At zero swirl, the results indicate that the jet’s coherent response is dominated by axisymmetric ( \(m=0\) ) structures, which are driven by the usual Kelvin–Helmholtz shear amplification mechanism. However, as swirl is increased, different coherent structures begin to dominate the response. For example, double and triple spiral ( \(m=2\) and \(m=3\) ) modes are identified as the dominant structures when the axial and azimuthal velocity maxima of the base flow are comparable. In this case, distinct co and counterrotating \(m=2\) modes experience vastly different degrees of amplification. The physics of this selection process involve several amplification mechanisms contributing simultaneously in different regions of the mode. This is analysed in more detail by comparing the alignment between the wavevector of the dominant response mode and the principal shear direction of the base flow. Additional discussion also considers the development of structures along the exterior of the jet nozzle.
In open flow simulations, the dispersion characteristics of disturbances near synthetic boundaries can lead to unphysical boundary scattering interactions that contaminate the resolved flow upstream by propagating numerical artifacts back into the domain interior. This issue is exacerbated in flows influenced by real or apparent body forces, which can significantly disrupt the normal stress balance along outflow boundaries and generate spurious pressure disturbances. To address this problem, this paper develops a zeroparameter, physicsbased outflow boundary condition (BC) designed to minimize pressure scattering from body forces and pseudoforces and enhance transparency of the artificial boundary. This “balanced outflow BC” is then compared against other common BCs from the literature using example axisymmetric and threedimensional open swirling flow computations. Due to centrifugal and Coriolis forces, swirling flows are known to be particularly challenging to simulate in open geometries, as these apparent forces induce nontrivial hydrostatic stress distributions along artificial boundaries that cause scattering issues. In this context, the balanced outflow BC is shown to correspond to a geostrophic hydrostatic stress correction that balances the induced pressure gradients. Unlike the alternatives, the balanced outflow BC yields accurate results in truncated domains for both linear and nonlinear computations without requiring assumptions about wave characteristics along the boundary.
A combined dataassimilation and linear meanflow analysis approach is developed to estimate coherent flow fluctuations from limited meanflow measurements. It also involves ReynoldsAveraged Navier–Stokes (RANS) modelling to efficiently tackle turbulent flows. Considering timeaveraged Particle Velocimetry Image (PIV) measurements of the nearstall flow past a NACA0012 airfoil at an angle of attack of \(10^{\circ }\) and in the chordbased Reynolds number range \(4.3 \cdot 10^4 \le Re \le 6.4 \cdot 10^4\) , data assimilation is first employed to correct RANS equations that are closed by the SpalartAllmaras model. The outputs of this procedure are a full meanflow description that matches the PIV data and a consistent turbulence model that provides not only a mean eddyviscosity field but also the perturbations of the latter with respect to meanflow modifications. Global stability and resolvent analyses are then performed based on the soobtained mean flow and model to satisfactorily predict nearstall lowfrequency phenomena, as confirmed through comparison with the Spectral Proper Orthogonal Decomposition (SPOD) of the PIV measurements. This comparison highlights the benefits in taking into account variations in the turbulent eddyviscosity over a frozen approach for the correct estimation of the present coherent lowfrequency oscillations.
A numerical study of yieldstress fluids flowing in porous media is presented. The porous media is randomly constructed by nonoverlapping monodispersed circular obstacles. Two class of rheological models are investigated: elastoviscoplastic fluids (i.e. Saramito model) and viscoplastic fluids (i.e. Bingham model). A wide range of practical Weissenberg and Bingham numbers is studied at three different levels of porosities of the media. The emphasis is on revealing some physical transport mechanisms of yieldstress fluids in porous media when the elastic behaviour of this kind of fluids is incorporated. Thus, computations of elastoviscoplastic fluids are performed and are compared with the viscoplastic fluid flow properties. At a constant Weissenberg number, the pressure drop increases both with the Bingham number and the solid volume fraction of obstacles. However, the effect of elasticity is less trivial. At low Bingham numbers, the pressure drop of an elastoviscoplastic fluid increases compared to a viscoplastic fluid, while at high Bingham numbers we observe drag reduction by elasticity. At the yield limit (i.e. infinitely large Bingham numbers), elasticity of the fluid systematically promotes yielding: elastic stresses help the fluid to overcome the yield stress resistance at smaller pressure gradients. We observe that elastic effects increase with both Weissenberg and Bingham numbers. In both cases, elastic effects finally make the elastoviscoplastic flow unsteady, which consequently can result in chaos and turbulence.
We perform a resolvent analysis of a compressible turbulent jet, where the optimisation domain of the response modes is located in the acoustic field, excluding the hydrodynamic region, in order to promote acoustically efficient modes. We examine the properties of the acoustic resolvent and assess its potential for jetnoise modelling, focusing on the subsonic regime. Resolvent forcing modes, consistent with previous studies, are found to contain supersonic waves associated with Mach wave radiation in the response modes. This differs from the standard resolvent in which hydrodynamic instabilities dominate. We compare resolvent modes with SPOD modes educed from LES data. Acoustic resolvent response modes generally have better alignment with acoustic SPOD modes than standard resolvent response modes. For the optimal mode, the angle of the acoustic beam is close to that found in SPOD modes for moderate frequencies. However, there is no significant separation between the singular values of the leading and suboptimal modes. Some suboptimal modes are furthermore shown to contain irrelevant structure for jet noise. Thus, even though it contains essential acoustic features absent from the standard resolvent approach, the SVD of the acoustic resolvent alone is insufficient to educe a lowrank model for jet noise. But because it identifies the prevailing mechanisms of jet noise, it provides valuable guidelines in the search of a forcing model (Karban et al. in J Fluid Mech 965:18, 2023).
This work presents a methodology to extract coherent structures from highspeed schlieren images of turbulent twin jets which are more physically interpretable than those obtained with currently existing techniques. Recently, Prasad and Gaitonde (J Fluid Mech 940:1–11, 2022) introduced an approach which employs the momentum potential theory of Doak (J Sound Vib 131(1):67–90, 1989) to compute potential (acoustic and thermal) energy fluctuations from the schlieren images by solving a Poisson equation, and combines it with spectral proper orthogonal decomposition (SPOD) to educe coherent structures from the momentum potential field instead of the original schlieren field. While the latter field is dominated by a broad range of vortical fluctuations in the turbulent mixing region of unheated highspeed jets, the momentum potential field is governed by fluctuations which are intimately related to acoustic emission, and its spatial structure in the frequency domain is very organized. The proposed methodology in this paper improves the technique of Prasad and Gaitonde (J Fluid Mech 940:1–11, 2022) in three new ways. First, the solution of the Poisson equation is carried out in the frequencywavenumber domain instead of the timespace domain, which simplifies and integrates the solution of the Poisson equation within the SPOD framework based on momentum potential fluctuations. Second, the issue of solving the Poisson equation on a finite domain with ad hoc boundary conditions is explicitly addressed, identifying and removing those unphysical harmonic components introduced in the solution process. Third, the solution of the SPOD problem in terms of momentum potential fluctuations is used to reconstruct schlieren SPOD fields associated with each mode, allowing the visualization of the obtained coherent structures also in terms of the density gradient. The method is applied here to schlieren images of a twinjet configuration with a small jet separation at two supersonic operation conditions: a perfectlyexpanded and an overexpanded one. The SPOD modes based on momentum potential fluctuations retain the wavepacket structure including the direct Machwave radiation, together with upstream and downstreamtraveling acoustic waves, similar to SPOD modes based on the schlieren images. However, for the same dataset, they result in a lowerrank decomposition than schlierenbased SPOD and provide an effective separation of twinjet fluctuations into independent toroidal and flapping oscillations that are recovered as different SPOD modes. These coherent structures are more consistent with twinjet wavepacket models available in the literature than those originally obtained with direct schlierenbased SPOD, facilitating their interpretation and comparison against theoretical analyses.
We present an extension of the RSVD \(\Delta t\) algorithm initially developed for resolvent analysis of statistically stationary flows to handle harmonic resolvent analysis of timeperiodic flows. The harmonic resolvent operator, as proposed by Padovan et al. (J Fluid Mech 900, 2020), characterizes the linearized dynamics of timeperiodic flows in the frequency domain, and its singular value decomposition reveals forcing and response modes with optimal energetic gain. However, computing harmonic resolvent modes poses challenges due to (i) the coupling of all \(N_{\omega }\) retained frequencies into a single harmonic resolvent operator and (ii) the singularity or nearsingularity of the operator, making harmonic resolvent analysis considerably more computationally expensive than a standard resolvent analysis. To overcome these challenges, the RSVD \(\Delta t\) algorithm leverages time stepping of the underlying timeperiodic linearized Navier–Stokes operator, which is \(N_{\omega }\) times smaller than the harmonic resolvent operator, to compute the action of the harmonic resolvent operator. We develop strategies to minimize the algorithm’s CPU and memory consumption, and our results demonstrate that these costs scale linearly with the problem dimension. We validate the RSVD \(\Delta t\) algorithm by computing modes for a periodically varying Ginzburg–Landau equation and demonstrate its performance using the flow over an airfoil.
This paper presents simulations of dambreak flows of Herschel–Bulkley viscoplastic fluids over complex topographies using the shallow water equations (SWE). In particular, this study aims to assess the effects of rheological parameters: powerlaw index (n), consistency index (K), and yield stress ( \(\tau _{c}\) ), on flow height and velocity over different topographies. Three practical examples of dambreak flow cases are considered: a dambreak on an inclined flat surface, a dambreak over a nonflat topography, and a dambreak over a wet bed (downstream containing an initial fluid level). The effects of bed slope and depth ratios (the ratio between upstream and downstream fluid levels) on flow behaviour are also analyzed. The numerical results are compared with experimental data from the literature and are found to be in good agreement. Results show that for both dry and wet bed conditions, the fluid front position, peak height, and mean velocity decrease when any of the three rheological parameters are increased. However, based on a parametric sensitivity analysis, the powerlaw index appears to be the dominant factor in dictating fluid behaviour. Moreover, by increasing the bed slope and/or depth ratio, the wavefrontal position moves further downstream. Furthermore, the presence of an obstacle is observed to cause the formation of an upsurge that moves in the upstream direction, which increases by increasing any of the three rheological parameters. This study is useful for an indepth understanding of the effects of rheology on catastrophic gravitydriven flows of nonNewtonian fluids (like lava or mud flows) for risk assessment and mitigation.
Employing direct numerical simulations, we investigate water and waterglycerol (85 wt%) droplets ( \(\sim \) 25 µL) moving on smooth surfaces, with contact angles of around 90 \(^{\circ }\) , at varying inclinations. Our focus is on elucidating the relative contribution of local viscous forces in the wedge and bulk regions in droplets to the total viscous force. We observe that, for fastmoving droplets, both regions contribute comparably, while the contribution of the wedge region dominates in slowmoving cases. Comparisons with existing estimates reveal the inadequacy of previous predictions in capturing the contributions of wedge and bulk viscous forces in fastmoving droplets. Furthermore, we demonstrate that droplets with identical velocities can exhibit disparate viscous forces due to variations in internal fluid dynamics.
We study generalised quasilinear (GQL) approximations applied to turbulent plane Couette flow. The GQL framework is explored in conjunction with a Galerkin reducedorder model (ROM) recently developed by Cavalieri and Nogueira (Phys Rev Fluids 7:102601, 2022), which considers controllability modes of the linearised Navier–Stokes system as basis functions, representing coherent structures in the flow. The velocity field is decomposed into two groups: one composed by highcontrollability modes and the other by lowcontrollability modes. The former group is solved with the full nonlinear equations, whereas the equations for the latter are linearised. We also consider a new GQL framework wherein the linearised equations for the lowcontrollability modes are driven by nonlinear interactions of modes in the first group, which are characterised by largescale coherent structures. It is shown that GQLROMs successfully recover the statistics of the full model with relatively high controllability thresholds and sparser nonlinear operators. Driven GQLROMs were found to converge more rapidly than standard GQL approximations, providing accurate description of the statistics with a larger number of linearised modes. This indicates that the forcing of linearised flow structures by largescale coherent structures is an important feature of turbulence dynamics that should be considered in GQL models. The results presented here reveal that further model reductions are attainable with GQLROMs, which can be valuable to extend these models to larger Reynolds numbers.