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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: 15 August 2024
Source: Computers & Fluids, Volume 280
Author(s): A. NavasMontilla, J. Guallart, P. SolánFustero, P. GarcíaNavarro
Publication date: 15 August 2024
Source: Computers & Fluids, Volume 280
Author(s): Chen Chen, Yu Sun
Publication date: 15 August 2024
Source: Computers & Fluids, Volume 280
Author(s): Ertiza Hossain Shopnil, Md. Nadeem Azad, Jahid Emon, A.K.M. Monjur Morshed
Publication date: 15 August 2024
Source: Computers & Fluids, Volume 280
Author(s): Will Trojak, Tarik Dzanic
Publication date: 15 August 2024
Source: Computers & Fluids, Volume 280
Author(s): Ke Zhang, Yiqing Shen
Publication date: 15 August 2024
Source: Computers & Fluids, Volume 280
Author(s): Arash Hajisharifi, Rahul Halder, Michele Girfoglio, Andrea Beccari, Domenico Bonanni, Gianluigi Rozza
Publication date: 15 August 2024
Source: Computers & Fluids, Volume 280
Author(s): Megala Anandan, S.V. Raghurama Rao
Publication date: 15 August 2024
Source: Computers & Fluids, Volume 280
Author(s): J.M. Catalán, S. Olivieri, M. GarcíaVillalba, O. Flores
Publication date: 15 August 2024
Source: Computers & Fluids, Volume 280
Author(s):
Publication date: Available online 25 July 2024
Source: Computers & Fluids
Author(s): Xiang Song, Linlin Fei, Haonan Peng, Xiaolong He
Firstly, an equivalent weighting formulation of WCNS is presented by explicitly including the wholepoint stencil into the set of candidate stencils. Secondly, motivated by the reorganization, the WCNSCU6 scheme is achieved in a more straightforward way. Thirdly, by introducing a TENO selection procedure in the framework of WCNSCU6Simplified, a TCNS6Simplified scheme is proposed, the resolution of which is comparable with the excellent TENO6 scheme, while the computational cost is much lower.
Weighted compact nonlinear schemes (WCNSs) are a popular family of highresolution shockcapturing schemes for simulating compressible flows, of which the nonlinear interpolation procedure is dominant for the performance. In this work, a simplified weighting strategy is introduced for the nonlinear interpolation procedure. Firstly, an equivalent weighting formulation of WCNS is presented by explicitly including the wholepoint stencil into the set of candidate stencils. Secondly, motivated by the reorganization of WCNS, the WCNSCU6 scheme is achieved in a more straightforward way. Thirdly, by introducing a TENO selection procedure in the framework of WCNSCU6Simplified, a TCNS6Simplified scheme is proposed, the resolution of which is comparable with the excellent TENO6 scheme, while the computational cost is much lower. The simplified schemes exhibit more outstanding, at least comparable, fidelity than the original schemes, however, with superior characteristics in terms of efficiency and simplicity. A variety of benchmark test problems are studied to demonstrate the behaviour of the simplified weighting strategy.
I propose a new framework of Lagrangian schemes to unify the SGH and CCH methods in one dimension. The scheme neither contains empirical parameters often contained in the SGH method nor solves Riemann problems frequently presented in the CCH method, which is a big difference from existing SGH/CCH methods and more general. The scheme is a new way to build the connection between SGH and CCH methods.
This paper focuses on a general computational framework to unify both Lagrangian staggeredgrid hydrodynamic (SGH) and cellcentered hydrodynamic (CCH) methods. One challenge is that artificial viscosity has contained empirical parameters in the SGH method for seven decades. To address this challenge, a new relationship between pressure and velocity is constructed using specific volume as a medium. Another challenge is that entropy is increasing in isentropic flows for the CCH method. To overcome this second challenge, the forces acting on a target cell are split into linear and quadratic terms in the CCH method. The numerical results of the two methods are almost identical. The scheme is more general than both existing SGH and CCH methods.
Waveletbased physicsinformed neural networks without utilizing any labeled data sets are employed to examine the study of nonNewtonian Maxwell fluid flow over a curved surface. We have used three different models to approximate different solutions to nonlinear coupled equations that were trained parallely. We have also employed a wavelet activation function for improved accuracy. The proposed method is very flexible to implement in comparison to the existing numerical schemes and gives accurate results for all the flow parameters.
Maxwell fluid flow over a curved surface with the impacts of nonlinear convection and radiation, temperaturedependent properties, and magnetic field are investigated. The governing equations of the physical system are solved using wavelet based physics informed neural network, a machine learning technique. This is an unsupervised method, and the solutions have been obtained without knowing the numerical solution to the problem. Given the nonlinearity of the coupled equations, the methodology used is flexible to implement, and the activation function used improves the accuracy of the solution. We approximate the unknown functions using different neural network models and determine the solution by training the network. The special case of the obtained results is examined with the available results in the literature for validation of the proposed methodology. It is observed that the proposed approach gives reliable results for the analyzed problem of study. Further, an analysis of the influence of flow parameters (deborah number, variable thermal conductivity and viscosity parameter, velocity slip parameter, temperature ratio parameter, suction parameter, and convection parameters) on temperature and fluid flow velocity is carried out. It is observed that as the flow parameter Deborah number, velocity slip parameter, and viscosity parameter increase, there is a decline in velocity and an enhancement in temperature. This study of fluid flow over a curved surface has applications in the polymer industry, which plays an important role in the manufacturing of contact lenses.
A directionallysplit volumeoffluid (VOF) technique is proposed to study the evolution of interfaces under selfgenerated curvaturedependent velocity. A topological volume conservation penalty is incorporated in the geometric VOF methodology by altering the advection equation using variational principles. Parallel implementation of the approach is validated with canonical level set (LS) evolution problems involving interface motion in the normal direction. Constrained curvature flow of different geometries is demonstrated with emphasis on the required numerical components for an accurate and stable solution.
A directionallysplit volumeoffluid (VOF) methodology for evolving interfaces under curvaturedependent speed is devised. The interface is reconstructed geometrically and the volume fraction is advected with a technique to incorporate a topological volume conservation constraint. The proposed approach uses the idea that the role of curvature in a speed function V$$ \mathbf{V} $$ is analogous to the role of viscosity in the corresponding hyperbolic conservation law to propagate complex interfaces where singularities may exist. The approach has the advantage of simple implementation and straightforward extension to more complex multiphase systems by formulating the interface evolution problem using energy functionals to derive an expression for the interfaceadvecting velocity. The numerical details of the volumeoffluid based formulation are discussed with emphasis on the importance of curvature estimation. Finally, canonical curves and surfaces traditionally investigated by the level set (LS) method are tested with the devised approach and the results are compared with existing work in LS.
The numerical study of flow around the multiple spheres is investigated by using a directforcing immersed boundary method. It conducted numerical analyses of flow past single sphere, tandem arrangements of two spheres, and a uniform array of nine spheres, under various flow conditions. An important characteristic of flow over the multiple spheres is devised by comparing with the drag, transverse and lift coefficients, as well as vortex shedding.
The numerical study of flow around a pair of spheres and a square array of spheres is investigated by using a directforcing immersed boundary method. Using high resolution threedimensional computations, we analyzed the flow around several configurations: a sphere, a pair of spheres in a tandem arrangement with centertocenter streamwise ratio L/D ranging from 1 to 6, and a square array with 9 spheres in a uniform arrangement. In the latter case, we explore the ratio of array diameter (D _{G}) to sphere diameter (D) at 4, 5, 6 and 7. The centertocenter streamwise and transverse pitch is the same, varied from L/D = 1.5, 2, 2.5 to 3, and they were arranged in a square periodic array to allow uniform distribution within the array. Based on the effective directforcing immersed boundary projection method, the fractional time marching methodology is applied for solving four field variables involving three velocities and one pressure component. The pressure Poisson equation is advanced in space by using the fast Fourier transform (FFT) and a tridiagonal matrix algorithm (TDMA), effectively solving for the diagonally dominant tridiagonal matrix equations. A directforcing immersed boundary method is involved to treat the interfacial terms by adding the appropriate sources as force function at the boundary, separating the phases. Geometries featuring the stationary solid obstacles in the flow are embedded in the Cartesian grid with special discretizations near the embedded boundary using a discrete Dirac delta function to ensure the accuracy of the solution in the cut cells. An important characteristic of flow over the multiple spheres is devised by comparing with the drag and lift coefficients, as well as vortex shedding.
A rigidperfectly plastic Bingham model is presented, and its implementation into an FVVoF procedure is validated for cohesive and noncohesive materials featuring different angles of repose. A close agreement of the predicted soil surface with experimental data is obtained for noncohesive material, and the failure lines, calculated from the introduced Euler–Almansi strain measure, coincide well with the experimental data. To verify the applicability to realistic problems, the current procedure is successfully verified in largescale dimensions against SPH simulations that use a more sophisticated material model.
Granular flow problems characterized by large deformations are widespread in various applications, including coastal and geotechnical engineering. The paper deals with the application of a rigidperfectly plastic twophase model extended by the Drucker–Prager yield criterion to simulate granular media with a finite volume flow solver (FV). The model refers to the combination of a Bingham fluid and an Eulerian strain measure to assess the failure region of granular dam slides. A monolithic volumeoffluid (VoF) method is used to distinguish between the air and granular phases, both governed by the incompressible Navier–Stokes equations. The numerical framework enables modeling of large displacements and arbitrary shapes for largescale applications. The displayed validation and verification focuses on the rigidperfectly plastic material model for noncohesive and cohesive materials with varying angles of repose. Results indicate a good agreement of the predicted soil surface and strain results with experimental and numerical data.
The staggered Legendre spectral element method is extended to the quasistatic magnetohydrodynamic (MHD) setting, which relative to hydrodynamics involves an additional Poissonlike problem for the electric potential. The proposed discretization is suitable for largescale simulations involving threedimensional geometries of arbitrary complexity that feature turbulent and/or transitional dynamics. The numerical solutions are shown to converge exponentially with polynomial order.
The classical staggered ℙNℙN−2$$ {\mathbb{P}}_N\hbox{} {\mathbb{P}}_{N2} $$ spectral element method (SEM) is revisited and extended to quasistatic magnetohydrodynamic (MHD) flows. In this realm, which is valid in the limit of vanishing magnetic Reynolds number, the evaluation of the Lorentz force in the momentum equation requires the electric current density, governed by Ohm's law and a charge conservation condition derived from Ampère's law, to be determined. Once discretized with the SEM, this translates into solving one additional problem for the electric potential involving the socalled consistent Poisson operator. The method is well suited for fully threedimensional flows in complex geometries. Changes in resolution requirements aside, consideration of the electromagnetic quantities is estimated to increase the computational cost associated with MHD by about 40% relative to hydrodynamics. The accuracy and the capabilities of the scheme is demonstrated on a set of common flows from the MHD literature. Exponential convergence with polynomial order is confirmed for the electric current density.
A large Courant–Friedrichs–Lewy (CFL) algorithm is presented for the explicit, finite volume solution of hyperbolic systems of conservation laws, with a focus on the shallow water equations. The scheme allows for CFL values up to 100, with reduced numerical diffusion compared to the original Godunov scheme. This plot shows a sample simulation for the 1D advection equation reported in the article.
A large Courant–Friedrichs–Lewy (CFL) algorithm is presented for the explicit, finite volume solution of hyperbolic systems of conservation laws, with a focus on the shallow water equations. The Riemann problems used in the flux computation are determined using averaging kernels that extend over several computational cells. The usual CFL stability constraint is replaced with a constraint involving the kernel support size. This makes the method unconditionally stable with respect to the size of the computational cells, allowing the computational mesh to be refined locally to an arbitrary degree without altering solution stability. The practical implementation of the method is detailed for the shallow water equations with topographical source term. Computational examples report applications of the method to the linear advection, Burgers and shallow water equations. In the case of sharp bottom discontinuities, the need for improved, wellbalanced discretisations of the geometric source term is acknowledged.
A novel interface reconstruction method is proposed to reconstruct the interface from volume fractions for use with Geometric VolumeofFluid algorithms. The algorithm uses a Marching Cube based isoAlpha method which uses a lookuptable based approach enabling fast and robust interface reconstruction. We highlight issues pertaining to the bracketability of the solution for certain interface configurations. These cases are isolated and handled using a ParkerYoung based interface reconstruction method. Finally static and dynamic interface reconstruction cases are demonstrated.
In modelling twophase flows, accurate representation of interfaces is crucial. A class of methods for interface reconstruction are based on isosurface extraction, which involves a noniterative, interpolation based approach. These approaches have been shown to be faster by an order of magnitude than the conventional PLIC schemes. In this work, we present a new isosurface extraction based interface reconstruction scheme based on the Marching Cubes algorithm (MC), which is commonly used in computer graphics for visualizing isosurfaces. The MC algorithm apriori lists and categorizes all possible interface configurations in a single grid cell into a Look Up Table (LUT), which makes this approach fast and robust. We also show that for certain interface configurations, the inverse problem of obtaining the isovalue from the cell volume fraction is not surjective, and a special treatment is required while handling these cases. We then demonstrate the capabilities of the method through benchmark cases for 2D and 3D static/dynamic interface reconstruction.
Publication date: Available online 2 August 2024
Source: Journal of Computational Physics
Author(s): Magnus Svärd
Publication date: Available online 2 August 2024
Source: Journal of Computational Physics
Author(s): Jonas Luther, Yijun Wang, Patrick Jenny
Publication date: Available online 2 August 2024
Source: Journal of Computational Physics
Author(s): Xavier Blanc, Francois Hermeline, Emmanuel Labourasse, Julie Patela
Publication date: Available online 2 August 2024
Source: Journal of Computational Physics
Author(s): Hamad El Kahza, William Taitano, JingMei Qiu, Luis Chacón
Publication date: Available online 2 August 2024
Source: Journal of Computational Physics
Author(s): Xu Guo, Shidong Jiang, Yunfeng Xiong, Jiwei Zhang
Publication date: Available online 2 August 2024
Source: Journal of Computational Physics
Author(s): Blaise Delmotte, Florencio Balboa Usabiaga
Publication date: Available online 2 August 2024
Source: Journal of Computational Physics
Author(s): Yang Kuang, Yedan Shen, Guanghui Hu
Publication date: Available online 25 July 2024
Source: Journal of Computational Physics
Author(s): Conghai Wu, Ruixuan Ma, Yimin Wang, Shuaibin Han, Shuhai Zhang
Publication date: Available online 20 July 2024
Source: Journal of Computational Physics
Author(s): Zhao Lanhao, Di Yingtang, Mao Jia
Publication date: Available online 29 July 2024
Source: Journal of Computational Physics
Author(s): C.B. TRANG, L. Jakabčin, T. Sayet, E. Blond, E. de Bilbao, A. Batakis
The effects of inlet Mach number on the unsteadiness of shockboundary layer interactions (SBLIs) over curved surfaces are investigated for a supersonic turbine cascade using wallresolved large eddy simulations. Three inlet Mach numbers, 1.85, 2.00, and 2.15 are considered at a chordbased Reynolds number 395,000. The curved walls of the airfoils impact the SBLIs due to the state of the incoming boundary layers and local pressure gradients. On the suction side, due to the convex wall, the boundary layer entering the SBLI evolves under a favorable pressure gradient and bulk dilatation. On the other hand, the concave wall on the pressure side imposes an adverse pressure gradient and bulk compression. Variations in the inlet Mach number induce different shock impingement locations, enhancing these effects. A detailed characterization of the suction side boundary layers indicates that a higher Mach number leads to larger shape factors, favoring separation and larger bubbles, while the reverse holds for the pressure side. A timefrequency analysis reveals the presence of intermittent events in the separated flow occurring predominantly at lowfrequencies on the suction side and at midfrequencies on the pressure side. Increasing the inlet Mach number leads to an increase in the time scales of the intermittent events on the suction side, which are associated with instants when highspeed streaks penetrate the bubble, causing local flow reattachment and bubble contractions. Instantaneous flow visualizations show the presence of streamwise vortices developing on the turbulent boundary layers on both airfoil sides and along the bubbles. These vortices influence the formation of the largescale longitudinal structures in the boundary layers, affecting the mass imbalance inside the separation bubbles.
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.
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 previously developed numericalmultilayer modeling approach for systems of governing equations is extended so that unwanted terms, resulting from vertical variations in certain background parameters, can be removed from the dispersionrelation polynomial associated with the system. The new approach is applied to linearized anelastic and compressible systems of governing equations for gravity waves including molecular viscosity and thermal diffusion. The ability to remove unwanted terms from the dispersionrelation polynomial is crucial for solving the governing equations when realistic background parameters, such as horizontal velocity and temperature, with strong vertical gradients, are included. With the unwanted terms removed, previously studied dispersionrelation polynomials, for which methods for defining upgoing and downgoing vertical wavenumber roots already exist, are obtained. The new methods are applied to a comprehensive set of mediumscale timewavepacket examples, with realistic background parameters, lower boundary conditions at 30 km altitude, and modeled wavefields extending up to 500 km altitude. Results from the compressible and anelastic model versions are compared, with compressible governingequation solutions understood as the more physically accurate of the two. The new methods provide significantly less computationally expensive alternatives to nonlinear timestep methods, which makes them useful for comprehensive studies of the behavior of viscous/diffusive gravity waves and also for large studies of cases based on observational data. Additionally, they generalize previously existing Fourier methods that have been applied to inviscid problems while providing a theoretical framework for the study of viscous/diffusive gravity waves.
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.
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.
Twodimensional freesurface flow past a submerged rectangular disturbance in an open channel is considered. The forced Korteweg–de Vries model of Binder et al. (Theor Comput Fluid Dyn 20:125–144, 2006) is modified to examine the effect of varying obstacle length and height on the response of the freesurface. For a given obstacle height and flow rate in the subcritical flow regime an analysis of the steady solutions in the phase plane of the problem determines a countably infinite set of discrete obstacle lengths for which there are no waves downstream of the obstacle. A rich structure of nonlinear behaviour is also found as the height of the obstacle approaches critical values in the steady problem. The stability of the steady solutions is investigated numerically in the timedependent problem with a pseudospectral method.
The generation mechanism of wall heat flux is one of the fundamental problems in supersonic/hypersonic turbulent boundary layers. A novel heat decomposition formula under the curvilinear coordinate was proposed in this paper. The new formula has wider application scope and can be applied in the configurations with grid deformed. The new formula analyzes the wall heat flux of an interaction between a shock wave and a turbulent boundary layer over a compression corner. The results indicated good performance of the formula in the complex interaction region. The contributions of different energy transport processes were obtained. While the processes by the mean profiles such as molecular stresses and heat conduction, can be ignored, the contributions by the turbulent fluctuations, such as Reynolds stresses and turbulent transfer of heat flux, were greatly increased. Additionally, the pressure work is another factor that affects the wall heat flux. The pressure work in the wallnormal direction is concentrated close to the reattachment point, while the pressure work in the streamwise direction acts primarily in the shear layer and the reattachment point.
In this paper we present a numerical scheme based on spectral collocation methods to investigate the flow of a piezoviscous fluid, i.e., a fluid in which the rheological parameters depend on the pressure. In particular, we consider an incompressible Navier–Stokes fluid with pressure dependent viscosity flowing in: (i) a twodimensional nonsymmetric planar channel; (ii) a threedimensional axisymmetric nonstraight conduit. For both cases we impose the Navier slip boundary conditions that can be reduced to the classical noslip condition for a proper choice of the slip parameter. We assume that the dependence of the viscosity on the pressure is of exponential type (Barus law), even though the model can be replaced by any other viscosity function. We write the mathematical problem (stress based formulation) and discretize the governing equations through a spectral collocation scheme. The advantage of this numerical procedure, which to the authors’ knowledge has never been used before for this class of fluids, lies in in the ease of implementation and in the accuracy of the solution. To validate our model we compare the numerical solution with the one that can be obtained in the case of small aspect ratio, i.e., the leading order lubrication solution. We perform some numerical simulation to investigate the effects of the pressuredependent viscosity on the flow. We consider different wall functions to gain insight also on the role played by the channel/duct geometry. In both cases (i), (ii) we find that the increase of the coefficient appearing in the viscosity function results in a global reduction of the flow, as physically expected.
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.