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Experimental observations unambiguously reveal quasi-frictionless water flow through nanometer-scale carbon nanotubes (CNTs). Classical fluid mechanics is deemed unfit to describe this enhanced flow, and recent investigations indicated that quantum mechanics is required to interpret the extremely weak water–CNT friction. In fact, by quantum scattering, water can only release discrete energy upon excitation of electronic and phononic modes in the CNT. Here, we analyze in detail how a traveling water molecule couples to both plasmon and phonon excitations within a sub-nanometer, periodic CNT. We find that the water molecule needs to exceed a minimum speed threshold of ∼50 m/s in order to scatter against CNT electronic and vibrational modes. Below this threshold, scattering is suppressed, as in standard superfluidity mechanisms. The scattering rates, relevant for faster water molecules, are also estimated. [ABSTRACT FROM AUTHOR]

The purpose of this research is to discuss a two-dimensional (2D), laminar, continuous flow of Casson liquid through a stretched porous wedge in the presence of chemical reaction and buoyancy effects over wedge. This research is aimed at analyzing chemically reacting flow of Casson model over a heated porous wedge in order to understand the features of dynamic wedge. The governing equations and involved parameters are nondimensionalized using transformations. Bvp4c, a numerical tool in Matlab is employed to assess the solution. Significant findings of the major dimensionless parameters on state profiles of velocity, temperature and concentration are drawn graphically. The principal results indicate the impacts of Casson parameter, Eckert and Prandtl number, R stretching parameter, K 1 chemical parameter, Sc Schmidt number, C mass transfer parameter, m wedge angle parameter on concentration, velocity and temperature field. The Sherwood, Nusselt number and skin friction numerical values are presented in tabular form. Major findings show that drag force at wedge declines for greater K 1 . Nusselt number shrinks for larger behavior for K 1 . Sherwood number upsurges for greater performance for chemical reaction parameter K 1 . Moreover, K 1 upsurges the temperature slowly but the impacts of K 1 on concentration show a decreasing behavior. [ABSTRACT FROM AUTHOR]

We introduce a vorticity Leray- α model with eddy viscosity depending on d (x , ∂ Ω) η where ∂ Ω is the boundary of the domain and η ∈ ] 0 ; 1 [ . We prove that this system admits fairly regular weak solutions converging when α goes to 0 to the solution of a reference system [ABSTRACT FROM AUTHOR]

In this paper, analytic solutions and dynamic properties of a variety of Boussinesq-type equations are established via the complete discrimination system for polynomial method. All the existing single traveling wave solutions to these equations as well as some new solutions are shown, and the Hamiltonian and topological properties to these equations are also presented. Considering the significance of the Boussinesq-type equations, our results would have wide applications in ocean engineering and fluid mechanics, like describing and predicting the solitary and periodic waves in various shallow water models. [ABSTRACT FROM AUTHOR]

The objective of this study was to explore the higher-order turbulence statistics of flow and turbulent length scales around a complex pier (CP) and compare the results with those for a simple pier (SP). The velocity data were recorded in a laboratory flume using particle image velocimetry (PIV). The PIV data were analysed to estimate the velocity fluctuations of third order, turbulence production and dissipation rates, turbulent length scales and the contributions of burst–sweep events to the total Reynolds shear stress around the piers mounted on a rigid flat surface. The skewness and advection coefficients indicated a more asymmetric distribution of velocity fluctuations for the SP than for the CP. Ejection and sweep events illustrated the dominance of similar strengths for an extended period, downstream of the piers. The upstream turbulent kinetic energy production was similar for both piers, while the upstream dissipation rate was higher for the CP. The length scales were greater at the upstream for the case of the SP while, downstream, they were greater for the CP. The findings of this work demonstrate the importance of a pile cap in restricting downward-moving flow by showing a lower magnitude of scour-inducing turbulence parameters for the CP as compared with the SP. [ABSTRACT FROM AUTHOR]

In smooth prismatic open channels, the boundary shear stress is obtained from continuity and momentum equations. The shear stress is a function of gravity, secondary flow and gradient velocity. In this research, semi-analytical equations were developed to estimate the average boundary shear stress in smooth rectangular and trapezoidal open channels with side slopes of 0.5, 1.0, 1.5 and 2.0 using conformal mapping techniques. After dividing the channel cross-section into bed and wall sub-sections, a previously presented method was used to estimate the average shear stress of the bed and the wall in open channels. For the studied case, in the first estimate of shear stress, the secondary current and constant eddy viscosity were neglected. After determining correction factors for secondary currents and eddy viscosity, the second estimation provided a good match with experimental measurements of the average shear stress for all aspect ratios. [ABSTRACT FROM AUTHOR]

We present a mathematical model of an experiment in which cells are cultured within a gel, which in turn floats freely within a liquid nutrient medium. Traction forces exerted by the cells on the gel cause it to contract over time, giving a measure of the strength of these forces. Building upon our previous work (Reoch et al. in J Math Biol 84(5):31, 2022), we exploit the fact that the gels used frequently have a thin geometry to obtain a reduced model for the behaviour of a thin, two-dimensional cell-seeded gel. We find that steady-state solutions of the reduced model require the cell density and volume fraction of polymer in the gel to be spatially uniform, while the gel height may vary spatially. If we further assume that all three of these variables are initially spatially uniform, this continues for all time and the thin film model can be further reduced to solving a single, non-linear ODE for gel height as a function of time. The thin film model is further investigated for both spatially-uniform and varying initial conditions, using a combination of analytical techniques and numerical simulations. We show that a number of qualitatively different behaviours are possible, depending on the composition of the gel (i.e., the chemical potentials) and the strength of the cell traction forces. However, unlike in the earlier one-dimensional model, we do not observe cases where the gel oscillates between swelling and contraction. For the case of initially uniform cell and gel density, our model predicts that the relative change in the gels’ height and length are equal, which justifies an assumption previously used in the work of Stevenson et al. (Biophys J 99(1):19–28, 2010). Conversely, however, even for non-uniform initial conditions, we do not observe cases where the length of the gel changes whilst its height remains constant, which have been reported in another model of osmotic swelling by Trinschek et al. (AIMS Mater Sci 3(3):1138–1159, 2016; Phys Rev Lett 119:078003, 2017). [ABSTRACT FROM AUTHOR]

• A partitioned fluid-structure interaction (FSI) framework is developed. • The meshless Vector Form Intrinsic Finite Element (VFIFE) is innovatively used as a solid solver. • Various benchmarks involving vortex-induced vibration phenomena are studied with the new algorithm. • Strong adaptability and accuracy of the VFIFE method are proved by numerical results. • An experimental case of flow past flexible curtain in a water tank is investigated. The Vector Form Intrinsic Finite Element (VFIFE) is an advanced meshless Lagrangian structural solver. This study introduces a partitioned framework to integrate Arbitrary Lagrangian-Eulerian and VFIFE methods into fluid-structure interaction (FSI) problems featured by large structural displacements and deformations. The VFIFE method enables the FSI simulations with deformable structures due to the nature of Lagrangian particles, which is challenging for traditional computational fluid mechanics techniques. In addition, the VFIFE can be effectively equipped with the partitioned coupling schemes because of the versatility of governing equations. In this algorithm system, several matrix problems in finite element methods and mapping and interpolation in the fluid-structure interface can be avoided. The significant potential of this algorithm in tackling complex FSI problems is demonstrated through various benchmarks, encompassing scenarios like Taylor-Green vortex, flow over a rigid cylinder (Re = 40 ∼ 200), forced vibration of a rigid cylinder, vortex-induced vibration (VIV) of an elastically mounted cylinder, and VIV of a rigid cylinder with an attached flexible cantilever beam. Finally, an experiment on flow past a curtain in a water tank is conducted to further evaluate the precision and stability of the current coupling strategy in three dimensions, demonstrating the feasibility of such methods in flexible structures. [ABSTRACT FROM AUTHOR]

With the rapid development of urban underground space, the construction of shield-driven cross-river twin tunnels is increasing, and the complex hydro-mechanical coupling effects and twin-tunnel interactions bring huge construction risks to such projects, which have attracted more and more attention. This study aims to understand the excavation effects induced by shield driving of cross-river twin tunnels through numerical simulation. A refined three-dimensional numerical model based on the fully coupled hydro-mechanical theory is established. The model considers the main components of the slurry pressure balance shield (SPBS) machine, including support force, jacking thrust, grouting pressure, shield-rock interaction and lining-grouting interaction, as well as the detailed construction process. The purpose is to examine the excavation effects during construction, including rock deformation around tunnels, the change in pore pressure, and the response of the lining. The results show the influence range of twin-tunnel excavation on rock deformation and pore pressure, as well as the modes of lining response. In addition, this study also systematically investigates the effects of water level fluctuation and burial depth on twin-tunnel excavation. The results indicate that the increase of water level or burial depth will enhance the excavation effects and strengthen the twin-tunnel interactions. These results provide useful insights for estimating the construction impact range and degree of twin tunnels, and serve as basic references for the design of cross-river twin tunnels. [ABSTRACT FROM AUTHOR]

In this work, we study a (2 + 1)-dimensional variable-coefficient Caudrey–Dodd–Gibbon–Kotera–Sawada equation in fluid mechanics. The new lump and lump-soliton solutions are obtained by the variable-coefficient polynomial function method. We used 3D graphs, contour plots and density graphs to show that the amplitude and velocity of solitons are affected by some variable coefficients. It is proved that the polynomial function method with variable coefficients is very direct and effective for solving lump-type solutions in variable coefficient integrable systems, and more new conclusions can be obtained. [ABSTRACT FROM AUTHOR]

Lid-driven cavity (LDC) flow is a significant area of study in fluid mechanics due to its common occurrence in engineering challenges. However, using numerical simulations (ANSYS Fluent) to accurately predict fluid flow and mixed convective heat transfer features, incorporating both a moving top wall and a heated hemispherical obstruction at the bottom, has not yet been attempted. This study aims to numerically demonstrate forced convection in a lid-driven square cavity (LDSC) with a moving top wall and a heated hemispherical obstacle at the bottom. The cavity is filled with a Newtonian fluid and subjected to a specific set of velocities (5, 10, 15, and 20 m/s) at the moving wall. The finite volume method is used to solve the governing equations using the Boussinesq approximation and the parallel flow assumption. The impact of various cavity geometries, as well as the influence of the moving top wall on fluid flow and heat transfer within the cavity, are evaluated. The results of this study indicate that the movement of the wall significantly disrupts the flow field inside the cavity, promoting excellent mixing between the flow field below the moving wall and within the cavity. The static pressure exhibits fluctuations, with the highest value observed at the top of the cavity of 1 m width (adjacent to the moving wall) and the lowest at 0.6 m. Furthermore, dynamic pressure experiences a linear increase until reaching its peak at 0.7 m, followed by a steady decrease toward the moving wall. The velocity of the internal surface fluctuates unpredictably along its length while other parameters remain relatively stable. [ABSTRACT FROM AUTHOR]

Oscillating-body viscometers have been used in the past to measure, in an absolute way, the viscosity of molten materials at high temperatures, from salts, metals, alloys, and semiconductors. However, the simultaneous use of basic or incomplete mathematical models, to mimic the experiment, and less careful engineering solutions for the design and operation of the instruments, led in the past to high discrepancies between the data obtained in several laboratories. This was caused by the incorrect use of the method's theory, less accurate solutions of the complex solutions, that involve solid state and fluid mechanics, and unreal instrument design. From these types of viscometers, oscillating-cup instruments have had the most success in measuring viscosity at high temperatures, and they will be the object of this paper. It was written as a resource for workers interested in transport properties of materials when considering its use for the absolute measurement of fluids viscosity in their work, or in judging the results of others' work when comparing data with their own. The paper starts with the most accurate theory of the method's description, followed by a discussion of its validity, application to instrument design, and consequent operation. Several constraints were identified and recommendations were made to minimize the effects of failing to satisfy them. Finally, a discussion about the uncertainty budget calculations for a real experiment is made. If all these points are followed in the design and operation of the instrument, results in global uncertainties Ur(η) between 0.02 and 0.04 are possible to obtain, up to high temperatures. If these constraints are not satisfied, erroneous measurements can be made, making comparisons and quality assessment difficult. [ABSTRACT FROM AUTHOR]

In this paper, a statistical physical derivation of thermodynamically consistent fluid mechanical equations is presented for non-isothermal viscous molecular fluids. The coarse-graining process is based on (i) the adiabatic expansion of the one-particle probability density function around local thermodynamic equilibrium, (ii) the assumption of decoupled particle positions and momenta, and (iii) the variational principle. It is shown that there exists a class of free energy functionals for which the conventional thermodynamic formalism can be naturally adopted for non-equilibrium scenarios, and describes entropy monotonic fluid flow in isolated systems. Furthermore, the analysis of the general continuum equations revealed the possibility of a non-local transport mode of energy in highly compressible dense fluids. [ABSTRACT FROM AUTHOR]

This manuscript delves into the examination of the stochastic fractional derivative of Drinfel'd-Sokolov-Wilson equation, a mathematical model applicable in the fields of electromagnetism and fluid mechanics. In our study, the proposed equation is through examined through various viewpoints, encompassing soliton dynamics, bifurcation analysis, chaotic behaviors, and sensitivity analysis. A few dark and bright shaped soliton solutions, including the unperturbed term, are also examined, and the various 2D and 3D solitonic structures are computed using the Tanh-method. It is found that a saddle point bifurcation causes the transition from periodic behavior to quasi-periodic behavior in a sensitive area. Further analysis reveals favorable conditions for the multidimensional bifurcation of dynamic behavioral solutions. Different types of wave solutions are identified in certain solutions by entering numerous values for the parameters, demonstrating the effectiveness and precision of Tanh-methods. A planar dynamical system is then created using the Galilean transformation, with the actual model serving as a starting point. It is observed that a few physical criteria in the discussed equation exhibit more multi-stable properties, as many multi-stability structures are employed by some individuals. Moreover, sensitivity behavior is employed to examine perturbed dynamical systems across diverse initial conditions. The techniques and findings presented in this paper can be extended to investigate a broader spectrum of nonlinear wave phenomena. [ABSTRACT FROM AUTHOR]

This work, in a pioneering approach, attempts to build a biometric system that works purely based on the fluid mechanics governing exhaled breath. We test the hypothesis that the structure of turbulence in exhaled human breath can be exploited to build biometric algorithms. This work relies on the idea that the extrathoracic airway is unique for every individual, making the exhaled breath a biomarker. Methods including classical multi-dimensional hypothesis testing approach and machine learning models are employed in building user authentication algorithms, namely user confirmation and user identification. A user confirmation algorithm tries to verify whether a user is the person they claim to be. A user identification algorithm tries to identify a user's identity with no prior information available. A dataset of exhaled breath time series samples from 94 human subjects was used to evaluate the performance of these algorithms. The user confirmation algorithms performed exceedingly well for the given dataset with over 97% true confirmation rate. The machine learning based algorithm achieved a good true confirmation rate, reiterating our understanding of why machine learning based algorithms typically outperform classical hypothesis test based algorithms. The user identification algorithm performs reasonably well with the provided dataset with over 50% of the users identified as being within two possible suspects. We show surprisingly unique turbulent signatures in the exhaled breath that have not been discovered before. In addition to discussions on a novel biometric system, we make arguments to utilise this idea as a tool to gain insights into the morphometric variation of extrathoracic airway across individuals. Such tools are expected to have future potential in the area of personalised medicines. [ABSTRACT FROM AUTHOR]

We are interested in the stability analysis of two-dimensional incompressible inviscid fluids. Specifically, we revisit a known recent result on the stability of Yudovich's solutions to the incompressible Euler equations in |$L^{\infty }([0,T];H^{1})$| by providing a new approach to its proof based on the idea of compactness extrapolation and by extending it to the whole plane. This new method of proof is robust and, when applied to viscous models, leads to a remarkable logarithmic improvement on the rate of convergence in the vanishing viscosity limit of two-dimensional fluids. Loosely speaking, this logarithmic gain is the result of the fact that, in appropriate high-regularity settings, the smoothness of solutions to the Euler equations at times |$t\in [0,T)$| is strictly higher than their regularity at time |$t=T$|⁠. This "memory effect" seems to be a general principle that is not exclusive to fluid mechanics. It is therefore likely to be observed in other setting and deserves further investigation. Finally, we also apply the stability results on Euler systems to the study of two-dimensional ideal plasmas and establish their convergence, in strong topologies, to solutions of magnetohydrodynamic systems, when the speed of light tends to infinity. The crux of this asymptotic analysis relies on a fine understanding of Maxwell's system. [ABSTRACT FROM AUTHOR]

The turbulent jet plays an important role in fluid mechanics since it is a prototype of free turbulent flow which presents many unsolved problems, among which the absence of closure of the governing equations. Despite the chaotic nature of turbulence, it is characterized by the existence of many universal structures, in particular dimensionless invariants such as its opening angle or the correlation coefficient of velocities. After having given new exact solutions of the Reynolds Averaged Navier–Stokes equations (RANS), we suggest a solution to this puzzle in the scale-relativity framework. In this theory, the time derivative of the Navier–Stokes equations is integrated in terms of a macroscopic Schrödinger equation acting in velocity-space. This equation involves a constant ℏ v which can be identified with the energy dissipation rate, while the pressure gradient manifests itself as a quantum harmonic oscillator (QHO) potential. The squared modulus of its solutions yields the probability density function (PDF) of velocities. The Reynolds stresses can then be derived from this PDF, so that the closure problem is solved in this case. This allows us to obtain a theoretical prediction for the turbulent intensity radial profile (and therefore for the pressure) which agrees with the experimental data. The ratio of axial over radial velocity fluctuations is found to be R = 1.3 – 1.4 from QHO properties, in good agreement with its experimental values; we theoretically predict a jet opening angle α = 1 / 2 R 3 accounting for its universal value ≈ 1 / 5 ; the mean ratio of turbulent intensity amplitudes over jet centerline axial velocity is predicted to be X = 19 / 80 , in good agreement with its universally measured value ≈ 1 / 4 ; from these parameters we derive possible values of the radial turbulent intensity amplitude μ = 0.19 – 0.22 consistent with experiments; finally, we find a correlation coefficient of velocities ρ = 1 / R 3 = 2 α , suggesting an explanation for the universal value ≈ 0.4 observed for the turbulent jet and for all free shear flows. [ABSTRACT FROM AUTHOR]

This paper applies fractional calculus to a practical example in fluid mechanics, illustrating its impact beyond traditional integer order calculus. We focus on the classic problem of a rigid body rotating within a uniformly rotating container, which generates a liquid vortex from an undisturbed initial state. Our aim is to compare the time evolutions of the physical system in fractional and integer order models by examining the torque transmission from the rotating body to the surrounding liquid. This is achieved through closed-form, time-developing solutions expressed in terms of Mittag–Leffler and Bessel functions. Analysis reveals that the rotational velocity and, consequently, the vortex structure of the liquid are influenced by three distinct time zones that differ between integer and noninteger models. Anomalous diffusion, favoring noninteger fractions, dominates at early times but gradually gives way to the integer derivative model behavior as time progresses through a transitional regime. Our derived vortex formula clearly demonstrates how the liquid vortex is regulated in time for each considered fractional model. [ABSTRACT FROM AUTHOR]

In this paper we study the dynamics of an incompressible viscous fluid evolving in an open-top container in two dimensions. The fluid mechanics are dictated by the Navier-Stokes equations. The upper boundary of the fluid is free and evolves within the container. The fluid is acted upon by a uniform gravitational field, and capillary forces are accounted for along the free boundary. The triple-phase interfaces where the fluid, air above the vessel, and solid vessel wall come in contact are called contact points, and the angles formed at the contact point are called contact angles. The model that we consider integrates boundary conditions that allow for full motion of the contact points and angles. Equilibrium configurations consist of quiescent fluid within a domain whose upper boundary is given as the graph of a function minimizing a gravity-capillary energy functional, subject to a fixed mass constraint. The equilibrium contact angles can take on any values between 0 and π depending on the choice of capillary parameters. The main thrust of the paper is the development of a scheme of a priori estimates that show that solutions emanating from data sufficiently close to the equilibrium exist globally in time and decay to equilibrium at an exponential rate. [ABSTRACT FROM AUTHOR]

When braided dense-mesh stents are used to treat carotid stenosis, the structural mechanics of vascular stents, the contact mechanics with blood vessels, and the fluid mechanics in the blood environment need to be studied in depth to reduce the damage of stents to blood vessels and the incidence of in-stent restenosis. Three types of braided stents with 8, 16, and 24 strands and laser-cut stents with the corresponding size parameters were designed, and the bending behavior of each of these types of stent, deployment, and fluid dynamic analysis of the 24-strand braided stent were simulated. The results show that the bending stress of the 8-, 16-, and 24-strand braided stents is 46.33%, 50.24%, and 31.86% of that of their laser-cut counterparts. In addition, higher strand density of the braided stents was associated with greater bending stress; after the 24-strand braided stent was expanded within the stented carotid artery, the carotid stenosis rate was reduced from 81.52% to 46.33%. After stent implantation, the maximum stress on the vessel wall in a zero-pressure diastolic environment decreased from 0.34 to 0.20 MPa, the maximum pressure on the intravascular wall surface decreased from 4.89 to 3.98 kPa, the area of high-pressure region decreased, the wall shear force of the stenotic segment throat decreased, and blood flow increased in the stenosis segments. The braided stent had less bending stress and better flexibility than the laser-cut stent under the same stent size parameters; after the 24-strand braided stent was implanted into the stented vessel, it could effectively dilate the vessel, and the blood flow status was improved. [ABSTRACT FROM AUTHOR]

Recent research has shown that individuals suffering from COVID-19 are accommodating an elevated level of blood viscosity due to the morphological changes in blood cells. As viscosity is a major flow parameter influencing the flow across a stenosis or an aneurysm, the examination of the significance of hyperviscosity in COVID patients is imperative in arterial pathologies. In this research, we have considered a patient-specific case in which the aneurysm is located along the abdominal aortal walls. Recent research on the side effects of COVID-19 voiced out the various effects on the circulatory system of humans. Also, as abdominal aneurysms exist very often among individuals, causing the death of 150–200 million every year, the hyper-viscous effects of blood on the flow across the diseased aorta are explored by considering the elevated viscosity levels. In vitro explorations contribute considerably to the clinical methods and treatments to be regarded. The objective of the present inquest is to research the flow field in aneurysmatic-COVID-affected patients considering the elastic nature of vessel walls, using the arbitrary Lagrangian-Eulerian approach. The study supports the various clinical findings that voiced the detrimental effects associated with blood hyperviscosity. The simulation results obtained, by solving the fluid mechanics' equations coupled with the solid mechanics' equations, employing a FEM solver suggest that the elevated stress imparted by the hyper-viscous flows on the walls of the aneurysmal aorta can trigger the fastening of the aneurysmal sac enlargement or rupture. [ABSTRACT FROM AUTHOR]

Fluid mechanics is a fundamental course in many disciplines such as civil engineering and hydraulic engineering, with broad applicability and practical significance in engineering. However, the abstractness and multiplicity of its basic concepts hinders students' first-hand experience during traditional classroom learning, and the time and space limitation of its offline experiment often results in unsatisfying teaching effectiveness. To address these challenges, a set of virtual simulation experiment system is developed for the course of fluid mechanics, along with an external support system to maximize its performance. Evaluation based on curriculum objective achievement shows that this experimental system has significantly improved the teaching effectiveness for the course of fluid mechanics. It promotes students' independent learning skills and their ability utilizing fluid mechanics knowledge to understand, simplify and solve practical engineering problems. [ABSTRACT FROM AUTHOR]

Liquid sodium hybrid bearing is mechanical pump shaft bottom key support components, that play a balanced radial force of the impeller by fluid effect, in order to improve the bearing performance, based on the calculation model, simulation analysis, structure improvement and other aspects of analysis, this paper based on the theory of fluid mechanics of bearing finite element model for numerical calculation and analysis of flow field. Under different eccentricities and vibration velocities, the influence of structure improvement on bearing capacity is analysed. The results show that the bearing capacity of the liquid sodium hybrid bearing is mainly the hydrostatic bearing capacity, and the hydrodynamic pressure only plays an auxiliary role. After the improvement of the load‐bearing structure, the load‐bearing capacity is increased by 4%–7.3%. And the leakage is reduced by 27%–38% when the depth of the annular groove is 0.6 mm. [ABSTRACT FROM AUTHOR]

The nonlinear evolution equations (NLEEs) play a significant role in applied mathematics, including ordinary and partial differential equations, which are frequently used in many disciplines of applied sciences. The Drinfeld–Sokolov–Wilson (DSW) equation and the Burgers equation are the fundamental equations occurring in various areas of physics and applied mathematics, such as nonlinear acoustics and fluid mechanics. The new generalized (G ′ / G) -expansion method is an effective and more powerful mathematical tool for solving NLEEs arising in applied mathematics and mathematical physics. In this article, we investigate further exact solutions as well as soliton solutions to these couple of nonlinear evolution equations by executing the new generalized (G ′ / G) -expansion method. A large number of soliton solutions, including single soliton, bell-shaped soliton, kink-shaped soliton, singular kink soliton, singular soliton, periodic soliton, irregular periodic soliton solutions, and others, have been retrieved. Each of the derived solutions includes an explicit function of the variables in the equations under consideration. We provide some 3D plots to visualize and realize the characteristics of these solutions. It has been established that the suggested techniques are more potential and successful at obtaining soliton solutions for nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

Compact heat exchangers are widely being used in various devices owing to its minimized size and efficient operation. The traditionally fitted circular tubes in heat exchanger have been modified as semi-circular tubes with slit. This newly proposed design offers added tubes surface area of 63.69% for better fluid flow and heat exchange. To investigate, two dimensional, unsteady, incompressible and isothermal computational studies have been carried out. The different confinements (BR= 1.54d, 2d and 3d) and gap ratios (g = 0.07, 0.14 and 0.21)have been preferred in order to mimic confined fluid environment in compact heat exchangers over the Reynolds numbers range of 50-200. Ansys Workbench 18 has been employed in modeling, meshing and carrying out the simulations of the problem formulated. Pressure and velocity were coupled using the SIMPLE algorithm. The convective and diffusive terms in the governing equations were discretized using second order upwind and central difference scheme. The time step size was fixed as 0.005 and the simulation was run until flow maturity. Results claim that flow sheds well nearer to tubes with slit at BR 1.54, which is not happening for circular tubes at same BR. The arrangement with the minimum BR and maximum gap ratio offers best performance. Semi-circle combination separated by 0.21d offers best heat transfer with an improvement of 10.51% as compared to circular components at a blockage (BR) ratio of 1.54 and Re of 200.The concept of tube splits instead of circular tubes is more effective in dissipating heat whenever the flow shedding is deteriorating or completely eliminated. The overall performance parameter (ɛ) for tube split is highest when BR 3 and g 0.21. [ABSTRACT FROM AUTHOR]

The melting of wall-mounted ice deep inside a water layer flow is investigated, the ice being initially in the form of a slender hump or step-up and the oncoming water upstream near the wall being warmer than the ice. The wall is at the same temperature as the oncoming water except beneath the ice where the wall temperature is the same as that of the ice. The unsteady interaction of the flow, heat transfer and phase change is studied analytically and computationally for a basic pure-ice model in two spatial dimensions at high flow rates. In-flow predictions of ice-shape evolution are presented along with the complete melting times and the vanishing points where melting is completed on the solid surface. This is for a range of initial conditions and background heat transfers. The unsteady movement of the contact points at the edges of the ice formation is determined explicitly for the cases of humps and steps, together with the ultimate behaviours of both the ice humps and the ice steps. Effects of reducing the sub-ice wall temperature and accretion leading to flow separation are also discussed. [ABSTRACT FROM AUTHOR]

An unstable density stratification between two fluids mixes spontaneously under the effect of gravity, a phenomenon known as Rayleigh--Taylor (RT) turbulence. If the two fluids are immiscible, for example, oil and water, surface tension prevents intermixing at the molecular level. However, turbulence fragments one fluid into the other, generating an emulsion in which the typical droplet size decreases over time as a result of the competition between the rising kinetic energy and the surface energy density. Even though the first phenomenological theory describing this emulsification process was derived many years ago, it has remained elusive to experimental verification, hampering our ability to predict the fate of oil in applications such as deep-water spills. Here, we provide the first experimental and numerical verification of the immiscible RT turbulence theory, unveiling a unique turbulent state that originates at the oil--water interface due to the interaction of multiple capillary waves. We show that a single, non-dimensional, and time-independent parameter controls the range of validity of the theory. Our findings have wide-ranging implications for the understanding of the mixing of immiscible fluids. This includes in particular oil spills, where our work enables the prediction of the oil--water interface dynamics that ultimately determine the rate of oil biodegradation by marine bacteria. [ABSTRACT FROM AUTHOR]

We consider the iterative solution of large linear systems of equations in which the coefficient matrix is the sum of two terms, a sparse matrix A and a possibly dense, rank deficient matrix of the form γUUT, where γ > 0 is a parameter which in some applications may be taken to be 1. The matrix A itself can be singular, but we assume that the symmetric part of A is positive semidefinite and that A+γUUT is nonsingular. Linear systems of this form arise frequently in fields like optimization, fluid mechanics, computational statistics, and others. We investigate preconditioning strategies based on an alternating splitting approach combined with the use of the Sherman-Morrison-Woodbury matrix identity. The potential of the proposed approach is demonstrated by means of numerical experiments on linear systems from different application areas. [ABSTRACT FROM AUTHOR]

Accurately simulating the airflow field at tower-line height of large field space in hilly and gully areas is key to studying the wind-induced vibration response and mechanical characteristics of high-voltage transmission lines and optimizing the tower-line coupling structure design, based on the relevant theory of computational fluid dynamics. However, due to the lack of systematic research on boundary effects, the simulation results of the flow field are not accurate or the model boundaries are excessively redundant and difficult to solve. In order to address this challenge, a typical region was modeled based on DEM data, and the influence of modeling methods and boundary effects on flow field simulation at specific height layers in complex terrain was systematically discussed through flow field simulation and boundary effect analysis. The results indicate that when the height of the calculation domain exceeds seven times the terrain height difference, the boundary effect is essentially eliminated. Furthermore, the distortion of the flow field caused by wall boundary constraints decreases as the redundant distance increases, with a redundant distance of 700 m being able to obtain a more stable wind field. It is concluded that the study effectively elucidates the impact of the calculation domain on the flow field and presents a method to mitigate the boundary effect of the fluid model. These findings hold valuable reference value for enhancing the stability and wind resistance of high-voltage transmission line structures. [ABSTRACT FROM AUTHOR]

In this paper, we propose, analyze and test numerically a pressure-robust stabilized finite element for a linearized problem in incompressible fluid mechanics, namely, the steady Oseen equation with low viscosity. Stabilization terms are defined by jumps of different combinations of derivatives for the convective term over the element faces of the triangulation of the domain. With the help of these stabilizing terms, and the fact the finite element space is assumed to provide a point-wise divergence-free velocity, an |$\mathcal O\big(h^{k+\frac 12}\big)$| error estimate in the |$L^2$| -norm is proved for the method (in the convection-dominated regime), and optimal order estimates in the remaining norms of the error. Numerical results supporting the theoretical findings are provided. [ABSTRACT FROM AUTHOR]

In urban water supply and drainage systems, rainwater channels or pipes are rectangular in design to help control the flow rate and adapt well to limited space. When the Bernoulli equation in fluid mechanics is used to solve the head loss of rectangular pipelines, the velocity parameter used in the kinetic energy term is usually the instantaneous or average velocity of the section at a certain point. Given that this velocity parameter is in exponential form, the smaller the error is, the greater the impact on the result will be. Thus, the kinetic energy term must be corrected. This study focuses on establishing a cross section velocity distribution model in a rectangular pipe and deriving the kinetic energy correction coefficient through the velocity distribution. Based on the Navier–Stokes equation, the partial differential equation describing the velocity distribution is further refined and simplified. Combined with the boundary conditions of the pipeline, the method of separating variables and Fourier transform are used to solve the equation. An example shows how to establish the velocity distribution model and find the analytical solution. Finally, the analytical formula of the kinetic energy correction factor of different cross section parameters and fluid properties is derived. To verify the accuracy of the analytical formula, the Fluent numerical simulation software is used for empirical verification, and then the Deming regression method is used to analyze the error between the theoretical and experimental values. The regression results of the kinetic energy correction coefficient prediction model established in this study are consistent with the actual values, and the confidence interval reaches 95%. This work provides strong guidance for the prediction of the kinetic energy correction coefficient in fluid mechanics and has an important theoretical and practical value. [ABSTRACT FROM AUTHOR]

Fluid mechanics is a branch of physics that focuses on the study of the behavior and laws of motion of fluids, including gases, liquids, and plasmas. The Yu–Toda–Sasa–Fukuyama equation, a class of Kadomtsev–Petviashvili type equations, is a significant integrable model with applications in fluids and other fields. In this paper, we study breather and soliton solutions of a generalized (3 + 1)-dimensional YTSF equation. By utilizing the Hirota bilinear method and Painlevé analysis, we construct solutions in the form of trigonometric and hyperbolic functions and analyze the interaction between waves graphically. We consider the characteristics of wave distribution along characteristic lines to obtain the distance between each wave and the angle generated, which is beneficial for understanding the ocean wave superposition effect. Additionally, we examine the dynamic characteristics of the wave, such as amplitude, velocity, period, shape, position, width, and phase. Furthermore, we investigate the effects of the system parameters on solitons and breathers. [ABSTRACT FROM AUTHOR]

Gravity currents are of high interest both for their relevance in natural scenarios and because varying horizontal buoyancy presents a canonical problem in fluid mechanics [Huppert, "Gravity currents: A personal perspective," J. Fluid Mech. 554, 299–322 (2006)]. In this paper, attention is directed to gravity currents with a full-depth lock release propagating into a linearly stratified ambient fluid. For the case of an unstratified ambient, similarity solutions are known to capture the evolving height profile of the gravity current. We will compare this solution class with numerical data from high fidelity simulations. The presence of ambient stratification (quantified by the stratification intensity, S) introduces internal gravity waves that interact with the propagating current head, which will inhibit Kelvin–Helmholtz billows, decelerate current propagation, and smooth the shape of the current head. We perform direct numerical simulations of planar two- and three-dimensional gravity currents released into stratified ambient fluid of varying S and analyze the gravity current kinematics. Our analysis complements existing findings from performed laboratory and numerical experiments [Dai et al., "Gravity currents propagating at the base of a linearly stratified ambient," Phys. Fluids 33, 066601 (2021)] that show a stratified ambient modifies the current front velocity. Previous literature employed has inconsistent Reynolds numbers and boundary conditions, complicating interpretations. In the present numerical campaign, a closer analysis clarifies influence of the top boundary condition choice on formation and structure of the internal gravity waves. While acknowledging there is no available choice for a high-accuracy simplified numerical representation of a free-surface, a family of profiles for internal wave formation emerges varying with buoyancy Reynolds number and top boundary condition selection. The subsequent results appraise similarity solutions for the distribution of the heavy fluid in the gravity current. Our results show that for unstratified and low stratification ambient fluid, height profiles permit a similarity solution but higher values of S are less amenable; these profiles suggest a continuing time dependency on the traveling internal wave. [ABSTRACT FROM AUTHOR]

In the field of fluid mechanics, traditional turbulence models such as those based on Reynolds-averaged Navier–Stokes (RANS) equations play a crucial role in solving numerous problems. However, their accuracy in complex scenarios is often limited due to inherent assumptions and approximations, as well as imprecise coefficients in the turbulence model equations. Addressing these challenges, our research introduces an innovative approach employing physics-informed neural networks (PINNs) to optimize the parameters of the standard k − ω turbulence model. PINNs integrate physical loss functions into the model, enabling the adaptation of all coefficients in the standard k − ω model as trainable parameters. This novel methodology significantly enhances the accuracy and efficiency of turbulent flow simulations, as demonstrated by our application to the flow over periodic hills. The two coefficients that have been modified considerably are σ ω and α, which correspond to the diffusion and production terms in the specific dissipation rate equation. The results indicate that the RANS simulation with PINNs coefficients (k − ω − PINNs simulation) improves the prediction of separation in the near-wall region and mitigates the overestimation of turbulent kinetic energy compared to the base RANS simulation. This research marks a significant advancement in turbulence modeling, showcasing the potential of PINNs in parameter identification and optimization in fluid mechanics. [ABSTRACT FROM AUTHOR]

This work examines the Painlevé integrability of a (3 + 1)-dimensional Boussinesq-type equation. Using the Mathematica program, we rigorously establish Painlevé's integrability for the suggested problem. By utilizing Hirota's bilinear technique, we obtain the dispersion relations and phase shifts, which enable us to derive multiple soliton solutions. In addition, we systematically derive a wide range of lump solutions using the Maple symbolic computation. The investigation extends to encompass a variety of exact solutions with distinct structural features, including kink, periodic, singular, and rational solutions. This comprehensive analysis illustrates the profound richness of the model's dynamics and its potential to elucidate diverse nonlinear wave phenomena across various physical contexts. Therefore, the results that we will obtain play a vital role in understanding the mechanism of generation and propagation of many mysterious phenomena that arise in various scientific fields, including plasma physics, fluid mechanics, and the propagation of waves on the surfaces of seas and oceans to optical fibers. [ABSTRACT FROM AUTHOR]

We generalize the multipole expansion and the structure of the Faxén operator in Stokes flows obtained for bodies with no-slip to generic boundary conditions, addressing the assumptions under which this generalization is conceivable. We show that a disturbance field generated by a body immersed in an ambient flow can be expressed, independently on the boundary conditions, as a multipole expansion, the coefficients of which are the moments of the volume forces. We find that the dualism between the operator giving the disturbance field of an nth order ambient flow and the nth order Faxén operator, referred to as the Hinch–Kim dualism, holds only if the boundary conditions satisfy a property that we call Boundary-Condition reciprocity (BC-reciprocity). If this property is fulfilled, the Faxén operators can be expressed in terms of the (m, n)th order geometrical moments of the volume forces (defined in the article). In addition, it is shown that in these cases, the hydromechanics of the fluid-body system is completely determined by the entire set of the Faxén operators. Finally, classical boundary conditions of hydrodynamic applications are investigated in light of this property: boundary conditions for rigid bodies, Newtonian drops at the mechanical equilibrium, porous bodies modeled by the Brinkman equations are BC-reciprocal, while deforming linear elastic bodies, deforming Newtonian drops, non-Newtonian drops, and porous bodies modeled by the Darcy equations do not have this property. For Navier-slip boundary conditions on a rigid body, we find the analytical expression for low order Faxén operators. By using these operators, the closed form expressions for the flow past a sphere with arbitrary slip length immersed in shear and quadratic flows are obtained. [ABSTRACT FROM AUTHOR]

The current revolution in the field of machine learning is leading to many interesting developments in a wide range of areas, including fluid mechanics. Fluid mechanics, and more concretely turbulence, is an ubiquitous problem in science and engineering. Being able to understand and predict the evolution of turbulent flows can have a critical impact on our possibilities to tackle a wide range of sustainability problems (including the current climate emergency) and industrial applications. Here, we review recent and emerging possibilities in the context of predictions, simulations, and control of fluid flows, focusing on wall-bounded turbulence. When it comes to flow control, we refer to the active manipulation of the fluid flow to improve the efficiency of processes such as reduced drag in vehicles, increased mixing in industrial processes, enhanced heat transfer in heat exchangers, and pollution reduction in urban environments. A number of important areas are benefiting from ML, and it is important to identify the synergies with the existing pillars of scientific discovery, i.e., theory, experiments, and simulations. Finally, I would like to encourage a balanced approach as a community in order to harness all the positive potential of these novel methods. [ABSTRACT FROM AUTHOR]

Definition: In young Maxwell's eyes, electricity, magnetism and fluid mechanics present analogies that let the first be mathematically grasped in a unitary way similarly to the latter. This entry sketches the first steps of James Clerk Maxwell's unitary view of electromagnetism and fluid mechanics, with long-lasting effects on understanding the physical world. In his very first paper on the subject, Maxwell interpreted Faraday's concept of lines of force of both electricity and magnetism as filaments of a flowing fluid. That is, Maxwell suggested to unify the previously distinct fields of electricity and magnetism, considering them as different aspects of the same entity, the 'electromagnetic field', which is mathematically described by four partial differential equations. In the literature there are several comprehensive works on Maxwell's mature exposition of his theory; however, the aim of this entry contribution is rather more limited. Indeed, it is restricted to examining the contributions of Maxwell's first paper towards developing the idea of electric current as the motion of an incompressible fluid. Thus, this entry highlights the strong connections of Maxwell's epistemological view with the 'mechanistic' approach of the time to every aspect of physical phenomenology. For this purpose, this entry mentions some historical context surrounding the emergence of Maxwell's innovative concepts. [ABSTRACT FROM AUTHOR]

The article provides a comprehensive account of Fritz Noether's life and career as a mathematician, focusing on his work in hydrodynamics and his struggle to find employment due to Nazi laws. Despite his sister Emmy Noether's efforts to secure a position for him in the United States, Fritz ultimately accepted an offer from the University of Tomsk in Siberia. Tragically, both Emmy and Fritz's wife Regina passed away, and Fritz himself was arrested by the NKVD and later discovered to have been wrongfully convicted and executed by the Soviets in 1941. [Extracted from the article]

This paper explains the importance and benefits of using AI in fluid mechanics, emphasizing its capability of finding the solution of fluid flow systems through iterative optimization techniques. It explores how AI can enhance the understanding of fluid dynamics to improve engineering processes. In the presented studies, the heat and mass transport of the Casson nanofluidic flow model on a nonlinear slanted extending sheet (HMT‐CNFM) via AI‐based Levenberg Marquard methodology with backpropagated trained neural networks (TNN‐BLMM) is studied. By applying an appropriate transformation, the governing PDEs representing HMT‐CNFM are converted into a system of nonlinear ODEs. The dataset for Levenberg Marquard methodology with backpropagated trained neural network (TNN‐BLMM) for all six scenarios of this proposed model via computational power of the Lobatto IIIA scheme using the "bvp4c" package in MATLAB and then graphically illustrate all these six scenarios through nftool to attain mean square error, regression, error histogram, performance, and fit curve. Training, testing, and validation processes of NN‐BLMM are organized for the investigation of the HMT‐CNFM model. [ABSTRACT FROM AUTHOR]

The efflux problem deals with the outflow of water through an orifice in a vessel, the flow over the crest of a weir and some other ways of discharge. The difficulties to account for such fluid motions in terms of a mathematical theory made it a notorious problem throughout the history of hydraulics and hydrodynamics. The treatment of the efflux problem, therefore, reflects the diverging routes along which hydraulics became an engineering science and hydrodynamics a theoretical science out of touch with applications. By the twentieth century, the presentation of the efflux problem in textbooks on hydraulics had almost nothing in common with that in textbooks on hydrodynamics. [ABSTRACT FROM AUTHOR]

This paper is concerned with quasilinear systems of partial differential equations consisting of two hyperbolic operators interacting dissipatively. Its main theorem establishes global-in-time existence and asymptotic stability of strong solutions to the Cauchy problem close to homogeneous reference states in d ≥ 3 space dimensions. Notably, the operators are not required to be symmetric hyperbolic, instead merely the existence of symbolic symmetrizers is assumed. The dissipation is characterized by algebraic conditions implying the uniform decay of all Fourier modes at the reference state. On a technical level, the theory developed herein uses para-differential operators as its main tool. Apparently being the first to apply such operators in the context of global-in-time existence of small solutions for quasi-linear hyperbolic systems, the present work contains a new version of the strong Gårding inequality. In the context of theoretical physics, the theorem applies to recent formulations for the relativistic dynamics of viscous, heat-conductive fluids such as notably that of Bemfica, Disconzi and Noronha (2018) [2]. [ABSTRACT FROM AUTHOR]

This research proposes a numerical approach to improve the thermal performance of shape memory polymers (SMPs) while their mechanical properties remain intact. Sixteen different 3D minichannel structures were numerically designed to investigate the impact of embedded water flow in microchannel networks on the thermal response and shape recovery of SMPs. This work employs two approaches, each with different physics: approach A focuses on solid mechanics analysis and, accordingly, thermal analysis in solids without considering the fluid. approach B tackles solid and fluid mechanics analysis and thermal analysis in both solid and fluid subdomains, which inherently calls for fluid–structure coupling in a uniform procedure. Finally, the results of these two approaches are compared to predict the SMP's thermal and mechanical behavior. The structural designs are then analyzed in terms of their shape recovery speed, recovery ratio, and recovery parameters. The results indicate that isotropic structures thermally outperform their anisotropic counterparts, exhibiting improved thermal characteristics and faster shape recovery. Additionally, it was observed that polymeric structures with a low volume fraction of embedded branches thermally perform efficiently. The findings of this study predict that the geometrical angle between the main branch and sub-branches of SMP favorably impacts the enhancement of thermal characteristics of the structure, accelerating its shape recovery. Approach B accelerates the shape recovery rate in SMPs due to fluid flow and uniform heat transfer within the structures. [ABSTRACT FROM AUTHOR]

The ideal fuel rail pressure is a significant component to keep the high-pressure common rail (HPCR) system work stably. The influence of time-varying fuel injection disturbance of the HPCR system is neither fully considered nor well dealt with in traditional rail pressure control approaches. To this end, the rail pressure tracking problem of an HPCR system is investigated in this paper using a generalized proportional integral observer (GPIO)-based composite control algorithm. A nonlinear model of the HPCR system is first established based on fluid dynamics and mechanics laws. Then, a GPIO is utilized to observe the time-varying fuel injection disturbance. Based on the design of a nonlinear sliding surface using the disturbance estimation, a GPIO-based nonsingular terminal sliding mode control (NTSMC) method is proposed to achieve a better rail pressure tracking control performance and a stronger robustness. Finally, a group of simulations in the MATLAB/Simulink environment and experiments in a more realistic Advanced Modeling Environment for performing Simulation of engineering systems (AMESim) environment are conducted, the results of which demonstrate the advantage and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a (3 + 1)-dimensional generalized variable coefficient Kadomtsev–Petviashvili equation is investigated systematically, which can characterize evolution of the long water waves and small amplitude surface waves with the weak nonlinearity, weak dispersion, and weak perturbation in fluid mechanics. We investigate one lump and lump molecules obtained from one breather and breather molecules by a new degenerating breather method, respectively. In addition, the bound state of lump molecules and other localized waves is derived theoretically by velocity resonance. Considering the condition of variable coefficient, the several sets of interesting solutions having a complex structure are obtained, which include the type of parabolic, S-shaped, and periodic. The analysis method can also help us to study lump molecules existing in other integrable systems from a new perspective. [ABSTRACT FROM AUTHOR]

In fluid mechanics research, data gathered from measurements and simulations may be challenging to interpret due to complexities such as transience, non-linearity, and high dimensionality. Velocity data from the airflow through an internal combustion engine often exhibit such properties; nevertheless, accurate characterizations of these airflows are required in order to correctly predict and control the subsequent combustion and emission processes in pursuit of net zero targets. The temporal mean is a common way of representing an ensemble of realizations of velocity fields, but the averaging process can artificially diminish the magnitudes of the resultant vectors. Accurate representation of these vector magnitudes is of particular importance, as the velocity magnitudes in the intake airflow are thought to be primary drivers of the subsequent variation in an engine flow, which influences emission formation and overall efficiency. As an alternative to the ensemble mean, this work proposes the application of a dimensionality reduction method known as the sparsity-promoting dynamic mode decomposition (SPDMD), which can extract core structures from an ensemble of velocity fields while retaining more realistic vector magnitudes. This is demonstrated for the first time with large-eddy simulation (LES) velocity data and compared to a corresponding set of experimental particle image velocimetry (PIV) data. The SPDMD 0 Hz modes are shown to be more representative of the velocity magnitudes present in both datasets. This facilitates more accurate quantification of the differences in vector magnitudes between simulations and experiments, and more reliable identification of which LES snapshots are closer to the PIV ensemble. [ABSTRACT FROM AUTHOR]

The present article examines the nonlinear stability of two viscoelastic electrified cylindrical fluids immersed in permeable media. The current structure consists of two endless vertical cylinders containing two electrified fluids. An axial unchanged electric field (EF) is applied to the entire construction; additionally, the impact of the surface tension is reflected. The main driving force for understanding this challenge has increasing significance in atmospheric and oceanic dynamics. The viscous potential theory is employed to ease the mathematical processes. The fundamental hydrodynamic equations are combined with Maxwell's equations in the quasi-static approximation to set the boundary-value problem. The appropriate boundary conditions (BCs) are expressed in a nonlinear form; this nonlinearity is achieved by addressing the linearized controlling equations of the motion. The viscoelastic impacts are considered to illustrate how the BCs produce their contributions. Consequently, the equations of motion are tackled without the effects of viscoelasticity parameters. The interface displacement consequently interacts vertically along with the cylindrical axis. The Rayleigh Helmholtz–Duffing oscillator describes the propagation of the interface between the two fluids. The non-perturbative approach (NPA), based on the He's frequency formula, transforms the typical nonlinear differential equation (NDE) into a linear one. The non-dimensional analysis reveals a lot of dimensionless physical numerals. These non-dimensional physical characteristics can be utilized to study the fundamental character of the liquid movement. They are also used to reduce the quantity of variables that are needed to comprehend the framework. A quick explanation of NPA is also presented. The stability study reveals the real/complex coefficients of the NDE. The numerical simulations show that there is a consistent solution and that the increases in the axial EF, as well as axial wavenumber, stabilize the system. The obtained findings help to understand and explain diverse nonlinear progressions that have taken place in fluid mechanics. To show the impact of the different factors and the efficiency of the stability approach, diverse PolarPlot diagrams are graphed for both actual and hypothetical portions. [ABSTRACT FROM AUTHOR]