Journal articles: 'Hydrodynamics linear stability analysis'

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VOLPERT, V. A., and A. I. VOLPERT. "Convective instability of reaction fronts: Linear stability analysis." European Journal of Applied Mathematics 9, no. 5 (October 1998): 507–25. http://dx.doi.org/10.1017/s095679259800357x.

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The paper is devoted to convective instability of reaction fronts. New approaches are developed to study some eigenvalue problems arising in chemical hydrodynamics. For gaseous combustion in the case of equality of transport coefficients, a linear stability analysis of an upward propagating front is carried out. A minimax representation of the stability boundary is obtained.

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Christian Oliver, Paschereit, Terhaar Steffen, Cosic Bernhard, and Oberleithner Kilian. "IL05 Application of Linear Hydrodynamic Stability Analysis to Reacting Swirling Combustor Flows." Proceedings of the International Conference on Jets, Wakes and Separated Flows (ICJWSF) 2013.4 (2013): _IL05–1_—_IL05–11_. http://dx.doi.org/10.1299/jsmeicjwsf.2013.4._il05-1_.

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Khayat, Roger E., and Byung Chan Eu. "Generalized hydrodynamics and linear stability analysis of cylindrical Couette flow of a dilute Lennard–Jones fluid." Canadian Journal of Physics 71, no. 11-12 (November 1, 1993): 518–36. http://dx.doi.org/10.1139/p93-081.

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Linear stability analysis is carried out for cylindrical Couette flow of a Lennard–Jones fluid in the density range from the dense liquid to the dilute gas regime. Generalized hydrodynamic equations are used to calculate marginal stability curves and compare them with those obtained by using the Navier–Stokes–Fourier equations for compressible fluids and also for incompressible fluids. In the low Reynolds or Mach number regime, if the Knudsen number is sufficiently low, the marginal stability curves calculated by the generalized hydrodynamic theory coincide, within numerical errors, with those based on the Navier–Stokes theory. But there are considerable deviations between them in the regimes beyond those mentioned earlier, since nonlinear effects manifest themselves in the laminar mean flow through the nonlinear dissipation term and normal stresses. There are three marginal stability curves obtained in contrast to the Navier–Stokes theory, which yields only two. The previously observed phase-transition-like behavior in fluid variables and the slip phenomenon are found to occur beyond the hydrodynamic stability point. The disturbance entropy production associated with the Taylor–Couette vortices is calculated to first order in disturbances in flow variables and is found to decrease as the number of vortices increases and thereby the dynamic structure is progressively more organized.

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Vanderhaegen, Guillaume, Corentin Naveau, Pascal Szriftgiser, Alexandre Kudlinski, Matteo Conforti, Arnaud Mussot, Miguel Onorato, Stefano Trillo, Amin Chabchoub, and Nail Akhmediev. "“Extraordinary” modulation instability in optics and hydrodynamics." Proceedings of the National Academy of Sciences 118, no. 14 (March 31, 2021): e2019348118. http://dx.doi.org/10.1073/pnas.2019348118.

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The classical theory of modulation instability (MI) attributed to Bespalov–Talanov in optics and Benjamin–Feir for water waves is just a linear approximation of nonlinear effects and has limitations that have been corrected using the exact weakly nonlinear theory of wave propagation. We report results of experiments in both optics and hydrodynamics, which are in excellent agreement with nonlinear theory. These observations clearly demonstrate that MI has a wider band of unstable frequencies than predicted by the linear stability analysis. The range of areas where the nonlinear theory of MI can be applied is actually much larger than considered here.

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Albert, C., A. Tezuka, and D. Bothe. "Global linear stability analysis of falling films with inlet and outlet." Journal of Fluid Mechanics 745 (March 24, 2014): 444–86. http://dx.doi.org/10.1017/jfm.2014.57.

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AbstractIn this paper, the stability of falling films with different flow conditions at the inlet is studied. This is done with an algorithm for the numerical investigation of stability of steady-state solutions to dynamical systems, which is based on an Arnoldi-type iteration. It is shown how this algorithm can be applied to free boundary problems in hydrodynamics. A volume-of-fluid solver is employed to predict the time evolution of perturbations to the steady state. The method is validated by comparison to data from temporal and spatial stability theory, and to experimental results. The algorithm is used to analyse the flow fields of falling films with inlet and outlet, taking the inhomogeneity caused by different inlet conditions into account. In particular, steady states with a curved interface are analysed. A variety of reasonable inlet conditions is investigated. The instability of the film is convective and perturbations at the inlet could be of importance since they are exponentially amplified as they are transported downstream. However, the employed algorithm shows that there is no significant effect of the inlet condition. It is concluded that the flow characteristics of falling films are stable with respect to the considered time-independent inlet conditions.

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Gong, Jinchou, Changxi Ma, and Chenqiang Zhu. "A modified two-lane lattice hydrodynamics model considering the downstream traffic conditions." Modern Physics Letters B 34, no. 24 (June 4, 2020): 2050250. http://dx.doi.org/10.1142/s0217984920502504.

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The difference between the optimal current difference and the actual current difference will be used as the correction item. The dynamic multiple current information about the front lattice will be considered. A modified lattice traffic hydrodynamics model is established by considering the downstream traffic conditions in the two-lane system. Through the stability analysis, it is found that the downstream traffic condition can be added as a correction term to increase the stability of the system. The area of the stable region on the phase diagram is enlarged by the derived stability. The mKdV equation, which can describe density wave, is derived by nonlinear analysis. Finally, the phase diagram of stability condition in linear analysis and the kink wave diagram of mKdV equation in nonlinear analysis are obtained by numerical simulation, which verifies the theoretical derivation of this paper. The results show that in the two-lane traffic flow expansion model, considering the downstream traffic conditions can effectively suppress traffic jams and make the traffic flow stable.

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Hernandez-Duenas, Gerardo, Leslie M. Smith, and Samuel N. Stechmann. "Stability and Instability Criteria for Idealized Precipitating Hydrodynamics." Journal of the Atmospheric Sciences 72, no. 6 (May 27, 2015): 2379–93. http://dx.doi.org/10.1175/jas-d-14-0317.1.

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Abstract A linear stability analysis is presented for fluid dynamics with water vapor and precipitation, where the precipitation falls relative to the fluid at speed VT. The aim is to bridge two extreme cases by considering the full range of VT values: (i) VT = 0, (ii) finite VT, and (iii) infinitely fast VT. In each case, a saturated precipitating atmosphere is considered, and the sufficient conditions for stability and instability are identified. Furthermore, each condition is linked to a thermodynamic variable: either a variable θs, which denotes the saturated potential temperature, or the equivalent potential temperature θe. When VT is finite, separate sufficient conditions are identified for stability versus instability: dθe/dz > 0 versus dθs/dz < 0, respectively. When VT = 0, the criterion dθs/dz = 0 is the single boundary that separates the stable and unstable conditions; and when VT is infinitely fast, the criterion dθe/dz = 0 is the single boundary. Asymptotics are used to analytically characterize the infinitely fast VT case, in addition to numerical results. Also, the small-VT limit is identified as a singular limit; that is, the cases of VT = 0 and small VT are fundamentally different. An energy principle is also presented for each case of VT, and the form of the energy identifies the stability parameter: either dθs/dz or dθe/dz. Results for finite VT have some resemblance to the notion of conditional instability: separate sufficient conditions exist for stability versus instability, with an intermediate range of environmental states where stability or instability is not definitive.

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GERKEMA, THEO. "A linear stability analysis of tidally generated sand waves." Journal of Fluid Mechanics 417 (August 25, 2000): 303–22. http://dx.doi.org/10.1017/s0022112000001105.

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A linear stability analysis is carried out to examine the initial stage of sand-wave growth under tidal flows and the occurrence of a preferred length scale. The fact that these bedforms typically have length scales small compared to the tidal excursion is exploited by adopting an asymptotic approach to solve the hydrodynamic part of the problem, i.e. to find the hydrodynamic response to an initially small bed perturbation. This method is shown to have important advantages over previously used methods, since it allows an exploration of the complete sand-wave regime (whereas other methods fail for short sand waves), and in general it is also more accurate. It is found that the selection of a preferred length scale depends mainly on only two parameters (the bed-slope coefficient, and the ratio of friction velocity to eddy viscosity), whereas there appears to be almost no dependence on the water depth.

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Jiang, Zhongzheng, Wenwen Zhao, Weifang Chen, and Zhenyu Yuan. "Eu's generalized hydrodynamics with its derived constitutive model: Comparison to Grad's method and linear stability analysis." Physics of Fluids 33, no. 12 (December 2021): 127116. http://dx.doi.org/10.1063/5.0071715.

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Das, S., S. K. Guha, and A. K. Chattopadhyay. "Linear stability analysis of hydrodynamic journal bearings under micropolar lubrication." Tribology International 38, no. 5 (May 2005): 500–507. http://dx.doi.org/10.1016/j.triboint.2004.08.023.

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Sinha, Aniruddha, Kristján Gudmundsson, Hao Xia, and Tim Colonius. "Parabolized stability analysis of jets from serrated nozzles." Journal of Fluid Mechanics 789 (January 15, 2016): 36–63. http://dx.doi.org/10.1017/jfm.2015.719.

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We study the viscous spatial linear stability characteristics of the time-averaged flow in turbulent subsonic jets issuing from serrated (chevroned) nozzles, and compare them to analogous round jet results. Linear parabolized stability equations (PSE) are used in the calculations to account for the non-parallel base flow. By exploiting the symmetries of the mean flow due to the regular arrangement of serrations, we obtain a series of coupled two-dimensional PSE problems from the original three-dimensional problem. This reduces the solution cost and manifests the symmetries of the stability modes. In the parallel-flow linear stability theory (LST) calculations that are performed near the nozzle to initiate the PSE, we find that the serrated nozzle reduces the growth rates of the most unstable eigenmodes of the jet, but their phase speeds are approximately similar. We obtain encouraging validation of our linear PSE instability wave results vis-à-vis near-field hydrodynamic pressure data acquired on a phased microphone array in experiments, after filtering the latter with proper orthogonal decomposition (POD) to extract the energetically dominant coherent part. Additionally, a large-eddy simulation database of the same serrated jet is investigated, and its POD-filtered pressure field is found to compare favourably with the corresponding PSE solution within the jet plume. We conclude that the coherent hydrodynamic pressure fluctuations of jets from both round and serrated nozzles are reasonably consistent with the linear instability modes of the turbulent mean flow.

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MONTANERO, J. M., and A. M. GAÑÁN-CALVO. "Viscoelastic effects on the jetting–dripping transition in co-flowing capillary jets." Journal of Fluid Mechanics 610 (August 8, 2008): 249–60. http://dx.doi.org/10.1017/s0022112008002681.

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Linear hydrodynamics stability analysis is used to determine the influence of elasticity on the jetting–dripping transition and on the temporal stability of non-axisymmetric modes in co-flowing capillary jets. The critical Weber number for which axisymmetric perturbations undergo a transition from convective to absolute instability is calculated from the spatio-temporal analysis of the dispersion relation for Oldroyd-B liquids, as a function of the density and viscosity ratios, and the Reynolds and Deborah numbers. Elasticity increases the critical Weber number for all cases analysed and, consequently, fosters the transition from jetting to dripping. The temporal analysis of the dispersion relation for them= 1 lateral mode shows that elasticity does not affect its stability.

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Vanegas, Juan M., David Peterson, Taras I. Lakoba, and Valeri N. Kotov. "Spinodal de-wetting of light liquids on graphene." Journal of Physics: Condensed Matter 34, no. 17 (February 25, 2022): 175001. http://dx.doi.org/10.1088/1361-648x/ac4f7e.

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Abstract We demonstrate theoretically the possibility of spinodal de-wetting in heterostructures made of light–atom liquids (hydrogen, helium, and nitrogen) deposited on suspended graphene. Extending our theory of film growth on two-dimensional (2D) materials to include analysis of surface instabilities via the hydrodynamic Cahn–Hilliard-type equation, we characterize in detail the spatial and temporal scales of the resulting spinodal de-wetting patterns. Both linear stability analysis and direct numerical simulations of the surface hydrodynamics show micron-sized (generally material dependent) patterns of ‘dry’ regions. The physical reason for the development of such instabilities on graphene can be traced back to the inherently weak van der Waals interactions between atomically thin materials and atoms in the liquid. Thus 2D materials could represent a new theoretical and technological platform for studies of spinodal de-wetting.

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Lu, Xiaoyi, and Carlos Pantano. "Linear stability analysis of a premixed flame with transverse shear." Journal of Fluid Mechanics 765 (January 19, 2015): 150–66. http://dx.doi.org/10.1017/jfm.2014.728.

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AbstractOne-dimensional planar premixed flames propagating in a uniform flow are susceptible to hydrodynamic instabilities known (generically) as Darrieus–Landau instabilities. Here, we extend that hydrodynamic linear stability analysis to include a lateral shear. This generalization is a situation of interest for laminar and turbulent flames when they travel into a region of shear (such as a jet or shear layer). It is shown that the problem can be formulated and solved analytically and a dispersion relation can be determined. The solution depends on a shear parameter in addition to the wavenumber, thermal expansion ratio, and Markstein lengths. The study of the dispersion relation shows that perturbations have two types of behaviour as wavenumber increases. First, for small shear, we recover the Darrieus–Landau results except for a region at small wavenumbers, large wavelengths, that is stable. Initially, increasing shear has a stabilizing effect. But, for sufficiently high shear, the flame becomes unstable again and its most unstable wavelength can be much smaller than the Markstein length of the zero-shear flame. Finally, the stabilizing effect of low shear can make flames with negative Markstein numbers stable within a band of wavenumbers.

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Khakimzyanov, Gayaz S., Zinaida I. Fedotova, Oleg I. Gusev, and Nina Yu Shokina. "Finite difference methods for 2D shallow water equations with dispersion." Russian Journal of Numerical Analysis and Mathematical Modelling 34, no. 2 (April 24, 2019): 105–17. http://dx.doi.org/10.1515/rnam-2019-0009.

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Abstract Basic properties of some finite difference schemes for two-dimensional nonlinear dispersive equations for hydrodynamics of surface waves are considered. It is shown that stability conditions for difference schemes of shallow water equations are qualitatively different in the cases the dispersion is taken into account, or not. The difference in the behavior of phase errors in one- and two-dimensional cases is pointed out. Special attention is paid to the numerical algorithm based on the splitting of the original system of equations into a nonlinear hyperbolic system and a scalar linear equation of elliptic type.

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Nold, Andreas, and Martin Oberlack. "Symmetry analysis in linear hydrodynamic stability theory: Classical and new modes in linear shear." Physics of Fluids 25, no. 10 (October 2013): 104101. http://dx.doi.org/10.1063/1.4823508.

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Hogg, Michael C., Martin C. Cook, Geoff D. Tansley, and John C. Woodard. "FULL NON-LINEAR STABILITY ANALYSIS OF THE VENTRASSIST HYDRODYNAMIC BEARING SYSTEM." ASAIO Journal 48, no. 2 (March 2002): 140. http://dx.doi.org/10.1097/00002480-200203000-00062.

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Rao, T. V. V. L. N., and Jerzy T. Sawicki. "Linear Stability Analysis for a Hydrodynamic Journal Bearing Considering Cavitation Effects." Tribology Transactions 45, no. 4 (January 2002): 450–56. http://dx.doi.org/10.1080/10402000208982573.

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PASCHEREIT, Christian Oliver, Steffen TERHAAR, Bernhard ĆOSIĆ, and Kilian OBERLEITHNER. "Application of linear hydrodynamic stability analysis to reacting swirling combustor flows." Journal of Fluid Science and Technology 9, no. 3 (2014): JFST0024. http://dx.doi.org/10.1299/jfst.2014jfst0024.

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Amamou, A., and M. Chouchane. "Non-linear stability analysis of floating ring bearings using Hopf bifurcation theory." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, no. 12 (July 25, 2011): 2804–18. http://dx.doi.org/10.1177/0954406211413520.

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Floating ring bearings are used to support and guide rotors in several high-speed rotating machinery applications. They are usually credited for lower heat generation and higher vibration suppressing ability. Similar to conventional hydrodynamic bearings, floating ring bearings may exhibit unstable behaviour above a certain stability critical speed. Linear stability analysis is usually applied to predict the stability threshold speed. Non-linear stability analysis, however, is needed to predict the presence and the size of stable limit cycles above the stability threshold speed or unstable limit cycles below the stability critical speed. The prediction of limit cycles is an important step in bearing stability analysis. In this article, a non-linear dynamic model is derived and used to investigate the stability of a perfectly balanced symmetric rigid rotor supported by two identical floating ring bearings near the critical stability boundaries. The fluid film hydrodynamic reactions of the floating ring bearings are modelled by applying the short bearing theory and the half Sommerfeld solution. Hopf bifurcation theory is then utilized to determine the existence and the approximate size of stable and unstable limit cycles in the neighbourhood of the stability critical speed depending on the bearing design parameters. Numerical integration of the non-linear equations of motion is then carried out in order to compare the trajectories obtained by numerical integration to those obtained analytically using Hopf bifurcation analysis. Stability boundary curves for typical bearing design parameters have been decomposed into boundaries with supercritical stable limit cycles and boundaries with subcritical unstable limit cycles. The shape and size of the limit cycles for selected bearing parameters are presented using both analytical and numerical approaches. This article shows that floating ring stability boundaries may exhibit either stable supercritical limit cycles or unstable subcritical limit cycles predictable by Hopf bifurcation.

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Wang, Haifei, Shimin Yang, and Tan Lu. "Performance-Matching Optimization Design of Loader-Hydraulic System Based on Hydrodynamics Analysis." Processes 10, no. 8 (August 3, 2022): 1524. http://dx.doi.org/10.3390/pr10081524.

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The study of the performance of dynamic hydraulic throttling under the condition of stable fluid is of great significance. The effect of a step change in pressure differences on the throttling performance of a hydraulic valve is studied. This paper studies the dynamic and static performance of a hydraulic-valve-outlet throttling-speed regulation system, builds a more accurate mathematical model, considers the linear factors of the flow of hydraulic-valve throttling, analyzes the influence of the step-load change in pressure difference on the stability of the hydraulic-valve movement speed, and constructs a nonlinear mathematical model of the speed-regulation system of the outlet throttling. A pressure sensor is used to measure the change in pressure overshoot, and the effect of a pressure-difference step change on the throttling performance of the hydraulic valve is studied under steady-fluid conditions. The theory is analyzed and verified by experiment, and the parameters of hydraulic components are modified using the dynamic-change rule of the hydraulic valve’s two-chamber pressure.

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AZAIEZ, J. "Linear stability of free shear flows of fibre suspensions." Journal of Fluid Mechanics 404 (February 10, 2000): 179–209. http://dx.doi.org/10.1017/s002211209900717x.

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A linear stability analysis of the mixing layer in the presence of fibre additives is presented. Using a formulation based on moments of the probability distribution function to determine the particle orientation, we extend the classical linear stability theory and derive a modified Orr–Sommerfeld equation. It is found that, for large Reynolds numbers, the flow instability is governed by two parameters: a dimensionless group H, analogous to a reciprocal Reynolds number representing the importance of inertial forces versus viscous forces associated with the anisotropic elongational viscosity of the suspension; and a coefficient CI that accounts for inter-particle hydrodynamic interactions. A parametric study reveals that both parameters can induce an important attenuation of the flow instability. Furthermore, we show that the stabilizing effects arise from the orientation diffusion due to hydrodynamic interactions, and not from the anisotropy induced by the presence of fibres in the flow, as speculated before. The examination of profile contours of different perturbation terms and the analysis of the rate of production of enstrophy show clearly that the main factor behind the reduction of the flow instability is associated with the fibre shear stress disturbance. This disturbance acts as a dissipative term as the fibres, due to the orientational diffusivity arising from hydrodynamic interactions, deviate from the fully aligned anisotropic orientation. On the other hand, fibre normal stresses act as a destabilizing factor and are important only in the absence of hydrodynamic interactions.

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Wang, Bo-Fu, Zhen-Hua Wan, Zhi-Wei Guo, Dong-Jun Ma, and De-Jun Sun. "Linear instability analysis of convection in a laterally heated cylinder." Journal of Fluid Mechanics 747 (April 17, 2014): 447–59. http://dx.doi.org/10.1017/jfm.2014.180.

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AbstractThe three-dimensional instabilities of axisymmetric flow are investigated in a laterally heated vertical cylinder by linear stability analysis. Heating is confined to a central zone on the sidewall of the cylinder, while other parts of the sidewall are insulated and both ends of the cylinder are cooled. The length of the heated zone equals the radius of the cylinder. For three different aspect ratios, $A= 1.92 $, 2, 2.1 ($A=\mathrm{height}$/radius), the dependence of the critical Rayleigh number on the Prandtl number (from 0.02 to 6.7) has been studied in detail. For such a kind of laterally heated convection, some interesting stability results are obtained. A monotonous instability curve is obtained for $A= 1.92 $, while the instability curves for $A= 2 $ and $A= 2.1 $ are non-monotonous and multivalued. In particular, an instability island has been found for $A=2$. Moreover, mechanisms corresponding to different instability results are obtained when the Prandtl number changes. At small Prandtl number, the flow is oscillatory unstable, which is dominated by hydrodynamic instability. At intermediate Prandtl number, the interaction between buoyancy and shear in the base flow plays a more important role than pure hydrodynamic instability. At even higher Prandtl number, Rayleigh–Bénard instability becomes the dominant process and the flow loses stability through steady bifurcation.

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SHORT, MARK, and D. SCOTT STEWART. "Cellular detonation stability. Part 1. A normal-mode linear analysis." Journal of Fluid Mechanics 368 (August 10, 1998): 229–62. http://dx.doi.org/10.1017/s0022112098001682.

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A detailed investigation of the hydrodynamic stability to transverse linear disturbances of a steady, one-dimensional detonation in an ideal gas undergoing an irreversible, unimolecular reaction with an Arrhenius rate constant is conducted via a normal-mode analysis. The method of solution is an iterative shooting technique which integrates between the detonation shock and the reaction equilibrium point. Variations in the disturbance growth rates and frequencies with transverse wavenumber, together with two-dimensional neutral stability curves and boundaries for all unstable low- and higher frequency modes, are obtained for varying detonation bifurcation parameters. These include the detonation overdrive, chemical heat release and reaction activation energy. Spatial perturbation eigenfunction behaviour and phase and group velocities are also obtained for selected sets of unstable modes. Results are presented for both Chapman–Jouguet and overdriven detonation velocities. Comparisons between the earlier pointwise determination of stability and interpolated neutral stability boundaries obtained by Erpenbeck are made. Possible physical mechanisms which govern the wavenumber selection underlying the initial onset of either regular or irregular cell patterns are also discussed.

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Turkyilmazoglu, Mustafa. "Single phase nanofluids in fluid mechanics and their hydrodynamic linear stability analysis." Computer Methods and Programs in Biomedicine 187 (April 2020): 105171. http://dx.doi.org/10.1016/j.cmpb.2019.105171.

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Qi, Xinyue, Rongjun Cheng, and Hongxia Ge. "Analysis of a novel two-lane lattice model with consideration of density integral and relative flow information." Engineering Computations 37, no. 8 (April 8, 2020): 2939–55. http://dx.doi.org/10.1108/ec-10-2019-0441.

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Purpose This study aims to consider the influence of density difference integral and relative flow difference on traffic flow, a novel two-lane lattice hydrodynamic model is proposed. The stability criterion for the new model is obtained through the linear analysis method. Design/methodology/approach The modified Korteweg de Vries (KdV) (mKdV) equation is derived to describe the characteristic of traffic jams near the critical point. Numerical simulations are carried out to explore how density difference integral and relative flow difference influence traffic stability. Numerical and analytical results demonstrate that traffic congestions can be effectively relieved considering density difference integral and relative flow difference. Findings The traffic congestions can be effectively relieved considering density difference integral and relative flow difference. Originality/value Novel two-lane lattice hydrodynamic model is presented considering density difference integral and relative flow difference. Applying the linear stability theory, the new model’s linear stability is obtained. Through nonlinear analysis, the mKdV equation is derived. Numerical results demonstrate that the traffic flow stability can be efficiently improved by the effect of density difference integral and relative flow difference.

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Mitarai, Namiko, and Hiizu Nakanishi. "Stability Analysis of Collisional Granular Flow on a Slope." International Journal of Modern Physics B 17, no. 22n24 (September 30, 2003): 4290–94. http://dx.doi.org/10.1142/s0217979203022337.

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We analyze the linear stability of a collisional granular flow on a slope under gravity using hydrodynamical equations based on kinetic theory of inelastic particles. It is shown that the steady, uniform flow is unstable against longitudinal long-wavelength perturbations in lower density region. The results are compared with the instabilities found in numerical simulations of granular flows.

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Kolmychkov, V. V. "COMPUTER SIMULATION FOR SUBCRITICAL CONVECTION IN MULTI‐COMPONENT ALLOYS." Mathematical Modelling and Analysis 11, no. 1 (March 31, 2006): 57–71. http://dx.doi.org/10.3846/13926292.2006.9637302.

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Subcritical convection with hexagonal flow pattern is registered in 3D computer simulation of convective mass transfer in ternary solution under phase transition conditions. The calculations are evaluated by the classical theory of hydrodynamic stability and display a good agreement with linear and finite amplitude stability analysis. Key words: convective instability, subcritical convection, computer simulation.

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GORDILLO, J. M., M. PÉREZ-SABORID, and A. M. GAÑÁN-CALVO. "Linear stability of co-flowing liquid–gas jets." Journal of Fluid Mechanics 448 (November 26, 2001): 23–51. http://dx.doi.org/10.1017/s0022112001005729.

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A temporal, inviscid, linear stability analysis of a liquid jet and the co-flowing gas stream surrounding the jet has been performed. The basic liquid and gas velocity profiles have been computed self-consistently by solving numerically the appropriate set of coupled Navier–Stokes equations reduced using the slenderness approximation. The analysis in the case of a uniform liquid velocity profile recovers the classical Rayleigh and Weber non-viscous results as limiting cases for well-developed and very thin gas boundary layers respectively, but the consideration of realistic liquid velocity profiles brings to light new families of modes which are essential to explain atomization experiments at large enough Weber numbers, and which do not appear in the classical stability analyses of non-viscous parallel streams. In fact, in atomization experiments with Weber numbers around 20, we observe a change in the breakup pattern from axisymmetric to helicoidal modes which are predicted and explained by our theory as having an hydrodynamic origin related to the structure of the liquid-jet basic velocity profile. This work has been motivated by the recent discovery by Gañán-Calvo (1998) of a new atomization technique based on the acceleration to large velocities of coaxial liquid and gas jets by means of a favourable pressure gradient and which are of emerging interest in microfluidic applications (high-quality atomization, micro-fibre production, biomedical applications, etc.).

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Wan, Jin, Xin Huang, Wenzhi Qin, Xiuge Gu, and Min Zhao. "An Improved Lattice Hydrodynamic Model by considering the Effect of “Backward-Looking” and Anticipation Behavior." Complexity 2021 (November 5, 2021): 1–12. http://dx.doi.org/10.1155/2021/4642202.

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In order to prevent the occurrence of traffic accidents, drivers always focus on the running conditions of the preceding and rear vehicles to change their driving behavior. By taking into the “backward-looking” effect and the driver’s anticipation effect of flux difference consideration at the same time, a novel two-lane lattice hydrodynamic model is proposed to reveal driving characteristics. The corresponding stability conditions are derived through a linear stability analysis. Then, the nonlinear theory is also applied to derive the mKdV equation describing traffic congestion near the critical point. Linear and nonlinear analyses of the proposed model show that how the “backward-looking” effect and the driver’s anticipation behavior comprehensively affect the traffic flow stability. The results show that the positive constant γ , the driver’s anticipation time τ , and the sensitivity coefficient p play significant roles in the improvement of traffic flow stability and the alleviation of the traffic congestion. Furthermore, the effectiveness of linear stability analysis and nonlinear analysis results is demonstrated by numerical simulations.

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Das, Subrata, and Sisir Kumar Guha. "Non-linear stability analysis of micropolar fluid lubricated journal bearings with turbulent effect." Industrial Lubrication and Tribology 71, no. 1 (January 14, 2019): 31–39. http://dx.doi.org/10.1108/ilt-07-2017-0212.

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Purpose The purpose of this paper is to investigate the effect of turbulence on the stability characteristics of finite hydrodynamic journal bearing lubricated with micropolar fluid. Design/methodology/approach The non-dimensional transient Reynolds equation has been solved to obtain the non-dimensional pressure field which in turn used to obtain the load carrying capacity of the bearing. The second-order equations of motion applicable for journal bearing system have been solved using fourth-order Runge–Kutta method to obtain the stability characteristics. Findings It has been observed that turbulence has adverse effect on stability and the whirl ratio at laminar flow condition has the lowest value. Practical implications The paper provides the stability characteristics of the finite journal bearing lubricated with micropolar fluid operating in turbulent regime which is very common in practical applications. Originality/value Non-linear stability analysis of micropolar fluid lubricated journal bearing operating in turbulent regime has not been reported in literatures so far. This paper is an effort to address the problem of non-linear stability of journal bearings under micropolar lubrication with turbulent effect. The results obtained provide useful information for designing the journal bearing system for high speed applications.

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Golovanov, А. V., L. V. Babakova, and I. A. Karpov. "Linear Stability Analysis of One-Dimensional Models of Magneto-Hydrodynamic Domains in Nematics." Liquid Crystals and their Application 15, no. 3 (September 18, 2015): 119–24. http://dx.doi.org/10.18083/lcappl.2015.3.119.

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Bagheri, Shervin. "Computational Hydrodynamic Stability and Flow Control Based on Spectral Analysis of Linear Operators." Archives of Computational Methods in Engineering 19, no. 3 (August 2, 2012): 341–79. http://dx.doi.org/10.1007/s11831-012-9074-0.

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Guha, S. K., and A. K. Chattopadhyay. "On the linear stability analysis of finite-hydrodynamic porous journal bearings under coupled stress lubrication." Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 221, no. 7 (July 1, 2007): 831–40. http://dx.doi.org/10.1243/13506501jet230.

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The objective of the present investigation is to study theoretically, using the finite-difference techniques, the dynamic performance characteristics of finite-hydrodynamic porous journal bearings lubricated with coupled stress fluids. In the analysis based on the Stokes micro-continuum theory of the rheological effects of coupled stress fluids, a modified form of Reynolds equation governing the transient-state hydrodynamic film pressures in porous journal bearings with the effect of slip flow of coupled stress fluid as lubricant is obtained. Moreover, the tangential velocity slip at the surface of porous bush has been considered by using Beavers-Joseph criterion. Using the first-order perturbation of the modified Reynolds equation, the stability characteristics in terms of threshold stability parameter and whirl ratios are obtained for various parameters viz. permeability factor, slip coefficient, bearing feeding parameter, and eccentricity ratio. The results show that the coupled stress fluid exhibits better stability in comparison with Newtonian fluid.

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35

Calvete, Daniel, Francesca Ribas, Huib E. De Swart, and Albert Falques. "EFFECT OF SURFACE ROLLERS ON THE FORMATION OF CRESCENTIC BARS." Coastal Engineering Proceedings 1, no. 33 (December 15, 2012): 51. http://dx.doi.org/10.9753/icce.v33.sediment.51.

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The formation of crescentic bars is examined using a morphodynamic model based in linear stability analysis. The effect of surface rollers for off-normal wave conditions is examined. The effect of the rollers is to increase the efolding times with increasing the angle of incidence. For angles large enough the formation of crescentic bars is even inhibit. The main effect of the rollers it be through hydrodynamics. The longitudinal changes in current produced by the rollers cause the maximum of sediment concentration to be shifted towards the coast with the final effect of prevent the formation of crecscentic bars.

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Zhai, Cong, and Weitiao Wu. "A modified two-dimensional triangular lattice model under honk environment." International Journal of Modern Physics C 31, no. 06 (June 2020): 2050089. http://dx.doi.org/10.1142/s0129183120500898.

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The honk effect is not uncommon in the real traffic and may exert great influence on the stability of traffic flow. As opposed to the linear description of the traditional one-dimensional lattice hydrodynamic model, the high-dimensional lattice hydrodynamic model is a gridded analysis of the real traffic environment, which is a generalized form of the one-dimensional lattice model. Meanwhile, the high-dimensional traffic flow exposed to the open-ended environment is more likely to be affected by the honk effect. In this paper, we propose an extension of two-dimensional triangular lattice hydrodynamic model under honk environment. The stability condition is obtained via the linear stability analysis, which shows that the stability region in the phase diagram can be effectively enlarged under the honk effect. Modified Korteweg–de Vries equations are derived through the nonlinear stability analysis method. The kink–antikink solitary wave solution is obtained by solving the equation, which can be used to describe the propagation characteristics of density waves near the critical point. Finally, the simulation example verifies the correctness of the above theoretical analysis.

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37

Llamoza, Johan, and Desiderio A. Vasquez. "Structures and Instabilities in Reaction Fronts Separating Fluids of Different Densities." Mathematical and Computational Applications 24, no. 2 (May 17, 2019): 51. http://dx.doi.org/10.3390/mca24020051.

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Density gradients across reaction fronts propagating vertically can lead to Rayleigh–Taylor instabilities. Reaction fronts can also become unstable due to diffusive instabilities, regardless the presence of a mass density gradient. In this paper, we study the interaction between density driven convection and fronts with diffusive instabilities. We focus in fluids confined in Hele–Shaw cells or porous media, with the hydrodynamics modeled by Brinkman’s equation. The time evolution of the front is described with a Kuramoto–Sivashinsky (KS) equation coupled to the fluid velocity. A linear stability analysis shows a transition to convection that depends on the density differences between reacted and unreacted fluids. A stabilizing density gradient can surpress the effects of diffusive instabilities. The two-dimensional numerical solutions of the nonlinear equations show an increase of speed due to convection. Brinkman’s equation lead to the same results as Darcy’s laws for narrow gap Hele–Shaw cells. For large gaps, modeling the hydrodynamics using Stokes’ flow lead to the same results.

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Khavasi, Ehsan, Bahar Firoozabadi, and Hossein Afshin. "Linear analysis of the stability of particle-laden stratified shear layers." Canadian Journal of Physics 92, no. 2 (February 2014): 103–15. http://dx.doi.org/10.1139/cjp-2013-0028.

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Hydrodynamic instabilities at the interface of stratified shear layers could occur in various modes and have an important role in the mixing process. In this work, the linear stability analysis in the temporal framework is used to study the stability characteristics of a particle-laden stratified two-layer flow for two different background density profiles: smooth (hyperbolic tangent) and piecewise linear. The effect of parameters, such as bed slope, viscosity, and particle size, on the stability is also considered. The pseudospectral collocation method employing Chebyshev polynomials is used to solve two coupled eigenvalue equations. Based on the results, there are some differences in the stability characteristics of the two density profiles. In the case of R = 1 (R is the ratio of the shear layer thickness to the density layer thickness), the stability boundary in smooth profile is the transition from the unstable flow (where the dominant unstable mode is Kelvin–Helmholtz) to the stable one where in the piecewise linear profile this boundary is the transition from Kelvin–Helmholtz to the Holmboe mode. It is also shown that the unstable region increases with the bed slope and unstable modes amplify as the bed slope increases. For R = 5 the flow does not become stable by increasing the stratification in nonzero bed slope, and in some wavenumbers the Kelvin–Helmholtz and Holmboe modes coexist. In addition, by increasing the bed slope the growth rate of the Holmboe mode and the range of its existence decrease. As expected, the viscosity makes the current more stable, and for large values of the viscosity (small Reynolds number) the flow becomes stable at long waves (small wave numbers) for all bulk Richardson numbers. Existence of small particles does not change the instability characteristics so much, however, large particles make the flow more unstable.

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Demyanko, Kirill V., Igor E. Kaporin, and Yuri M. Nechepurenko. "Inexact Newton method for the solution of eigenproblems arising in hydrodynamic temporal stability analysis." Journal of Numerical Mathematics 28, no. 1 (March 26, 2020): 1–14. http://dx.doi.org/10.1515/jnma-2019-0021.

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AbstractThe inexact Newton method developed earlier for computing deflating subspaces associated with separated groups of finite eigenvalues of regular linear large sparse non-Hermitian matrix pencils is specialized to solve eigenproblems arising in the hydrodynamic temporal stability analysis. To this end, for linear systems to be solved at each step of the Newton method, a new efficient MLILU2 preconditioner based on the multilevel 2nd order incomplete LU-factorization is proposed. A special variant of Krylov subspace method IDR2 with right preconditioning is developed. In comparison with GMRES it requires much smaller workspace while may converge considerably faster than BiCGStab. The effectiveness of the proposed methods is illustrated with matrix pencils of order up to 3.1 ⋅ 106 arising in the temporal linear stability analysis of a typical hydrodinamic flow.

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Ghosh, Abhishek, and Sisir Kumar Guha. "Linear stability analysis of finite hydrodynamic journal bearing under turbulent lubrication with coupled-stress fluid." Industrial Lubrication and Tribology 68, no. 3 (April 11, 2016): 386–91. http://dx.doi.org/10.1108/ilt-07-2015-0094.

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Purpose Several researchers have observed that to satisfy modern day’s need, it is essential to enhance the characteristics of journal bearing, which is used in numerous applications. Moreover, the use of Newtonian fluid as a lubricant is diminishing day by day, and the use of Non-Newtonian fluids is coming more into picture. Furthermore, if turbo-machinery applications are taken into account, then it can be seen that journal bearings are used for high speed applications as well. Thus, neglecting turbulent conditions may lead to erroneous results. Hence, this paper aims to present focuses on studying the stability characteristics of finite hydrodynamic journal bearing under turbulent coupled-stress lubrication. Design/methodology/approach First, the governing equation relevant to the problem is generated. Then, the dynamic analysis is carried out by linear perturbation technique, leading to three perturbed equations, which are again discretized by finite difference method. Finally, these discretized equations are solved with the help of Gauss-Seidel Iteration technique with successive over relaxation scheme. Consequently, the film response coefficients and the stability parameters are evaluated at different parametric conditions. Findings It has been concluded from the study that with increase in value of the coupled-stress parameter, the stability of the journal may increase. Whereas, with increase in Reynolds number, the stability of the journal decreases. On the other hand, stability increases with increasing values of slenderness ratio. Originality/value Researches have been performed to study the dynamic characteristics of journal bearing with non-Newtonian fluid as the lubricant. But in the class of non-Newtonian lubricants, the use of coupled-stress fluid has not yet been properly investigated. So, an attempt has been made to perform the stability analysis of bearings with coupled-stress fluid as the advanced lubricant.

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Moreno-Boza, D., W. Coenen, A. Sevilla, J. Carpio, A. L. Sánchez, and A. Liñán. "Diffusion-flame flickering as a hydrodynamic global mode." Journal of Fluid Mechanics 798 (June 15, 2016): 997–1014. http://dx.doi.org/10.1017/jfm.2016.358.

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The present study employs a linear global stability analysis to investigate buoyancy-induced flickering of axisymmetric laminar jet diffusion flames as a hydrodynamic global mode. The instability-driving interactions of the buoyancy force with the density differences induced by the chemical heat release are described in the infinitely fast reaction limit for unity Lewis numbers of the reactants. The analysis determines the critical conditions at the onset of the linear global instability as well as the Strouhal number of the associated oscillations in terms of the governing parameters of the problem. Marginal instability boundaries are delineated in the Froude number/Reynolds number plane for different fuel jet dilutions. The results of the global stability analysis are compared with direct numerical simulations of time-dependent axisymmetric jet flames and also with results of a local spatio-temporal stability analysis.

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42

Han, Xiang Lin, and Cheng Ouyang. "A Lattice Hydrodynamic Model Considering the Following Lattice and its Stability Analysis." Applied Mechanics and Materials 444-445 (October 2013): 293–98. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.293.

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Incorporating the ITS in traffic flow, two lattice hydrodynamic models considering the following lattice are proposed to study the influence of the following lattice on traffic flow stability. The results from the linear stability theory show that considering the following lattice could lead to the improvement of the traffic flow stability. The modified Korteweg-de Vries equations (the mKdV equation, for short) near the critical point are derived by using the nonlinear perturbation method to show that the traffic jam could be described by the kink-antikink soliton solutions for the mKdV equations.

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Wang, Feng-Hui, Yu-Chuan Zhu, Zhan-Hong Wan, and Song He. "Stability analysis of a two-phase suspension between rotating porous cylinder with the radial flow." Modern Physics Letters B 29, no. 05 (February 20, 2015): 1550014. http://dx.doi.org/10.1142/s0217984915500141.

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The hydrodynamic stability analysis of viscous flow between rotating porous cylinder has been researched for a long time by many researchers. But little works have been carried out about the linear stability analysis of the two-phase suspension. When the radial flow is present, the linear hydrodynamic stability analysis of suspension has been carried out between rotating porous cylinder. We know that the continuous and Stokes equations cannot only solve the stability problem of the continuous fluid phase, but also solving the stability problem of the discontinuous particle phase. The stability equations from an eigenvalue problem that was solved by a numerical technique based on Wan's method. The results reveal that the radial Reynolds number have a great effect on the critical Taylor number in the suspension. In this paper, we also researched on how the critical Taylor number changes as the radius ratio η, the axial wave number k, the particle concentration and the circumferential direction wave number happen to change with the radial Reynolds number increasing range from -5 to 5. Thus, our research discovered the radial inflow and outflow have a stabilizing effect on the two-phase suspension and the circumferential direction wave number also has a stabilizing effect.

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44

He, Yu-Chu, Geng Zhang, and Dong Chen. "Effect of density integration on the stability of a new lattice hydrodynamic model." International Journal of Modern Physics B 33, no. 09 (April 10, 2019): 1950071. http://dx.doi.org/10.1142/s0217979219500711.

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A novel traffic lattice hydrodynamic model considering the effect of density integration is proposed and analyzed in the paper. Via linear stability theory, linear stability condition of the new model is derived, which reveals an improvement of traffic stability by considering the integration of continuous historical density information. Moreover, the nonlinear properties of the extended model are revealed through nonlinear analysis. The propagating backwards kink–antikink waves are generated by deriving the mKdV equation near the critical point and verified by numerical simulation. All the results show that the density integration effect can suppress traffic congestion efficiently in traffic lattice hydrodynamic modeling.

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45

Feng, Yue-Hong, Ming Mei, and Guojing Zhang. "Nonlinear structural stability and linear dynamic instability of transonic steady-states to hydrodynamic model for semiconductors." Journal of Differential Equations 344 (January 2023): 131–71. http://dx.doi.org/10.1016/j.jde.2022.10.038.

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46

Boyadjiev, Christo, and Maria Doichinova. "A method for stability analysis of the non-linear heat and mass transfer processes." Thermal Science 8, no. 1 (2004): 95–105. http://dx.doi.org/10.2298/tsci0401095b.

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Many systems with non-linear heat and mass transfer processes might be unstable at certain conditions. Small disturbances might bring out them of their equilibrium state, after which they achieve itself to a new stable state. The method developed here concerns a non-linear analysis of hydrodynamic stability of the systems with intensive heat and mass transfer. It al lows the determination of the kinetic energy distribution between the main flow and the disturbance, when the equilibrium value of the disturbance amplitude is determined.

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Bansal, Pikesh, Ajit K. Chattopadhayay, and Vishnu P. Agrawal. "Linear Stability Analysis of Hydrodynamic Journal Bearings with a Flexible Liner and Micropolar Lubrication." Tribology Transactions 58, no. 2 (January 7, 2015): 316–26. http://dx.doi.org/10.1080/10402004.2014.969817.

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48

Rukes, Lothar, Christian Oliver Paschereit, and Kilian Oberleithner. "An assessment of turbulence models for linear hydrodynamic stability analysis of strongly swirling jets." European Journal of Mechanics - B/Fluids 59 (September 2016): 205–18. http://dx.doi.org/10.1016/j.euromechflu.2016.05.004.

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Vorobyov, Eduard, and Christian Theis. "Structure Formation in Anisotropic Disks." Proceedings of the International Astronomical Union 2, S235 (August 2006): 143. http://dx.doi.org/10.1017/s1743921306005758.

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The majority of normal disk galaxies are characterized by non-axisymmetric structures like spirals or bars. These structural elements have been widely discussed in the literature as a result of gravitational instabilities which are connected to growing density waves or global instabilities of disks. A first insight into the properties of galactic discs was provided by linear stability analysis. However, a disadvantage of linear stability analysis remained its restriction to small perturbations, both in amplitude and wavelength. Thus, numerical simulations, especially hydrodynamical and stellar-hydrodynamical simulations became a primary tool for the analysis of galactic evolution.

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Emerson, Benjamin, Tim Lieuwen, and Matthew P. Juniper. "Local stability analysis and eigenvalue sensitivity of reacting bluff-body wakes." Journal of Fluid Mechanics 788 (January 8, 2016): 549–75. http://dx.doi.org/10.1017/jfm.2015.724.

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This paper presents an experimental and theoretical investigation of high-Reynolds-number low-density reacting wakes near a hydrodynamic Hopf bifurcation. This configuration is applicable to the wake flows that are commonly used to stabilize flames in high-velocity flows. First, an experimental study is conducted to measure the limit-cycle oscillation of this reacting bluff-body wake. The experiment is repeated while independently varying the bluff-body lip velocity and the density ratio across the flame. In all cases, the wake exhibits a sinuous oscillation. Linear stability analysis is performed on the measured time-averaged velocity and density fields. In the first stage of this analysis, a local spatiotemporal stability analysis is performed on the measured time-averaged velocity and density fields. The stability analysis results are compared to the experimental measurement and demonstrate that the local stability analysis correctly captures the influence of the lip-velocity and density-ratio parameters on the sinuous mode. In the second stage of the analysis, the linear direct and adjoint global modes are estimated by combining the local results. The sensitivity of the eigenvalue to changes in intrinsic feedback mechanisms is found by combining the direct and adjoint global modes. This is referred to as the eigenvalue sensitivity throughout the paper for reasons of brevity. The predicted global mode frequency is consistently within 10 % of the measured value, and the linear global mode shape closely resembles the measured nonlinear oscillations. The adjoint global mode reveals that the oscillation is strongly sensitive to open-loop forcing in the shear layers. The eigenvalue sensitivity identifies a wavemaker in the recirculation zone of the wake. A parametric study shows that these regions change little when the density ratio and lip velocity change. In the third stage of the analysis, the stability analysis is repeated for the varicose hydrodynamic mode. Although not physically observed in this unforced flow, the varicose mode can lock into longitudinal acoustic waves and cause thermoacoustic oscillations to occur. The paper shows that the local stability analysis successfully predicts the global hydrodynamic stability characteristics of this flow and shows that experimental data can be post-processed with this method in order to identify the wavemaker regions and the regions that are most sensitive to external forcing, for example from acoustic waves.

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Journal articles on the topic 'Hydrodynamics linear stability analysis'

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