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Journal articles on the topic 'Hydrodynamic stability theory'

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Published: 6 September 2023

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1

Georgescu, A., and J. T. Stuart. "Hydrodynamic Stability Theory." Journal of Applied Mechanics 54, no. 1 (March 1, 1987): 250. http://dx.doi.org/10.1115/1.3172987.

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2

Dauchot, Olivier, and Paul Manneville. "Local Versus Global Concepts in Hydrodynamic Stability Theory." Journal de Physique II 7, no. 2 (February 1997): 371–89. http://dx.doi.org/10.1051/jp2:1997131.

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3

Malik, Mujeeb R. "Review of "Theory and Computation in Hydrodynamic Stability."." AIAA Journal 43, no. 4 (April 2005): 924–25. http://dx.doi.org/10.2514/1.16537.

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4

Yano, Masayuki, and Anthony T. Patera. "A space–time variational approach to hydrodynamic stability theory." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2155 (July 8, 2013): 20130036. http://dx.doi.org/10.1098/rspa.2013.0036.

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We present a hydrodynamic stability theory for incompressible viscous fluid flows based on a space–time variational formulation and associated generalized singular value decomposition of the (linearized) Navier–Stokes equations. We first introduce a linear framework applicable to a wide variety of stationary- or time-dependent base flows: we consider arbitrary disturbances in both the initial condition and the dynamics measured in a ‘data’ space–time norm; the theory provides a rigorous, sharp (realizable) and efficiently computed bound for the velocity perturbation measured in a ‘solution’ space–time norm. We next present a generalization of the linear framework in which the disturbances and perturbation are now measured in respective selected space–time semi-norms ; the semi-norm theory permits rigorous and sharp quantification of, for example, the growth of initial disturbances or functional outputs. We then develop a (Brezzi–Rappaz–Raviart) nonlinear theory which provides, for disturbances which satisfy a certain (rather stringent) amplitude condition, rigorous finite-amplitude bounds for the velocity and output perturbations. Finally, we demonstrate the application of our linear and nonlinear hydrodynamic stability theory to unsteady moderate Reynolds number flow in an eddy-promoter channel.
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5

Heng, Zhou, and K. Fujimura. "Further improvement of weakly nonlinear theory of hydrodynamic stability." Science in China Series A: Mathematics 41, no. 1 (January 1998): 84–92. http://dx.doi.org/10.1007/bf02900777.

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6

Shao, Song Shi, Jiong Sun, and Kai Liu. "Bifurcation Analysis for Sailing Stability of Autonomous Underwater Vehicle." Applied Mechanics and Materials 44-47 (December 2010): 1682–86. http://dx.doi.org/10.4028/www.scientific.net/amm.44-47.1682.

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There are several nonlinear elements in the equations of Autonomous Underwater Vehicle(AUV) movements. It is difficult to deal nonlinear problem with traditional methods. A hydrodynamic parameter interference is chosen as bifurcation parameter at first. Then the sailing stability of AUV with proportional-derivative controller is analysed by bifurcation theory. The center manifold theory is used to get the expression of system state parameters. And the Hopf bifurcation of system is analysed. The result is verified by numerical simulations. It shows that the hydrodynamic parameter’s changing will bring Hopf bifurcation for depthkeeping saiiling. And the range of hydrodynamic parameter value that insures AUV sailing stability is given.
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7

Andreichenko, D. K., and K. P. Andreichenko. "On the theory of stability of a cylindrical hydrodynamic suspension." Fluid Dynamics 44, no. 1 (February 2009): 10–21. http://dx.doi.org/10.1134/s0015462809010025.

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8

Chow, Carson C., and Terence Hwa. "Defect-mediated stability: an effective hydrodynamic theory of spatiotemporal chaos." Physica D: Nonlinear Phenomena 84, no. 3-4 (July 1995): 494–512. http://dx.doi.org/10.1016/0167-2789(95)00072-c.

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9

Kuhlmann, H. C., and H. J. Rath. "Hydrodynamic instabilities in cylindrical thermocapillary liquid bridges." Journal of Fluid Mechanics 247 (February 1993): 247–74. http://dx.doi.org/10.1017/s0022112093000461.

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The hydrodynamic stability of steady axisymmetric thermocapillary flow in a cylindrical liquid bridge is investigated by linear stability theory. The basic state and the three-dimensional disturbance equations are solved by various spectral methods for aspect ratios close to unity. The critical modes have azimuthal wavenumber one and the most dangerous disturbance is either a pure hydrodynamic steady mode or an oscillatory hydrothermal wave, depending on the Prandtl number. The influence of heat transfer through the free surface, additional buoyancy forces, and variations of the aspect ratio on the stability boundaries and the neutral mode are discussed.
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10

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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11

Heng, Zhou. "The re-examination of the weakly nonlinear theory of hydrodynamic stability." Applied Mathematics and Mechanics 12, no. 3 (March 1991): 219–25. http://dx.doi.org/10.1007/bf02098051.

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12

Kim, Daejong, Sanghoon Lee, Michael D. Bryant, and Frederick F. Ling. "Hydrodynamic Performance of Gas Microbearings." Journal of Tribology 126, no. 4 (October 1, 2004): 711–18. http://dx.doi.org/10.1115/1.1792676.

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Hydrodynamic performance of gas microbearings, fabricated with deep X-ray lithography and electroplating, will be presented in this article. Static performance in terms of load parameters and attitude angles was calculated using Molecular Gas Lubrication (MGL) theory. Threshold speed and allowable rotor mass were calculated to investigate safe operating conditions of the fabricated gas microbearings using orbit simulation. Finally, improved bearing designs were proposed to increase stability.
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13

LAMBELIN, JEAN-PIERRE, FRANÇOIS NADAL, ROMAIN LAGRANGE, and ARTHUR SARTHOU. "Non-resonant viscous theory for the stability of a fluid-filled gyroscope." Journal of Fluid Mechanics 639 (October 16, 2009): 167–94. http://dx.doi.org/10.1017/s0022112009990978.

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In the case of a gyroscope including a cylindrical fluid-filled cavity, the classic Poinsot's coning motion can become unstable. For certain values of the solid inertia ratio, the coning angle opens under the effect of the hydrodynamic torque. The coupled dynamics of such a non-solid system is ruled by four dimensionless numbers: the small viscous parameter ε = Re−1/2 (where Re denotes the Reynolds number), the fluid–solid inertia ratio κ which quantifies the proportion of liquid relative to the total mass of the gyroscope, the solid inertia ratio σ and the aspect ratio h of the cylindrical cavity. The calculation of the hydrodynamic torque on the solid part of the gyroscope requires the preliminary evaluation of the possibly resonant flow inside the cavity. The hydrodynamic scaling used to derive such a flow essentially depends on the relative values of κ and ε. For small values of the ratio /ε (compared to 1), Gans derived an expression of the growth rate of the coning angle. The principles of Gans' approach (Gans, AIAA J., vol. 22, 1984, pp. 1465–1471) are briefly recalled but the details of the whole calculation are not given. At the opposite limit, that is for large values of /ε, the dominating flow is given by a linear inviscid theory. In order to take account of viscous effects, we propose a direct method involving an exhaustive calculation of the flow at order ε. We show that the deviations from Stewartson's inviscid theory (Stewartson, J. Fluid Mech., vol. 5, 1958, p. 577) do not originate from the viscous shear at the walls but rather from the bulk pressure at order ε related to the Ekman suction. Physical contents of Wedemeyer's heuristic theory (Wedemeyer, BRL Report N 1325, 1966) are analysed in the view of our analytical results. The latter are tested numerically in a large range of parameters. Complete Navier–Stokes (NS) equations are solved in the cavity. The hydrodynamic torque obtained by numerical integration of the stress is used as a forcing term in the coupled fluid–solid equations. Numerical results and analytical predictions show a fairly good quantitative agreement.
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14

Akhmetov, Vadim. "HYDRODYNAMIC STABILITY OF SWIRLING FLOWS WITH AXIAL RECIRCULATION ZONES." International Journal for Computational Civil and Structural Engineering 19, no. 1 (March 29, 2023): 14–22. http://dx.doi.org/10.22337/2587-9618-2023-19-1-14-22.

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The problem of the motion of a viscous incompressible swirling flow in an axisymmetric channel has been numerically investigated. Various flow regimes have been obtained, including those with the formation of the axial recirculation zones. In the framework of linear theory, the stability of the obtained calculated flows with respect to non-axisymmetric perturbations is investigated on the assumption of local parallelism. The growth rates and phase velocities of unstable disturbances are calculated. In the presence of a reverse flow zone, the disturbances growth rates are increased significantly.
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15

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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16

Bojadjiev, Chr. "Nonlinear mass transfer and hydrodynamic stability in solubility phenomena." Pure and Applied Chemistry 74, no. 10 (January 1, 2002): 1801–10. http://dx.doi.org/10.1351/pac200274101801.

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The dissolution of gases, liquids,or solids in liquids is a heterogeneous reaction, and in many cases, the reaction rate is limited by a diffusive transfer of substance in the boundary layer at the face interphase. In modern industry, intensive interphase mass transfer processes are accomplished by large concentration gradients. This can result in a set of nonlinear effects and the difference between experimental data and predictions of the linear mass transfer theory. One of the main nonlinear effects is a result of the induction of a secondary flow at the interface boundary. This can lead to essential changes of the dissolution rate and the hydrodynamic stability of the system.
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17

Lattanzio, J. C., and E. R. Keto. "Collisions Between High Latitude Clouds: Theory Meets Observations." International Astronomical Union Colloquium 120 (1989): 460. http://dx.doi.org/10.1017/s025292110002426x.

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We report on fully three-dimensional hydrodynamic and radiative transfer simulations of collisions between high latitude clouds. Our model uses the smoothed particle hydrodynamics code described by Lattanzio and Henriksen (1988) to compute the velocity, temperature, and density fields in the impacted clouds and a recently developed radiative transfer code to compute 13 CO line radiation from the simulated source. By including the instrumental effects involved in a particular observations we can make detailed comparisons with the observations. The model shows that: 1) The previously unexplained energy source for the broad CO line wings reported by Blitz, Magnani, and Wandel (1988) derives from the collisions. 2) Collisions can induce rapid gravitational collapse and star formation in these clouds which are otherwise supported against gravitational contraction via their internal energy content. 3) The external pressure due to intercloud HI, firts proposed for these objects by Keto and Myers (1986), plays a significant role in the stability and evolution of the high latitude clouds.
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18

Speziale, Charles G., Ridha Abid, and Gregory A. Blaisdell. "On the consistency of Reynolds stress turbulence closures with hydrodynamic stability theory." Physics of Fluids 8, no. 3 (March 1996): 781–88. http://dx.doi.org/10.1063/1.868861.

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19

Makov, Yu N. "Analogy between shear flow stratification and compressibility effects in hydrodynamic stability theory." Fluid Dynamics 25, no. 2 (1990): 313–16. http://dx.doi.org/10.1007/bf01058986.

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20

Eckert, M. "The troublesome birth of hydrodynamic stability theory: Sommerfeld and the turbulence problem." European Physical Journal H 35, no. 1 (April 24, 2010): 29–51. http://dx.doi.org/10.1140/epjh/e2010-00003-3.

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21

Huet, Patrick, K. Kajantie, Robert G. Leigh, Bao-Hua Liu, and L. McLerran. "Hydrodynamic stability analysis of burning bubbles in electroweak theory and in QCD." Physical Review D 48, no. 6 (September 15, 1993): 2477–92. http://dx.doi.org/10.1103/physrevd.48.2477.

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22

MATSUI, N., K. MIMA, M. HONDA, and A. NISHIGUCHI. "Analysis of rippled shock-wave propagation and ablation-front stability by theory and hydrodynamic simulation." Journal of Plasma Physics 61, no. 1 (January 1999): 43–50. http://dx.doi.org/10.1017/s0022377898007260.

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The hydrodynamic start-up problem is one of the most crucial issues in laser-driven symmetrical implosion. The target-surface roughness and initial imprint by nonuniform laser irradiation result in Rayleigh–Taylor instability in the acceleration and deceleration phase. To estimate the tolerance of the target-surface roughness, the temporal behaviour of corrugated ablation surface and rippled shock-wave propagation are investigated using a perturbation analysis of the fluid equation, which is solved under the boundary model of a fire-polished ablation surface. The results show good agreement with two- dimensional hydrodynamic simulation and experimental results [T. Endo et al., Phys. Rev. Lett.74, 3608 (1995)].
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23

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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24

Kim, Boo-Ki, and Michael M. Bernitsas. "Effect of Memory on the Stability of Spread Mooring Systems." Journal of Ship Research 43, no. 03 (September 1, 1999): 157–69. http://dx.doi.org/10.5957/jsr.1999.43.3.157.

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The importance of including the hydrodynamic memory effect in modeling and analysis of spread mooring systems (SMS) is assessed based on the design methodology for mooring systems developed at the University of Michigan. The memory effect is modeled by the hydrodynamic radiation forces expressed in terms of added mass at infinite frequency and convolution integrals of impulse response functions. The convolution integrals, which are explicit functions of time, are converted to autonomous excitation by the method of extended dynamics. For a given SMS configuration, nonlinear stability and bifurcation theory are used to produce catastrophe sets in the parametric design space separating regions of qualitatively different system dynamics. This approach reveals the complete picture of nonlinear phenomena associated with system dynamics and eliminates the need for extensive simulations. Catastrophe sets are developed in several parametric design spaces, providing fundamental understanding of the memory effects on SMS nonlinear dynamics. The mathematical model is based on the slow-motion maneuvering equations in the horizontal plane, including hydrodynamic memory effect and third-order quasi-steady hydrodynamic forces. Mooring lines are modeled by synthetic fiber ropes attached to surface terminals and deep-water catenary chains with touchdown and nonlinear drag. Environmental loads consist of time-independent current, wind, and mean wave drift forces.
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25

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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26

Zhu, Lailai, and Howard A. Stone. "Rotation of a low-Reynolds-number watermill: theory and simulations." Journal of Fluid Mechanics 849 (June 15, 2018): 57–75. http://dx.doi.org/10.1017/jfm.2018.416.

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Recent experiments have demonstrated that small-scale rotary devices installed in a microfluidic channel can be driven passively by the underlying flow alone without resorting to conventionally applied magnetic or electric fields. In this work, we conduct a theoretical and numerical study on such a flow-driven ‘watermill’ at low Reynolds number, focusing on its hydrodynamic features. We model the watermill by a collection of equally spaced rigid rods. Based on the classical resistive force (RF) theory and direct numerical simulations, we compute the watermill’s instantaneous rotational velocity as a function of its rod number $N$, position and orientation. When $N\geqslant 4$, the RF theory predicts that the watermill’s rotational velocity is independent of $N$ and its orientation, implying the full rotational symmetry (of infinite order), even though the geometrical configuration exhibits a lower-fold rotational symmetry; the numerical solutions including hydrodynamic interactions show a weak dependence on $N$ and the orientation. In addition, we adopt a dynamical system approach to identify the equilibrium positions of the watermill and analyse their stability. We further compare the theoretically and numerically derived rotational velocities, which agree with each other in general, while considerable discrepancy arises in certain configurations owing to the hydrodynamic interactions neglected by the RF theory. We confirm this conclusion by employing the RF-based asymptotic framework incorporating hydrodynamic interactions for a simpler watermill consisting of two or three rods and we show that accounting for hydrodynamic interactions can significantly enhance the accuracy of the theoretical predictions.
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27

KOCH, DONALD L., and ASHOK S. SANGANI. "Particle pressure and marginal stability limits for a homogeneous monodisperse gas-fluidized bed: kinetic theory and numerical simulations." Journal of Fluid Mechanics 400 (December 10, 1999): 229–63. http://dx.doi.org/10.1017/s0022112099006485.

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A linear stability analysis is performed for the homogeneous state of a monodisperse gas-fluidized bed of spherical particles undergoing hydrodynamic interactions and solid-body collisions at small particle Reynolds number and finite Stokes number. A prerequisite for the stability analysis is the determination of the particle velocity variance which controls the particle-phase pressure. In the absence of an imposed shear, this velocity variance arises solely due to the hydrodynamic interactions among the particles. Since the uniform state of these suspensions is unstable over a wide range of values of particle volume fraction φ and Stokes number St, full dynamic simulations cannot be used in general to characterize the properties of the homogeneous state. Instead, we use an asymptotic analysis for large Stokes numbers together with numerical simulations of the hydrodynamic interactions among particles with specified velocities to determine the hydrodynamic sources and sinks of particle-phase energy. In this limit, the velocity distribution to leading order is Maxwellian and therefore standard kinetic theories for granular/hard-sphere molecular systems can be used to predict the particle-phase pressure and rheology of the bed once the velocity variance of the particles is determined. The analysis is then extended to moderately large Stokes numbers for which the anisotropy of the velocity distribution is considerable by using a kinetic theory which combines the theoretical analysis of Koch (1990) for dilute suspensions (φ [Lt ] 1) with numerical simulation results for non-dilute suspensions at large Stokes numbers. A linear stability analysis of the resulting equations of motion provides the first a priori predictions of the marginal stability limits for the homogeneous state of a gas-fluidized bed. Dynamical simulations following the detailed motions of the particles in small periodic unit cells confirm the theoretical predictions for the particle velocity variance. Simulations using larger unit cells exhibit an inhomogeneous structure consistent with the predicted instability of the homogeneous gas–solid suspension.
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28

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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29

Sun, Di-Hua, Geng Zhang, Min Zhao, Sen-Lin Cheng, and Jian-Dong Cao. "Stability analysis of feedforward anticipation optimal flux difference in traffic lattice hydrodynamic theory." Communications in Nonlinear Science and Numerical Simulation 56 (March 2018): 287–95. http://dx.doi.org/10.1016/j.cnsns.2017.08.004.

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30

Heng, Zhou, and You Xueyi. "On problems in the weakly nonlinear theory of hydrodynamic stability and its improvement." Acta Mechanica Sinica 9, no. 1 (February 1993): 1–12. http://dx.doi.org/10.1007/bf02489156.

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31

Албагачиев, Али, Ali Albagachiev, Владимир Данилов, and Vladimir Danilov. "MAGNETIC LIQUID IN HYDRODYNAMIC LUBRICATION MODE OF SPHERICAL SURFACES." Bulletin of Bryansk state technical university 2016, no. 3 (September 30, 2016): 90–93. http://dx.doi.org/10.12737/22017.

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From the position of the hydrodynamic lubrication theory are considered the peculiarities of magnetoliquid lubrication in a point contact determined with a complicated character of the interaction of hydrodynamic and magnetic forces in a lubrication layer. The pressure distribution in a lubrication layer of magnetic liquid is considered as a superposition of the augend and addend pr and pm induced with hydrodynamic and magnetic forces. The contribution of the constituent pr is described by Reynolds equation in accordance with the classic hydrodynamic theory. At the saturation of magnetic liquid the constituent pm is presented as a function of the magnetic field strength, saturation magnetization of magnetic liquid and its viscosity and also velocity of rolling. As a result of the solution of a hydrodynamic problem through a numerical method there are defined conditions under which a lubrication layer loses its stability that is followed with the loss of carrying capacity in areas with negative pressure. The dependences of resistance to rolling forces, and sliding ones in a contact of spherical surfaces.
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32

Oza, Anand U., Rodolfo R. Rosales, and John W. M. Bush. "A trajectory equation for walking droplets: hydrodynamic pilot-wave theory." Journal of Fluid Mechanics 737 (November 27, 2013): 552–70. http://dx.doi.org/10.1017/jfm.2013.581.

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AbstractWe present the results of a theoretical investigation of droplets bouncing on a vertically vibrating fluid bath. An integro-differential equation describing the horizontal motion of the drop is developed by approximating the drop as a continuous moving source of standing waves. Our model indicates that, as the forcing acceleration is increased, the bouncing state destabilizes into steady horizontal motion along a straight line, a walking state, via a supercritical pitchfork bifurcation. Predictions for the dependence of the walking threshold and drop speed on the system parameters compare favourably with experimental data. By considering the stability of the walking state, we show that the drop is stable to perturbations in the direction of motion and neutrally stable to lateral perturbations. This result lends insight into the possibility of chaotic dynamics emerging when droplets walk in complex geometries.
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33

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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34

MILLER, M. D., and E. KROTSCHECK. "THEORY OF THIRD SOUND AND STABILITY OF THIN 3He–4He SUPERFLUID FILMS." International Journal of Modern Physics B 21, no. 13n14 (May 30, 2007): 2091–102. http://dx.doi.org/10.1142/s021797920704349x.

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In this paper, we summarize the results of recent studies of third sound in thin, superfluid 3 He -4 He mixture films and the relation of the third sound spectrum to the question of the films' thermodynamic stability. We have considered films on several representative substrates: Nuclepore, glass, Li and Na . Our approach utilizes the variational, hypernetted chain/Euler-Lagrange (HNC–EL) theory as applied to inhomogeneous boson systems to calculate chemical potentials for both the 4 He superfluid film and the physisorbed 3 He . Numerical density derivatives of the chemical potentials lead to the sought-after third sound speeds. On all substrates, the third sound speeds show a series of oscillations as a function of film coverage that is driven by the layered structure of the 4 He film. We find that the effect on the third sound response of adding a small amount of 3 He to the 4 He film can depend sensitively on the particular 4 He film coverage. The third sound speed can either increase or decrease. In fact, in some regimes, the added 3 He destabilizes the film and can drive "layering transitions" leading to quite complicated geometric structures of the film in which the outermost layer consists of phase–separated regimes of 3 He and 4 He . Finally, we examine the range of applicability of the usual film–averaged hydrodynamic description. We find that at least up to film thicknesses of six liquid layers, there is no regime in which this hydrodynamic description is applicable.
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35

Li, Lixiang, Hongxia Ge, and Rongjun Cheng. "Analysis of the predictive effect and feedback control in an extended lattice hydrodynamic model." Engineering Computations 37, no. 5 (December 16, 2019): 1645–61. http://dx.doi.org/10.1108/ec-07-2019-0297.

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Purpose This paper aims to put forward an extended lattice hydrodynamic model, explore its effects on alleviating traffic congestion and provide theoretical basis for traffic management departments and traffic engineering implementation departments. Design/methodology/approach The control method is applied to study the stability of the new model. Through nonlinear analysis, the mKdV equation representing kink-antikink soliton is acquired. Findings The predictive effect and the control signal can enhance the traffic flow stability and reduce the energy consumption. Originality/value The predictive effect and feedback control are first considered in lattice hydrodynamic model simultaneously. Numerical simulations demonstrate that these two factors can enhance the traffic flow stability.
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36

Chung, Jin-Sug, and Michael M. Bernitsas. "Hydrodynamic Memory Effect on Stability, Bifurcation, and Chaos of Two-Point Mooring Systems." Journal of Ship Research 41, no. 01 (March 1, 1997): 26–44. http://dx.doi.org/10.5957/jsr.1997.41.1.26.

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The stability properties of two-point mooring systems governed by their slow horizontal motions are studied theoretically. The often-neglected memory effect due to hydrodynamic wave loads change—in some cases critically—the stability boundaries in the system design space. The third-order maneuvering equations and a nonlinear elastic spring model are used to describe the dynamics of the moored vessel and the mooring lines, respectively. The resulting model accurately represents a two-point mooring system and can be used for stability analysis in the sense of Lyapunov. The stability charts of mooring systems with memory effects exhibit considerable differences from systems without memory in local regions of bifurcation diagrams. Further, the pattern of these changes of stability boundaries varies with the hydrodynamic properties of the moored vessel and/or the environmental conditions. The findings of this study suggest that the number of influencing design parameters can be much more than the present stability theory of dynamical systems can handle. They prove, however, that neglecting the memory effect may result in selecting unsafe configurations of two-point mooring systems.
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37

Sun, Dianfeng, Jianjun Sun, Fei Liu, Xiaohua Xu, and Dongliang Zhang. "Stability Analysis of Hydrodynamic Mechanical Seals in Multifrequency Excitation." Coatings 13, no. 7 (June 26, 2023): 1157. http://dx.doi.org/10.3390/coatings13071157.

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The dynamic characteristics of the complex relationship among the sealing system, excitation, and response have a considerable impact on the operational reliability of hydrodynamic mechanical seals, which is a critical issue in the field of sealing theory and technology. Scholars at home and abroad have established dynamic models and calculated the displacement responses of dynamic and static rings in the time domain based on the force on these rings so that the response results can be used for system stability analysis. Neither are the excitation characteristics of cavitation load extracted, nor are the distance response and system leakage rate of the dynamic and static rings analyzed under coupled cavitation and random excitation. In this study, under different operating conditions of the hydrodynamic mechanical seal system, the liquid film evaporation load and seismic load are applied to study the frequency domain response of the distance between the dynamic and static rings and the system leakage rate. The following conclusions have been obtained: Assuming that the chamber pressure is 0.5 MPa and the spring specific pressure is 0.055 MPa, during stable operation, the distance between the moving and stationary rings at 1500 rpm~3000 rpm speeds is 1.12 μm~3.05 μm. For a specific spring pressure of 0.055 MPa, medium pressures of 0.2 MPa~1.0 MPa, and spindle speeds of 1500 rpm~3000 rpm, the excitation force is 30 N, and the frequency is 30 Hz, And the seismic load is assumed to be sinusoidal, the excitation force is 6 N, the fundamental frequency is 120 Hz, and the system leak rate is in 0.1 mL/min~1.3 mL/min. Under multi-frequency excitation coupling, the distance between the dynamic and static rings will decrease as the pressure of the medium in the sealing cavity increases, and this will increase with the increase in the rotating speed. The leakage rate of the system will increase with the increase in the rotating speed and the pressure of the medium, and the test value is largely consistent with the theoretical value.
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38

Chung, J. S. "Stability-Based Design of Two-Point Mooring Systems With Hydrodynamic Memory." Journal of Offshore Mechanics and Arctic Engineering 119, no. 1 (February 1, 1997): 61–69. http://dx.doi.org/10.1115/1.2829047.

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A systematic method of determining the design parameter values of two-point mooring (TPM) systems is presented. The conclusions of nonlinear stability analysis of horizontal plane slow motion dynamics of TPM systems with hydrodynamic memory are used to guide selection of the design variables. Specifically, within the stable regions of bifurcation diagram, a set of parameter values is chosen systematically to examine the corresponding TPM system. Then, each TPM system is simulated and the results are evaluated in terms of given criteria such as tension level of the mooring line or offset of the moored vessel. The hydrodynamic memory effect due to the oscillatory motions of moored vessel is included in the formulation. The memory effect influences the stability properties of TPM systems and alters the design chart/bifurcation diagram and particularly the static loss and dynamic loss of stability. The significance of hydrodynamic memory on several TPM systems is illustrated by comparing the statistics of the simulations. The design approach implemented in this work shows that nonlinear stability theory can be used effectively in the actual design process of mooring systems to reduce dramatically the number of simulations required. It is also shown that the often inconclusive nonlinear time simulations can be guided by theoretical nonlinear stability analysis of system dynamics to produce improved design values of system parameters of TPM systems.
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39

Georgievskii, D. V., W. H. Müller, and B. E. Abali. "Eigenvalue problems for the generalized Orr-Sommerfeld equation in the theory of hydrodynamic stability." Doklady Physics 56, no. 9 (September 2011): 494–97. http://dx.doi.org/10.1134/s1028335811090023.

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40

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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41

Skobelev, B. Yu. "Nonlinear theory of hydrodynamic stability and bifurcations of solutions of the Navier-Stokes equations." Fluid Dynamics 25, no. 1 (1990): 6–11. http://dx.doi.org/10.1007/bf01051290.

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42

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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43

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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44

Wang, Tian Ying, Jian Zhang, and Jin Kun Liu. "Concept Design of a New Non-Ship-Shaped FPSO." Applied Mechanics and Materials 170-173 (May 2012): 2222–27. http://dx.doi.org/10.4028/www.scientific.net/amm.170-173.2222.

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In order to give full play to the advantages of FPSOs in the development of offshore oilfields, a new non-ship-shaped FPSO concept named IQFP is put forward through intensive study on various factors affecting the performance of FPSOs. Then, the optimized IQFP general design of a project case is presented based on the IQFP concept. The intact stability and damage stability of the IQFP are calculated and checked according to IMO rules. The hydrodynamic performance in frequency domain is simulated using the three-dimensional potential flow theory and compared with that of a ship-shaped FPSO with similar tonnage. The results indicate that the IQFP has a large stability margin and more excellent hydrodynamic performance than the ship-shaped FPSO. Through the research of this paper, the excellent characteristic of the new FPSO concept IQFP is verified and the basis and foundation are provided for the further studies.
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45

Yao, Tao, and Zong Yu Chang. "Simulations and Stability Analysis of Wave-Induced Motions of a Freely Floating Body Using ADINA." Applied Mechanics and Materials 775 (July 2015): 14–18. http://dx.doi.org/10.4028/www.scientific.net/amm.775.14.

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In this article, a direct numerical method is developed to solve two-dimensional interaction problems of wave and floating body with ADINA software. Motion’s equation of the floating body and hydrodynamic parameters are expressed based on potential flow theory. The force and response on the floating body boundary is described in terms of linear minor wave theory. The numerical test is carried out. The result intuitively shows the dynamic response and the stability of floating body under incident waves.
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46

Zhang, Fan, and Lan Yin. "Phonon Stability of Quantum Droplets in Dipolar Bose Gases." Chinese Physics Letters 39, no. 6 (June 1, 2022): 060301. http://dx.doi.org/10.1088/0256-307x/39/6/060301.

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Stabilized by quantum fluctuations, dipolar Bose–Einstein condensates can form self-bound liquid-like droplets. However in the Bogoliubov theory, there are imaginary phonon energies in the long-wavelength limit, implying dynamical instability of this system. A similar instability appears in the Bogoliubov theory of a binary quantum droplet, and is removed due to higher-order quantum fluctuations as shown recently [Gu Q and Yin L 2020 Phys. Rev. B 102 220503(R)]. We study the excitation energy of a dipolar quantum droplet in the Beliaev formalism, and find that quantum fluctuations significantly enhance the phonon stability. We adopt a self-consistent approach without the problem of complex excitation energy in the Bogoliubov theory, and obtain a stable anisotropic sound velocity which is consistent with the superfluid hydrodynamic theory, but slightly different from the result of the extended Gross–Pitaevskii equation due to quantum depletion. A modified Gross–Pitaevskii equation in agreement with the Beliaev theory is proposed, which takes the effect of quantum fluctuations into account more completely.
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47

Shi, Sheng-zhe, Xian-Jiao Gao, Ting Jiang, and Teng-jiao Sang. "The Stability of Longitudinal Motion of Amphibious Aircraft During Takeoff." Journal of Physics: Conference Series 2569, no. 1 (August 1, 2023): 012070. http://dx.doi.org/10.1088/1742-6596/2569/1/012070.

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Abstract In this paper, the mathematical model of the takeoff of an amphibious aircraft was established. On this basis, the hydrodynamic coefficients in the pitch and heave motion equation were calculated using the strip theory. The stability criterion was used to analyze the longitudinal motion stability of the amphibious aircraft during takeoff, and three characteristic parameters of the general stability of longitudinal motion were obtained: natural period, half-decay period, and damping ratio. The result showed that the motion of amphibious aircraft was stable during takeoff.
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48

Norman, Colin A. "Theory of bipolar flows and jets from young stars." Symposium - International Astronomical Union 122 (1987): 51–59. http://dx.doi.org/10.1017/s0074180900155901.

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Current thinking on the origin, evolution and stability of stellar jets and bipolar flows is reviewed. Particular emphasis is given to the driving mechanisms of bipolar molecular and ionised gas outflows from young stellar objects. General constraints on both hydrodynamic and magnetohydrodynamic flows are presented. The interrelationship between the protostellar outflows and others such as those associated with powerful, highly collimated outflows in active galactic nuclei are discussed. Intimately connected phenomena such as maser sources and Herbig-Haro objects are briefly treated and finally, areas of potentially interesting future research are indicated.
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49

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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50

Feola, Roberto, Felice Iandoli, and Federico Murgante. "Long-time stability of the quantum hydrodynamic system on irrational tori." Mathematics in Engineering 4, no. 3 (2021): 1–24. http://dx.doi.org/10.3934/mine.2022023.

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<abstract><p>We consider the quantum hydrodynamic system on a $ d $-dimensional irrational torus with $ d = 2, 3 $. We discuss the behaviour, over a "non-trivial" time interval, of the $ H^s $-Sobolev norms of solutions. More precisely we prove that, for generic irrational tori, the solutions, evolving form $ \varepsilon $-small initial conditions, remain bounded in $ H^s $ for a time scale of order $ O(\varepsilon^{-1-1/(d-1)+}) $, which is strictly larger with respect to the time-scale provided by local theory. We exploit a Madelung transformation to rewrite the system as a nonlinear Schrödinger equation. We therefore implement a Birkhoff normal form procedure involving small divisors arising form three waves interactions. The main difficulty is to control the loss of derivatives coming from the exchange of energy between high Fourier modes. This is due to the irrationality of the torus which prevents to have "good separation'' properties of the eigenvalues of the linearized operator at zero. The main steps of the proof are: (i) to prove precise lower bounds on small divisors; (ii) to construct a modified energy by means of a suitable high/low frequencies analysis, which gives an a priori estimate on the solutions.</p></abstract>
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