方柱尾流流态对床面冲淤形态的影响

应用平面二维悬沙数学模型对方柱尾流区的泥沙输运及床面调整进行了数值模拟，并对重要物理参数做了分析说明。数值计算采用时间分裂一全隐式有限差分格式，流场的计算基于沿水深平均的RANS方程。通过系统的数值模拟，揭示了不同来流情况下，方柱尾流区的流态变化，及与之相应的床面变化规律，并对不同流态下的泥沙运动作了分析。计算结果表明在方柱尾流区，不同的流场流态对尾流区的床面调整有明显影响。流场较弱的情况下，尾流区中湍动强度相应较弱，此时悬浮泥沙由于流速减小而普遍落淤，床面应力的减小也致使床面冲刷量减小。随着流场强度的逐渐增大，尾流区中湍动强度相应增强，床面应力增大，同时湍流的强烈交换作用增强了对泥沙的输运作用，床面变化不再是简单的淤积状态，部分区域出现了冲刷。     

Kinematic Characteristics of Fluid Flow in a Channel with a Profiled Bottom

The results of an experimental investigation of fluid flow in a channel with an erodible and profiled rigid bottom are presented. The kinematic parameters of the flow were measured with a laser Doppler anemometer. The experimental data were interpreted using a linear model of potential flow over bottom roughness.     

Incompressible Limit for the Compressible Flow of Liquid Crystals

The connection between the compressible flow of liquid crystals with low Mach number and the incompressible flow of liquid crystals is studied in a bounded domain. In particular, the convergence of weak solutions of the compressible flow of liquid crystals to the weak solutions of the incompressible flow of liquid crystals is proved when the Mach number approaches zero; that is, the incompressible limit is justified for weak solutions in a bounded domain.     

可塌陷气管的p—V关系和极限流量

通过对正常大鼠气管在不同轴向伸长比条件下作液体灌注实验,并对所得压力-容积数据进行最小二乘拟合,得到包含在拟合函数关系式中的大鼠气管材料常数,文章详细分析这些材料常数的力学含义,并对可塌陷气管的顺应性和极限流量进行讨论,文章结果为分析气管在特定力学环境中的适应性生长和塌陷特性提供重要的信息。     

The Slow Erosion Limit in a Model of Granular Flow

We study a 2 × 2 system of balance laws that describes the evolution of a granular material (avalanche) flowing downhill. The original model was proposed by Hadeler and Kuttler (Granul Matter 2:9–18, 1999). The Cauchy problem for this system has been studied by the authors in recent papers (Amadori and Shen in Commun Partial Differ Equ 34:1003–1040, 2009; Shen in J Math Anal Appl 339:828–838, 2008). In this paper, we first consider an initial-boundary value problem. The boundary condition is given by the flow of the incoming material. For this problem we prove the global existence of BV solutions for a suitable class of data, with bounded but possibly large total variations. We then study the “slow erosion (or deposition) limit”. We show that, if the thickness of the moving layer remains small, then the profile of the standing layer depends only on the total mass of the avalanche flowing downhill, not on the time-law describing the rate at which the material slides down. More precisely, in the limit as the thickness of the moving layer tends to zero, the slope of the mountain is provided by an entropy solution to a scalar integro-differential conservation law.     

Higher-Order Terms in the Capillary Limit Approximation of Viscous-Capillary Flow

We propose a new approximation to the solution of the steady state equations describing two-phase immiscible flow in a porous medium. It is demonstrated that the general procedure contains the capillary equilibrium approximation as a special case. The solution is approximated by a perturbation series in a parameter related to the capillary number. The expansion of the solution results in a sequence of decoupled linear elliptic boundary value problems. This sequence is solved numerically by a Finite Element method, and the accuracy of the approximations is evaluated.     

Justification of the Averaging Method for Multifrequency Systems with Pulse Action

We prove new estimates for the error of the averaging method for oscillation systems with slowly varying frequencies subjected to pulse action at fixed times. The main assumption is imposed not on all harmonics of the right-hand side of the system but only on resonance ones.__________Translated from Neliniini Kolyvannya, Vol. 8, No. 1, pp. 61–79, January–March, 2005.     

Justification of the kinematic assumptions for thin-walled rods with shallow profile

In this Note we present a justification of the kinematic assumptions for thin-walled rods with shallow profile. These assumptions are fundamental to writing the one-dimensional equilibrium equations for such structures. The obtained kinematics are different from the Vlassov case, which is only valid for strongly curved profiles. They are also different from the that classically used in shell theory. The justification given in this Note is based on an asymptotic approach. To cite this article: L. Grillet et al., C. R. Mecanique 333 (2005).     

Vortex Funnel Formation by a Mass Sink within the Shallow-Water Model

The problem of the evolution of an axisymmetric vortex in the presence of given mass sinks is considered within the shallow-water model. Using the cyclostrophic balance approximation, i.e. the balance between pressure gradient and centrifugal force, the nonlinear process of development of a steady vortex flow regime (vortex funnel) is described.     

Justification of the drift-flux model for two-phase flow in a circular pipe

A flow of a gas-liquid dispersed mixture in a circular pipe with a variable inclination to the horizon, as applied to oil and gas flows in wells, is considered. Within the framework of a multi- fluid approach, the equations of an asymptotic drift-flux model, which contains an algebraic relation between the phase velocities and one momentum equation for the volume-averaged velocity of the mixture, are derived. It is shown that the drift-flux model in this formulation strictly follows from the balance laws under assumption of inertialess velocity slip of the phases in case of validity of one of the following conditions: (i) the dispersed-phase volume fraction is small; (ii) the phase velocity slip may be neglected; or (iii) the flow regime is inertialess and the acceleration of the mixture can be neglected. A numerical algorithm based on the SIMPLE method is implemented for solving the obtained equations of the drift-flux model. The possibility of modeling the gravitational segregation and the pressure buildup in a shut-in well and transient slug flows is demonstrated.     

Resolution Effects and Enslaved Finite-Difference Schemes for a Double Gyre, Shallow-Water Model

We study numerical solutions of the reduced-gravity shallow-water equation on a beta plane, subjected to a sinusoidally varying wind forcing leading to the formation of a double gyre circulation. As expected the dynamics of the numerical solutions are highly dependent on the grid resolution and the given numerical algorithm. In particular, the statistics of the solutions are critically dependent on the scheme's ability to resolve the Rossby deformation radius. We present a method, applicable to any finite-difference scheme, which effectively increases the spatial resolution of the given algorithm without changing its temporal stability or memory requirements. This enslaving method makes use of properties of the governing equations in the absence of time derivatives to reduce the overall truncation error. By examining statistical measures of stochastic solutions at resolutions near the Rossby radius, we show that the enslaved schemes are capable of reproducing statistics of standard schemes computed at twice the resolution. Received 29 August 1996 and accepted 6 March 1997     

Experimental Study of Sediment Flow Discharge in New System of Bottom Intakes with Porous Media

Bottom rack intake is one of the most popular structures for diverting water in steep rivers. The problems of corrosion, deformity, and clogging of the bottom racks in long term inspire a new system of bottom intake in which a filled trench of porous media replaces the bottom racks. Diversion of a specified amount of water through the porous media, when the void space in the granular material is filled with fine sediments in comparison to the bottom racks, requires much larger structure. For the proposed water intake, lower cost of construction and maintenance and higher compatibility with the river morphology are considered as major advantages. This research deals with an experimental model with two-story channel, the lower one is used to convey diverted water through the porous media and the upper one is used to carry the remained flow to downstream. Measurements of the diverted discharge were performed for different rates of flow, grain, and sediment size distributions as well as surface slopes of intake. Results show that despite clogging of the suspended sediments in porous media, using appropriate grain size with a surface slope of the porous media increases the discharge coefficient of system. In comparison to the clear water flow, the diverted discharge reduction induced by clogging is not significant and the efficiency of system in long term with no operation effort is confirmed. An empirical formulation has been proposed based on the concept of Darcy’s law for surface infiltration. The equation is found to be dependent on size ratio, Reynolds number, and hydraulic gradient. The theoretical predictions in comparison with the experimental results have shown a good consistency.     

The Zero Surface Tension Limit of Two-Dimensional Interfacial Darcy Flow

We perform energy estimates for a sharp-interface model of two-dimensional, two-phase Darcy flow with surface tension. A proof of well-posedness of the initial value problem follows from these estimates. In general, the time of existence of these solutions will go to zero as the surface tension parameter vanishes. We then make two additional estimates, in the case that a stability condition is satisfied by the initial data: we make an additional energy estimate which is uniform in the surface tension parameter, and we make an estimate for the difference of two solutions with different values of the surface tension parameter. These additional estimates allow the zero surface tension limit to be taken, showing that solutions of the initial value problem in the absence of surface tension are the limit of solutions of the initial value problem with surface tension as surface tension vanishes.     

Numerical Simulation of the Fall of a Body with a Corrugated Bottom on Water

A numerical model is proposed for the potential flow of an ideal incompressible fluid produced by impact of a body with concave bottom on water. Compression of the entrapped air is taken into account. The algorithm is based on joint solution of the equations of motion for the body and the fluid by the finite difference method with approximation in time. At each time, the boundaryvalue problem for the Laplace equation is solved by the boundaryelement method. Calculation results are given. The effects of the air layer, dimensions and shape of the corrugations, initial velocity, and other parameters on the impact process are shown.     

On the Justification of Plate Models

In this paper, we will consider the modelling of problems in linear elasticity on thin plates by the models of Kirchhoff–Love and Reissner–Mindlin. A fundamental investigation for the Kirchhoff plate goes back to Morgenstern (Arch. Ration. Mech. Anal. 4:145–152, 1959) and is based on the two-energies principle of Prager and Synge. This was half a century ago.     

Quasi-Neutral Limit for a Model of Viscous Plasma

We perform a rigorous analysis of the quasi-neutral limit for a model of viscous plasma represented by the Navier–Stokes–Poisson system of equations. It is shown that the limit problem is the Navier–Stokes system describing a barotropic fluid flow, with the pressure augmented by a component related to the nonlinearity in the original Poisson equation.     

Hydrodynamic Limit for a Hamiltonian System with Boundary Conditions and Conservative Noise

We study the hyperbolic scaling limit for a chain of N coupled anharmonic oscillators. The chain is attached to a point on the left and there is a force (tension) τ acting on the right. In order to provide good ergodic properties to the system, we perturb the Hamiltonian dynamics with random local exchanges of velocities between the particles, so that momentum and energy are locally conserved. We prove that in the macroscopic limit the distributions of the elongation, momentum and energy converge to the solution of the Euler system of equations in the smooth regime.     

Limit cycles of a double pendulum with nonlinear springs

The limit cycles of a double pendulum with hard, soft, or linear springs subject to a follower force are drawn using computer simulation     

Mathematical Justification of the Obstacle Problem in the Case of a Shallow Shell

This paper deals with the asymptotic formulation and justification of a mechanical model for a shallow shell in frictionless unilateral contact with an obstacle. The first three parts of the paper concern the formulation of the equilibrium problem. Special attention is paid to the contact conditions, which are usual within two or three dimensional elasticity, but which are not so usual in shell theories. Lastly the limit problem is formulated in the main part of the paper and a convergence result is presented. Two points are worth stressing here. First, we point out that unlike classical bilateral shell models justifications, the functional framework of the present analysis involves cones. Secondly, while the cones result from a positivity condition on the boundary as long as the thickness parameter is finite, leading to a Signorini problem in the Sobolev space H ¹, the cone results from a positivity condition in the domain, giving rise to a so-called obstacle problem in the Sobolev space H ² at the limit.