Numerical Simulation of Coherent Structures over Plant Canopy

This paper reports large eddy simulations of the interaction between an atmospheric boundary layer and a canopy (representing a forest cover). The problem is studied for a homogeneous configuration representing the situation encountered above a continuous forest cover, as well as for a heterogeneous configuration representing the situation similar to an edge or a clearing in a forest. The numerical results reproduces correctly all the main characteristics of this flow as reported in the literature: the formation of a first generation of coherent structures aligned transversally with the wind flow direction, the reorganization and the deformation of these vortex tubes into horse-shoe structures. The results obtained when introducing a discontinuity in the canopy (reproducing a clearing or a fuel break in a forest), are compared with the experimental data collected in a wind tunnel; here, the results confirm the existence of a strong turbulence activity inside the canopy at a distance equal to 8 times the height of the canopy, referenced in the literature as the Enhance Gust Zone (EGZ) characterized by a local peak of the skewness factor.     

New solutions of classical problems in rigid body dynamics

The equations of motion of a rigid body acted upon by general conservative potential and gyroscopic forces were reduced by Yehia to a single second-order differential equation. The reduced equation was used successfully in the study of stability of certain simple motions of the body. In the present work we use the reduced equation to construct a new particular solution of the dynamics of a rigid body about a fixed point in the approximate field of a far Newtonian centre of attraction. Using a transformation to a rotating frame we also construct a new solution of the problem of motion of a multiconnected rigid body in an ideal incompressible fluid. It turns out that the solutions obtained generalize a known solution of the simplest problem of motion of a heavy rigid body about a fixed point due to Dokshevich.     

A Lagrangian finite element method for the simulation of flow of non-newtonian liquids

A Lagrangian method for the simulation of flow of non-Newtonian liquids is implemented. The fluid mechanical equations are formulated in the form of a variational principle, and a discretization is performed by finite elements.The method is applied to the slow of a contravariant convected Maxwell liquid around a sphere moving axially in a cylinder. The simulations show that the friction factor for a sphere in a narrow cylinder is a rapidly decreasing function of the Deborah number, while the friction factor for a sphere in a very wide cylinder is not significantly affected by fluid elasticity. It is demostrated that the simulated wall effect on the motion of the sphere may be utilized in an experimental identification of a time constant for a given liquid.     

Ideal gas flow behind a finite-amplitude shock wave

The equations of one-dimensional (with a plane of symmetry) adiabatic motion of an ideal gas are transformed to a form convenient for studying flows between a moving piston and a shock wave of variable intensity. The solution is found for the equations of a motion containing a shock wave which propagates through a quiescent gas with variable initial density and constant pressure. This solution contains four arbitrary constants and, in a particular case, gives an example of adiabatic shockless compression by a piston of a gas initially at rest.     

Three-dimensional isothermal lava flows over a non-axisymmetric conical surface

Within the thin-layer approximation for a highly-viscous heavy incompressible fluid, a hydrodynamicmodel of a 3D isothermal lava flow over a non-axisymmetric conical surface is constructed. Using analytical methods, a self-similar solution for the law of leading-edge propagation is obtained in the case of a flow from a non-axisymmetric source located at the apex of a conical surface with smoothly varying properties. In the case of a flow over a substantially non-axisymmetric surface, it is shown that there exists a self-similar solution for the free-surface shape and the law of leading-edge motion. This solution is studied numerically for particular examples of the substrate surface and the source. In the general case of a non-self-similar flow over a substantially non-axisymmetric conical surface, a local analytical solution is obtained for the free-surface shape and the velocity field near the leading flow front.     

A Eulerian/Lagrangian model to calculate the evolution of a water droplet spray

We introduce a Eulerian/Lagrangian model to compute the evolution of a spray of water droplets inside a complex geometry. To take into account the complex geometry we define a rectangular mesh and we relate each mesh node to a node function which depends on the location of the node. The time-dependent incompressible and turbulent Navier-Stokes equations are solved using a projection method. The droplets are regarded as individual entities and we use a Lagrangian approach to compute the evolution of the spray. We establish the exchange laws related to mass and heat transfer for a droplet by introducing a mass transfer coefficient and a heat transfer coefficient. The numerical results from our model are compared with those from the literature in the case of a falling droplet in the atmosphere and from experimental investigation in a wind tunnel in the case of a polydisperse spray. The comparison is fairly good. We present the computation of a water droplet spray inside a complex and realistic geometry and determine the characteristics of the spray in the vicinity of obstacles.     

Practical techniques for a three‐dimensional FEM analysis of incompressible fluid flow contained with slip walls and a downstream tube bundle

Two practical techniques are proposed in this paper to simulate a flow contained in a plenum with a downstream tube bundle under a PC environment. First, a technique to impose slip wall conditions on smooth‐faced planes and sharp edges is proposed to compensate for the mesh coarseness relative to boundary layer thickness. In particular, a new type of Poisson equation is formulated to simultaneously satisfy both such velocity boundary conditions on walls and the incompressibility constraint. Second, a numerical model for a downstream tube bundle is proposed, where hydraulic resistance in a tube is imposed as a traction boundary condition on a fluid surface contacting the tube bundle end. The effectiveness of the techniques is numerically demonstrated in the application to a flow in a condenser water box. Copyright © 2001 John Wiley & Sons, Ltd.     

Penetration of a cumulative jet into a barrier

A solution is given to the problem of the penetration of a cumulative jet with an arbitrary distribution of the velocity along it, taking account of the strength properties of the barrier. Using the example of a jet with a linear distribution of the velocity, the article demonstrates the possibility of obtaining a large puncturing capacity due to a change in the gradient along the jet as a function of the physicomechanical properties of the barrier and the jet. In addition, a distribution of the velocity along the jet is obtained which assures a maximal penetration in a barrier, arranged at a distance where a limiting elongation is not attained either partially or completely over the whole jet.     

Draft of a nozzle with the circulating outflow of a vortical flow of gas

The presence of circulation in an outflowing gas leads to a change in the working parameters of a nozzle. The question of the mass flow rate and the draft of a nozzle without a diffusor (a point) for twisted flows has been studied theoretically and experimentally [1–6]. The use of nozzles with a supersonic part introduces a considerable degree of complication into the method for the analytical calculation of the draft characteristics and the program for their experimental investigation. In [2, 7], a theory of a nozzle is formulated for a model of a potential circulating flow of gas; in [5, 8], an electronic computer was used to solve the complete system of the equations of gasdynamics for the motion of a rotating flow along a nozzle; in [7, 9], an investigation was made of a variational problem of the shaping of a diffusor for a circulation flow. The calculation of the draft, carried out in the above-mentioned communications (with the exception of [2], in which a study was made of a partial model of an eddyless rotational motion), is bound up with labor-consuming computer calculations. In the present article, in a development of [3, 6], a quasi-one-dimensional theory of a supersonic nozzle for a vortical flow of gas is formulated and verified experimentally.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 145–149, September–October, 1975.     

Weak–Strong Uniqueness of Dissipative Measure-Valued Solutions for Polyconvex Elastodynamics

For the equations of elastodynamics with polyconvex stored energy, and some related simpler systems, we define a notion of a dissipative measure-valued solution and show that such a solution agrees with a classical solution with the same initial data, when such a classical solution exists. As an application of the method we give a short proof of strong convergence in the continuum limit of a lattice approximation of one dimensional elastodynamics in the presence of a classical solution. Also, for a system of conservation laws endowed with a positive and convex entropy, we show that dissipative measure-valued solutions attain their initial data in a strong sense after time averaging.     

Standing Pulse Solutions to FitzHugh–Nagumo Equations

Reaction–diffusion systems serve as relevant models for studying complex patterns in several fields of nonlinear sciences. A localized pattern is a stable non-constant stationary solution usually located far away from neighborhoods of bifurcation induced by Turing’s instability. In the study of FitzHugh–Nagumo equations, we look for a standing pulse with a profile staying close to a trivial background state except in one localized spatial region where the change is substantial. This amounts to seeking a homoclinic orbit for a corresponding Hamiltonian system, and we utilize a variational formulation which involves a nonlocal term. Such a functional is referred to as Helmholtz free energy in modeling microphase separation in diblock copolymers, while its global minimizer does not exist in our setting of dealing with standing pulse. The homoclinic orbit obtained here is a local minimizer extracted from a suitable topological class of admissible functions. In contrast with the known results for positive standing pulses found in the literature, a new technique is attempted by seeking a standing pulse solution with a sign change.     

Effect of boundaries of various shapes on vortex dynamics

The motion of a vortex near a boundary of arbitrary shape is considered within the framework of a two-dimensional problem. Integrable differential equations of motion are obtained. Two forms of the algebraic equation of the vortex trajectories are derived. Examples of vortex motion near a straight-line boundary, in a channel, in an angular domain, in the neighborhood of a flat edge, in a round basin, and near a parabolic boundary.     

Bifurcations of rotating structures in a parabolic functional differential equation

We investigate the Andronov-Hopf bifurcation of the birth of a periodic solution from a space-homogeneous stationary solution of the Neumann problem on a disk for a parabolic equation with a transformation of space variables in the case where this transformation is the composition of a rotation by a constant angle and a radial contraction. Under general assumptions, we prove a theorem on the existence of a rotating structure, deduce conditions for its orbital stability, and construct its asymptotic form. __________ Translated from Neliniini Kolyvannya, Vol. 9, No. 2, pp. 155–169, April–June, 2006.     

The extension and oscillation of a non-Hooke's law spring

We derive a wave equation for small-amplitude, undamped, extensional oscillation of a spring-mass system consisting of a mass suspended on a spring governed by a quadratic force-extension relationship. We justify this quadratic model using a Taylor series expansion of the general elasticity equations for a helical spring. Transformation of the equation of motion of the spring leads to a separable wave equation with the spacial component being a transformation of Bessel's equation. The model is successful in predicting static extension and period of oscillation of a helical wire spring for which the wave equation based on Hooke's law is inadequate.     

Configurations of gas-liquid two-phase bubbles in immiscible liquid media

The configuration of a “two-phase bubble” constituted of a gas phase and a liquid phase in an immiscible liquid medium is classified into three types: complete engulfing of a gas bubble inside a liquid shell, partial coalescence of a gas bubble and a liquid drop forming a three-phase contact line, and non-coalescence whereby a gas bubble and a liquid drop remain separated. Simple criteria have been presented by which the favorable type of configuration in a given system is predicted from the values of the spreading coefficients characterizing the system. Experiments using some combinations of liquids as well as air suggest the general validity of the criteria.     

Single-strand strainwire technique: Comparison with existing methods and a proposed photostrain technique

This paper is the third of three papers evaluating a refined internal strainwire technique. This final paper evaluates the technique by comparing it with two elastic solutions, with a photoelastic solution, and with a new proposed photostrain technique. The problem chosen as the basis of comparison was a plane-stress problem of a plate with a circular hole under uniform tension. The proposed technique is experimental in nature and combines parts of the results of a photoelastic solution with those yielded by a three-wire internal strain-gage-rosette analysis to completely fix the state of stress in the model. The scientific techniques used to compare the three-wire strain technique and photostrain technique are as follows: two elastic solutions, one evaluated at a point and one arrived at by integrating the stress functions over a finite length; a finite-element solution; a photoelastic analysis using the shear-difference technique to separate the principal stresses; and a three-wire-rosette analysis. A comparison is made of the values of principal stresses yielded by these methods.     

粘性金属中的正激波稳定性问题

G.H.Miller等把高压金属中的粘性激波作为强间断面处理,解析推论出:在大粘性系数条件下小扰动激波是不稳定的,物质粘性是导致失稳的因素。本文中针对平面正激波,认为高压金属中的粘性激波的物理量是连续变化的,利用线性稳定性理论,用数值解推论出:在有粘性条件下小扰动激波都是稳定的,物质粘性是致稳的因素。指出G.H.Miller等获得错误结论的原因在于:从无粘流动解推出的小扰动边界条件导致粘性激波小扰动增长。给出实验确定的小扰动速度梯度的边界条件,这样既可以把粘性正激波作为强间断面处理,也能够保证粘性正激波的稳定性。     

Deformability of thin metal films on elastomer substrates

Recent applications in flexible electronics require that thin metal films grown on elastomer substrates be deformable. However, how such laminates deform is poorly understood. While a freestanding metal film subject to tension will rupture at a small strain by undergoing a necking instability, we anticipate that a substrate will retard this instability to an extent that depends on the relative stiffness and thickness of the film and the substrate. Using a combination of a bifurcation analysis and finite element simulations, we identify three modes of tensile deformation. On a compliant elastomer, a metal film forms a neck and ruptures at a small strain close to that of a freestanding film. On a stiff elastomer, the metal film deforms uniformly to large strains. On an elastomer of intermediate compliance, the metal film forms multiple necks, deforms much beyond the initial bifurcation, and ruptures at a large strain. Our theoretical predictions call for new experiments.     

On configurational balance in slender bodies

We propose a new derivation of the evolution equation of a sharp, coherent interface in a two-phase body having elongated shape, a body which we regard as a one-dimensional micropolar continuum. To this aim, we introduce a system of forces acting at the interface, and we apply the method of virtual powers to derive a balance law involving these forces. By exploiting the dissipation inequality, we manage to write this balance law in terms of a scalar field whose form is reminiscent of a well-known expression for the configurational stress in three dimensional micropolar continua.     

Establishment of Waves Generated by a Pulsating Source in a Finite-Depth Fluid

A correct solution of Sretenskii’s plane problem of a source pulsating in a finite-depth fluid is derived. The solution is found using generalized functions as a limit in the infinite future of a wave regime generated by a source which starts to execute pulsations in a fluid initially at rest at a certain moment of time.