Vanishing Viscosity with Short Wave–Long Wave Interactions for Systems of Conservation Laws

Motivated by Benney’s general theory, we propose new models for short wave–long wave interactions when the long waves are described by nonlinear systems of conservation laws. We prove the strong convergence of the solutions of the vanishing viscosity and short wave–long wave interactions systems by using compactness results from compensated compactness theory and new energy estimates obtained for the coupled systems. We analyze several of the representative examples, such as scalar conservation laws, general symmetric systems, nonlinear elasticity and nonlinear electromagnetism.     

A note on vortex breakdown incipience and Long’s jet

An extension of Long’s jet model is presented. This is formulated from the modified set of quasi-cylindrical (QC) equations proposed by Berger and Erlebacher (1995) [8] from an order-of-magnitude balance of the equations of motion near the vortex core breakdown. The new set of equations reveals the key role of the radial viscous term of the radial momentum equation around the vortex breakdown fold. So retaining this term, the third branch (solutions of Type III), corresponding to the full Navier–Stokes equations, and not observed by the slender Long’s model, could be obtained.     

Analysis and Optimization of Plane Cable Trusses∗

ABSTRACT

A method for the optimization of plane cable trusses with loads distributed along the cables according to any arbitrary law, as well as a suitable finite element model for the individual cable section, is presented. The optimization method is divided into two steps. In the first, the structure is optimized through the use of a simplified model in which the two main cables are considered continuously connected by an infinite number of vertical inex-tensible wires. In the second step the optimal solution obtained for the simplified model serves as the point of departure for the optimization of the real structure, using Powell's method of conjugate directions. Suitable external penalty functions guarantee that the solution is feasible. A numerical example is also given.     

Properties of the “Non-Free” Shock Wave/Boundary Layer Interaction on a Swept Plate

A comprehensive experimental investigation of the transition from the free to the non-free regime of interaction between a plane shock and a boundary layer in a conical flow and the non-free interaction properties has been carried out. A theoretical model is constructed and used to calculate the transition parameters and determine the range on which the non-free interaction can exist, together with its basic characteristics.     

Wave forces on a submerged horizontal plate–Part II: Solitary and cnoidal waves

This paper is the companion to Part I under the same title, and is mainly concerned with wave loads due to nonlinear waves of solitary and cnoidal type propagating over a submerged, horizontal and thin plate. Following the development of the nonlinear model (via the Level I Green–Naghdi theory) for the flow of an incompressible and inviscid fluid given in Part I, the wave-induced loads on the submerged, fixed (and rigid) plate are calculated, and results are compared with the available laboratory data, and with linear solutions of the problem. Dependence of the loads on wave conditions (wave height and wavelength) and plate characteristics (submergence depth and plate width) are studied for both the solitary and cnoidal wave cases.     

Computer simulation and measurement of microaccelerations on the “Mir” orbital station

The causes of microaccelerations on board earth satellites: motion about the center of mass, gravity field gradient, atmospheric drag, etc. are considered. Methods of determining the low-frequency component of the microacceleration on the Mir orbital station from three-component magnetometer and angular-velocity sensor measurements are described together with the results of microacceleration measurements made using an accelerometer.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 5–14, September–October, 1994.     

Impulsive Tension of Hexane and Glycerol under Shock‐Wave Loading

The strength of hexane and glycerol was measured under impulsive tension produced by interaction of a triangular compression pulse with a free surface. The tests were performed for strain rates of 10⁴–10⁵ sec^–1. It is established that the strength of hexane is equal to 14 MPa and does not depend on the strain rate, whereas the strength of glycerol increases from 57 to 142 MPa with an order of magnitude increase in the strain rate. The possibility of using the model of homogeneous nucleation to interpret the data obtained is discussed.     

Wave propagation in nonlinear and hysteretic media––a numerical study

This paper considers the problem of one dimensional wave propagation in nonlinear, hysteretic media. The constitutive law in the media is prescribed by an integral relationship based on the Duhem model of hysteresis. It is found that the well known nonlinear elastic stress–strain relationship is a special case of this integral relationship. It is also shown that the stress–strain relationship from the McCall and Guyer model of hyesteretic materials can also be derived from this integral stress–strain relationship. The first part of this paper focuses on a material with a quadratic stress–strain relationship, where the initial value problem is formulated into a system of conservation laws. Analytical solutions to the Riemann problem are obtained by solving the corresponding eigenvalue problem and serve as reference for the verification and illustration of the accuracy obtained using the applied numerical scheme proposed by Kurganov and Tadmor. The second part of this research is devoted to wave propagation in hysteretic media. Several types of initial excitations are presented in order to determine special characteristics of the wave propagation due to material nonlinearity and hysteresis. The results of this paper demonstrate the accuracy and the robustness of this numerical scheme to analyze wave propagation in nonlinear materials.     

Wave regimes on a ferromagnetic viscous‐fluid film flowing down a vertical cylinder

Axially symmetrical waves on the surface of a ferromagnetic viscousfluid film flowing down a cylindrical conductor with alternating current are considered. In this case, in addition to the gravitational force, the film is affected by a spatially nonuniform timedependent magnetic field. The film thickness was assumed to be small compared to the radius of the conductor. In the longwave approximation, a model equation for the deviation of the film thickness from its undisturbed value is obtained. Some numerical solutions of this equations are reported.     

“Equilibrium”and“non-equilibrium”turbulence

We review the concept of ‘‘equilibrium' in turbulence. It generally means a property of the energy spectrum, it can also be understood in terms of a scalar property, the Taylor–Kolmogorov formula relating the dissipation rate to the total energy and integral length scale. The implications of equilibrium and strong departure from equilibrium for turbulence modeling are stressed.     

Impulsive efects on global stability of models based on impulsive diferential equations with “supremum” and variable impulsive perturbations

Sufcient conditions are investigated for the global stability of the solutions to models based on nonlinear impulsive diferential equations with "supremum" and variable impulsive perturbations. The main tools are the Lyapunov functions and Razumikhin technique. Two illustrative examples are given to demonstrate the efectiveness of the obtained results.     

Plane acoustic wave propagation through a composite of elastic and Kelvin–Voigt viscoelastic material layers

The problem of plane wave propagation through a plane composite layer of thickness h is considered. The composite consists of periodically repeated elastic and Kelvin–Voigt viscoelastic material layers, and all layers are either parallel or perpendicular to the incident wave front. Moreover, it is assumed that the thickness of each separate layer of the composite is much less than the acoustic wave length and the thickness h of the entire composite. We study the problem by using a homogenized model of the composite, which allows us to find the reflection and transmission factors and the variation in the sound intensity level as it propagates though the composite layer of thickness h.     

Problem on Minimum Wave Speed for a Lotka–Volterra Reaction–Diffusion Competition Model

In this paper, by the instruction of an upper and a lower solutions and with the use of monotone iteration approach we obtain the precise minimum wave speed for the Lotka–Volterra competition model under some conditions on the parameters. Our results extended the known results in literature.