Non-linear shallow water theory

The equations controlling the three dimensional motion of a viscous, incompressible fluid in shallow water, are derived for use in any orthogonal coordinate system. Simplified equations for two dimensional motion are also developed. The equations are developed in terms of special coordinate dependent functions.     

On the theory of the vibropump

The problem of vibratory lifting of a fluid was considered in [1] on the assumption of incompressibility of the pump tubing. In the present paper account is taken of the elasticity of the tubing materal. This leads to the consideration of forced oscillation regimes in two elastic media coupled by nonlinear conditions on one of the boundaries. In this case there is an ambiguity in the relations between the unknowns and governing quantities which leads to a hysteresis effect.     

On the theory of rolling waves

The problem of rolling waves in a sheet of fluid flowing in a vertical plane [1] is treated on the basis of the complete Navier-Stokes equations with conditions on the unknown free boundary. The existence of a one-parameter family of rolling waves, bifurcating from the Poiseuille flow, is proved.     

On the dual-phase-lag thermoelasticity theory

The uniqueness and reciprocal theorems are proved without the use of Laplace Transforms for the Dual-Phase-Lag thermoelasticity theory. Variational principle is established for a linear anisotropic and inhomogeneous thermoelastic solid. The dissipative inequality is used to obtain a continuous dependence result for isotropic solid.     

On the theory of material inhomogeneities

The theory of material inhomogeneities, according to Noll’s approach, is revisited in detail and its interpretations in the recent literature on material anelastic behaviors, growth and phase transition phenomena are critically discussed.     

On the theory of long waves

A new method of studying plane steady wave motion of a gravity fluid is elucidated in this paper. This method succeeds in establishing the existence of a solitary wave, for example, and in giving the first complete foundation for the approximate Rayleigh theory [1], which concerns the theory of finite-amplitude long waves. Underlying the method are general boundary properties of univalent functions, used earlier by the author to construct a qualitative theory of jet fluid motions [2].     

On the theory of the acousto-electric effect

Summary The electric field along the direction of propagation to which a travelling longitudinal acoustic wave passing through an insulated solid conductor gives rise is calculated both for a metal and a semi-conductor at temperatures greater than the Debije temperature. The field is found to be proportional to the acoustic intensity and the frequency of the wave. Numerical estimates show that in a rod of copper of reasonable length the resulting potential difference between the ends will be difficult to demonstrate experimentally on account of its small size, while for germanium it should be larger by several orders of magnitude.To Prof. Dr. M. J. Druyvesteyn, under whose direction experiments are being performed to demonstrate and measure the acousto-electric effect, I am greatly obliged for valuable discussions. My sincere thanks are due to Prof. Dr. R. Kronig for his advice and criticisms regarding the calculations here presented.     

On the reliability theory of the structures

Summary The researches into the reliability theory of the structures, in hypothesis of elasto-plastic material, compels one to determine the probability function of structural resistance. As it is very difficult to find this function exactly, various authors approximate its values following different methods.The paper starts from the comparison among these ways and proposes as more efficient a simulation method based on parametric linear programming. To the latter it gives an appropriate physical interpretation that allows one to be able to control the computational process.

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Sommario Le difficoltà di determinare la distribuzione di probabilità della resistenza di strutture elasto-plastiche (costruite con materiale a resistenza aleatoria) hanno spinto molti autori a mettere a punto metodi approssimati. Partendo da un esame comparativo si propone, in questa sede, una tecnica di simulazione, che sembra dotata di particolare efficienza computazionale, basata sulla programmazione lineare parametrica. Di essa viene data anche una interpretazione fisica che consente di controllare il processo di calcolo.

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Research conducted under a grant of C.N.R. and accepted by the 15th Polish Solid Mechanics Conference. Zakopane, September 1973.     

On the theory of the dynamic viscometer

Summary It is shown that by using a dynamic viscometer, complex dynamic viscosities can be determined rather easily over a wide frequency range. Expansions of the exact solution which takes inertia effects into account are in the case of small gap widths almost identical for low and high frequencies. For intermediate frequencies the deviation from this limiting behavior is only a few percent.

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Zusammenfassung Die Anwendung von dynamischen Viskometern ermöglicht eine einfache Bestimmung von komplexen dynamischen Viskositäten über einen weiten Frequenzbereich. Reihenentwicklungen der exakten Lösung, welche Trägheitseffekte berücksichtigt, sind für den Fall enger Zylinder-Spalte für niedrige und hohe Frequenzen fast identisch. Aber auch bei Frequenzen im Zwischenbereich weichen die Ergebnisse nur um einige Prozent ab.

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With 1 figure     

On the structure of the theory of viscoplasticity

In various formulations of plasticity, there is evident a structure embracing several features, including inviscidity, a yield condition, and a constitutive inequality. By means of these features the constitutive equations of plasticity are derived. In the present paper we introduce a viscoplastic counterpart of the constitutive inequality of plasticity, and we consider its physical significance. We also present a theory of viscoplasticity having a structure similar to that of plasticity and its relation with the Hohenemser-Prager prototype of viscoplastic constitutive relations is considered.     

On the transient non-Fickian dispersion theory

The Fickian dispersion equation is the basic relationship used to describe the nonconvective mass flux of a solute in a porous medium. This equation prescribes a linear relationship between the dispersive mass flux and the concentration gradient. An important characteristic of the Fickian relationship is that it is independent of the history of dispersion (e.g. the time rate of change of the dispersion flux). Also, the dispersivities are supposed to be medium constants and invariant with temporal and spatial scales of observation. It is believed that in general these restrictions do not hold. A number of authors have proposed various alternative relationships. For example, differential equations have been employed that prescribe a relationship between the dispersion flux and its time and space derivatives. Also, stochastic theories result in integro-differential equations in which dispersion tensor grow asymptotically with time or distance. In this work, three different approaches, which lead to three different non-Fickian equations with a transient character, are discussed and their primary features and differences are highlighted. It is shown that an effective dispersion tensor defined in the framework of the transient non-Fickian theory, grows asymptotically with time and distance; a result which also follows from stochastic theories. Next, principles of continuum mechanics are employed to provide a solid theoretical basis for the non-Fickian transient dispersion theory. The equation of motion of a solute in a porous medium is used to provide a rigorous derivation of various dispersion relationships valid under different conditions. Under various simplifying assumptions, the generalized theory is found to agree with the conventional Fickian theory as well as several other non-Fickian relationships found in the literature. Moreover, it is shown that for nonconservative solutes, the traditional dispersion tensor is affected by the rate of mass exchange of the solute.Also with National Institute of Public Health and Environmental Protection (RIVM), PO Box 1; 3720BA Bilthoven, The Netherlands