Propagation of a bore produced by the sudden break of a dam

In this paper we study the progress of a bore, produced by the sudden break of a dam, when there is a flow of water ahead of the dam and the bed has a mild slope and offers resistance, employing Whitham's rule. We first derive certain interesting results from the general discussion of the differential equation, expressing the variation of the bore strength with the undisturbed Froude number, M0, ratio of bedslope to bed resistance, gα/R = a2 and the bore strength M(x) Ξ {h(x)/h0(x)} where h(x) and h0(x) are the bore height and the undisturbed height of the water immediately ahead of the bore, the horizontal distance x being measured from the dam. The parameters M0 and a2 combine to influence the bore strength in a very special way. We also examine the asymptotic cases when the bore strength M and M 1. The intermediate cases are investigated numerically to bring out the effects of the parameters, α, a2, M0 and the dam height on the strength of the bore, its velocity and the fluid velocity behind it

Study of self-similar and steady flows near singularities

One-dimensional steady state flow or a self-similar flow is represented by an integral curve of the system of ordinary differential equations and, in many important cases, the integral curve passes through a singular point. Kulikovskii & Slobodkina (1967) have shown that the stability of a steady flow near the singularity can be studied with the help of a simple first-order partial differential equation. In section 2 of this paper we have used their method to study steady transonic flows in radiation-gas-dynamics in the neighbourhood of the sonic point. We find that all possible one-dimensional steady flows in radiation-gas-dynamics are locally stable in the neighbourhood of the sonic point. A continuous disturbance on a steady flow, while decaying and propagating, may develop a surface of discontinuity within it. We have determined the conditions for the appearance of such a discontinuity and also the exact position where it appears. In section 3 we have shown that their method can be easily generalized to study the stability of self-similar flows. As an example we have considered the stability of the self-similar flow behind a strong imploding shock. In this case we find that the flow is stable with respect to radially symmetric disturbances

Transport processes in dense gases

A simple and direct procedure for evaluating the properties of dense gases has been attempted based on the BBGKY hierarchy of equations. The basic idea of Enskog, namely that increasing the density affects the behaviour of the assembly, mainly by reducing the specific volume and by providing a certain amount of shielding to molecular interactions, has been developed at length in this investigation. The decrease in specific volume allows one to approximate the three-particle distribution function in terms of one-particle and two-particle distribution functions. These distribution functions are expanded in terms of generalized Hermite polynomials to study small departures from equilibrium. In the simple Couette flow and one-dimensional heat flux problems, explicit expressions for viscosity and heat conductivity have been obtained. This enables one to study the variation of these with density and temperature. Numerical results are compared with experimental values for simple gases like argon, neon and helium. The values for the inverse-power-law forces behave monotonically and approach the Enskog curve. The Lennard-Jones potential shows, as density increases, an increase of viscosity and heat conductivity that is less rapid than for other power laws. The experimental values agrees well for the force laws studied here

Study of self-similar and steady flows near singularities. II. A case of multiple characteristic velocity

We consider here a system of first-order quasilinear partial differential equations in two independent variables: t, time and x, spatial coordinate. In many physically realistic problems in fluid mechanics, a singularity of the system of ordinary differential equations representing the steady solutions represents a critical state where one of the characteristic velocities vanishes (e.g. sonic point in fluid mechanics). Kulikovskii & Slobodkina (1967) have shown that the stability of all the steady solutions near a singularity can be studied with the help of a simple first-order quasi-linear partial differential equation. The simplicity of their method lies in the fact that all the results can be deduced from the phase-plane of the steady equations. The analysis of Kulikovskii & Slobodkina is valid for any system of equations, totally hyperbolic or mixed type with the only assumption that the characteristic velocity under consideration is real and not multiple. We have earlier (1970, to be referred to as part I) extended their treatment to self-similar flows. In this paper we have shown that in the case of a characteristic velocity of multiplicity s (s > 1), it is still possible to approximate the system provided there exists exactly s linearly independent eigenvectors corresponding to this characteristic velocity. The approximate system consists of s quasi-linear equations and we have to consider the s + 1 dimensional phase-space of the steady equations. In the end we have also discussed two illustrative examples

Radio and near-infrared observations of the steep spectrum Galactic plane radio source WKB 0314+57.8

Radio and near-infared observations towards the steep spectrum Galactic plane radio source WKB 0314+57.8 are presented, in order to clarify the nature of this source. The radio observations include archival and survey data, together with new Giant Metrewave Radio Telescope observations at 617 MHz. The near-infrared observations are in the J and K bands, from the Gemini instrument on the Shane 3-m telescope. The radio observations show that WKB 0314+57.8 is extended, with an very steep spectrum (with flux density proportional to frequency to -2.5 power between 40 MHz and 1.5 GHz). The colour--magnitude diagram constructed from near-infrared observations of the field suggests the presence of a z approx 0.08 galaxy cluster behind the Galactic plane, reddened by about 6 magnitudes of visual extinction. Although the steep spectrum source has no obvious identification, two other radio sources in the field covered by the near-infrared observations have tentative identifications with galaxies. These observations indicate that WKB 0314+57.8 is a relic source in a cluster of galaxies, not a pulsar.Comment: 6 pages, to appear in MNRAS, typos correcte

On the BGK collision model for a two-component assembly

This article does not have an abstract

Reduction of spurious velocity in finite difference lattice Boltzmann models for liquid - vapor systems

The origin of the spurious interface velocity in finite difference lattice Boltzmann models for liquid - vapor systems is related to the first order upwind scheme used to compute the space derivatives in the evolution equations. A correction force term is introduced to eliminate the spurious velocity. The correction term helps to recover sharp interfaces and sets the phase diagram close to the one derived using the Maxwell construction.Comment: 22 pages, 10 figures (submitted to International Journal of Modern Physics C- Physics and Computers