Uma Basu

Oblique interface-wave diffraction by a small bottom deformation in two superposed fluids

The problem of diffraction of oblique interface-waves by a small bottom deformation of the lower fluid in two superposed fluids has been investigated here assuming linear theory and invoking a simplified perturbation analysis. First order corrections to the velocity potentials in the two fluids are obtained by using the Greens integral theorem in a suitable manner. The transmission and reflection coefficients are evaluated approximately. These reduce to the known results for a single fluid in the absence of the upper fluid.

Incompressible Viscoelastic Flow of a Generalised Oldroyed-B Fluid through Porous Medium between Two Infinite Parallel Plates in a Rotating System

ABSTRACT Incompressible viscous fluid flow through a porous medium between two infinite parallel plates with moving upper plate in a rotating system has been studied here. The exact solution of the governing equation for the velocity field has been obtained by using Laplace and finite Fourier sine transformations in series form in terms of Mittage-Leffler function. It can be found that the fluid velocity decreases with the increasing values of fractional calculus parameter α and the permeability of the porous medium K. It can be also observed that the fluid velocity increases with the higher values of the viscosity of the porous medium. The dependence of the velocity field on fractional calculus parameters as well as material parameters has been illustrated graphically. Keywords Caputo operator; Generalised Oldroyed-B fluid; Laplace transformation: Finite Fourier sine transformation; porous medium . 1. INTRODUCTION In fluid dynamics the study of non-Newtonian fluid flow through porous medium has applications in different fields such as purification of crude oil, petroleum industry, polymer technology, electrostatic precipitation, irrigation, sanitary engineering, food industry etc. The flow behavior of non-Newtonian fluids cannot be described by Newtonian fluid model. For this reason various types of constitutive equations have been proposed and Oldroyed-B fluid model is one of them that has some success in describing non-Newtonian fluids. In recent years fractional calculus approach is found to be quite flexible in describing the viscoelastic fluids. In the approach the time derivative of integer order in the constitutive equation is replaced by Caputo fractional calculus operator. Charyulu and Ram [1] have investigated laminar flow of an incompressible micro polar fluid between two parallel plates with porous lining. Fetecau

Waves due to a line source in the presence of small bottom deformation

Abstract This paper is concerned with the effect of a small deformation at the bottom on a submerged oscillating line source. A simplified perturbation analysis is employed to reduce the problem to two independent boundary value problems up to first order involving water of uniform finite depth. The first order corrections to the velocity potential and the wave amplitudes radiated at infinity from the oscillating line source on its two sides are obtained in terms of integrals involving the shape function describing the bottom deformation. For two particular forms of the shape function, the corrections to the wave amplitudes are evaluated explicitly.

A plane vertical submerged barrier in surface water waves

By a simple application of Greens integral theorem, amplitude of the radiated waves at infinity due to a line source in the presence of a fixed vertical plane barrier completely submerged in deep water is obtained. KEYS WORDS AND PHRASES. Line source, submerged baer, velocity pote, Greens theorem, amplitude of radiated wav.

Propagation of magnetohydrodynamic dispersive waves on a running stream

A study is made of the propagation and generation of the Alfven gravity waves on a running stream of inviscid electrically conducting liquid of finite depth by an oscillating pressure distribution on the free surface of the liquid. It is shown that the ultimate steady state solution consists of either two or four Alfven gravity waves depending on the relative value of U and its critical value. The parametric equations of the critical curve which separates these two possible states are obtained.

Waves due to initial disturbances at the inertial surface in a stratified fluid of finite depth

This paper is concernedwith a Cauchy-Poisson problem in a weakly stratified ocean of uniform finite depth bounded above by an inertial surface (IS). The inertial surface is composedof a thin but uniform distribution of noninteracting materials. The techniques of Laplace transform in time andeither Greens integral theorem or Fourier transform have been utilizedin the mathematical analysis to obtain the form of the inertial surface in terms of an integral. The asymptotic behaviour of the inertial surface is obtainedfor large time and distance and displayed graphically. The effect of stratification is discussed.

ON GENERATION AND PROPAGATION OF TSUNAMIS IN ASHALLOW RUNNING OCEAN

A theory is presented of the generation and propagation of the two and the three dimensional tsunamis in a shallow running ocean due to the action of an arbitrary ocean floor or ocean surface disturbance. Integral solutions for both two and three dimensional problems are obtained by using the generalized Fourier and Laplace transforms. An asymptotic analysis is carried out for the investigation of the principal features of the free sur- face elevation. It is found that the propagation of the tsunamis depends on the relative magnitude of the given speed of the running ocean and the wave speed of the shallow ocean. When the speed of the running ocean is less than the speed of the shallow ocean wave, both the two and the three dimensional

Reflection of internal waves by sand ripples

An investigation is made to study the diffraction of a train of time harmonic progressive waves propagating along the surface of separation of two superposed fluids which are laterally unbounded, the upper fluid being extended infinitely upwards, the lower fluid being of finite depth with sand ripples at the bottom. The first order correction to the velocity potential for the problem of diffraction of interface waves in the presence of bottom deformation is obtained by integral transform technique after introduction of a linear frictional term in the kinematic boundary condition at the surface of separation following Lamb (1932), and the reflection and transmission coefficients are estimated for a patch of sand ripples.

Investigation of the problem of singularities in general relativity

Recently Addy and Datta have obtained a linearized solution for isentropic motions of a perfect fluid by assigning Cauchy data on the hypersurfacex4=0 and by imposing a restriction on the equation of state. In the present paper we pursue this study and discuss the problem of singularities from the standpoint of a local observer for which a singularity is defined as a state with an infinite proper rest mass density. It is shown that for a closed universe with any distribution of matter whatsoever there occurred a singularity in the past in the nonrotating parts of the universe and it must recur in the future. Furthermore, the collapse of a rotating fluid to a singularity seems inevitable when the relativistic equation of state is considered.

Unsteady Flows in an Elastico-Viscous Fluid Induced by Torsional Oscillations of a Plate

A study is made of the unsteady flows in an electrically conducting elastico-viscous rotating liquid in the presence of a uniform magnetic field due to small amplitude torsional oscillations of an infinite, rigid non-conducting plate. This analysis is aimed at finding the general features of the steady as well as the unsteady velocity field, and the structure of the associated boondary layers on the plate. The significant interaction of rotation, hydromagnetic and elastic parameters involved in the problem is examined. The velocity field related to the small elastic parameter is calculated with physical significance. The Ekman suction velocity is calculated as the limit of w(z, t) when z→∞t→∞ and is shown to be non-zero. It is shown that the non-zero Ekman suction velocity represents the generation of an axial inflow toward the boundary layers, Several limiting results are shown to follow as special cases of this analysis.