Stratified fluid motion in a channel with reference to the flow towards a sink and flow past a dipole and solid bodies

Abstract

The present piece of work of the thesis is on the study of the steady two-dimensional stratified flow of an inviscid incom-oressible non-diffusive fluid in an infinite channel. In all the problems discussed here, the flow is assumed to be laminar. The stratification is also assumed to be stable with density decreas-ing upwards. Attention is paid mainly on the mathematical charac-ter of the problem rather than the underlying physical ideas. The first chapter deals with the general introduction, the general equation of the inviscid fluid motion, discussion on the general equation, particular case for the two-dimensional flow, reduction to the pseudo-flow and hence the linearization of the resulting equation in the line shown by Long and Yih. The second chapter is on the study of two-dimensional stratified flow of an incomeressible inviscid fluid from x = +_ towards a sink placed at the origin at the bottom of an infinite channel formed by lt x lt and o lt y lt d. The problem is solved by using the two-way Fourier transform and its inversion. The streamlines are drawn for different values of B (B being the invense of the Froude number and is assumed to be less than n) and the flow pattern is found to differ from that obtained by Yih for a semi-infinite channel (- lt x lt o, lt y lt d). The first part of the third chapter is on the consiceration of the two-dimensional stratified flow over a dipole of strength u (the density of the fluid in the dipole flow is assumed cons-tant being equal to that of the lowermost layer of fluid in the stratified flow) placed at the origin at the bottom of the channel Streamlines are drawn for different values of u for fixed B ( lt n). For some values of the flow parameters B and u, there is a possibility of blocking. So, for small B (implying small stratification or learge U), a relationship between the dipole strength and the pressure at infinity is established for the non-occurence of blocking. In the second part, the dividing curve between the stratified flow and the dipole flow is...