Stratified Flow Over A Dipole And Conditions For The Non-Occurrence Of Blocking

Abstract

In the study on two-dimensional stratified flow in a channel, Dube (2002) and Yih (1960) proposed that the two-dimensional stratified flow over a barrier in a channel can be investigated by taking a suitable combination of sources, sink and doublets in place of barrier. Trustrum (1964) and then Dube (2023 & 2025) considered, however independently, the problem of two-dimensional channel flow over a barrier by applying an oseen-type approximation to the general flow and discussed the Long’s hypothesis. Our work is to examine and find out relation between the pressure at infinity, Fourde number and the strength of dipole for a non-occurrence of blocking by assuming the dipole to be placed at the bottom of the channel with its axis parallel to it and directed against the uniform flow.

If the pseudo-velocity at infinity on the negative side (i.e. at ) be not large enough, then there is apparently a possibility that a layer of the stratified fluid in the lower region of the channel may not be able to cross the diploe. This will result in what may be called the blocking of the incoming fluid by the diploe. This leads to a contradiction to the work of Trustrum (1964) that if the axis of the dipole be parallel to the channel wall then there is no possibility of blocking. So we restudy the problem of the stratified flow over a dipole placed at the bottom of the infinite channel with its axis parallel to the uniform flow at infinity. We shall also try to find out analytically relation between the pressure condition at infinity (on the negative side) and the strength of the dipole for the non-occurrence of blocking.