Two-Dimensional Steady Flow of Stably Stratified Incompessibile Inviscid Towards a Sink- Investigation of Role of Stream Function and Velocity
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Dube & Kumari (2023) work is further taken up to investigate the role of stream function y , Pseudo stream function y ¢ and velocity v (vertical and horizontal components). They considered the problem of steady two-dimensional flow of a stably stratified, incompressible inviscid fluid towards a sink situated at the middle point (origin) of the lower horizontal boundary of an infinite channel. They studied the flow pattern only. The problem is investigated by the physical flow to a pseudo-flow as Yih (1958) and Dube (2002) did in the semi-infinite channel problem. The solution of the pseudo-flow is obtained first by the linearizing its equation and then by using the Fourier transforms.
The pseudo-flow is characterized by one parameter b , which is the inverse of the internal Froude number F . When b = 0 , the stratified fluid flow reduces to the homogeneous irrotational fluid flow (unaffected directly by gravity).
Their solution for b for one-half of the channel agrees well with that of Yih and Dube. But when b ¹ 0
, our solution differs greatly from Yih and Dube . It is found that as soon as b becomes non-zero, a central core in the form of a cone not occupied by the fluid starts developing around the vertical line through the sink. The top of the core becomes wider and wider as b goes on increasing towards p . The
reason for the development of core may be attributed to gravity effect.
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