https://doi.org/10.1140/epjp/s13360-022-03563-0
Regular Article
Two-layer flow of uniformly rotating immiscible second-grade and viscous fluid layers
Department of Mathematics and Statistics, International Islamic University, 44000, Islamabad, Pakistan
Received:
12
October
2022
Accepted:
25
November
2022
Published online:
8
December
2022
This study reveals the flow of two immiscible uniformly rotating layers of second-grade and viscous fluids. The second-grade fluid in the upper layer is rotating with angular velocity 
over another immiscible viscous fluid layer rotating with angular velocity 
. The flows are co-rotating at 
and counter-rotating at 
, where 
(angular velocities ratio). The parameter limitation that 
causes the similarity solutions to exist over a flat interface at 
, where 
(densities ratio). A well-known finite-difference technique called the Keller–Box method is applied to solve the resultant system of nonlinear ODEs. The numerical results show that similarity solutions are present for all co-rotating flows (i.e., 
) but solutions exist only up to the critical values of 
in the case of counter-rotation (i.e., 
) this is due to the creation of a large shear flow across the interface. The prime objective of the current article is to investigate and address certain important flow characteristics such as recirculation regions, inward and outward “wall” jets, the creation of strong shear flow across the interface, and the relationship of inflow/outflow behavior with the oceanographic context under the impact of second-grade fluid parameter 
, fluid viscosity ratio 
, and angular velocities ratio that are very important in scientific and industrial applications.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
