Two-layer flow of uniformly rotating immiscible second-grade and viscous fluid layers

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 omega(1) over another immiscible viscous fluid layer rotating with angular velocity omega(2). The flows are co-rotating at sigma > 0 and counter-rotating at sigma < 0, where sigma = omega(2)/omega(1) (angular velocities ratio). The parameter limitation that sigma(2) rho = 1 causes the similarity solutions to exist over a flat interface at z = 0, where rho = rho(2) / rho(1) (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., 0 <= sigma <= 1) but solutions exist only up to the critical values of sigma in the case of counter-rotation (i.e., sigma(c) <= sigma <= 1) 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 K-1, fluid viscosity ratio mu = mu(2)/mu(1), and angular velocities ratio sigma that are very important in scientific and industrial applications.

Automated summary

This study investigates the flow characteristics of two immiscible rotating layers of fluids and explores their behaviors under co-rotation and counter-rotation. The findings have significant implications for scientific and industrial applications.