Flow characteristics in spin-up of a three-layer fluid

Abstract

A numerical study is made of the spin-up from rest of a three-layer fluid in a closed, vertically-mounted cylinder. The densities in the upper layer rho(1), middle layer rho(2) and lower layer rho(3) are rho(3)>rho(2)>rho(1), and the kinematic viscosities are left arbitrary. The representative system Ekman number is small. Numerical solutions are obtained to the time-dependent axisymmetric Navier-Stokes equations, and the treatment of the interfaces is modeled by use of the Height of Liquid method. Complete three-component velocity fields, together with the evolution of the interface deformations, are depicted. At small times, when the kinematic viscosity in the upper layer is smaller than in the middle layer, the top interface rises (sinks) in the central axis (peripheral) region. When the kinematic viscosity in the lower layer is smaller than in the middle layer, the bottom interface rises (sinks) in the periphery (axis) region. Detailed shapes of interfaces are illustrated for several cases of exemplary viscosity ratios.