Numerical analysis clarifying non-equilibrated periodic flows generated by dual-scaling Taylor’s analytical solution

Abstract

Abstract This study investigates the properties of a flow field derived from the multiplexed Taylor solution, focusing on its impact on established equilibrium relationships. We numerically analyse a multiplexed flow field by introducing a secondary flow with twice the period of the original Taylor solution, hypothesising that this dualisation affects the balance between transient and viscous terms. The visualisation of the flow field and the time evolution of the kinetic energy are investigated. Using second and sixth order central differences and the fractional step method with BiCGStab, we analyse three flow fields with different coefficients in a two-dimensional periodic domain. The study shows that the dualisation of the flow field disturbs the equilibrium between the unsteady and viscous terms. The time-averaged kinetic energy shows that the evolution of the dualised field approaches the kinetic energy distribution of the analytical solution, with variations depending on the coefficient of the quadratic term. The spatial distribution of the kinetic energy in fully developed fields is also compared with the analytical solution.