Chaos in Wavy-Stratified Fluid-Fluid Flow

Abstract

We perform a non-linear analysis of a fluid-fluid wavy-stratified flow using a simplified two-fluid model, i.e., the fixed-flux model (FFM) which is an adaptation of shallow water theory for the two-layer problem. Linear analysis using the perturbation method illustrates the short-wave physics leading to the Kelvin-Helmholtz instability (KHI). The interface dynamics are chaotic and analysis beyond the onset of instability is required to understand the non-linear evolution of waves. The two-equation FFM solver based on a higher-order spatio-temporal finite difference discretization scheme is used in the current simulations. The solution methodology is verified and the results are compared with the measurements from a laboratory-scale experiment. The Finite-Time Lyapunov Exponent (FTLE) based on simulations is comparable and slightly higher than the Autocorrelation function (ACF) decay rate, consistent with findings from previous studies. Furthermore, the FTLE is observed to be a strong function of the angle of inclination, while the root mean square (RMS) of the interface height exhibits a square-root dependence. It is demonstrated that this simple 1-D FFM captures the essential chaotic features of the interfacial behavior.