Chaos in wavy-stratified fluid-fluid flow

VAIDHEESWARAN, AVINASH; CLAUSSE, ALEJANDRO; FULLMER, WILLIAM D.; MARINO, RAUL; DE BERTODANO, MARTIN LOPEZ

CHAOS AN INTERDISCIPLINARY JR OF NONLINEAR SCIENCE

AMER INST PHYSICS

Año: 2019 vol. 29 p. 331211 - 331217

1054-1500

 We perform a nonlinear analysis of a uid-uid wavy-stratied ow using a simplied two-uid model (TFM), i.e., the xed-ux model (FFM), which is an adaptation of the shallow water theory for the two-layer problem. Linear analysis using the perturbation method illustrates the shortwave 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 nonlinear evolution of waves. The two-equation FFM solver based on a higher-order spatiotemporal nite difference scheme is used in the current simulations. The solution methodology is veried, and the results are compared with the measurements from a laboratory-scale experiment. The nite-time Lyapunov exponent (FTLE) based on simulations is comparable and slightly higher than the autocorrelation function decay rate, consistent with previous ndings. Furthermore, the FTLE is observed to be a strong function of the angle of inclination, while the root mean square 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 interface dynamics. This study also adds to a growing body of work indicating that a TFM with appropriate short wavelength physics is well-behaved and chaotic beyond the KHI.