Chaos in wavy-stratified fluid-fluid flow

Area of Science:

• Fluid Dynamics
• Nonlinear Dynamics
• Computational Physics

Background:

• Kelvin-Helmholtz instability (KHI) drives chaotic dynamics in fluid interfaces.
• Understanding nonlinear wave evolution beyond KHI requires advanced analysis.
• Simplified two-fluid models (TFM) offer computational advantages for complex fluid flows.

Purpose of the Study:

• To perform a nonlinear analysis of fluid-fluid wavy stratified flow.
• To investigate the capabilities of the fixed-flux model (FFM) in capturing chaotic interface dynamics.
• To compare simulation results with experimental data and analyze key parameters.

Main Methods:

• Utilized a simplified two-fluid model (FFM), an adaptation of shallow water theory.
• Employed a higher-order spatiotemporal finite difference scheme for simulations.
• Applied linear analysis via perturbation methods and calculated finite-time Lyapunov exponents (FTLE).

Main Results:

• The FFM successfully captures essential chaotic features of interface dynamics beyond KHI.
• FTLE values from simulations correlate well with experimental autocorrelation decay rates.
• FTLE is sensitive to the angle of inclination, while interface height shows a square-root dependence.

Conclusions:

• The 1-D FFM is a viable tool for studying chaotic fluid dynamics.
• The study validates the FFM's ability to model complex interfacial phenomena.
• Appropriate short-wavelength physics in TFMs leads to well-behaved, chaotic dynamics post-instability.