The coupled Kuramoto–Sivashinsky (CKS) equations for multilayer downflowing
films are derived and explored. The CKS equations exhibit a wealth of dynamical
behaviour, displaying travelling periodic waves, regular and chaotic-like patterns,
coexistence of different attractors, and perfect and imperfect synchronization of the
interfaces. New physical effects are found, such as suppression of the Rayleigh–Taylor
instability for heavy-top stratified films, and new surface-tension-driven instability.
Abstract
The boundary roughness effects on nonlinear saturation of Rayleigh-Taylor instability (RTI) in couple-stress fluid have been studied using numerical technique on the basis of stability of interface between two fluids of the system. The resulting fourth order ordinary nonlinear differential equation is solved using Adams-Bashforth predictor and Adams-Moulton corrector techniques numerically. The various surface roughness effects and surface tension effects on nonlinear saturation of RTI of two superposed couple-stress fluid and fluid saturated porous media are well investigated. At the interface, the surface tension acts and finally stability of the problem is discussed in detail.
Effect of boundary roughness on nonlinear saturation of Rayleigh-Taylor instability in couple-stress fluid
