Nonlinear dynamics of unstably stratified two-layer shear flow in a horizontal channel

The Rayleigh–Taylor instability at the interface of two sheared fluid layers in a horizontal channel is investigated absence inertia. dynamics flow described by nonlinear lubrication equation which solved numerically for adverse density stratifications. early-time features number finger-like protrusions different heights interface. fingers travel speeds leading to sequence merging events after eventually settles near-saturated state, comprising only one finger that includes most lower fluid. For sufficiently large stratifications, final state spans height and thin films each wall, both undergo chaotic dynamics, but finite-time touch-down/touch-up shown be precluded shear flow. An asymptotic analysis large-Bond-number limit (intense stratification) reveals finer structure including Landau–Levich-type connection regions. solutions are compared with numerical results model as well direct simulations, excellent agreement observed between three terms interfacial structure, wave speed film thicknesses.