On a generalized approach to the linear stability of spatially nonuniform thin film flows

Abstract

The presence of a deformable free surface in thin films driven to spread by body or shear forces gives rise to base states that are spatially nonuniform. This nonuniformity produces linearized disturbance operators that are non-normal and an eigenvalue spectrum that does not necessarily predict stability behavior. The falling film provides a simple example for demonstrating a more generalized, rigorous nonmodal approach to linear stability for free surface flows. Calculations of the pseudospectra and maximum disturbance amplification in this system, however, reveal weak effects of non-normality and transient growth such that the modal growth rate is rapidly recovered. Subdominant modes contribute little energy to the leading eigenvector because the oscillatory behavior is rapidly damped by surface tension. Generalization of these results to numerous other lubrication flows involving surface tension suggests similarly weak non-normality and transient growth.