Role of unsteadiness in shear instability: exhalation flow analog

Shear-instabilities at the interface of two fluids, such as the classical Kelvin-Helmholtz (KH) instability, can lead to fluid fragmentation critical in a wide range of physical, environmental, and biological applications. While many insights into such instabilities are derived using the assumption of steady background forcing flow, unsteady impulse flows are ubiquitous in environmental and physiological processes, such as exhalations. Yet, little is understood on the role of unsteadiness in shaping the outcome of the interface's topological change and its destabilization. In this combined theoretical and numerical study, we study the fundamentals of a liquid-air interface exposed to unsteady shear flows that mimic exhalation impulses. Evolution of the perturbed interface is formulated as an impulse-driven initial value problem using both linearized potential flow equations and nonlinear boundary integral methods. We show that the unsteadiness of the forcing can lead to surprising outcomes with the amplitude of the interface's inherent gravity-capillary wave being amplified, up to wave-breaking transition by the imparted unsteady flow, even in the equivalent regime that would be stable under classical linear KH theory. We discuss how it is, in fact, the cumulative history of the unsteady forcing that is key to this amplification and transition. The insights gained are discussed in the context of interface distortion and destabilization relevant for mucosalivary fluid fragmentation.