Liquid Surface Wave Band Structure Instabilities

TL;DR

This paper investigates how periodic shear flows at fluid interfaces lead to unique band structure instabilities, revealing new oscillating and nonoscillating modes distinct from classical Kelvin-Helmholtz instabilities.

Contribution

It introduces a band structure analysis of interfacial instabilities in periodically sheared ideal fluids, highlighting novel instability modes and their suppression mechanisms.

Findings

Identification of nonhermitian band structure causing instabilities

Enhanced instabilities near Bragg planes due to periodicity

Periodic flows can suppress classical KH instabilities

Abstract

We study interfacial instabilities between two spatially periodically sheared ideal fluids. Bloch wavefunction decompositions of the surface deformation and fluid velocities result in a nonhermitian secular matrix with an associated band structure that yields both linear oscillating and nonoscillating instabilities, enhanced near Bragg planes corresponding to the periodicity determined by converging or diverging surface flows. The instabilities persist even when the dynamical effects of the upper fluid are neglected, in contrast to the uniform shear Kelvin-Helmholtz (KH) instability. Periodic flows can also couple with uniform shear and suppress standard KH instabilities.