Shear Instabilities

Kelvin–Helmholtz instability billows rolling up at a shear interface — Numerical simulation of Kelvin–Helmholtz instability. Turbulent billows arise from shear at a density interface. Animation *KHI.gif* by Bdubb12, via Wikimedia Commons (public domain).

In this work, we carried out a complete analysis of a hydrodynamic shear instability entirely in the Lagrangian frame (to our knowledge, the first).

This Lagrangian framework, including the particular asymptotic expansion and various other mathematical details, can be applied to other canonical shear instabilities, or, more generally, instabilities in some way dependent on a background shear flow (some of this work is currently being undertaken).

Viewed this way, the Miles wind–wave instability is one member of a broader family of shear instabilities that can all be studied within a unified Lagrangian framework, which could reveal new insights into the underlying physics of these processes.