Interactions between Wind and Water Waves near Circular Flows

TL;DR

This paper investigates the complex interactions between wind and water waves near circular flows, analyzing stability and instability conditions through linearized models and deriving criteria for wave instability.

Contribution

It provides a detailed derivation of linearized two-phase flow problems and establishes new instability criteria for wind-perturbing water waves near circular flows.

Findings

Semi-circle result on unstable mode locations

Necessary and sufficient conditions for wave instability

Analysis of instability in Taylor-Couette flow context

Abstract

This manuscript concerns the dynamical interactions between wind and water waves, which are characterized through two-phase free interface problems for the Euler equations. We provide a comprehensive derivation on the linearized problems of general two-phase flows. Then, we study the instability issues of perturbing waves around circular steady solutions, and we demonstrate a semi-circle result on the possible locations of unstable modes. We also present necessary conditions and sufficient ones for the instability of wind-perturbing water waves near Taylor-Couette flows.