Coupled in air and in water Orr-Sommerfeld (OS) solver

Viscous wind wave stability analysis using coupled OS equations

This MATLAB code solves the linear stability problem of wind-generated water waves under viscous flow conditions. The formulation is based on the coupled Orr-Sommerfeld equations, accounting for the interaction between the air and water velocity profiles across the interface. The primary objective is to evaluate the growth rates and phase speeds of interfacial waves by solving a generalized eigenvalue problem for each prescribed wavenumber. Discretization of the coupled air-water domain using Chebyshev collocation methods and solution of the coupled eigenvalue problem to obtain complex wave speeds, where the imaginary part indicates growth or decay rates.

The numerical scheme implemented in the code follows the methodology described in Zeisel et al, Viscous effects on wave generation by strong winds. J. Fluid Mech 2008, 597, 343–369.