Generalized Stability Analysis of Wind Generated Surface Water Waves

The shear instability mechanism for generation of surface water waves (Miles 1957) is re-examined in light of the nonnormality of the underlying linear operator. The associated eigenproblem and adjoint eigenproblem are solved numerically and a clarification to previous perturbation solutions of the eigenproblem discussed. The optimal excitation problem is solved in the asymptotic limit t → ∞ and the optimal perturbation growth is compared with eigenmode growth. Transient growth rates are found to substantially exceed exponential growth rates suggesting a role for transient growth processes in the generation of surface water waves.