Generation and Breakdown of Surface Streaks in Wind-Driven Aqueous Flow

TL;DR

This study models wind-driven aqueous flow to understand how surface streaks form and break down, revealing the mechanisms behind wave initiation observed in experiments.

Contribution

It introduces a boundary layer model with optimal perturbations to explain the formation of surface streaks and their instabilities in wind-driven flows.

Findings

High-speed streaks penetrate deeper water layers.

Sinuous instabilities resemble experimental wave patterns.

Lateral undulations at the surface precede wave onset.

Abstract

A bypass transition scenario in a wind-stress driven aqueous flow is analysed using a temporally developing boundary layer model with accelerating surface drift velocity. The parameters of the model are selected to mimic a wave-tank experiment with a reference wind speed of 5 m/s. To study the boundary layer processes in isolation, a flat free surface is adapted, which inhibits the initiation of waves. First, preferred initial perturbations to which the boundary layer is the most sensitive are identified using linear non-normal growth theory. These perturbations are arranged as streamwise-constant vortex pairs located adjacent to the free surface. Subsequently, direct numerical simulations are initialized with these optimal perturbations and streamwise streaks are generated. High-speed streaks penetrate into deeper water layers and undergo sinuous instabilities reminiscent of the instabilities developing on low-speed streaks in wall-bounded flows. Streak instabilities induce lateral undulations at the free surface, which closely resemble the dye patterns before the onset of waves in wind-wave-tank experiments. The present analysis provides a theoretical background for these experimental observations.