Air-sea surface stress in the presence of air flow and surface separation

The oceanic surface stress and corresponding drag on the atmospheric flow are important parameters relevant to many air-sea exchange problems such as the prediction of ocean waves and sea states, short term weather variations, and long term climate trends. This problem has received considerable attention in the past few years, especially in the context of high wind speed conditions where the drag coefficient reduction had previously been predicted but has only recently been observed. Historically, our understanding of air-sea surface stress stems from turbulent boundary layer theory over smooth, flat, solid surfaces. Unlike models for surface stress over a flat plate, however, prediction of the air-sea surface stress is more complicated and currently less accurate due to the presence of surface waves that form, grow, interact, and break. The presence of waves creates additional stress components such as wave-induced and separation stresses. Moreover, surface separation in the form of sea spray droplets has recently been postulated to carry a significant fraction of the surface stress in extreme wind speed conditions. While these additional stresses might represent some of the physics that occurs at the ocean surface, a simple linear addition of more stresses appears to be inadequate. This postulation is intuitive when considering that all of these additional stresses depend on and modify the sea state.

In recent years, different authors have used air flow separation over steep and breaking waves to account for both an increase and a decrease in the drag coefficient relative to extrapolated, bulk values at high wind speeds. Such a disparity inspires this attempt to incorporate feedback between the different stress components, which is based not only on recent measurements but also on the simple logic that dictates, for example, that the viscous stress at the surface should be reduced if the air flow separates. Naturally, the inclusion of feedback between the stress components leads to a simple nonlinear formulation of the surface stress.

Our nonlinear stress parameterization, developed for use in a sea spray model, incorporates both air flow separation and feedback. Even though empirical wave spectra and breaking wave statistics are extrapolated beyond known limits, our model, which explicitly includes air flow separation, appears to reproduce a decreasing drag coefficient at high wind speeds. We conclude that air flow and surface separation and accompanying feedback may account for a significant portion of the physics that drive the observed trends in the drag coefficient.