Estimating the volume and surface area of air bubbles entrained by breaking waves from whitecap observations: With implications on the characteristic breaking wave speed and breaking strength parameter

TL;DR

This paper develops a model linking whitecap coverage to bubble entrainment, estimating bubble volume and surface area, and exploring implications for wave speed and breaking strength, with findings supported by observations and high-speed videos.

Contribution

Introduces a conceptual model quantifying bubble entrainment and its effects on wave energy dissipation and breaking properties from whitecap data.

Findings

Bubble surface area per sea surface area increases dramatically with wind speed.

Effective entrainment depth is approximately 0.11 m, nearly independent of wind speed.

Breaking wave speeds are narrowly distributed between 2 and 3.5 m/s, weakly dependent on wind speed.

Abstract

A conceptual model relating the whitecap coverage to the bubble plume buoyancy is developed following the observation that the entrained bubble plume buoyancy constitutes a large portion of the breaking wave energy dissipation. The formulation leads to estimations of an effective or equivalent-buoyancy depth of bubble entrainment as well as the volume and surface area of bubbles entrained by surface wave breaking. The results show that the air-water interface area per unit sea surface area is enhanced dramatically by the entrained bubbles: on the order of 10 m^2 at about 15 m/s wind speed. The effective entrainment depth represents the vertical reach of the bubble plume as if all the bubbles were collected into this depth. Based on empirical observations of whitecaps and breaking wave energy dissipation, it is about 0.11 m and relatively independent on wind speed. The void fraction of the top meter ocean layer is related linearly to the whitecap coverage with a proportionality factor of 0.11. The nearly-constant effective entrainment depth essentially renders the bubble entrainment process during the active wave breaking stage into a lateral 2D problem. Published high speed video recordings of bubble plume evolution appear to support this conclusion. Consistent with the nearly-constant effective entrainment depth, relevant breaking wave speeds are within a narrow range between about 2 and 3.5 m/s and depend on wind speed only weakly. Whitecap observations can also be used to quantify some elusive breaking properties such as the breaking strength parameter b relating the breaking energy dissipation rate and length of breaking front.