Scaling the Bubble Penetration Depth in the Ocean

Bubble plume penetration depths have been identified as a key parameter linking subsurface turbulent kinetic energy (TKE) dissipation rates and whitecaps. From data collected in the Atlantic sector of the Southern Ocean, nominally 50 degrees S 40 degrees W, bubble plume penetration depths were estimated from Acoustic Doppler Current Profiler measurements of the acoustic backscatter anomaly. Bubble presence at depth was corroborated using independent measurements of optical scattering. Here, an effective wavelength, observations of significant wave height and atmospheric forcing were used to scale penetration depths of breaking waves under open ocean conditions. The parameterization was developed assuming a correlation between the observed penetration depth and an estimate of the TKE dissipation rate enhancement under breaking waves. The effective wavelength was defined from the effective phase speed based on a momentum and energy balance across the atmospheric wave boundary layer and was considered to be the largest actively wind-coupled wave and representative of large-scale breaking for wave ages ranging from 15 to 35 (i.e., 15 = = 35). This yields a dimensional penetration depth parameterization in terms of inverse wave age and the length scales under consideration. The parameterization captures the bubble plume penetration depth with stronger forcing leading to deeper injections, reaching up to 9 m. Both length scales are effective at defining the depth of a wave-affected layer in terms of bubble presence with the effective wavelength better collapsing the data under mixed conditions with deeper plumes associated to larger fractional whitecap coverage.