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THE ACOUSTICAL AND PHYSICAL CHARACTERIZATION OF
WAVE-INDUCED BUBBLE PLUMES

 

IMT Lab investigators conducted studies of the the role of bubble production and distribution within high air void fraction whitecaps and sub-surface bubble plumes on acoustical scattering at the ocean surface and the generation of noise by bubbles. An additional research focus was to relate bubble production and plume properties such as penetration depth and acoustical scattering strength to the state of the ocean surface wave field. This project was funded by the Office of Naval Research.

RESEARCH OBJECTIVES
The objectives of the research were as follows:

  • relate the acoustical scattering from high void fraction bubble plumes to measured plume properties,
  • determine the relationship between specific, measured plume properties, such as penetration depth, plume volume, plume void fraction and bubble size distributions to surface wave conditions
  • relate bubble production within plumes to the generation of ambient noise.

SCIENTIFIC APPROACH

Two different strategies were undertaken to achieve successful results in this research project. The first was to conduct a series of wave tank studies at the Scripps Institution of Oceaography's hydraulic laboratory glass flume facility. The laboratory experiments were designed to study the basic physics of air entrainment and bubble production within plunging breakers.

The second strategy was to conduct open-ocean measurements of whitecaps in the Woods Hole Oceanographic Institution Underwater Acoustics Observatory of Martha’s Vineyard during October and November of 2002. The experiment (called Surface Processes and Acoustic Communications 2002, or SPACE02) was hosted by Dr. James Preisig at WHOI. Dr. David Farmer from the University of Rhode Island and Dr. Svein Vagle from the Institute of Ocean Sciences, British Colombia also participated.

Underwater acoustic sources and hydrophone arrays were deployed to study surface, bottom and volume acoustic channel properties simultaneously with our whitecap measurements. During the experiment surface processes, but at length and time scales an order of magnitude longer than our measurements. Our whitecap measurements taken together with the extensive marine boundary layer characterizations of Farmer and Vagle provided a complete surface characterization.

The core sensor system for the whitecap studies was the Advanced Plume Imaging System (APEX), developed and funded by a DURIP award through ONR. APEX was deployed with acoustic wave field meters and a blimp-mounted camera to characterize the 2D surface wave spectrum and the distribution and rates of wave breaking.

APEX, a multi-sensor package designed to probe the structure of dense bubble plumes directly beneath ocean whitecaps on several simultaneous scales, consists of two surface-following platforms deployable in high sea states to measure internal and macroscopic plume properties. The instruments on both frames include an optical bubble counter, an array of conductivity sensors, a conductivity/temperature sensor, an acoustic Doppler velocity profiler, an acoustic system for measuring plume scattering cross-section, and an underwater video camera. These sensors simultaneously measure bubble size distribution and void fraction of air within whitecap plumes, the size of the plumes and scaling of plume size with sea state, the acoustical roughness scales of the plume boundaries and the noise radiated during plume formation.

EXPERIMENTS

Two series of experiments were conducted in the seawater wave flume (33 m long, 0.5 m wide, 0.6 m deep) at Scripps Institution of Oceanography. Wave packets were generated at one end of the flume using a computer-controlled wave paddle, which produced plunging breakers approximately 10 cm in height. The amplitude and phase of the wave-packet frequency components were generated so that they added constructively at the wave break point, producing a breaking wave.

Breaking events were studied with a high-speed video camera and front and back lighting to produce images of the complicated two-phase flow occurring a few centimeters (2.5-18 cm) away from the glass-walled side of the flume. From this work, we have been able to determine the scale dependence of bubble creation mechanisms in breaking waves, as described in the next section.

RESULTS

Using the data from the laboratory wave-tank experiments and our these prior open-ocean whitecap studies, we have made a fundamental advance in our understanding of air entrainment and bubble formation in breaking waves. We found that there are two distinct mechanisms controlling the size distribution of bubbles, depending on bubble size. Turbulent fragmentation determines the size distribution for bubbles larger than about 1mm radius, resulting in a bubble density proportional to bubble radius to the power of –10/3. Smaller bubbles are created by jet and drop impact on the wave face with a –3/2 power scaling law. The length scale that separates these processes is the scale at which the forces of turbulent fragmentation are balanced by bubble surface tension, also known as the Hinze scale.

Bubble Size Distributions inside Breaking Waves

Three important quantative findings supported our findings:

  1. The transition between bubbles stabilized by surface tension and bubbles subject to fragmentation by turbulence results in a change in the power law scaling of bubble size from –3/2 to –10/3. The transition between the scaling laws occurs at bubble radius equal to the Hinze scale, which varies from about 0.5 mm to 1.5 mm for open-ocean whitecaps. We observed evidence of the Hinze scale in bubble size spectra taken from breaking waves in the laboratory, the open-ocean, and the surf zone, implying a common mechanism that operates within waves occurring in these three very different environments. In addition, the turbulent dissipation rate within the laboratory waves implied by the observed Hinze scale is consistent with measurements of the dissipation rate within breaking wave crests made by Melville and his co-workers.
  2. We observed a significant result in bubbles in the process of fragmenting. We were able to estimate the Webber number, Reynolds number and probability density of bubble eccentricity for a number of individual fragmenting bubbles within a breaking wave crest. Theoretical predictions of these variables based on prior work in the literature are in good agreement with our observations, which supports the idea that the population of bubbles larger than the Hinze scale is controlled by turbulent fragmentation.
  3. Our results were in excellent agreement between the bubble size distribution scaling law predicted by Garrett, Li and Farmer (radius to the power of –10/3) for bubbles fragmentedby turbulence and our observed distributions.

IMPACT/APPLICATIONS

There are a number of significant impacts arising from the bubble creation work and our discovery of simple scaling laws for bubble number density separated by a length scale that depends only on the turbulent dissipation rate. One of them is an opportunity to understand and model the fundamental physical processes leading to the –5/3 power law scaling of the wind-driven, oceanic ambient noise level with frequency. This property of oceanic noise, known for over 50 years as the Knudsen spectrum, is not well understood.

Since the noise radiated by whitecaps is driven by bubble creation rates, our new understanding of bubble formation processes in whitecaps will provide new insight into the origin of the Knudsen spectrum. The results also have important application to modeling the bubble-mediated transfer of greenhouse gases and aerosol production, both important for global climate change.

PUBLICATIONS
Grant B. Deane and M. Dale Stokes, “Scale dependence of bubble creation mechanisms in breaking waves”, Nature, Vol. 418, pp. 839-844 (2002). (PDF Format 408K)

Grant B. Deane and M. Dale Stokes, “A robust single cable sensor array for oceanographic use”, IEEE J. Ocean. Eng., Vol. 27(3), pp. 760-767 (2002). (PDF Format 280K)