- Analysis and Modeling of Surf-Zone Bubble Populations
To investigate the acoustical properties of this area, a multi-investigator experiment was performed near the Scripps Pier, March 1-12, 1997 (Scripps Pier Experiment). Our efforts included both measurements of bubbles using a newly developed acoustic technique as well as the measurement of a number of supporting environmental parameters including the incident wind and wave field, long-shore and cross-shore currents (using four 300 kHz acoustic Doppler current profilers and an electromagnetic current meter), and surf-zone bathymetry. Bubbles were measured using a newly developed broadband acoustic technique (Terrill & Melville 1998) which was deployed in a four-channel configuration from a compliant platform fixed to the seabed approximately 120m from the breaking surf in water of 6 m depth. Each channel of the system allows the determination of the bubble size distribution at a discrete depth via inversion of the measured sound speed and attenuation across a frequency band 4 kHz - 100 kHz. The data can be inverted using both a resonant approximation (Wildt 1946, Clay and Medwin 1979) or a finite-element method which considers the off-resonant contribution of bubbles (Commander and McDonald 1991). The ability to measure the attenuation and sound speed at rates of a few Hz allows us to resolve the bubble field with similar resolution. A unique feature of this data is that they are the first known measurements of the vertical gradients of the bubble populations in shallow water. Note that the acoustic technique has been tested beneath laboratory generated breaking waves and found to have close agreement with independent optical measurements of the bubble field (Melville, Terrill, & Veron 1997).
Our initial analysis of the data shows that high concentrations of bubbles offshore the surf-zone are typically a result of being transported from the breakpoint of the waves by offshore flow associated with rip currents. Due to the event-like nature of this offshore flow, the presence of bubbles is transient in time when measured from the fixed location. Several of these 'bubble events' were measured on 3/7 and 3/8 when we had the largest waves (H1/3~1m) and lowest spring tides (-0.41m) during the experiment. The bubble populations that advected through the measurement site resulted in frequency and depth dependent attenuations ranging from O(1) - O(100) dB/m with the largest attenuations typically occurring at frequencies in the 30 - 80 kHz band at the shallowest depths. The bubble size distributions were found to follow a power law of approximately a-5 for the larger radii, with a break in the slope occurring near radii of 100 mm. The void fractions of the episodic bubble 'clouds' advecting from the surf-zone were typically found to range from O(10-6-10-5) and have a strong vertical dependence. Scaling the bubble size distribution by the volume contribution has shown that bubbles with a radius of approximately 100 mm (corresponding to the break in the slope of the size distribution) contribute most to the total void fraction. This peak in the volume contribution curves is found to shift towards smaller radii with depth, a shift that can not be explained by compressional effects alone (Boyle's law). An analytical solution to the turbulent-transport equation of bubbles advecting offshore has demonstrated that the depth dependence of the volume contribution peak can be explained by the level of turbulent mixing inside the rip current (Terrill 1998). Behavior of the peak of the volume contribution curves has acoustical importance as the resonant frequency of this bubble size corresponds to the frequency of maximum attenuation.