A STOCHASTIC-MODEL FOR SCATTERING FROM THE NEAR-SURFACE OCEANIC BUBBLE LAYER

A stochastic scattering model is derived in which the backscatter from the near-surface oceanic bubble layer is written directly in terms of an integral over the wave-number spectrum (''power'' spectrum) of the sound-speed fluctuations in the layer. A factored form is given for the integral that allows the backscatter cross section per unit area to be expressed as the product of a ''geometric factor'' and an effective horizontal wave-number spectrum. Because a power spectrum formulation is statistical, there are no assumptions about the geometry of the bubble layer (e.g., hemispherical or cylindrical plumes are not assumed). By dividing measured data for backscatter versus frequency by the geometric factor, scattering data from 12 different deep-ocean reverberation measurements were inverted, and the wave-number spectrum of the sound speed in the bubble layer was directly inferred. For all 12 measurements, the inferred wave-number spectrum is an inverse power law of the form P(K) = AK(-beta), where A is a strength parameter, K is the horizontal wave number for a Fourier component of the sound-speed distribution, and the mean value of the spectral roll-off exponent beta is 3.86 +/- 0.45. The consistency in the inferred wave-number spectrum strongly suggests that on scales of less than half an acoustic wavelength (5 to 10 m), the sound-speed structure in the bubble layer is governed by turbulence in the inertial subrange (Kolmogorov subrange) which has a universal value of beta = 11/3 = 3.67 for fully developed isotropic turbulence. Using Von Karman's interpolation formula for Kolmogorov turbulence, together with oceanographically constrained input parameters, theoretical backscatter cross sections were computed and compared with the empirical fits of Ogden and Erskine to Critical Sea Test data. It is shown that with no adjustable parameters, the stochastic scattering model gives a good account of the observed backscatter, as a function of both frequency and grazing angle.