Attenuation Measurements Across Surface-Ship Wakes and Computed Bubble Distributions and Void Fractions

Abstract

A surface ship's wake is composed of several hydrodynamic phenomena. A large part of that wake contains a mixture of air bubbles of various sizes in turbulent water. Eventually, as the wake ages, the turbulence subsides and bubbles begin to rise at rates that are determined by their sizes. These bubbles of various sizes and concentrations control the propagation of acoustic signals inside and across a wake. To further our understanding of these phenomena, a series of three continuous-wave (CW)-pulsed signals were transmitted across a wake as the wake aged. Each transmission contained a set of four 0.5-ms-long pulses. The 12 pulses ranged over frequencies from 30 to 140 kHz in 10-kHz steps. The acoustic attenuations across wakes that were due to varying bubble-size densities within the wakes were determined experimentally. From those data, estimates of the bubble densities as functions of the speed of the wake-generating ship, the wake's age, and acoustic frequency were calculated. From the bubble-density results, power-law fits and void fractions are calculated. The attenuation measurements were taken at 7.5-m intervals behind the wake-generating ship and continued for about 2 km. The experiment was run for wakes generated at ship speeds of 12- and 15-kn wakes, and the 15-kn run was repeated for consistence determination. The bubble densities were observed to have power-law forms with varying parameters with the strongest, for early ages, having an exponent of -3.6 and a void fraction of 4 x 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-7</sup> , and with both diminishing for older wakes, as might be expected.