Low-Frequency Resonant Scattering of Bubble Clouds

Paul A. Hwang Oceanography Division, Naval Research Laboratory, Stennis Space Center, Mississippi

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William J. Teague Oceanography Division, Naval Research Laboratory, Stennis Space Center, Mississippi

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Abstract

The acoustic properties of water can be drastically modified by a small amount of air content in the fluid. The dynamics of bubble clouds and their collected oscillation mechanisms are among topics of active research in underwater acoustics. In the ocean, bubble clouds are long lasting, and most of the time can be considered as passive scatterers. Solutions of the key parameters such as resonance frequencies, sound speed, and target strength can be derived from treating the bubble cloud as a homogeneous medium with proper effective bulk properties. In this paper, the resonance frequency and target strength are derived from computations based on a classical solution for acoustic scattering of elastic spheres. The range of void fractions covers four orders of magnitude and includes single air bubbles as its asymptotic condition of void fraction equals unity.

Based on these computations, it is found that the isothermal condition is approached only at very low void fraction levels (<10−4). At high void fraction (>3 × 10−1), the cloud oscillation gradually approaches adiabatic condition. Within the broad range of void fraction from 2 × 10−4 to 3 × 10−1, the effective polytropic coefficient of the bubble cloud is approximately 1.2, which is halfway between adiabatic and isothermal conditions. Also, two simple scaling laws for the resonance characteristics of a spherical bubble cloud are revealed: (i) the dimensionless resonance wavenumber is uniquely determined by the void fraction, and (ii) the backscattering cross section is uniquely determined by the resonance frequency.

Corresponding author address: Dr. Paul Hwang, Meso- and Finescale Ocean Physics Section, Oceanography Division, Department of the Navy, Naval Research Laboratory, Stennis Space Center, MS 39529-5004.

Email: paul.hwang@nrlssc.navy.mil

Abstract

The acoustic properties of water can be drastically modified by a small amount of air content in the fluid. The dynamics of bubble clouds and their collected oscillation mechanisms are among topics of active research in underwater acoustics. In the ocean, bubble clouds are long lasting, and most of the time can be considered as passive scatterers. Solutions of the key parameters such as resonance frequencies, sound speed, and target strength can be derived from treating the bubble cloud as a homogeneous medium with proper effective bulk properties. In this paper, the resonance frequency and target strength are derived from computations based on a classical solution for acoustic scattering of elastic spheres. The range of void fractions covers four orders of magnitude and includes single air bubbles as its asymptotic condition of void fraction equals unity.

Based on these computations, it is found that the isothermal condition is approached only at very low void fraction levels (<10−4). At high void fraction (>3 × 10−1), the cloud oscillation gradually approaches adiabatic condition. Within the broad range of void fraction from 2 × 10−4 to 3 × 10−1, the effective polytropic coefficient of the bubble cloud is approximately 1.2, which is halfway between adiabatic and isothermal conditions. Also, two simple scaling laws for the resonance characteristics of a spherical bubble cloud are revealed: (i) the dimensionless resonance wavenumber is uniquely determined by the void fraction, and (ii) the backscattering cross section is uniquely determined by the resonance frequency.

Corresponding author address: Dr. Paul Hwang, Meso- and Finescale Ocean Physics Section, Oceanography Division, Department of the Navy, Naval Research Laboratory, Stennis Space Center, MS 39529-5004.

Email: paul.hwang@nrlssc.navy.mil

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