FUNDAMENTALS OF OCEAN ACOUSTICS

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1 FUNDAMENTALS OF OCEAN ACOUSTICS Third Edition L.M. Brekhovskikh Yu.P. Lysanov Moscow, Russia With 120 Figures Springer

2 Contents Preface to the Third Edition Preface to the Second Edition Preface to the First Edition v vii ix 1 The Ocean as an Acoustic Medium Sound Velocity in Sea Water Typical Vertical Profiles of Sound Velocity and Corresponding Conditions of Sound Propagation Underwater Sound Channel (USC) Surface Sound Channel USC with Two Axes Antiwaveguide Propagation Propagation-of Sound in Shallow Water Absorption of Sound Variability of the Ocean and Its Effect on Acoustics Large-Scale Currents and Frontal Zones Synoptic (Meso-Scale) Eddies Internal Waves Fine Vertical Structure of Waters Small-Scale Turbulence Ocean Surface Sound Scattering at the Ocean Surface Sound Scattering by Air Bubbles Deep-Scattering Layers (DSL) Ocean Bottom Ambient Noise Intrathermocline Lenses 32 2 Ray Theory of the Sound Field in the Ocean Wave Equation for an Inhomogeneous Medium Simplest Solutions of the Helmholtz Equation Refraction of Sound Rays 38 XI

3 xii Contents 2.3 Horizontal Distance Covered by a Ray Constant-Gradient Approximation of the Sound Velocity Profile Sound Intensity, Focusing Factor, and Caustics "Three-Dimensional" Refraction Snell's Law for the Range-Dependent Ocean Ocean Acoustic Tomography Weakly Divergent Bundles of Rays 56 3 Reflection of Sound from the Surface and Bottom of the Ocean: Plane Waves Reflection and Transmission Coefficients at an Interface Separating Two Liquids Transmission of a Sound Wave from Water into Air and Vice Versa Sound Wave Reflection from an Ocean Bottom Consisting of Liquid Layers Reflection from a Homogeneous Layer Reflection from an Arbitrary Number of Layers Sound Reflection from a Solid Analysis of the Reflection Coefficient Surface Rayleigh and Stonely Waves Reflection from a Continuously Layered Medium 78 4 Reflection of Sound from the Surface and Bottom of the Ocean: Point Source Sound Field of an Underwater Source Located Near the Water Surface Wave Representations L2 Ray Representation Directional Pattern Radiated Power Expansion of a Spherical Wave into Plane Waves Reflected Wave Lateral Wave Reflection from the Layered Inhomogeneous Half-Space: Caustics 95 5 Propagation of Sound in Shallow Water Ray Representation of the Sound Field in a Layer: Image Sources Integral Representation of the Field in the Layer Normal Modes in the Ocean with a Perfectly Reflecting Bottom Relation Between the Different Representations of the Field

4 Contents xiii 5.5 Normal Modes in a Two-Layered Liquid Averaged Decay Law Homogeneous Layer (c = c\ = c/,) Layer with Negative Refraction Underwater Sound Channel Simple Ray Theory of the USC: Trapping Coefficient of the USC "Linear" Model of the USC Travel Time Canonical Underwater Sound Channel Convergence Zones Field of a Point Source in the Underwater Sound Channel as a Sum of Normal Waves (Modes) Integral Representation of the Sound Field in the USC Transformation of the Integral Representation into the Sum of Normal Modes Linear Waveguide Normal Modes in the WKB Approximation: Phase Integral Normal Modes and Rays Spatial Periods of Interference 143 Range-Dependent Waveguide Normal Modes in an Almost Stratified Medium: Reference Waveguide Method Adiabatic Approximation: Ray Invariant Ray Invariant An Example of Using the Ray Invariant Conditions for the Validity of the Adiabatic Approximation and Ray Invariant Coupled Modes... A Rays in a Horizontal Plane The Case of a Coastal Wedge Parabolic Equation Method 163 Antiwaveguide Sound Propagation Linear Antiwaveguide Adjacent to Water Surface Symmetric Antiwaveguide: Quasi-Modes Symmetric Antiwaveguide: Lateral Wave 179 Scattering of Sound at Rough Surfaces Rayleigh Parameter Method of Small Perturbation (MSP) Average Intensity An Infinite Surface Bounded Scattering Surface: Far Zone 187

5 xiv Contents Correlation Function of the Scattered Field Scattering Coefficient for the Ocean Surface Frequency Spectrum of the Scattered Field Reflection Coefficient in the Specular Direction Method of Tangent Plane: Basic Concept Average Field Scattering Coefficient of High-Frequency Sound Scattering Pattern Frequency Spectrum Sound Scattering from a Surface with Two Scales of Roughness Surface Channel with a Rough Boundary Attenuation Along a Single Ray Averaged Decay Law for a Coherent Field Fore-reverberation of Sound in the Ocean Small-Slope Approximation in Wave Scattering by Rough Surfaces Sound Propagation in the Random Ocean Amplitude and Phase Fluctuations Phase Fluctuations Amplitude Fluctuations Scattering of Sound by Random Inhomogeneities..., Average Intensity of a Scattered Field Volume Scattering Coefficient Sound Scattering by Highly Anisotropic Inhomogeneities with a Fractal Spectrum Attenuation of Low-Frequency Sound in an Underwater Sound Channel Phase Fluctuations due to Internal Waves Fluctuations in Multipath Propagation Scattering and Absorption of Sound by Gas Bubbles in Water Sound Scattering by a Single Ideal Bubble Scattering and Absorption of Sound by a Real Bubble Dispersion of Sound Velocity Sound Scattering by an Air Bubble Near a Sea Surface Collective Bubble Oscillations 262 References 265 Index 275

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