Effects of the sound speed vertical profile on the evolution of hydroacoustic waves

We present a novel analytical model for the evolution of hydroacoustic waves in weakly compressible fluids characterised by depth variations of the sound speed profile. Using a perturbation expansion in terms of the small vertical variation of the sound speed, we derive a novel expression for the se...

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Bibliographic Details
Published in:Journal of fluid mechanics 2020-01, Vol.883, Article A28
Main Authors: Michele, S., Renzi, E.
Format: Article
Language:English
Subjects:
Acoustics
Compressible fluids
Earthquakes
Emergency communications systems
Emergency warning programs
Evolution
Fluids
Gravity
Mathematical models
Propagation
Salinity
Schrodinger equation
Sound
Sound velocity
Underwater acoustics
Variation
Velocity
Velocity potential
Vertical profiles
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Summary:We present a novel analytical model for the evolution of hydroacoustic waves in weakly compressible fluids characterised by depth variations of the sound speed profile. Using a perturbation expansion in terms of the small vertical variation of the sound speed, we derive a novel expression for the second-order velocity potential and show that this solution does not exist in the case of homogeneous sound speed. At the third order, we derive a linear Schrödinger equation governing the evolution of the wave envelope for large length and time scales, which features new terms depending on the sound speed distribution. We show that for generalised sound speed vertical profiles the frequency of the hydroacoustic signal can increase or decrease with respect to the constant sound speed case, depending on the profile. This has substantial implications on the speed of the wavetrain envelope. Our findings suggest the need to extend existing models that neglect the sound speed vertical variation, especially in view of applications to tsunami early warning.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2019.907