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

Published online by Cambridge University Press:  26 November 2019

S. Michele Open the ORCID record for S. Michele [Opens in a new window]  and
E. Renzi
S. Michele*
Affiliation:
Department of Mathematical Sciences, Loughborough University, LoughboroughLE11 3TU, UK
E. Renzi
Affiliation:
Department of Mathematical Sciences, Loughborough University, LoughboroughLE11 3TU, UK
*
†Email address for correspondence: s.michele@lboro.ac.uk
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Abstract

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.

JFM classification

Waves/Free-surface Flows: Waves/Free-surface Flows Compressible Flows: Compressible Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 883 , 25 January 2020 , A28
Copyright
© 2019 Cambridge University Press

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