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

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journal contribution
posted on 24.10.2019 by Simone Michele, Emiliano Renzi
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 Schr¨odinger 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.

Funding

Royal Society - CNR International Fellowship

EPSRC (First Grant EP/R015899/1)

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Fluid Mechanics

Volume

883

Publisher

Cambridge University Press (CUP)

Version

AM (Accepted Manuscript)

Rights holder

© Cambridge University Press

Publisher statement

This article has been published in a revised form in Journal of Fluid Mechanics https://doi.org/10.1017/jfm.2019.907. This version is published under a Creative Commons CC-BY-NC-ND. No commercial re-distribution or re-use allowed. Derivative works cannot be distributed. © Cambridge University Press.

Acceptance date

19/10/2019

Publication date

2019-11-26

Copyright date

2019

ISSN

0022-1120

eISSN

1469-7645

Language

en

Depositor

Dr Emiliano Renzi. Deposit date: 22 October 2019

Article number

A28

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