Michele_Renzi_JFM_2019.pdf (506.37 kB)
Effects of the sound speed vertical profile on the evolution of hydroacoustic waves
journal contribution
posted on 2019-10-24, 11:22 authored by Simone Michele, Emiliano RenziWe 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 MechanicsVolume
883Publisher
Cambridge University Press (CUP)Version
- AM (Accepted Manuscript)
Rights holder
© Cambridge University PressPublisher 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
2019-10-19Publication date
2019-11-26Copyright date
2019ISSN
0022-1120eISSN
1469-7645Publisher version
Language
- en
Depositor
Dr Emiliano Renzi. Deposit date: 22 October 2019Article number
A28Usage metrics
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