Translator Disclaimer
2021 Near-critical reflection of internal waves
Roberta Bianchini, Anne-Laure Dalibard, Laure Saint-Raymond
Anal. PDE 14(1): 205-249 (2021). DOI: 10.2140/apde.2021.14.205

Abstract

Internal waves describe the (linear) response of an incompressible stably stratified fluid to small perturbations. The inclination of their group velocity with respect to the vertical is completely determined by their frequency. Therefore the reflection on a sloping boundary cannot follow Descartes’ laws, and it is expected to be singular if the slope has the same inclination as the group velocity. We prove that in this critical geometry the weakly viscous and weakly nonlinear wave equations have actually a solution which is well approximated by the sum of the incident wave packet, a reflected second harmonic and some boundary layer terms. This result confirms the prediction by Dauxois and Young, and provides precise estimates on the time of validity of this approximation.

Citation

Download Citation

Roberta Bianchini. Anne-Laure Dalibard. Laure Saint-Raymond. "Near-critical reflection of internal waves." Anal. PDE 14 (1) 205 - 249, 2021. https://doi.org/10.2140/apde.2021.14.205

Information

Received: 27 March 2019; Accepted: 7 October 2019; Published: 2021
First available in Project Euclid: 23 March 2021

Digital Object Identifier: 10.2140/apde.2021.14.205

Subjects:
Primary: 35Q35 , 35Q86 , 76D10

Keywords: boundary layers , Boussinesq approximation , internal waves , near-critical reflection

Rights: Copyright © 2021 Mathematical Sciences Publishers

JOURNAL ARTICLE
45 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.14 • No. 1 • 2021
MSP
Back to Top