On the interaction of short linear internal waves with internal solitary waves
We study the interaction of small-scale internal wave packets with a large-scale internal solitary wave using high-resolution direct numerical simulations in two dimensions. A key finding is that for wave packets whose constituent waves are short in comparison to the solitary wave width, the inter...
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
Copernicus Publications
2018-01-01
|
Series: | Nonlinear Processes in Geophysics |
Online Access: | https://www.nonlin-processes-geophys.net/25/1/2018/npg-25-1-2018.pdf |
id |
doaj-be5d0835db314191b7012513eda9ff25 |
---|---|
record_format |
Article |
spelling |
doaj-be5d0835db314191b7012513eda9ff252020-11-25T00:46:10ZengCopernicus PublicationsNonlinear Processes in Geophysics1023-58091607-79462018-01-012511710.5194/npg-25-1-2018On the interaction of short linear internal waves with internal solitary wavesC. Xu0M. Stastna1Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, CanadaDepartment of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, CanadaWe study the interaction of small-scale internal wave packets with a large-scale internal solitary wave using high-resolution direct numerical simulations in two dimensions. A key finding is that for wave packets whose constituent waves are short in comparison to the solitary wave width, the interaction leads to an almost complete destruction of the short waves. For mode-1 short waves in the packet, as the wavelength increases, a cutoff is reached, and for larger wavelengths the waves in the packet are able to maintain their structure after the interaction. This cutoff corresponds to the wavelength at which the phase speed of the short waves upstream of the solitary wave exceeds the maximum current induced by the solitary wave. For mode-2 waves in the packet, however, no corresponding cutoff is found. Analysis based on linear theory suggests that the destruction of short waves occurs primarily due to the velocity shear induced by the solitary wave, which alters the vertical structure of the waves so that significant wave activity is found only above (below) the deformed pycnocline for overtaking (head-on) collisions. The deformation of vertical structure is more significant for waves with a smaller wavelength. Consequently, it is more difficult for these waves to adjust to the new solitary-wave-induced background environment. These results suggest that through the interaction with relatively smaller length scale waves, internal solitary waves can provide a means to decrease the power observed in the short-wave band in the coastal ocean.https://www.nonlin-processes-geophys.net/25/1/2018/npg-25-1-2018.pdf |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
C. Xu M. Stastna |
spellingShingle |
C. Xu M. Stastna On the interaction of short linear internal waves with internal solitary waves Nonlinear Processes in Geophysics |
author_facet |
C. Xu M. Stastna |
author_sort |
C. Xu |
title |
On the interaction of short linear internal waves with internal solitary waves |
title_short |
On the interaction of short linear internal waves with internal solitary waves |
title_full |
On the interaction of short linear internal waves with internal solitary waves |
title_fullStr |
On the interaction of short linear internal waves with internal solitary waves |
title_full_unstemmed |
On the interaction of short linear internal waves with internal solitary waves |
title_sort |
on the interaction of short linear internal waves with internal solitary waves |
publisher |
Copernicus Publications |
series |
Nonlinear Processes in Geophysics |
issn |
1023-5809 1607-7946 |
publishDate |
2018-01-01 |
description |
We study the interaction of small-scale internal wave packets with a large-scale internal solitary wave using
high-resolution direct numerical simulations in two dimensions. A key finding is that for wave packets whose constituent
waves are short in comparison to the solitary wave width, the interaction leads to an almost complete destruction of the
short waves. For mode-1 short waves in the packet, as the wavelength increases, a cutoff is reached, and for larger
wavelengths the waves in the packet are able to maintain their structure after the interaction. This cutoff corresponds to
the wavelength at which the phase speed of the short waves upstream of the solitary wave exceeds the maximum current
induced by the solitary wave. For mode-2 waves in the packet, however, no corresponding cutoff is found. Analysis based on
linear theory suggests that the destruction of short waves occurs primarily due to the velocity shear induced by the
solitary wave, which alters the vertical structure of the waves so that significant wave activity is found only above
(below) the deformed pycnocline for overtaking (head-on) collisions. The deformation of vertical structure is more
significant for waves with a smaller wavelength. Consequently, it is more difficult for these waves to adjust to the new
solitary-wave-induced background environment. These results suggest that through the interaction with relatively smaller
length scale waves, internal solitary waves can provide a means to decrease the power observed in the short-wave band in
the coastal ocean. |
url |
https://www.nonlin-processes-geophys.net/25/1/2018/npg-25-1-2018.pdf |
work_keys_str_mv |
AT cxu ontheinteractionofshortlinearinternalwaveswithinternalsolitarywaves AT mstastna ontheinteractionofshortlinearinternalwaveswithinternalsolitarywaves |
_version_ |
1725266472700215296 |