The Breaking and Scattering of the Internal Tide on a Continental Slope
JODY M. KLYMAK,* MATTHEW H. ALFORD,1 ROBERT PINKEL,# REN-CHIEH LIEN,1
YUNG JANG YANG,@ AND TSWEN-YUNG TANG&
* School of Earth and Ocean Sciences, University of Victoria, Victoria, British Columbia, Canada
1 Applied Physics Laboratory, University of Washington, Seattle, Washington
# Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California
@ Department of Marine Science, Naval Academy, Kaohsiung, Taiwan
& Institute of Oceanography, National Taiwan University, Taipei, Taiwan
(Manuscript received 12 May 2010, in final form 22 November 2010)
ABSTRACT
Astrong internal tide is generated in the Luzon Strait that radiates westward to impact the continental shelf of
the South China Sea. Mooring data in 1500-m depth on the continental slope show a fortnightly averaged
incoming tidal flux of 12 kW m21, and amooring on a broad plateau on the slope finds a similar flux as an upper
bound. Of this, 5.5 kW m21 is in the diurnal tide and 3.5 kW m21 is in the semidiurnal tide, with the remainder
in higher-frequencymotions. Turbulence dissipationmaybe as high as 3 kW m21. Local generation is estimated
from a linear model to be less than 1 kW m21. The continental slope is supercritical with respect to the diurnal
tide, implying that there may be significant back reflection into the basin. Comparing the low-mode energy of
a horizontal standing wave at the mooring to the energy flux indicates that perhaps one-third of the incoming
diurnal tidal energy is reflected. Conversely, the slope is subcritical with respect to the semidiurnal tide, and the
observed reflection is very weak. A surprising observation is that, despite significant diurnal vertical-mode-2
incident energy flux, this energy did not reflect; most of the reflection was in mode 1.
The observations are consistent with a linear scattering model for supercritical topography. Large fractions of
incoming energy can reflect depending on both the geometry of the shelfbreak and the phase between themodal
components of the incoming flux. If the incident mode-1 andmode-2 waves are in phase at the shelf break, there
is substantial transmission onto the shelf; if they are out of phase, there is almost 100% reflection. The obser-
vations of the diurnal tide at the site are consistent with the first case: weak reflection, with most of it in mode 1
and almost no reflection in mode 2. The sensitivity of the reflection on the phase between incident components
significantly complicates the prediction of reflections from continental shelves.
Finally, a somewhat incidental observation is that the shape of the continental slope has large regions that are
near critical to the dominant diurnal tide. This implicates the internal tide in shaping of the continental slope.
1. Introduction
The tides are believed to be a significant source of en-
ergy to the deep ocean, energizing the mixing between
watermasses that drives theoverturning circulation (Huang
1994; Munk and Wunsch 1998). In the deep ocean, an
important mechanism of energizing the mixing is via the
creation of internal tides. Two end points of internal tide
generation have been considered, generation over rough
but not very steep topography (St. Laurent and Garrett
2002) and generation over abrupt topographic features
(Llewellyn Smith and Young 2003; St. Laurent et al. 2003).
The latter process has been studied in fjords (Klymak and
Gregg 2004; Inall et al. 2005) and more recently at Hawaii
(Merrifield and Holloway 2002; Rudnick et al. 2003).
Interestingly, both fjord studies and the observations at
Hawaii indicate that most of the energy lost from the
barotropic conversion at abrupt topography radiates away
as low-mode internal tides rather than dissipating locally
(Klymak and Gregg 2004; Klymak et al. 2006a). Recent
numerical modeling supports the inferences from obser-
vations (Carter et al. 2008) and offers a simple theoretical
explanation (Klymak et al. 2010b) in terms of trapped
lee waves (Nakamura et al. 2000; Legg and Klymak 2008;
Klymak et al. 2010a).
Because so much of the energy radiates away from
abrupt topography, considerable attention has been
Corresponding author address: JodyM. Klymak, School of Earth
and Ocean Sciences, University of Victoria, P.O. Box 3055 STN
CSC, Victoria BC V8W 3P6, Canada.
E-mail: jklymak@uvic.ca
926 JOURNAL OF PHYS ICAL OCEANOGRAPHY VOLUME 41
DOI: 10.1175/2010JPO4500.1
 2011 American Meteorological Society

placed on understanding where that energy eventually
dissipates.One hypothesis is that there are dissipative losses
when the tides scatter at isolated seamounts (Johnston and
Merrifield 2003) or when they impact continental slopes
(Nash et al. 2004, 2007; Martini et al. 2010, manuscript
submitted to J. Phys. Oceanogr.; Kelly et al. 2010). When
internal waves impact a slope, the behavior depends on
whether the slope is supercritical (b , dh/dx) or sub-
critical (b . dh/dx) with respect to the incoming waves,
where b 5 [(N2 2 v2)/(v2 . f 2)]1/2 is the aspect ratio of
energy propagation of internal waves and dh/dx is the
local topographic slope (N is the local buoyancy fre-
quency, v is the tidal frequency and f is the Coriolis fre-
quency). For subcritical slopes, presumably much of the
energy scatters upslope onto the continental shelf, where
it likely dissipates in shallow water, whereas for super-
critical slopes an undetermined amount of energy will
reflect back into the basin. In both cases, there is pres-
ently no method for predicting a priori how much energy
is dissipated locally, though laboratory experiments in-
dicate that near-critical topographies will have significant
nonlinearities (McPhee-Shaw and Kunze 2002).
In this paper, we consider observations of the internal
tide impacting the continental slope on thewest side of the
South China Sea (SCS). The site is directly west of the
Luzon Strait, a region of very strong internal tide gener-
ation (Niwa and Hibiya 2004; Jan et al. 2007). This leads
to large-amplitude nonlinear internal waves propagating
across the basin (Zhao et al. 2004; Ramp et al. 2004;
Klymak et al. 2006b; Alford et al. 2010) and impacting
the continental slope (Lien et al. 2005; Chang et al. 2006;
St. Laurent 2008). The exact interplay between these
nonlinear waves and the internal tide is still being in-
vestigated, but it seems the nonlinear waves are largely
derived from the steeper semidiurnal tide rather than the
diurnal tide (Farmer et al. 2009; Alford et al. 2010;
Buijsman et al. 2010).
This paper examines what happens when this strong
internal tide impacts the continental slope, beginningwith
a description of our mooring and ship-based operations
(section 2). The observations indicate that there is sig-
nificant reflection from the continental slope in addition
to substantial local dissipation (section 3). These obser-
vations compare favorably to a linear reflection model
that indicates that for this stratification and continental
shelf depth there should be significant reflection of in-
coming internal tides (section 4), and we conclude with a
discussion of the results (section 5).
2. Experiment
We took part in a two-week experiment aboard the
OceanResearcher Iwith observations centered just east of
Dong Sha Island (Fig. 1).A line ofmooringswas deployed
along approximately 218N, with most of the moorings
being deployed farther upslope. Here we will concentrate
on a mooring deployed near the 1500-m isobath (MP1,
Fig. 1b), a ship survey made on the 700-m isobath, and a
mooring placed on theDongsha Plateau in 580 mofwater
(LR1, Fig. 1b).
The site of mooringMP1was chosen as part of an array
of sensors meant to understand the evolution of solitary
waves impacting the slope, the subject of other papers.
Here we were interested in the fate of the internal tide
and, at sea, decided to occupy a gap in ourmooring array.
It appears that the east–west profile of the slope at this
latitude has a region that is very near critical to the K1
internal tide (Fig. 2). This was only apparent when ship-
board bathymetry became available, and it supports the
idea of Cacchione et al. (2002) that internal tides smooth
FIG. 1. Experiment site in the SCS, approximately 450 km west of the Luzon Strait where strong internal tides
originate. Arrows are vertically integrated energy fluxes from a numerical model (courtesy H. Simmons 2010,
personal communication). The mooring locations on the continental slope are indicated in the right-hand panel.
MAY 2011 KLYMAK ET AL . 927