Erika McPheeShaw Institute for Computational Earth Systems Science, University of California Santa B

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Internal Waves over Continental Slopes
Implications for the Suspension and Transport of
Sediment
Erika McPhee-Shaw - Institute for
Computational Earth Systems Science, University
of California Santa Barbara
Abstract Critical reflection of internal
tides from continental margins and other
topographic features transfers energy from
low-wavenumber tidal frequencies directly to high
wavenumbers, leading to increased shear and
strain. This process has been linked to sediment
erosion and the generation of intermediate
nepheloid layers. Recent observations from the
northern California margin show episodic pulses
of baroclinic semidiurnal energy, with bottom
intensification of cross-isobath velocity and
bore-like behavior suggestive of reflection of
the semidiurnal internal tide. Observations of
intermediate nepheloid layer generation and
regions of relatively high erosion suggest a
response of sediment associated with this
process. The effect on sediment is twofold.
Near-critical reflection amplifies wave
velocities near the region of reflection. This
can impart a bottom shear stress high enough to
erode sediment from the seafloor. Secondly,
sediment suspended within the water column can
also be affected by internal wave interaction
with topography. Elevated turbulence can prevent
particles from settling. Relaxation or
restratification following mixing events near or
within the boundary layer can increase horizontal
diffusivity, possibly resulting in the formation
of intermediate nepheloid layers. Laboratory and
numerical experiments on internal wave reflection
have shown that the magnitude of turbulent
dissipation, and associated along-isopycnal
spreading or horizontal diffusivity, are
proportional to the divergence of internal wave
energy density flux at the boundary. Quantifying
the energy flux divergence is necessary before we
can predict sediment fluxes due to this process,
either for ocean margins in general, or for a
particular location. The geographic distribution
of energy flux in internal tides is related to
factors such as regional topographic roughness,
latitude, and spatial distribution of
stratification. Internal wave spectra near
margins and rough topography such as canyons are
often dominated by peaks at the semidiurnal and
tidal harmonics. The description of energy
transfer into turbulence in these conditions
differs from parameterizations applied in the
open ocean, and may require direct measurements
in the field. In addition to critical reflection,
other mechanisms which transfer internal wave
energy to small scales near topography should
also be considered.
Evidence for interaction between topography and
internal tides at the Northern California Margin
Observations of intermediate nepheloid layers and
M2-critical topography over the northern
California margin
Measurements CTD and current meter time series
from the Y-450 mooring, located at 450-m depth
(see map). Instruments packages were at 60, 180,
and 435-m depth, with the deepest instruments
located 15 meters above the bottom. Periods of
energetic internal tide activity occurred in
episodic pulses throughout the record.
CTD and transmissometer surveys were undertaken
over the Eel River margin (near Eureka,
California) between October 1998 and August 1999,
in order to investigate the characteristics and
seasonal nature of intermediate nepheloid layers
(INLs) over the outer shelf and upper-
continental slope. One goal of these surveys was
to ascertain whether there was a relationship
between regions of INL generation on the slope
and regions where slope topography was
near-critical for internal tides.
M2-critical topography on the continental slope
The panels on the left show a 15-day time series
from the Y-450 mooring, during August-September,
1996. This episode was characterized by high
internal semidiurnal energy. Cross-isobath
velocity, u, density perturbation, ?, and
vertical isopycnal displacement, ?z from 180-m
depth are plotted in a c, and from 435-m depth
in d e (The bottom depth was 450 meters). Note
the bottom amplification of cross-isobath
currents, and the high isopycnal displacements
near the bottom. Also note the asymmetric wave
shape observed at the bottom current meter and
CTD. The panels on the right show a contrasting
15-day time series. This segment, from
November-December, 1996, was characterized by
relatively weak semidiurnal internal energy.
"High Energy period"
"Low Energy period"
Variance-preserving spectra from two 40-day
periods (one "low-energy" and the other
"high-energy") from the Eel River mooring.
Spectra from near-bottom (435 m) velocity are
shown in blue, and mid-depth velocity (180 m)
spectra are in red.
The two cross-slope transects covered in the CTD-
transmissometer surveys are shown with the maroon
lines. The contours from these transects are
shown in the figures below, and are referred to
as the "O sites" or the "North sites." The black
circle marks the location of the Y-450 mooring,
at 450-m depth. Data from this mooring are shown
to the right. The shaded areas on each map mark
the regions where slope topography was
near-critical for the semidiurnal (M2) tide for
each season surveyed. The color designates the
value of w/wc, i.e. the proximity to critical.
Cacchione et al., 2002, show a similar analysis
for the outer shelf on this margin. There is
some variation in the location of critical
topography due to seasonal changes in
stratification. Of the four surveys, August 1999
was characterized by the highest portion of
near-critical topography (near-critical is
defined as 0.8 lt w/wc lt 1.3. For slope depths
between 200 and 1000 m, and between 40.4o and
41.6o N, approximately 37 of the continental
slope topography was near-critical during August.
In contrast, the portion of the same topography
that was near-critical during October '98,
January '99, and March ranged from 24 to 27.
Boundary layer intrusions generated by internal
wave interaction with topography
Evidence Bottom-trapped energy at the semidiurnal
frequency. During these episodes, M2 energy was
preferentially amplified in the across-isobath
velocity component over along-isobath component.
This was observed at the deep sensor, but not at
mid-depth. Semidiurnal vertical isopycnal
displacement (z' ?'/d?/dz, gradient estimated
from nearby, 1996 CTD profiles) was as high as
100 meters near the slope. This vertical
displacement is consistent with the across-slope
excursion that would result from the measured,
near-bed, cross-isobath currents of 20
cm/s. Asymmetry between up-going and down-going
phase. Shown theoretically and in laboratory
experiments to be a feature of near-critical
internal wave reflection (Thorpe, 1987, Thorpe,
1992). Bottom-trapped energy in tidal-harmonic
frequencies. Observed amplification at harmonic
frequencies suggests nonlinear interactions at
tidal frequencies. This implies that 1) beams
crossed each other, which in turn suggests
reflection and/or generation nearby, and 2)
energy might be transferred via nonlinear
processes into high wavenumbers while remaining
at low frequencies. This is important for
generating instabilities and turbulent
dissipation.
Here we focus on mechanism 2 - dispersal of
mixed boundary layer water caused by relaxation
or gravitational collapse of diapycnal mixing
events.
Successive mixing events and subsequent collapse
lead to gradual dispersal of boundary layer fluid
away from margin
Internal wave breaking mixes stratified fluid
near boundary
Observations of intermediate nepheloid layers
over the slope
INLs in Winter
INLs in Summer
Nonlinear energy transfer at low frequencies,
high wavenumbers? Reflected beams trapped near
the slope. Increased likelihood of nonlinear
interactions within this region. Transfer of
energy directly to small spatial scales while
still at low frequencies could be an important
part of the dissipation process that is not
included in fine-scale parameterization of
dissipation. (Müller and Liu, 1999, Garrett and
St. Laurent, 2002, Kunze et al., 2002)
Example analytical solutions for linear internal
wave reflection at subcritical conditions.
Reflected beams propagate within the vicinity of
the boundary.
3 cm
10 cm
Photographs from laboratory experiments. The
picture on left is a shadowgraph image of an
internal wave breaking against a sloping
boundary. In this situation, the wave was
subcritical, with w/wc 0.7 the angle of the
incident wave beam is slightly less steep than
the angle of the boundary. The panels on the
right show photographs, progressing in time, of
fluorescein-dyed boundary layer fluid spreading
into the interior.
The change in potential energy within a mixing
patch is described by
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The future of internal wave - nepheloid layer
studies?
The perturbation kinetic energy balance is given
by
We need measurements of energy density flux
divergence over boundary regions (following
methods of Kunze et al, 2002, in Monterey
Canyon). These measurements are necessary to
quantify the energy available for mixing.
Ideally, the generation of INLs would be
assessed, possibly via a dye-dispersal study,
along with a concurrent mooring array and set of
fine- and micro-structure measurements to obtain
energy fluxes and turbulent dissipation rates.
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Cross-slope transmissometer and CTD transects
from the Eel River Margin, 1998 to 1999. SPM
concentration contours are shaded in gray.
Potential density contours are shown with the
solid lines. The colorbar on the right of each
panel shows magnitude of the SPM concentration
anomaly, in mg/l. For both the "North transects"
and the "O transects" the distance across the
slope is in kilometers from a zero-point at
approximately 50-m depth on the continental
shelf. Intermediate nepheloid layers were
observed over the continental slope during most
seasons. In winter, the suspended particulate
signal was dominated by INLs generated over the
outer shelf and spreading out over deeper waters
at depths of 70 to 150 meters. During summer
and fall, INLs from the deeper continental slope
were prevalent, and were often associated with
regions of M2- critical topography. The strongest
slope-depth INLs were observed during August,
coincident with the period characterized by the
largest swaths (highest percent surface area) of
critical topography.
Following Kunze et al (1995) we assume that the
internal wave energy flux divergence term is the
primary source for perturbation kinetic energy
near the boundary, and thus the loss terms
(dissipation and buoyancy flux) are proportional
to the flux divergence over the dissipation
region (McPhee-Shaw and Kunze, 2002). Thus, 1
becomes
Acknowledgements and citations This project was
funded by the office of Naval Research, through
an AASERT grant associated with the STRATAFORM
program. Thanks go to Eric Kunze, and to Richard
Sternberg, Andrea Ogston, Peter Rhines, Eric
Lindahl, Dave Cacchione, Beth Mullenbach, and
Chuck Nittrouer for help with the laboratory and
field aspects of this study.
Cacchione, Pratson, and Ogston, 2002. The shaping
of continental slopes by internal tides. Science,
296, 724-727. Garrett and St. Laurent, 2002.
Aspects of deep ocean mixing. J. Phys. Ocean. 58,
11-24 Kunze, Rosenfeld, Carter, and Gregg, 2002.
Internal waves in Monterey Canyon. J. Phys.
Ocean, 32, 1890-1913. McPhee-Shaw and Kunze,
2002. Boundary layer intrusions from a sloping
bottom a mechanism for generating intermediate
nepheloid layers. J. Geophys. Res., 107, C6.
10.1029/2001JC000801 Muller and Liu, 1999.
Scattering of internal waves at finite topography
in two dimensions. Part II Spectral calculations
and boundary mixing. J. Phys. Ocean, 30,
550-563 Thorpe, 1992. Thermal fronts caused by
internal gravity waves reflecting from a slope.
J. Phys. Ocean., 22, 105-108
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and the spreading rate, U, of the collapsing,
newly-mixed volume of fluid is proportional to
the internal wave energy flux divergence
(Where Rf is the Richardson flux number, N the
buoyancy frequency, L the overturn length scale,
and ltupgt is the pressure flux, or energy density
flux)
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Intrusion spreading rate can we
predict Nepheloid Layer spreading rate?