INTRODUCTION Given appropriate slope, the ocean responds to

INTRODUCTION Given appropriate slope, the ocean responds to

INTRODUCTION
Given appropriate slope, the ocean
responds to a tropical storm with motions of
sub-inertial frequencies trapped over a
continental slope, the coastally trapped
waves. It is speculated that in a low-latitude
region a storm can excite bottom-intensified
topographic Rossby waves whose theory has
been outlined by Rhines (1970). In order for
a continental shelf to support baroclinic
topographic waves it should (1) respond as a
baroclinic ocean, and (2) have a slope steep
enough to dominate the planetary -effect
but small enough to prevent internal Kelvintype modes. The low-latitude Nicaragua shelf
region in the Caribbean Sea matches those
criteria.
CLASSIFICATION
OF COASTALLY

Generation of Topographic Waves by a Tropical
Cyclone Impacting a Low-Latitude Continental Shelf
Dmitry Dukhovskoy, Steven Morey, James OBrien
Center for Ocean-Atmospheric Prediction Studies
The Florida State University
MODEL EXPERIMENT

1
3

TRAPPED WAVES

Based on: Gill and Clarke, 1974; Wang and
Mooers, 1976; Huthnance, 1978; Mysak,
1980.
SCALE ANALYSIS
1) Barotropic vs Baroclinic
2

Ri N H
Burger Number: Bu

L fL

2

When Bu >> 1, the shelf response should
predominantly be baroclinic. Baroclinic
modes should be considered for the
Nicaragua Shelf (Bu > 1).
2) Coastal wall effect (Allen, 1980):

Ri B

B H H

If > 1, the continental margin acts like a
vertical wall to a wave allowing the
existence of internal Kelvin wave modes.
For the Nicaragua Shelf, coastal wall
effect can be neglected (Figure 1).
3) Anticipated modal structure of the
topographic Rossby waves on the
Nicaragua slope (Figure 6):
Topographic Rossby wave motions
over the Nicaragua shelf will have
barotropic mode over the upper part
of the slope (local Ri < L) and baroclinic (bottom-intensified) mode over the deeper part of the slope (Ri > L).

Table 1. Characteristics of baroclinic
topographic wave simulated in the
model 10-5, T, k 10-5, l 10-5, , , C,
Points

rad s-1

h

rad m-1

rad m-1

km

Dgr

m s-1

2
3
4

0.86
1.14
1.14

202
153
153

-1.1
-1.8
-2

10.5
7
8.6

59
87
73

119
127
126

0.08
0.16
0.13

The Nicaragua Shelf region with simplified bathymetry (Figure 2) is modeled using
Navy Coastal Ocean Model. The model is forced with the wind field computed from
the gradient wind balance applied to the analytical pressure field in a hurricane
(OBrien and Reid, 1967). The storm translates over the region with speed 6 km/h
(Figure 4 a).

Figure 1. Bathymetry of the
Nicaragua Shelf region. The
dashed box marks the region
approximated by the model
domain. Values for coastal wall
effect scale analysis are
shown.

Bottom
intensified
(trapped) wave
Ri > L

Barotropic
shelf wave,
Ri < L Figure 6. The alongshore velocity of the topographic Rossby wavemode 1. From: Wang and Mooers, 1976. K Cg Figure 7. Wavenumber vector (K) estimates from time series analysis. Note the length scale of the wave is the reciprocal of the shown vectors. The red arrow indicates the orientation of the group velocity Figure 4. Evolution in time (in columns) of the simulated fields (in rows). Upper row (a, b, c): potential -density field at 300 m depth. Bottom row (d, e, f): the 22, 11, and 6C isotherms. Figure 3. Geometry and fluxes of a fixed volume element used for calculating energetics of the topographic waves. Figure 2. Model domain. Location of the points used for the time series analysis. ANALYSIS OF THE MODEL RESULTS Formation of internal waves trapped along the slope is well observed in the plot of the potential density field at -300 m depth (Figure 4 a-c) and three-dimensional diagrams of the temperature and potential density surfaces (Figure 4 d-f). The wavelet transforms (Figure 5, the first 180 hours are not shown) demonstrate that the motions are dominated by slow-oscillating modes (> 100 hours period). For
frequencies identified from spectra, the wave-number vectors are derived (Figure 7
and Table 1, details are in Dukhovskoy et al., 2007). The orientation of the wavenumber vector agrees well with the result of the rotary spectral analysis (Figure 8).

Figure 5. Morlet
wavelet transform of
the along-isobath
component of the
near-bottom velocity.

ENERGETICS OF THE TOPOGRAPHIC WAVES
The direction of the group velocity vector (Cg) of
the topographic Rossby wave

C g KK
are
N horthogonal
cos .
corresponds to the direction of energy flux. Cg and
and

Thus when the wavenumber vector is directed upslope the group
velocity vector is directed downslope. The energy is propagated by the
topographic waves with the shallowTo
water
to the right.
demonstrate
the energy propagation by the
waves, the energy budget is computed for a
volume element along the continental slope
(Figure 3). The energy fluxes through the

Figure 9. (a) Time series of the energy
fluxes through the volume faces. The fluxes
are normalized by the area of the face (J/s
m2). Segments of the time series within the
black box are shown in (b) for right and left
faces, and (c) for front and back faces.

faces oriented across the slope (right and
left faces) have the largest magnitudes
and are equal in magnitude and opposite in
ACKNOWLEDGMENTS
sign (Figure 9 a). Dominant low-frequency
study was supported by NASA Physical Oceanography and by
oscillations (~150 h) are evident in the time This
funding through the NOAA ARC. The authors would like to thank Paul
Martin and Alan Wallcraft at the Naval Research Laboratory for the
series of the fluxes through the right and
NCOM development and assistance with the model.
left faces (Figure 9 b). Along the isobaths,
REFERENCES
the energy is propagated with the shallow
Allen, J.S., 1980. Models of wind-drive currents on the continental shelf. Ann.
Rev. Fluid Mech., 12, 389-433.
There to
is an
water
theobvious
right. tendency for the fluxes
Buchwald, V.T., and J.K. Adams, 1968. The propagation of continental shelf
Figure 8. Near-bottom current
through the front and back faces to be antiwavs. Proc. Roy. Soc. London, A305, 235-250.
ellipses of the rotary constituent at correlated (Figure 9 c). When the energy flux Charney, J.G., 1955. The generation of ocean currents by wind. J. Mar. Res., 14,
433-498.
the frequency (, Table 1) of the
Dukhovskoy, D.S., S.L. Morey, and J.J. OBrien, 2007. Generation of
through the back face is positive and the
Topographic Waves by a Tropical Cyclone Impacting a Low-Latitude
maximum spectral peak for points energy flux through the front face is negative,
Continental Shelf. Cont. Shelf Res., accepted.
Gill, A.E., and A.J. Clarke, 1974. Wind-induced upwelling, coastal currents and
1 to 4 shown in Figure 2. The
the energy is propagated downslope.
sea level changes. Deep-Sea Res. 21, 325-345.
horizontal bar indicates the length Presumably this is related to the topographic Mysak, L.A., 1980. Topographically trapped waves. Ann. Rev. Fluid Mech. 12,
45-76.
of the axis for the specified value
Rhines, P.B., 1970. Edge-, bottom-, and Rossby waves in a rotating stratified
Rossby waves whose wave-number vector
fluid, Geophys. Fluid. Dyn. 1, 273-302.
2
2
(cm / s cph).
D.-P., and C.N.K. Mooers, 1976. Coastal-trapped waves in a continuously
estimates (Figure 7) suggest that the energy is Wang,
stratified ocean, J. Phys. Oceanogr. 6 (6), 853-863.

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