Dmitry Dukhovskoy, Steven Morey, James O

1
Generation of Topographic Waves by a Tropical
Cyclone Impacting a Low-Latitude Continental Shelf
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
Kelvin-type modes. The low-latitude Nicaragua
shelf region in the Caribbean Sea matches those
criteria.
Dmitry Dukhovskoy, Steven Morey, James
OBrien Center for Ocean-Atmospheric Prediction
Studies The Florida State University
MODEL EXPERIMENT 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 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.
CLASSIFICATION OF COASTALLY TRAPPED WAVES
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.
Based on Gill and Clarke, 1974 Wang and Mooers,
1976 Huthnance, 1978 Mysak, 1980.
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 (gt 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 wave-number 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.
Figure 6. The alongshore velocity of the
topographic Rossby wavemode 1. From Wang and
Mooers, 1976.
To 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 faces oriented
across the slope (right and left faces) have
the largest magnitudes and are equal in magnitude
and opposite in sign (Figure 9 a). Dominant
low-frequency oscillations (150 h) are evident
in the time series of the fluxes through the
right and left faces (Figure 9 b). Along the
isobaths, the energy is propagated with the
shallow water to the right.
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.
ACKNOWLEDGMENTS This study was supported by NASA
Physical Oceanography and by funding through the
NOAA ARC. The authors would like to thank Paul
Martin and Alan Wallcraft at the Naval Research
Laboratory for the NCOM development and
assistance with the model.
Figure 7. Wave-number 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 vector (Cg).
REFERENCES Allen, J.S., 1980. Models of
wind-drive currents on the continental shelf.
Ann. Rev. Fluid Mech., 12, 389-433. Buchwald,
V.T., and J.K. Adams, 1968. The propagation of
continental shelf wavs. Proc. Roy. Soc. London,
A305, 235-250. Charney, J.G., 1955. The
generation of ocean currents by wind. J. Mar.
Res., 14, 433-498. Dukhovskoy, D.S., S.L. Morey,
and J.J. OBrien, 2007. Generation of Topographic
Waves by a Tropical Cyclone Impacting a
Low-Latitude Continental Shelf. Cont. Shelf Res.,
accepted. Gill, A.E., and A.J. Clarke, 1974.
Wind-induced upwelling, coastal currents and sea
level changes. Deep-Sea Res. 21, 325-345. Mysak,
L.A., 1980. Topographically trapped waves. Ann.
Rev. Fluid Mech. 12, 45-76. Rhines, P.B., 1970.
Edge-, bottom-, and Rossby waves in a rotating
stratified fluid, Geophys. Fluid. Dyn. 1,
273-302. Wang, D.-P., and C.N.K. Mooers, 1976.
Coastal-trapped waves in a continuously
stratified ocean, J. Phys. Oceanogr. 6 (6),
853-863.
There is an obvious tendency for the fluxes
through the front and back faces to be
anti-correlated (Figure 9 c). When the energy
flux through the back face is positive and the
energy flux through the front face is negative,
the energy is propagated downslope. Presumably
this is related to the topographic Rossby waves
whose wave-number vector estimates (Figure 7)
suggest that the energy is propagated downslope.
Figure 8. Near-bottom current ellipses of the
rotary constituent at the frequency (?, Table 1)
of the maximum spectral peak for points 1 to 4
shown in Figure 2. The horizontal bar indicates
the length of the axis for the specified value
(cm2/ s2 cph).