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

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