INTRODUCTION Given appropriate slope, the ocean responds to
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
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
Based on: Gill and Clarke, 1974; Wang and
Mooers, 1976; Huthnance, 1978; Mysak,
1) Barotropic vs Baroclinic
Ri N H
Burger Number: Bu
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):
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
Table 1. Characteristics of baroclinic
topographic wave simulated in the
model 10-5, T, k 10-5, l 10-5, , , C,
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
Ri > L
Ri < L
Figure 6. The alongshore
velocity of the topographic
Rossby wavemode 1. From:
Wang and Mooers, 1976.
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 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
component of the
ENERGETICS OF THE TOPOGRAPHIC WAVES
The direction of the group velocity vector (Cg) of
the topographic Rossby wave
C g KK
corresponds to the direction of energy flux. Cg 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
to the right.
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
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,
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.
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,
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,
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.
(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.
A team effort between the CAFC, the CCFM&FM and our funders Canadian Safety and Security Centre, DRDC and Public Safety Canada. 3. Why . ... Calgary. Hassan. Wildland Fire-induced Risk Modelling Framework for the Greater Athabasca Oil Sand Region. 6.
HATS ARE NOT ALLOWED(Even if they're this cute) Make sure you are not falling out either end. Easy on the makeup! Please hide your tats! DON'T GO THERE! Shirts should be pulled down! ... What not to wear… Last modified...
Westerns vs. Action-Adventure. Western focused on taming nature or the natural inhabitants. Today's Action-Adventure is more about wars over oil reserves, mineral deposits and preservation of homeland security. The modern movie has given way to spreading democracy and clashing against...
Autotuning Sparse Matrix and Structured Grid Kernels Samuel Williams1,2, Richard Vuduc3, Leonid Oliker1,2, John Shalf2, Katherine Yelick1,2, James Demmel1,2, Jonathan Carter2, David Patterson1,2 1University of California Berkeley 2Lawrence Berkeley National Laboratory 3Georgia Institute of Technology [email protected]
Why is plain language important? Accessibility demands it. Writing for a wide audience with diverse abilities requires clarity and efficiency. 20% of your audience may have some form of visual or cognitive impairment, and that number is expected to grow
In non-O-O languages, e.g. C and Matlab, there is no notion of agent, but you can pass a routine as argument to another routine, as in. integral (& f, a, b) where. f. is the function to integrate.& f (C...
Spinach Chromatography. Lab Objective. Separate pigments from spinach using paper chromatography. Calculate R. f values of separated pigments*R. f = distance substance travels distance solvent front travels. Materials. Chromatography paper strips. Petroleum Ether: Acetone Solution. 1 vial spinach leaf extract....
Ready to download the document? Go ahead and hit continue!