ATMOSPHERIC AND OCEANIC WAVES

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ATMOSPHERIC AND OCEANIC WAVES
B. N. Goswami
Centre for Atmospheric and Oceanic
Sciences Indian Institute of Science
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wavelength
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Fig.1
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Fig.2
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Fig.3 High frequency radar measurements of
line-of-sight velocities at heights between 78
and 94 km in the upper mesosphere measured in two
directions, equally inclined at small angles to
the vertical. Top panels show data filtered to
include only periods longer than 8 hr and bottom
panels show data filtered to include only periods
from 8 min to 8 hr. The data were collected
during May 11-14, 1981
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Fig.4
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Fig.5 Polar stereographic projection of
geopotential height at 500 hPa in the NH on a
typical day. The large scale waves with
wavelength 3000-4000 km are seen.
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Fig.6 Polar stereographic projection of
geopotential height at 500 hPa in the SH on a
typical day. The large scale waves with
wavelength 3000-4000 km are seen.
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An example of long waves in the middle latitude
westerlies
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The wave shown in Fig.7 is known as tropical
instability wave (TIW). Some characteristics of
the wave can be derived from time-longitude plot
of SST at a latitude close to the equator and
shown in Fig.8.
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Fig.7
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Fig. 8 Slope of alternating high and low SST
show westward propagation of the wave. Phase
Speed distance traveled/timegt approximately
0.35 m/s Wavelength distance between two
minima or maxima , 1100 km
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• Why do we want to study these waves? The waves
  influence the weather and climate. Better
  understanding of these waves can improve our
  prediction capability of weather and climate.
• In this talk, we shall introduce
• 1. Gravity Waves, example of small scale, high
  frequency waves. These waves are important for
  many processes in the mesosphere and
  thermosphere. Rotation of earth not so important.
• 2. Rossby Waves, Kelvin waves and mixed
  Rossby-Gravity waves, examples of large scale
  waves. Effect weather and climate. Earths
  rotation is important.

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What kind of waves are allowed by the atmosphere
and the Ocean? How do we answer this
question? As any motion in the atmosphere or the
ocean is governed by the basic equations of
motion, we start with the basic equations of
motion and write them for small perturbations
(called linearization). As we are interested in
waves, we look for wave solutions of these linear
equations consistent with given boundary
conditions.
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?ln?/ ?z
exp(i(wtkxmz))
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LARGE SCALE ATMOSPHERIC AND OCEANIC WAVES To
describe the large scale atmospheric and oceanic
waves, we shall consider two situations
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z
h
H
y
x
Geometry of the shallow water model
The infinite channel of width L rotating with
angular speed f/2
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Summary Waves in a Middle Latitude Beta-plane
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of Rossby waves
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Dispersion relation of waves for middle latitude
shallow water channel.
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the
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Do we see these waves predicted by theory in the
Atmosphere ? Wavenumber-frequency spectra of
twice daily OLR in tropics showing Kelvin, Rossby
and MRG waves (Weickman and Kiladis, JAS,1999,
vol.56,374pp)
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Cp(Rossby)
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Time longitude section of sea-level anomalies
from TOPEX/POSEIDON along equator (bottom) and 4N
(top). Eastward propagating Kelvin wave along the
equator and Rossby wave propagating westward at
4N are seen. Rossby waves emanate after the
Kelvin waves reach the eastern boundary. Phase
speed of the Rossby wave is appox. 1/3 that of
Kelvin wave.
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Time-height sections of equatorial lower
stratosphere showing the evidence of Kelvin-wave
activity. a) zonal wind and b) temperature at
Canton island. Downward propagation of westerly
phase of QBO is also seen. Phase difference
between U and T is consistent with Kelvin wave.
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Time-longitude section of sea level anomalies
from TOPEX/POSEIDON along 21N, 32N and 39N. Slope
of the line shows that phase speed of the Rossby
waves decreases northwards.
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Two snapshots of sea level anomalies from
TOPEX. The front of the Rossby wave in the top
panel is due to the difference in phase speed of
Rossby wave as one goes away from the
equator. The lower panel shows Rossby wave front
reaching the western boundary. A reflected Kelvin
wave signal propagates quickly eastward.
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Thank you!