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8/2/2019 AEP 06 Rossby Gravity Waves1
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Atmospheric and
environmental Physics
PH3022
6
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Waves in the Atmosphere
Perturbation method
Properties of wave
Shallow water gravity wave
Planetary Rossby wave
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Assumptions Basic state variables must satisfy the governing
equations when perturbations are set to zero The perturbation fields must be small enough so that all
terms in the governing equations that involve products of
the perturbations can be neglected
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Perturbation method
If the terms that are products of the perturbation
variables are neglected, the nonlinear governingequations are reduced to linear differential
equations in the perturbation variables inn which
the basic state variables are specifiedcoefficients
The equations can then be solved by standard
methods to determine the character andstructure of the perturbations in terms of the
known basic state
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Perturbation method
For equations with constant coefficients
the solutions are sinusoidal in character
Solution determines propagation speed,
vertical structure, conditions for growth ordecay of waves
Useful in studying the stability of a given
basic state flow with respect to smallsuperposed perturbations
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Atmospheric waves Perturbations in the atmosphere can be represented as
Fourier series of sinusoidal components. IfL isdistance around latitude circle,s is planetary wave
number (an integer designating number of waves
around latitude circle) then:
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Atmospheric waves
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For a group of waves added together eachcomponent has its own wavenumber and phase speed
Waves in which the phase speed varies with karecalled dispersive. Various sinusoidal componentsoriginating at a given location are found in different
places at a later time For non-dispersive waves phase speeds are
independent of the wave number
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Vorticity Absolute vorticity is sum of the vorticity of air
relative to Earth and Earths vorticity (relativevorticity+coriolis parameter)
Absolute vorticity will change if air mass is
stretched or compressed. But if it is divided bythe vertical spacing between levels of constantentropy (or potential temperature) then the
result is a conserved quantity of adiabatic flowcalledpotential vorticity
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is called stream function.
Velocity of flow can be
represented as partial
derivatives of streamfunction at a given point