AEP 06 Rossby Gravity Waves1

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

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AEP 06 Rossby Gravity Waves1