Atmospheric Waves Questions and Answers

Q: A wave whose phase speed depends on its wavelength is described as _____.

Dispersion means the phase speed varies with wavenumber, so a packet spreads and the group velocity differs from the phase velocity. Rossby and gravity waves are dispersive while sound and equatorial Kelvin waves are not. Trapping and evanescence describe how the amplitude varies in space rather than how the speed varies with wavelength.

Q: The level at which the mean flow speed equals the wave phase speed is called a _____ level.

At a critical level the intrinsic frequency vanishes, the vertical wavelength shrinks and the wave is absorbed, depositing its momentum into the mean flow. Reflecting levels turn waves back by a different mechanism, the steering level is a synoptic concept for system movement, and the level of non-divergence concerns the vertical structure of the divergence field. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Q: Arrange the following waves in order of increasing typical period. 1. Rossby 2. Acoustic 3. Inertial 4. Gravity Select the correct sequence.

Acoustic waves have periods of seconds, gravity waves minutes to hours, inertial oscillations about a day, and Rossby waves days to weeks, giving the order 2, 4, 3, 1. The ladder spans some six orders of magnitude, and placing any newly encountered phenomenon on it from an estimate of its timescale is a quick way to identify which family it belongs to.

Q: Match each wave with its restoring mechanism. List I A. Acoustic B. Internal gravity C. Rossby List II P. buoyancy Q. compressibility R. potential vorticity gradient Select the correct match.

Acoustic waves are restored by compressibility, internal gravity waves by buoyancy, and Rossby waves by the meridional gradient of potential vorticity. Organising the wave family by restoring force rather than by name makes the dispersion relations far easier to reconstruct, since each follows directly from the physics of what returns a displaced parcel towards its original position. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Q: Match each equatorial wave with its propagation direction. List I A. Kelvin B. Equatorial Rossby C. Mixed Rossby-gravity List II P. westward phase Q. eastward only R. westward phase with upward energy Select the correct match.

The Kelvin wave travels eastward only, the equatorial Rossby wave westward, and the mixed Rossby-gravity wave has westward phase propagation while carrying energy upward. The opposing directions of the first two produce the east-west asymmetry of the Gill response to tropical heating, and the momentum carried by the first and third drives the quasi-biennial oscillation. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Q: Which model error results from omitting gravity wave drag?

The cold pole problem, in which the modelled winter polar vortex is too strong and too cold, was a longstanding defect traced directly to missing wave drag. Adding an orographic gravity wave drag scheme largely resolved it. The other errors listed arise from quite different deficiencies in convection, microphysics and numerical conservation.

Q: Which quantity does a gravity wave drag scheme compute?

The scheme launches a wave momentum flux at the source level and computes where it is deposited, the vertical divergence of that flux being the drag applied to the resolved flow. Saturation criteria determine the deposition level. Counting individual crests is neither possible nor meaningful at model resolution, and the surface amplitude is an input rather than the output of the calculation. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Q: Which quantity is the wavenumber of a wave?

The wavenumber is defined as two pi divided by the wavelength and gives the number of radians of phase per unit distance. The number of oscillations per second is the frequency, and the distance travelled per oscillation is the wavelength itself. In meteorology a zonal wavenumber is often quoted instead as the number of complete waves around a latitude circle, which is a different convention worth noticing when reading the literature. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Q: Which meaning does zonal wavenumber three carry in meteorology?

Meteorologists count the number of complete waves fitting around the globe, so wavenumber three means three ridges and three troughs at that latitude. At 45 degrees north the corresponding wavelength is about 9400 kilometres. This planetary convention differs from the mathematical wavenumber and both appear in the literature, so checking which is meant is worthwhile. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

61.

A wave whose phase speed depends on its wavelength is described as _____.

A.dispersive
B.trapped, meaning that its amplitude decays away from a boundary or from the equator on either side
C.evanescent
D.non-dispersive, so that every component of a wave packet travels at exactly the same speed as the rest

Answer: A

Dispersion means the phase speed varies with wavenumber, so a packet spreads and the group velocity differs from the phase velocity. Rossby and gravity waves are dispersive while sound and equatorial Kelvin waves are not. Trapping and evanescence describe how the amplitude varies in space rather than how the speed varies with wavelength.

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62.

The level at which the mean flow speed equals the wave phase speed is called a _____ level.

A.non-divergent level, at which the horizontal divergence of the flow vanishes throughout the layer
B.critical
C.reflecting level, at which the wave is turned back rather than absorbed into the mean flow above it
D.steering

Answer: B

At a critical level the intrinsic frequency vanishes, the vertical wavelength shrinks and the wave is absorbed, depositing its momentum into the mean flow. Reflecting levels turn waves back by a different mechanism, the steering level is a synoptic concept for system movement, and the level of non-divergence concerns the vertical structure of the divergence field. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Discuss in Forum

63.

Arrange the following waves in order of increasing typical period.

1. Rossby

2. Acoustic

3. Inertial

4. Gravity

Select the correct sequence.

A.2, 3, 4, 1
B.4, 2, 1, 3
C.2, 4, 3, 1
D.1, 2, 3, 4

Answer: C

Acoustic waves have periods of seconds, gravity waves minutes to hours, inertial oscillations about a day, and Rossby waves days to weeks, giving the order 2, 4, 3, 1. The ladder spans some six orders of magnitude, and placing any newly encountered phenomenon on it from an estimate of its timescale is a quick way to identify which family it belongs to.

Discuss in Forum

64.

Match each wave with its restoring mechanism.

List I

A. Acoustic

B. Internal gravity

C. Rossby

List II

P. buoyancy

Q. compressibility

R. potential vorticity gradient

Select the correct match.

A.A-P, B-Q, C-R
B.A-R, B-P, C-Q
C.A-Q, B-R, C-P
D.A-Q, B-P, C-R

Answer: D

Acoustic waves are restored by compressibility, internal gravity waves by buoyancy, and Rossby waves by the meridional gradient of potential vorticity. Organising the wave family by restoring force rather than by name makes the dispersion relations far easier to reconstruct, since each follows directly from the physics of what returns a displaced parcel towards its original position. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Discuss in Forum

65.

Match each equatorial wave with its propagation direction.

List I

A. Kelvin

B. Equatorial Rossby

C. Mixed Rossby-gravity

List II

P. westward phase

Q. eastward only

R. westward phase with upward energy

Select the correct match.

A.A-Q, B-P, C-R
B.A-P, B-Q, C-R
C.A-R, B-P, C-Q
D.A-Q, B-R, C-P

Answer: A

The Kelvin wave travels eastward only, the equatorial Rossby wave westward, and the mixed Rossby-gravity wave has westward phase propagation while carrying energy upward. The opposing directions of the first two produce the east-west asymmetry of the Gill response to tropical heating, and the momentum carried by the first and third drives the quasi-biennial oscillation. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Discuss in Forum

66.

Which parameterisation must climate models include for the middle atmosphere?

A.Aerosol indirect effects, through which particles modify the reflectivity and lifetime of a cloud layer
B.Gravity wave drag
C.Convective momentum transport, which redistributes horizontal momentum vertically within a deep cloud
D.Cloud microphysics

Answer: B

Unresolved gravity waves generated by orography and convection deposit momentum in the stratosphere and mesosphere, and without a parameterisation of that drag models produce a polar vortex far too strong and a mesosphere far from observation. The other processes are important elsewhere in the model but do not control the middle atmosphere circulation in the same way. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

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67.

Which model error results from omitting gravity wave drag?

A.Excessive rainfall
B.A surface pressure field that drifts steadily away from observation over the course of the integration
C.A polar night jet that is much too strong
D.A tropical circulation that is far too weak because the momentum transport into the tropics is missing

Answer: C

The cold pole problem, in which the modelled winter polar vortex is too strong and too cold, was a longstanding defect traced directly to missing wave drag. Adding an orographic gravity wave drag scheme largely resolved it. The other errors listed arise from quite different deficiencies in convection, microphysics and numerical conservation.

Discuss in Forum

68.

Which quantity does a gravity wave drag scheme compute?

A.The number of individual wave crests present within each grid box at each time step of the integration
B.The wave amplitude at the surface
C.The total energy carried upward by the wave field through the whole depth of the atmospheric column
D.The vertical divergence of the wave momentum flux

Answer: D

The scheme launches a wave momentum flux at the source level and computes where it is deposited, the vertical divergence of that flux being the drag applied to the resolved flow. Saturation criteria determine the deposition level. Counting individual crests is neither possible nor meaningful at model resolution, and the surface amplitude is an input rather than the output of the calculation. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Discuss in Forum

69.

Which quantity is the wavenumber of a wave?

A.Two pi divided by the wavelength
B.The number of complete oscillations that pass a fixed point in one second as the wave travels past it
C.The wavelength itself
D.The distance the wave travels during one complete oscillation of the fluid at a fixed point in space

Answer: A

The wavenumber is defined as two pi divided by the wavelength and gives the number of radians of phase per unit distance. The number of oscillations per second is the frequency, and the distance travelled per oscillation is the wavelength itself. In meteorology a zonal wavenumber is often quoted instead as the number of complete waves around a latitude circle, which is a different convention worth noticing when reading the literature. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Discuss in Forum

70.

Which meaning does zonal wavenumber three carry in meteorology?

A.A wave whose phase advances by three degrees of longitude during each hour of its eastward progress
B.Three complete waves around a latitude circle
C.A wavelength of three thousand kilometres measured along the latitude circle at the level concerned
D.Three radians per metre

Answer: B

Meteorologists count the number of complete waves fitting around the globe, so wavenumber three means three ridges and three troughs at that latitude. At 45 degrees north the corresponding wavelength is about 9400 kilometres. This planetary convention differs from the mathematical wavenumber and both appear in the literature, so checking which is meant is worthwhile. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Discuss in Forum

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