Atmospheric Waves Questions and Answers

Q: Analysis of an atmospheric variable shows prominent modes at 5, 40 and 1460 days. These modes correspond respectively to

The modes are synoptic, MJO and ENSO.A period of about 5 days is typical of synoptic weather systems, the passage of mid-latitude cyclones and anticyclones. About 40 days falls in the 30 to 60 day band of the Madden-Julian Oscillation. 1460 days is 4 years, within the 2 to 7 year period of El Nino-Southern Oscillation.Tides have periods of about half a day and a day, not 5 days. Milankovitch cycles last tens of thousands of years, and decadal variability means about 10 years or more, far longer than 4 years.

Q: P and Q respectively describe flow fields corresponding to

P and Q are equatorial Rossby and equatorial Kelvin waves.Both patterns are organised about the equator, so they are equatorially trapped waves, not mid-latitude or polar ones. In P the pressure cells lie off the equator with opposite signs to north and south, with flow circling each cell and crossing the equator: the Rossby-type equatorial wave with cross-equatorial flow (the mixed Rossby-gravity, or Yanai, wave). In Q the highs and lows are centred on the equator and the wind is purely east-west, in geostrophic balance with the north-south pressure gradient: the equatorial Kelvin wave, which has no meridional velocity.Option D reverses the two, and options A and C name mid-latitude and polar waves, which these equator-centred patterns are not.

Q: Which of the following is not Dispersive wave ?

The non-dispersive wave is the shallow water gravity wave.A wave is dispersive when its speed depends on its wavelength. In shallow water the speed of a gravity wave is\[ c = \sqrt{g h} \]which depends only on depth, so all wavelengths travel together; tsunamis are the classic example.Deep-water gravity waves travel at \(c = \sqrt{g\lambda/2\pi}\), so long waves outrun short ones. Rossby waves (printed Russby) and inertia (inertia-gravity) waves also have speeds that depend on wavelength, so they are dispersive.

Q: The effects of gravity acting on perturbations to a density gradient in vertical are referred as :

They are Gravity waves, also called buoyancy waves.In a stably stratified fluid, a parcel displaced vertically is pushed back by buoyancy and overshoots, so it oscillates. These oscillations, where gravity acts on disturbances to the vertical density gradient, propagate as internal gravity waves in the atmosphere and ocean; lee waves over mountains are an example.Rossby waves arise from the variation of the Coriolis effect with latitude, Kelvin waves are trapped against a coast or the equator by rotation, and inertia waves are oscillations driven by the Earth's rotation alone.

Q: The Madden-Julian Oscillations (MJO) has a zonal wavenumber 1 with maximum amplitude in the deep tropics, and it moves eastward around the equator with a period of :

The MJO has a period of 30-60 days.The Madden-Julian Oscillation, discovered by Roland Madden and Paul Julian in 1971, is the dominant intraseasonal variation in the tropics: an eastward-moving envelope of enhanced and suppressed convection that travels around the globe in about 30 to 60 days (often quoted as 30-90 days). It affects the active and break phases of the Indian monsoon and tropical cyclone formation.10-20 days is the period of the quasi-biweekly mode of the monsoon, a different oscillation. 70-80 and 80-90 days lie beyond the MJO's usual range.

Q: Which restoring force acts on an acoustic wave?

Sound waves are restored by the pressure changes that accompany compression and rarefaction of the air, and they travel at about 340 metres per second near the surface. Buoyancy restores gravity waves, the Coriolis force restores inertial oscillations, and the planetary vorticity gradient restores Rossby waves. Classifying each wave by its restoring mechanism is the most reliable way to keep the whole family straight, since the mathematics of each follows directly from the physics of what pushes the parcel back.

Q: Which restoring force acts on an internal gravity wave?

A parcel displaced upward in a stably stratified atmosphere becomes denser than its surroundings and sinks back, overshooting and oscillating at the buoyancy frequency. That oscillation propagating through the fluid is an internal gravity wave. Compressibility gives sound waves, the latitudinal variation of the Coriolis parameter gives Rossby waves, and friction damps waves rather than restoring them. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Q: Which frequency bounds an internal gravity wave from above?

The dispersion relation gives the frequency as the buoyancy frequency times the cosine of the angle the wavenumber vector makes with the vertical, so no internal gravity wave can exceed the buoyancy frequency. In the troposphere that corresponds to a period of about ten minutes. The Coriolis parameter bounds the frequency from below once rotation is included, giving the inertia-gravity wave band. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Q: Which direction does the energy of an internal gravity wave travel?

For internal gravity waves the group velocity is perpendicular to the wavenumber vector, so energy propagates at right angles to the direction in which the crests move. Downward phase propagation therefore corresponds to upward energy propagation, which is how waves generated in the troposphere are identified in stratospheric observations. This counterintuitive property is one of the most distinctive features of the wave type. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Analysis of an atmospheric variable shows prominent modes at 5, 40 and 1460 days. These modes correspond respectively to

A.Tidal, MJO and ENSO
B.Synoptic, MJO and ENSO
C.Synoptic, MJO and Decadal
D.Tidal, Milankhovich and ENSO

Exam Year(s)

GATE XE - 2018,

Answer: B

The modes are synoptic, MJO and ENSO.

A period of about 5 days is typical of synoptic weather systems, the passage of mid-latitude cyclones and anticyclones. About 40 days falls in the 30 to 60 day band of the Madden-Julian Oscillation. 1460 days is 4 years, within the 2 to 7 year period of El Nino-Southern Oscillation.

Tides have periods of about half a day and a day, not 5 days. Milankovitch cycles last tens of thousands of years, and decadal variability means about 10 years or more, far longer than 4 years.

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Two flow patterns: P with closed high (H) and low (L) pressure cells centred off the equator, opposite in sign across it, with circulation round each cell and north-south flow crossing the equator between cells; Q with an L and an H centred on the equator with east-west winds only

P and Q respectively describe flow fields corresponding to

A.Mid latitude Rossby and Polar gravity waves
B.Equatorial Rossby and Equatorial Kelvin waves
C.Midlatitude gravity and Polar Rossby waves
D.Equatorial Kelvin and Equatorial Rossby waves

Exam Year(s)

GATE XE - 2018,

Answer: B

P and Q are equatorial Rossby and equatorial Kelvin waves.

Both patterns are organised about the equator, so they are equatorially trapped waves, not mid-latitude or polar ones. In P the pressure cells lie off the equator with opposite signs to north and south, with flow circling each cell and crossing the equator: the Rossby-type equatorial wave with cross-equatorial flow (the mixed Rossby-gravity, or Yanai, wave). In Q the highs and lows are centred on the equator and the wind is purely east-west, in geostrophic balance with the north-south pressure gradient: the equatorial Kelvin wave, which has no meridional velocity.

Option D reverses the two, and options A and C name mid-latitude and polar waves, which these equator-centred patterns are not.

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Rossby waves depend fundamentally upon the variation of the Coriolis parameter with latitude, known as :

A.Alfa effect
B.Gamma effect
C.Beta effect
D.Lambda effect

Exam Year(s)

MH SET - 2019, SET Exam - 2019,

Answer: C

The variation of the Coriolis parameter with latitude is the beta effect.

The Coriolis parameter is \(f = 2\Omega\sin\phi\), and its northward gradient is \(\beta = df/dy\). As an air or water parcel moves north or south, conservation of absolute vorticity makes its relative vorticity change, and this restoring tendency is what produces westward-propagating Rossby waves. The beta-plane approximation is named after it.

'Alfa', 'gamma' and 'lambda' effects are not the name given to this gradient.

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Which of the following is not Dispersive wave ?

A.Russby wave
B.Deep water gravity wave
C.Shallow water gravity wave
D.Inertia wave

Exam Year(s)

MH SET - 2021, SET Exam - 2021,

Answer: C

The non-dispersive wave is the shallow water gravity wave.

A wave is dispersive when its speed depends on its wavelength. In shallow water the speed of a gravity wave is

\[ c = \sqrt{g h} \]

which depends only on depth, so all wavelengths travel together; tsunamis are the classic example.

Deep-water gravity waves travel at \(c = \sqrt{g\lambda/2\pi}\), so long waves outrun short ones. Rossby waves (printed Russby) and inertia (inertia-gravity) waves also have speeds that depend on wavelength, so they are dispersive.

Discuss in Forum

The effects of gravity acting on perturbations to a density gradient in vertical are referred as :

A.Rossby waves
B.Kelvin waves
C.Gravity waves
D.Inertia waves

Exam Year(s)

MH SET - 2024, SET Exam - 2024,

Answer: C

They are Gravity waves, also called buoyancy waves.

In a stably stratified fluid, a parcel displaced vertically is pushed back by buoyancy and overshoots, so it oscillates. These oscillations, where gravity acts on disturbances to the vertical density gradient, propagate as internal gravity waves in the atmosphere and ocean; lee waves over mountains are an example.

Rossby waves arise from the variation of the Coriolis effect with latitude, Kelvin waves are trapped against a coast or the equator by rotation, and inertia waves are oscillations driven by the Earth's rotation alone.

Discuss in Forum

The Madden-Julian Oscillations (MJO) has a zonal wavenumber 1 with maximum amplitude in the deep tropics, and it moves eastward around the equator with a period of :

A.10-20 days
B.70-80 days
C.30-60 days
D.80-90 days

Exam Year(s)

MH SET - 2025, SET Exam - 2025,

Answer: C

The MJO has a period of 30-60 days.

The Madden-Julian Oscillation, discovered by Roland Madden and Paul Julian in 1971, is the dominant intraseasonal variation in the tropics: an eastward-moving envelope of enhanced and suppressed convection that travels around the globe in about 30 to 60 days (often quoted as 30-90 days). It affects the active and break phases of the Indian monsoon and tropical cyclone formation.

10-20 days is the period of the quasi-biweekly mode of the monsoon, a different oscillation. 70-80 and 80-90 days lie beyond the MJO's usual range.

Discuss in Forum

Which restoring force acts on an acoustic wave?

A.Compressibility of the air
B.Buoyancy, which returns a displaced parcel towards its original level within a stratified atmosphere
C.The Coriolis force
D.The meridional gradient of planetary vorticity, which turns a displaced parcel back towards its latitude

Answer: A

Sound waves are restored by the pressure changes that accompany compression and rarefaction of the air, and they travel at about 340 metres per second near the surface. Buoyancy restores gravity waves, the Coriolis force restores inertial oscillations, and the planetary vorticity gradient restores Rossby waves. Classifying each wave by its restoring mechanism is the most reliable way to keep the whole family straight, since the mathematics of each follows directly from the physics of what pushes the parcel back.

Discuss in Forum

Which restoring force acts on an internal gravity wave?

A.The variation of the Coriolis parameter with latitude across the region in which the wave is travelling
B.Buoyancy in a stably stratified fluid
C.Compressibility, which is what allows the wave to propagate through the air at the speed of sound
D.Friction

Answer: B

A parcel displaced upward in a stably stratified atmosphere becomes denser than its surroundings and sinks back, overshooting and oscillating at the buoyancy frequency. That oscillation propagating through the fluid is an internal gravity wave. Compressibility gives sound waves, the latitudinal variation of the Coriolis parameter gives Rossby waves, and friction damps waves rather than restoring them. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Discuss in Forum

Which frequency bounds an internal gravity wave from above?

A.The acoustic cut-off frequency
B.The inertial frequency multiplied by the ratio of the vertical to the horizontal wavenumber involved
C.The Brunt-Vaisala frequency
D.The Coriolis parameter, which sets the lowest frequency at which the wave is able to propagate freely

Answer: C

The dispersion relation gives the frequency as the buoyancy frequency times the cosine of the angle the wavenumber vector makes with the vertical, so no internal gravity wave can exceed the buoyancy frequency. In the troposphere that corresponds to a period of about ten minutes. The Coriolis parameter bounds the frequency from below once rotation is included, giving the inertia-gravity wave band. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Discuss in Forum

10.

Which direction does the energy of an internal gravity wave travel?

A.Parallel to the phase propagation, in the same direction and at the same speed as the crests move
B.Vertically only
C.In the direction of the mean flow, being carried passively by the wind through which the wave passes
D.Perpendicular to the phase propagation

Answer: D

For internal gravity waves the group velocity is perpendicular to the wavenumber vector, so energy propagates at right angles to the direction in which the crests move. Downward phase propagation therefore corresponds to upward energy propagation, which is how waves generated in the troposphere are identified in stratospheric observations. This counterintuitive property is one of the most distinctive features of the wave type. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Discuss in Forum

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