Atmospheric Waves Questions and Answers

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.

Q: Which observation identifies upward propagating gravity wave energy?

Because the group velocity is perpendicular to the phase velocity and directed on the opposite side of the horizontal, a wave carrying energy upward shows phase lines descending with time. Radiosonde and radar time-height sections are read this way routinely. Amplitude does grow with height as the density falls, but that is a separate consequence of energy conservation rather than an indicator of direction. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Q: Which consequence follows from that amplitude growth?

Once the wave amplitude is large enough to overturn the isentropes, the wave breaks, generating turbulence and depositing its momentum flux into the mean flow. This drag is the principal driver of the mesospheric circulation and must be parameterised in climate models. Reflection occurs at certain levels for other reasons, and smooth dissipation is far too slow to matter at these altitudes. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Q: Which circulation is driven largely by breaking gravity waves?

Gravity wave drag in the mesosphere forces a meridional circulation from the summer to the winter pole, which drives the summer mesopause to the coldest temperatures found anywhere in the atmosphere. Without the wave drag the mesosphere would be far closer to radiative equilibrium. The Hadley, Walker and Ferrel cells are tropospheric features driven by quite different mechanisms. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Q: Which feature of the summer mesopause demonstrates this driving?

Despite continuous sunlight, the summer mesopause reaches about 130 kelvin, far colder than the winter mesopause, because the wave-driven circulation forces strong ascent and adiabatic cooling there. It is the coldest place in the Earth's atmosphere and is where noctilucent clouds form. This departure from radiative expectation is the clearest evidence of the wave driving. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Q: Which cloud type forms at the summer mesopause?

Noctilucent or polar mesospheric clouds form near 83 kilometres in the extremely cold summer mesopause and are visible from high latitudes after sunset. Polar stratospheric and nacreous clouds form much lower, around 20 kilometres in the winter stratosphere, and cirrus is a tropospheric cloud. Their existence is direct evidence of the extreme cold that wave driving produces. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

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.

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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.

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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.

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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

Which observation identifies upward propagating gravity wave energy?

A.Downward phase propagation in a time-height section
B.Upward phase propagation, since energy and phase must always travel in the same direction as one another
C.Stationary phase lines
D.A steady increase in the amplitude of the oscillation with time at a fixed height above the ground

Answer: A

Because the group velocity is perpendicular to the phase velocity and directed on the opposite side of the horizontal, a wave carrying energy upward shows phase lines descending with time. Radiosonde and radar time-height sections are read this way routinely. Amplitude does grow with height as the density falls, but that is a separate consequence of energy conservation rather than an indicator of direction. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

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Which effect causes gravity wave amplitude to grow with height?

A.The reduction of the horizontal wavelength as the wave propagates upward through the atmosphere above
B.The decrease of density with height
C.The increase of the buoyancy frequency with height as the atmosphere becomes more stably stratified
D.The decrease of temperature

Answer: B

Conservation of wave energy flux requires the amplitude to grow as the inverse square root of density, so a wave with a one metre per second velocity perturbation in the troposphere reaches tens of metres per second in the mesosphere. That growth eventually leads to breaking. The buoyancy frequency does increase into the stratosphere but the density effect is far larger and is the conventional explanation. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

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Which consequence follows from that amplitude growth?

A.The wave dissipates smoothly
B.The wave slows down until it becomes stationary relative to the ground at the level of maximum amplitude
C.The wave eventually breaks and deposits its momentum
D.The wave is reflected back downward once its amplitude exceeds a critical threshold at some level

Answer: C

Once the wave amplitude is large enough to overturn the isentropes, the wave breaks, generating turbulence and depositing its momentum flux into the mean flow. This drag is the principal driver of the mesospheric circulation and must be parameterised in climate models. Reflection occurs at certain levels for other reasons, and smooth dissipation is far too slow to matter at these altitudes. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Discuss in Forum

Which circulation is driven largely by breaking gravity waves?

A.The Hadley circulation, whose ascending branch lies beneath the intertropical convergence zone below
B.The Walker circulation
C.The Ferrel cell, which is the indirect meridional circulation found in the middle latitudes of each hemisphere
D.The mesospheric summer to winter pole circulation

Answer: D

Gravity wave drag in the mesosphere forces a meridional circulation from the summer to the winter pole, which drives the summer mesopause to the coldest temperatures found anywhere in the atmosphere. Without the wave drag the mesosphere would be far closer to radiative equilibrium. The Hadley, Walker and Ferrel cells are tropospheric features driven by quite different mechanisms. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Discuss in Forum

Which feature of the summer mesopause demonstrates this driving?

A.It is colder than the winter mesopause
B.It is warmer than the winter mesopause, as would be expected from the distribution of solar heating there
C.It has the same temperature
D.It shows no seasonal variation at all because the radiative timescale at that altitude is extremely long

Answer: A

Despite continuous sunlight, the summer mesopause reaches about 130 kelvin, far colder than the winter mesopause, because the wave-driven circulation forces strong ascent and adiabatic cooling there. It is the coldest place in the Earth's atmosphere and is where noctilucent clouds form. This departure from radiative expectation is the clearest evidence of the wave driving. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Discuss in Forum

10.

Which cloud type forms at the summer mesopause?

A.Nacreous cloud, whose iridescent appearance results from diffraction by uniformly sized ice particles
B.Noctilucent cloud
C.Polar stratospheric cloud, which forms in the winter stratosphere at temperatures below about 195 kelvin
D.Cirrus

Answer: B

Noctilucent or polar mesospheric clouds form near 83 kilometres in the extremely cold summer mesopause and are visible from high latitudes after sunset. Polar stratospheric and nacreous clouds form much lower, around 20 kilometres in the winter stratosphere, and cirrus is a tropospheric cloud. Their existence is direct evidence of the extreme cold that wave driving produces. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

Discuss in Forum

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