Atmospheric Waves Questions and Answers

Answer: C

The stationary pattern forced by the Rockies, the Tibetan Plateau and the land-sea contrasts is dominated by the longest waves, principally wavenumbers one to three. Only these are long enough to satisfy the Charney-Drazin criterion and propagate into the stratosphere. Wavenumbers five to seven describe the travelling synoptic waves, and wavenumber zero is the zonal mean rather than a wave at all. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Answer: D

Substituting a wave solution into the linearised equations yields an algebraic relation between frequency and wavenumber that must hold for the solution to exist. That dispersion relation encodes the whole propagation behaviour of the wave type. Continuity, hydrostatic balance and the thermal wind relation are among the equations from which the dispersion relation is derived rather than substitutes for it. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Answer: A

Small perturbations are superposed on a specified basic state, products of perturbations are discarded, and a solution proportional to a complex exponential is substituted, giving an algebraic condition on frequency and wavenumber. This is the standard method throughout the subject. Numerical integration and observational averaging can confirm the result but do not derive it. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Answer: B

Linearisation requires the perturbation to be small enough that products of perturbation quantities may be neglected, which fails once a wave grows to large amplitude or begins to break. A moving basic state is perfectly acceptable and simply Doppler shifts the frequency. Stationarity and barotropy are special cases rather than requirements of the method.

Answer: C

Breaking occurs when the wave amplitude becomes large enough to overturn the isentropes, at which point the linear assumption fails completely and turbulence is generated. Linear theory can predict where breaking will begin but not what happens afterwards. Propagation, Doppler shifting and ducting are all well described by linear theory.

Answer: D

Saturation is reached when the wave induced vertical displacement is large enough to make the total potential temperature gradient vanish, and the ratio of actual to saturation amplitude measures how close that is. Parameterisation schemes limit the wave flux to keep the ratio at or below one. The Rossby and Froude numbers measure quite different competitions, though the Froude number does govern whether flow surmounts a barrier at all. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

Answer: A

When the kinetic energy of the approaching flow is insufficient to lift it over the barrier against the stratification, the air is deflected around the ends instead, which is the low Froude number regime. Barrier jets and gap winds result. At high Froude number the flow surmounts the ridge and generates the mountain wave field. Recognising the regime from the flow speed and stratification is a practical forecasting skill in mountainous terrain.

Answer: B

Blocked flow accelerating through a gap can produce winds far stronger than the ambient flow, and such gap winds are a recognised hazard in fjords, straits and mountain passes. The foehn descends the lee slope after crossing the crest, while sea breezes and katabatic winds are driven by thermal contrasts rather than by dynamical channelling.

Answer: C

When the horizontal scale of the terrain matches a trapped wave mode of the atmospheric profile, the lee wave response is resonantly amplified and can produce severe downslope windstorms. The Boulder windstorm of 1972 is the classic documented example. Buoyancy frequency matching describes a different situation and the other options have no dynamical basis.

Answer: D

Downslope windstorms with gusts exceeding 50 metres per second occur on the lee slopes of major ranges when the wave response is amplified and breaks, and they cause substantial damage in places such as Boulder and the Alpine valleys. Tornadoes, microbursts and squall lines are all convective phenomena with quite different dynamics.