Adiabatic Processes and Lapse Rates Questions and Answers

Answer: D

Large eddy simulation resolves eddies larger than the grid and parameterises only the smaller ones, which is feasible for the boundary layer where the energy containing eddies are hundreds of metres across. Direct numerical simulation resolves everything but is limited to laboratory Reynolds numbers. Reynolds averaging parameterises the whole spectrum. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Answer: A

The Obukhov length compares the turbulence generated mechanically by shear with that generated thermally by buoyancy, and its sign indicates whether the surface layer is stable or unstable. Above that height buoyancy dominates. It is the fundamental scaling parameter of Monin-Obukhov similarity theory, which underlies every surface layer parameterisation. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Answer: B

The Obukhov length is negative when the surface heat flux is upward, which is the unstable daytime case, and positive at night when the flux is downward. Neutral conditions correspond to an infinite length. The sign convention is arbitrary but universal, and remembering that daytime is negative saves confusion when reading the literature.

Answer: C

Monin and Obukhov showed that the dimensionless wind and temperature gradients in the surface layer are universal functions of height divided by the Obukhov length. The theory reduces the whole surface layer problem to a pair of empirically determined functions. Mixing length ideas are one ingredient and Kolmogorov theory concerns the inertial subrange of the turbulence spectrum. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Answer: D

In neutral conditions the wind increases as the logarithm of height divided by the roughness length, which follows from the constant stress assumption and dimensional analysis. Stability modifies the profile through the Monin-Obukhov functions. The logarithmic law is one of the most robust results in boundary layer meteorology and underpins the estimation of surface stress. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Answer: A

The roughness length is the height at which the extrapolated logarithmic profile reaches zero wind, ranging from a fraction of a millimetre over calm water to a metre over forest. The displacement height is a companion parameter needed over tall canopies, which makes it a reasonable alternative. Albedo and Bowen ratio describe radiative and energetic rather than aerodynamic properties. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Answer: B

Calm water is aerodynamically very smooth, but the roughness length increases with wind speed as waves develop, which is the Charnock relation. This dependence on the wind itself makes the ocean surface unusual, since over land the roughness is fixed by the terrain and vegetation. It matters greatly for the drag coefficient in strong winds.

Answer: C

The bulk aerodynamic formula writes the stress as the density times a drag coefficient times the square of the wind speed at a reference height, usually ten metres. The drag coefficient depends on roughness and on stability, and over the ocean it depends on the wind speed itself because the waves grow with it. Squaring the wind means that a doubling of the speed quadruples the stress, which is why storm surges and wave heights respond so sharply to increases in wind.

Answer: D

Measurements in hurricanes show the drag coefficient saturating and even declining above about 33 metres per second, probably because sea spray and foam smooth the effective surface. This was an unexpected finding with important consequences for hurricane intensity prediction. Without it, models would predict weaker storms than are observed.

Answer: A

Reduced drag at extreme wind speeds means less frictional dissipation, so the ratio of enthalpy input to momentum loss rises and the maximum potential intensity increases. Emanuel's theory of maximum potential intensity depends explicitly on this ratio. The discovery reconciled theoretical intensity limits with the strongest storms actually observed.