01. General
It is well-known that the airflow over mountainous terrain is often more disturbed than over level country, particularly when the winds are strong a great deal of turbulence and drafts is produced. If the air is unstable the mechanical turbulence will be carried upwards to great heights and will combine with the turbulence produced by the convective activity likely over the mountains and to the windward.
If a strong wind current of stable air, however, flows at right or nearly right angles to a mountain barrier, and certain other conditions are met, the airflow up to very high levels is organized in a standing wave pattern to the lee of the ridge. The waves are known as mountain waves, also referred to as “lee waves” and “standing waves”. They frequently occur to the lee of hills and mountains in all parts of the world. The waves are stationary with the air flowing right through them in a manner similar to water flowing through the standing wave pattern downstream from a submerged rock.
Strong mountain waves can be a hazard to aircraft because of the combined effect of the severe turbulence they sometimes generate, the vertical currents they set up, and the pressure altimeter errors involved. The really powerful waves generated by the larger mountain ranges, such as the Sierra Nevada and Rocky Mountains, at their worst cause as violent a form of turbulence as any thunderstorm. They should be avoided, particularly if terrain clearance is marginal. While strong mountain wave activity is relatively rare at turbojet cruising levels, it happens often enough to warrant attention. Modern jet transport have suffered structural damage and have had passengers injured, when their cabins were thrown into chaotic disarray by strong mountain waves.
02. Structure
A schematic diagram of the flow pattern and conditions associated with a typical mountain wave is shown in Fig. 1.
Unless the air mass is exceptionally dry, the deformation of the airstreams by hills or mountains is visibly revealed in a variety of orographic clouds whose form and characteristics tell a great deal about the nature of the airflow. Being linked to the terrestrial relief they remain stationary and are continually being formed at the windward side and dissolving at the downwind side.
Clouds peculiar to the mountain wave are the following:
Cap clouds
Cap clouds, hugging the top of the mountains may be several thousand feet thick. The upper surface often reflects the shape of the topography below. On the windward slopes prolonged precipitation may occur, whilst the cloud appears to flow over the leeward edge like a waterfall (fohn wall). Violent downdrafts, up to 5000 ft/min may exist in the cloud waterfall region down steep lee slopes. Some distance down wind from the ridge the air sweeps up again, forming:
Rotor or roll clouds
Rotor clouds often form in the waveflow of moderate and large mountains beneath the crests of large amplitude lee waves. The rolls have the appearance of a line of ragged cumulus or stratocumulus parallel to and downwind of the mountain range. The base is usually near the level of the crest whilst the top may be several thousand feet higher, sometimes to twice the height of the crest. In extreme cases the rotor clouds may build up to such a height that thunderstorms form and such “wave thunderstorms” are not uncommon in the Andes wave.
While often appearing very harmless and difficult to identify, because of the close resemblance to fair weather cumulus or stratocumulus, the rotor cloud zone is extremely turbulent with strong up and downdrafts (up to 5000 ft per minute). There is a constant boiling motion in and below this stationary cloud. Frequently there are a number of roll cloud lines each marking a wave crest. The most powerful rotor is the one beneath the first lee wave crest downstream of the mountain ridge.
Lenticular clouds
Lenticular clouds, or lens shaped clouds above the rotor are a distinctive feature of the mountain wave. They may occur at any altitude up to the tropopause. Several lenticulars are sometimes seen in a wave condition, stacked one above the other.
The lenticulars generally have characteristically smooth outlines indicative of the usually smooth laminar wave flow in this section; indeed flights through this part of the wave are often characterized by marked smoothness.
At times severe turbulence is encountered in the tropopause layer above the smooth lenticulars, especially so if a jet stream shear situation overlaps the mountain wave in the upper troposphere. This might be revealed by the turbulent structure of any lenticular cirrus clouds at these levels.
As has been noted above, flight in the tropospheric part of wave flow bounded by the turbulent rotor zone and tropopause layer, is often markedly smooth. This, however, is not always the case. The abrupt breakdown of smooth wave flow into chaotic turbulence throughout a considerable depth of the troposphere is a phenomenon which is known to occur occasionally, but the process is imperfectly understood and there is no basis as yet for forecasting such developments. When this condition occurs it may be spotted visually from the ragged appearance of the lenticulars, if any.
Mountain waves most commonly have a horizontal wave length in the range 3-15 miles with a majority around 5-8 miles. The wave length varies with the stability of the atmosphere and with the wind speed. A lesser stability and greater windspeed favour a longer wave length.
The amplitude of the waves, i.e. the vertical interval between the troughs and crests, depends in a complex way on both the topography as well as the properties of the airstream. The amplitude usually increases from the ground upwards to achieve some maximum in the middle troposphere and then slowly decreases with height. However, with strong winds over large mountains having steep lee slopes the maximum amplitude may be attained in the upper troposphere.
The vertical double amplitude may reach 7000 ft or more, whilst the maximum vertical currents measured are around 5000 ft/min (an estimate in the Sierra Nevada goes as high as 7000-8000 ft/min). Naturally such extremes only occur in the lee of the highest mountain ridges which lie across the temperate latitude westerlies, but intensities represented by about half those values are often attained in many parts of the world. The vertical currents in mountain waves have carried gliders to the stratosphere in several parts of the world, and to more than 15,000 ft over moderate hills.
03. Requirements for Formation
Meteorological conditions
Any range of high ground with crests of 500 ft or higher can produce lee waves. Necessary conditions are as follows:
Wind
The wind direction through a considerable depth of the troposphere must be at right or nearly right angles to the mountain range with speeds at crest level exceeding 15 kt in the case of small mountains and 30 kt for large mountains such as the Rockies. Speeds must increase upwards. This wind profile is frequently associated with a jet stream.
Stability
The air must be stably stratified, though not necessarily extending downwards to the surface, and more particularly there should be marked stability, preferably a sharp inversion, at levels slightly above crest level.
The requirement of stability is easily understood when it is realized that whenever a parcel of air is lifted in a stable environment and released, it will tend to fall back toward its original level but because of its momentum will overshoot like a pendulum, oscillating back and forth below and above its equilibrium position. Successive waves are present downstream, each being of smaller amplitude than the preceding one until the wave motion is damped out.
Since the above necessary conditions are most liable to occur during the colder part of the year, it follows that the mountain wave is mainly a wintertime phenomenon. Similarly, conditions are most favourable during the night. The diurnal effect, however, is almost irrelevant for large mountains where waves may form irrespective of the time of day and night.
Topographical effects
The width of the mountain range must match the wave length of the air stream for strong, i.e. large amplitude waves. This resonance effect is of great importance in wave development and the strongest waves in an air stream are not necessarily associated with the largest mountains. The larger the mountains the stronger the wind necessary for large amplitude waves. Thus for large mountains the maximum effect is usually obtained when there is a jet stream over the mountain range.
Successive terrain features may amplify or damp the lee waves, depending upon the spacing of the ridges with respect to the wave length of the airflow.
Terrain features believed to be ideal in producing moderate to strong wave activity are shown in Fig. 2. Relevant assumptions are the following:
- The mountain profile should show a drop of at least 3000 ft on the lee side.
- Waves will be stronger in the lee of a ridge, than of an isolated peak of similar cross-section, will extend higher and will carry a greater distance down wind.
- Waves will be stronger when the mountain barrier is concave toward the wind direction than in case of a convex crest line; this is related to the fact that some of the air is able to avoid flowing over the summit by passing around the sides of the ridge.
- Waves will be stronger when there is a second ridge or hill down wind and in phase to act as an accelerator to the ascending air in forming the return upswing or jump.
- Waves will be strongest in the lee of a pass lying between two prominent peaks; this is related to the accelerated flow of stable air through the pass.
- Strong waves will be made stronger by the resonance effect at times where three or more parallel ridges lie the same distance apart.
- Glaciated ridges are better wave producers than bare ones.
04. Turbulence
A general account of the distribution of wave turbulence is already included in para 02.
Flying conditions in the higher levels of a mountain wave are often remarkably smooth. Yet mountain waves also generate violent turbulence. The transition from smooth to turbulent flow can be quite abrupt. Although wave turbulence can occur at any height, most turbulent areas are the rotor zone and the tropopause layer.
Rotor zone
Rotor turbulence can be extremely severe in waves generated by the larger mountain ranges. Effective gust velocities of 40 ft per second have been computed from aircraft observations during the Sierra Wave Project (US), while stronger gusts have been estimated. Vertical accelerations of 2g to 4g were common in rotor zones in the Sierra Nevada mountains and French Alps.
A frequently applied thumb rule in avoiding the worst rotor turbulence is to plan through a suspected mountain wave condition at an altitude at least 50% higher than the height of the mountain range with respect to the surrounding terrain. This procedure will also permit safe clearance of the mountain range despite strong downdrafts and altimeter errors.
Tropopause layer
The tropopause layer is frequently turbulent in mountain wave conditions, especially if there is a jet stream over the area. Tropopause turbulence may be as severe as in the rotor, and in rare cases has been classed as extreme. An effective gust velocity of 37 ft per second was measured by the Mountain Wave Project near Bishop, California, at 38,000 ft in strong wave conditions.
Much study on mountain wave occurrence at jet cruising levels has previously taken place in the US. Certain emphasis is being placed on the role played by the tropopause in generating or intensifying latent turbulent situations. Statistics show a maximum of CAT (Clear Air Turbulence) in the vertical which is found close to the mean height of the tropopause. Fig. 3 shows the distribution of CAT pilot reports made over Central Colorado during 13 full-winter-spring months over a couple of years; the peak at 37,000 ft is not considered to be due to any bias in actual flight frequencies; the ratio of over-flights to descending and climbing flights was three to two.
A number of US airlines recommend to avoid the tropopause zone whenever mountain waves are expected and to exercise extra flightplanning caution in case of down wind flights. This is because in a stationary wave flow it is the aircraft’s ground speed that determines the severity of the turbulence – not, as is normally the case in turbulence penetration, the airspeed. Since the tropopause varies about ± 4000 ft in height in mountain wave conditions, the recommended procedure is to operate, in suspected strong wave conditions, some 4000 or 5000 ft above or below the average tropopause altitude. Special care must be exercised in flightplanning at very high levels under wave conditions. At these levels the safety margins are reduced, since the problem of Mach buffet and low speed buffet may cause control difficulties if the aircraft in fact encounters turbulence.
Outside the rotor zone and tropopause layer smooth airflow normally exists, but with strong up and downdrafts. On occasions these flight levels may be turbulent. A visual clue is the presence of lenticulars with ragged edges.
Though the normal mountain wave is marked by characteristic cloud forms, one should be aware of the possible existence of wave conditions without these visual clues whenever strong winds blow over mountainous terrain.
05. Altimeter Errors
Pressure altimeter errors are induced by disturbed airflow over mountainous terrain. The effects are the lowering of the pressure over and to the lee of high ground in strong winds and the local lowering of pressure in turbulent eddies. Thus the altimeter will read erroneously on the unsafe side. The total error, caused by the disturbed airflow effects, however, is believed not to exceed 1000 ft. Yet, figures as high as 2500 ft have been claimed by pilots approaching the mountains from leeside, but these figures could be explained when one considers an up wind flight in the strong downdraft area on the leeside of the mountains while the altimeter was read shortly before. In such conditions, when the aircraft approaches the mountains at minimum clearance altitude, it will be hard to climb through the strong downdrafts along the mountain slope and it is very likely that the plane is simply pushed steadily toward the mountain peak that are hidden most of the time by the cap cloud. Therefore a much higher than normal flight altitude should be flown to cross the mountain range at minimum altitudes from down wind side whenever wave conditions are indicated.
Additionally, large principal errors are likely in mountain wave conditions, due to the air being colder than standard and a pressure altimeter setting that could be too high for the region. For the latter errors, to which pressure altimeters are always subject, allowance should invariably be made when planning safety heights.
06. Aircraft Icing
In general, icing is more likely and tends to be more intense over mountainous terrain than is usual under identical conditions over low flat terrain. This is because the orographically induced updrafts permit the air to support larger cloud droplets and greater liquid water contents.
At the higher levels icing in a typical mountain wave is not a problem. Under certain conditions, however, icing may exist down to very low temperatures.
07. Peel-off Turbulence
A very special case of mountain wave exists around the isolated top of the Fuji Yama in Japan. The Japanese National Meteorological Institute has conducted thorough research on this mysterious form of air turbulence.
The research work indicates that rotor turbulence can produce vertical velocities of up to 100 ft/sec, which can cause structural damage to, or may even break up, an aircraft. Obviously this theory can also be applied to any isolated peak of the same order of magnitude.
The research resulted in the conclusion that this clear air turbulence can be caused by a peculiar air flow, called “peel-off”. This “peel-off” turbulence is more severe than air turbulence within cumulo nimbus clouds.
Previously, it was simply conceived that the air turbulence around Mount Fuji was the mountain wave. But much remained to be solved according to the mountain wave theory, because Mount Fuji is a solitary peak, and not a mountain range.
Wind tunnel tests proved that this strange phenomenon – “peel-off” turbulence – could arise around isolated mountain peaks.
In winter, strong westerly winds blow against the slope of Mount Fuji and pass over the mountain after hitting the top.
At this moment, a strong air flow develops on the leeside of the mountain and blows up along the slope near the summit (peel-off phenomenon).
This strong air-current blowing upwards causes numerous vortices to develop east of the mountain top.
This CAT is peculiar to the 3776 m high peak and arises in an area 1 km wide and 15-20 km long, east of the mountain summit, when westerly winds of more than 50 kt blow. This turbulence is severest ever observed by meteorologists.
On clear winter days, therefore, aircraft flying close to Mount Fuji should steer clear of an area stretching at an angle of 60 degrees from the top (30 degrees on both sides of the line extending east from the top and along the wind line), and should keep at least 20 km away from the summit. They are also advised to fly at an altitude of at least 15,000 ft near the mountain.