The non-linear interaction of a gravity wave with the vortical modes

The wave-wave interaction theory has been used successfully in describing one class of weakly non-linear wave phenomena. The application of this theory to the atmosphere shows the possibilities of energy and momentum transfer among three interacting gravity waves, as well as from the gravity wave to the other modes of motion. It has been found that the non-resonant interaction of a gravity wave with two vortical modes can proceed at a reasonably rapid rate. With the gravity wave viewed as the primary wave and the two vortical modes as the secondary waves, the interaction equation can be linearized and solved. The resulting analytic formula gives the growth rate of the interaction. In the absence of the Earth's rotation, the growth is limited to a threshold effect. The theory shows that whenever the horizontal air parcel velocity of a gravity wave exceeds a factor of √2 times the horizontal trace velocity of the wave, energy and momentum transfer from the gravity wave to the vortical modes can proceed. The rotation of the Earth will blur this threshold effect by making the interaction more likely to occur. Thus, through this mechanism, a gravity wave can transfer its energy and momentum to the horizontal velocity field in the vortical mode. In this sense, the small scale vortical motions would serve as the sink of both energy and momentum of a propagating gravity wave. When scales of vortical modes reach sufficiently small values, dissipation through viscosity becomes important. At this scale and smaller, the vortical modes are damped out quickly and its energy spectrum must exhibit a sharp decay.     

Comprehensive meteorological modelling of the middle atmosphere: a tutorial review

This paper reviews the current state of comprehensive, three-dimensional, time-dependent modelling of the circulation in the middle and upper atmosphere from a meteorologist's perspective. The paper begins with a consideration of the various components of a comprehensive model (or general circulation model, GCM), including treatments of processes that can be explicitly resolved and those that occur on scales too small to resolve (and that must be parameterized). The typical performance of GCMs in simulating the tropospheric climate is discussed. Then some important background on current ideas concerning the general circulation of the stratosphere and mesosphere is presented. In particular, the transformed-Eulerian mean flow formalism, the role of vertically-propagating internal gravity waves in driving the large-scale circulation, and the notion of a stratospheric surf zone are all briefly reviewed. Using this background as a guide, some middle atmospheric GCM results are discussed, with a focus on simulations made recently with the GFDL ‘SKYHI’ troposphere-stratosphere-mesosphere GCM. The presentation attempts to emphasize the interaction between theory and comprehensive modelling. Many theoretical notions cannot be confirmed in detail from observations of the real atmosphere due to the various limitations in the observational methods, but can be very completely examined in GCMs in which every atmospheric variable is known perfectly (within the limits of the numerical methods). It will be shown that our understanding of both the role of gravity waves in the general circulation and the nature of the stratospheric surf zone has benefited from analysis of GCM results.From the point of view of the upper atmosphere, one of the most interesting aspects of GCMs is their ability to generate a self-consistent field of upward-propagating gravity waves. This paper concludes with a discussion of the gravity wave field in the middle atmosphere of GCMs. Comparisons of the explicitly-resolved gravity wave field in the SKYHI model with observations are quite encouraging, and it seems that the model is capable of producing a gravity wave field with many realistic features. However, the simulated horizontal spectrum of the eddy momentum fluxes associated with the waves is quite shallow, suggesting that much of the spectrum that is important for maintaining the mean circulation is not explicitly resolvable in current GCMs. A brief discussion of current efforts at parameterizing the mean flow effects of the unresolvable gravity waves is presented.     

Contributions of gravity waves to the momentum,heat and turbulent energy budget of the upper mesosphere and lower thermosphere

The role of gravity waves for the momentum and heat budget of the atmosphere between approximately 70 and 110 km height is considered. Parameterization schemes for vertical gravity wave diffusivity, generalized Rayleigh friction, viscous force, heat conduction and kinetic energy dissipation are reviewed. Eddy diffusion parameterization and its relation to the gravity wave approach is also discussed and it is shown that principal similarities exist in both concepts, especially when irregular (stochastic) contributions to the perturbations are modeled. Special attention is paid to the dissipation of perturbation kinetic energy and its contribution to the heat budget of the mesopause region. It is concluded that the amount of energy which can be attributed to the part of the gravity wave spectrum contributing to generalized Rayleigh friction above the mesopause is of the order of 10% of the total perturbation energy.     

A simple model of gravity-wave momentum and energy fluxes transferred through the middle atmosphere to the upper atmosphere

Vertical fluxes of momentum and energy through the middle atmosphere are calculated by using a simple semi-empirical model of quasi-monochromatic internal gravity waves with dominant vertical wavenumbers. In this model those dominant gravity waves are assumed to saturate and break at each observational altitude by an effective critical-layer mechanism. The dominant value of the vertical wave-number is expressed by an exponential function of altitude, decreasing upward with a scale height of 34 km. This expression gives the momentum and energy flux densities decreasing upward with scale heights of 12 and 18 km, respectively, and typical values at 100 km altitude are estimated as 4 × 10⁻⁵ Pa and 4 × 10⁻³ W/m². A heat flux induced by wavebreaking turbulence also has an order of magnitude similar to that of the wave energy flux. Variabilities around these values and comparisons with other momentum and heat inputs to the upper atmosphere are only briefly discussed.     

Variations of the gravity wave characteristics with height,season and latitude revealed by comparative observations

This paper reviews some recent observations of gravity wave characteristics in the middle atmosphere, revealed by co-ordinated observations with the MU radar in Shigaraki (35°N, 136°E) and nearby rocketsonde experiments at Uchinoura (31°N, 131°E). We further summarize the results of comparative studies on the latitudinal variations of the gravity wave activity, which were detected by additionally employing data obtained with MF radars at Adelaide (35°S, 139°E) and Saskatoon (52, 107W) and lidar observations at Haute Provence (44, 6E).The seasonal variation of gravity wave activity detected with the MU radar in the lower stratosphere showed a clear annual variation with a maximum in winter, and coincided with that for the jet-stream intensity, indicating a close relation between the excitation of gravity waves and jet-stream activity at middle latitudes. The long-period (2–21 h) gravity waves seemed to be excited near the ground, presumably due to the interaction of flow with topography, and the short-period (5 min 2 h) components had the largest kinetic energy around the peak of jet-stream.We found an increase with height in the vertical scales of dominant gravity waves, which can be explained in terms of a saturation of upward propagating gravity waves. The values of the horizontal wind velocity variance generally increased in the stratosphere and lower mesosphere, but they became fairly constant above about 65 km due to the wave saturation, resulting in the active production of turbulent layers.Although the gravity wave energy showed an annual variation in the lower atmosphere, it exhibited a semiannual variation in the mesosphere, with a large peak in summer and a minor enhancement in winter. Lidar observations reasonably interpolated the seasonal variations in the intermediate height regions.The gravity wave energy in the mesosphere, with periods less than about 2 h, was consistently larger in summer than in winter at all the stations, i.e. at 35N, 44N,52 N and 35 S. However, the values were generally larger at 35 N than at 52 N. which was found from a comparison of l-yr observations at Shigaraki and Saskatoon. Furthermore, a comparison between Shigaraki and Adelaide, located at the conjugate points relative to the equator, revealed that the gravity-wave energy in the mesosphere was found to be fairly similar, when we compared the values in summer/winter in each hemisphere.     

Gravity wave saturation and eddy diffusion in the middle atmosphere

A discussion is given of gravity wave saturation and its relation to eddy diffusion in the middle atmosphere. Attention is focused on the saturation process and some of its observable manifestations. It does not serve as a review of all related work. Although a theoretical point of view is taken, the emphasis is on which wave parameters need be measured to predict quantitatively the influence of gravity waves on eddy transport. The following considerations are stressed: the variation of spectra with observation time T; that eddy diffusivities are determined by velocity spectra; the anisotropic nature of diffusivity; a unified approach to saturation; an attempt to make eddy diffusivity more precise; the relationship between eddy diffusivity and wave dissipation.The subjects of ‘wave drag’ (momentum flux deposition) and heat flux need only be treated briefly, because they are related to eddy diffusivity in simple ways. Consideration is also given to two different theoretical mechanisms of wave saturation—wave induced convective instability and strong nonlinear wave interactions. The saturation theory is then used to predict a globally averaged height profile of vertical diffusivity in the middle atmosphere. This calculation shows that gravity waves are a major contributor to eddy diffusion from heights of 40–110 km, and that they are significant down to 20 km. A more detailed calculation of wave induced eddy diffusion, including latitudinal and seasonal variations, can be made if wave velocity spectra become available. The paper closes with recommendations for future research.     

Gravity waves from O2 nightglow during the AIDA '89 campaign III: effects of gravity wave saturation

The O₂ atmospheric (0–1) night airglow emitted within the gravity wave saturation region at ∼90–100 km can serve as a means of studying the wave activity. In this analysis, the atmospheric motions were described by a mean spectral model and an algorithm was developed to infer the wave kinetic energy density and momentum flux from variations in O₂ (0–1) airglow emission rate and rotational temperature. The method was applied to eight nights of data collected by MORTI, a mesopause oxygen rotational temperature imager, during the AIDA campaign of 1989 in Puerto Rico (18°N, 67°W). The observed r.m.s. fractional fluctuations of airglow emission rate and rotational temperature were of the order of ∼0.07–0.15 and ∼0.02–0.04, respectively, and the characteristic vertical wavelengths were estimated at ∼10 2 -20 km. The inferred r.m.s. horizontal velocities and velocity variances were found to be ∼12–25 m/s and ∼150–600 m²/s², with the majority of the horizontal velocity and its variance associated with low-frequency, large-scale wave motions. The estimated momentum fluxes, mainly contributed by high-frequency, small-scale waves, were ∼2–10 m²/s². These results are in good agreement with those obtained from other measurements using different observational methods at low and mid-latitudes.     

On the structure and circulation of the polar thermosphere under magnetically quiet conditions

A theoretical study is presented bearing on the thermospheric circulation and composition at polar latitudes. The observed motions and density perturbations in N₂, O and He have signatures which may be understood in terms of two different source mechanisms. We consider electric field momentum coupling and Joule heating as well as interactions between both processes. A spectral model in terms of vector spherical harmonics (with magnetic coordinates) is used, delineating the diurnal and mean (time independent) components. The important non-linearities are evaluated in configuration space. The electric field model of Volland and the global average density and temperature variations of Hedin (MSIS) are adopted as input. Our analysis leads to the following conclusions. (1) The vortex type double cell polar circulation (zonal wave number m = 1) is primarily driven by collisional momentum transfer from electric field induced ion convection. (2) Because of the thermospheric low pass filter, a large time independent component (zonal wave number m = 0) is produced by Joule heating; the heavier species (N₂) being concentrated where the lighter ones (O, He) are depleted, and vice versa due to wind induced diffusion (3) The electric field driven vortex circulation redistributes the mass and energy in the time independent density and temperature variations (from Joule heating), producing primarily diurnal variations (m = 1) in the temperature and composition near the pole and at auroral latitudes, again the heavier and lighter species varying out of phase. The above results are in substantial agreement with observations. It is worth noting that momentum rectification associated with the diurnally varying electric field and conductivity induces a weak zonally symmetric (single cell) prograde polar vortex. However, this motion is partially compensated by a retrograde vortex from geostrophic balance due to Joule heating, which dominates near the pole. These motions are small compared with the diurnally varying component in the polar circulation.     

Vertical propagation characteristics of internal gravity waves around the mesopause observed by the Arecibo UHF radar

A high resolution wind observation of the mesosphere and lower thermosphere (73–95 km) was conducted with the aid of the high power UHF Doppler radar at Arecibo (18.4°N, 66.8°W). Zonal wind velocities were continuously observed during day-time hours on 1–15 August 1980. We discuss here the observed wind fluctuations with periods of 1–4 h in the light of internal gravity waves. The phase propagation associated with these fluctuations is, on average, shown to be downward, indicating an upward energy flux. A space-time spectral analysis shows that waves with vertical wavelengths shorter than 10 km disappear around the mesopause (about 85km), while those with longer vertical wavelengths exist throughout the observational height. This result is explained in terms of wave absorption at a critical layer where the mean zonal wind has a westerly shear with height. This feature is consistent with the behavior expected for internal gravity waves around the summer mesopause in order to explain general circulation models.     

Generation of sporadic sodium layers via turbulent heating of the atmosphere?

When a gravity wave breaks down, its energy is dumped in a narrow altitude range initiating an increase in temperature, which may consequently generate sporadic sodium layers (SSL) through temperature sensitive chemistries. In order to estimate the temperature change resulted from gravity wave breakdown, the energy dissipation through viscous process is discussed. We show that SSLs can be successfully siimulated by solving the continuity equation with a temperature dependent production function. The generation of the largest SSL observed at Arecibo is shown to be associated with gravity waves exhibiting very short vertical wavelength. Simultaneous sodium and temperature measurements suggest that the heating mechanism proposed here as a possible explanation to the occurrence of SSLs, if viable, is more applicable to low and middle latitudes than high latitudes.     

Interference of tidal and gravity waves in the ionosphere and an associated sporadic E-layer

Observations made on 10 July 1987 with the EISCAT UHF radar are presented. The F-region measurements of both electron density and field-aligned ion velocity show that an upward propagating gravity wave with a period of about 1 h is present. The origin of the gravity wave is probably auroral. The E-region ion velocities show a tidal wave and both upward and downward propagating gravity waves. The gravity waves have three dominant periods with a possible harmonic relationship and similar vertical wavelengths. These waves are either reflected at a single reflection level, ducted between two levels, or they are generated in a non-linear interaction between gravity and tidal waves. The E-region electron density is dominated by particle precipitation. After a short burst of more intense precipitation, a sporadic E-layer forms at 105km and then disappears 40min later. Within this time, the layer rises and falls by a few kilometres, following closely the motion of a convergent null in the velocity profile. We suggest that the formation and destruction of this layer is controlled by both the precipitation, which indirectly provides a source of metal ions through charge exchange, and the superposition of gravity waves and the tidal wave.     

Permanent monitoring of the upper mesosphere and lower thermosphere wind fields (prevailing and semidiurnal tidal components) obtained from LF D1 measurements in 1991 at the Collm Geophysical Observatory

The wind field of the upper mesosphere and lower thermosphere region (85–105 km) over Central Europe (52°N, 15°E) has been continually and reliably recorded by regular daily D1 radio wind measurements in the LF range (177, 225 and 270 kHz) using commercial radio transmitters. These measurements show the prevailing winds, the tidal wind components and the effects of internal gravity waves, as well as the seasonal and irregular variations of these parameters. The height of the wind measurements is determined by measuring the travel time differences between corresponding modulation bursts in the sky wave and in the ground wave. Using a quasi-online calculation procedure, the results are available immediately. Therefore they are useful for monitoring the upper atmospheric circulation with regard to upper atmosphere meteorology in the future. Vertical profiles of the wind field parameters can be derived with the aid of the combined wind and height measurements. Height-time cross-sections of the monthly mean prevailing winds and semidiurnal wind components have been calculated almost continuously for the last 10 years. The present paper deals with recent results for the year 1991.     

Gravity wave activity in the upper mesosphere over Urbana,Illinois: lidar observations and analysis of gravity wave propagation models

We analyze 375 h of Na Wind/Temperature lidar measurements of the mesopause region (≈ 80–105 km) Na density and temperature profiles on 57 nights distributed over 2 yr at Urbana, Illinois. These observations yield a high-resolution seasonal data set of gravity wave activity in the upper mesosphere. From this data, we present measurements of the Brunt-Väisälä period, the relative atmospheric density perturbations and their spectra, and the parameters of 143 quasi-monochromatic gravity waves. The direct measurement of the Brunt-Väisälä period allows accurate calculation of the horizontal velocity perturbations and vertical displacement perturbations from the density measurements. The horizontal velocity and vertical displacement vertical wave number spectrum magnitudes and indices show considerable seasonal and nightly variability. The gravity wave amplitudes, wavelengths, and observed periods exhibit systematic relationships similar to those found in previous studies, and are consistent with the MU radar measurements of intrinsic gravity wave parameters. Here, we present a detailed analysis of the observations in terms of Diffusive-Filtering Theory models of gravity wave propagation. The magnitudes of the vertical wave number spectrum, the form of the joint vertical wave number and frequency spectrum, and the systematic relationships between the monochromatic gravity wave parameters are consistent with the Diffusive-Filtering model. We compare these results with a variety of radar, lidar, and airglow observations from other sites. This observational study suggests that the complex nonlinear interactions of the gravity wave field may be modeled successfully as a diffusive damping process, where the effective diffusivity is a function of the total wave variance.     

Climatology of gravity waves in the middle atmosphere

An attempt is made at the statistical analysis of small-scale disturbances in the stratosphere and mesosphere with the aid of meteorological rocket observations at many stations from 77°N to 8°S for several years.By applying a high-pass filter to daily rocket data in the height range 20–65 km, wind and temperature fluctuations with characteristic vertical scales close to or less than 10 km are obtained, which are considered to be due to internal gravity waves. Results are expressed in terms of parameters which tend to emphasize smallscale vertical fluctuations and which should provide qualitative measures of gravity wave activity.It is found that the gravity wave activity shows a notable annual cycle in higher latitudes with the maximum in wintertime, while it shows a semiannual cycle in lower latitudes with the maxima around equinoxes. It is also found from the standard deviation around the monthly mean that the temporal variability of gravity waves is very large.     

Gravity-wave motions in the mesosphere and lower thermosphere observed at Mawson,Antarctica

We present the results of MF radar observations of mean winds and waves in the height range 78–108 km at Mawson (67°S, 63°E), Antarctica. The measurements were made in the period from 1984 to 1990. Climatologies of the prevailing zonal and meridional circulations made with a 12-day time resolution show that the mean circulation remained relatively stable over the 6 yr of observation. Climatologies of gravity-wave motions in the 1–24 h period range were also generated. These reveal that the r.m.s. amplitudes of horizontal wave motions near the mesopause (~90 km) are about 30 m s⁻¹, and that there is some anisotropy in the motions, especially at heights below 90 km. Meridional amplitudes are larger than zonal amplitudes, which suggests a preference for wave propagation in the north-south direction. Comparisons with MST radar wind observations made near the summer solstice at Poker Flat, Alaska (65°N) and at Andøya, Norway (69°N) show similarities with the Mawson observations, but the wave amplitudes and mean motions are larger in magnitude at the northern sites. This suggests hemispheric differences in wave activity that require further study.     

A spectral approach for studying middle and upper atmospheric phenomena

We report on the application of a newly developed spectral code to the study of the middle/upper atmosphere. The spectral approach offers conceptual and practical convenience for analyzing the generation and interaction of different components of atmospheric activity through the decomposition of the dynamical fields into components with different zonal wave numbers (m). As examples and tests, we obtain solutions for the m = 0 (the mean circulation) and 1 (the diurnal tides) components separately (no mutual interactions), as well as the m = 1 component under the influence of the mean circulation. By simulating gravity wave effects with Rayleigh friction and eddy diffusion peaking near 90 km altitude, the mean circulation thus generated can reproduce the observed mesospheric temperature anomaly under solstice conditions. The computed diurnal tides are in good agreement with results obtained earlier by other authors. The large temperature gradient (associated with the m = 0 component) set up by the mesospheric temperature anomaly under solstice conditions creates a condition favorable for the development of baroclinic instabilities in the mesopause layer, especially near the summer pole. In our time dependent calculation, waves with approximately 4-day period are generated in the m = 1 component, superimposing with the 1-day period tides.     

Angle-of-arrival oscillations in the mesosphere as seen by medium frequency (MF) radar

The Saskatoon MF radar operates continuously in the spaced antenna mode with 5 min resolution, primarily for horizontal wind analysis at mesospheric heights. Mean Doppler frequency and antenna-pair phase difference are available as byproducts. Clear oscillations are sometimes seen in the latter. Spectral analysis shows that these also occur in the Doppler and extend over a range of heights. The two cases shown are almost certainly perturbations in specular reflecting layers moving with horizontal velocity close to that of the wind. Downward phase propagation is apparent, and when the oscillations are present, the wind appears to be decelerating. The tentative explanation of a breaking gravity wave decelerating the mean flow is put forward, although the relations between frequency, and horizontal and vertical wavelengths, contradict linear gravity wave theory.     

Heights of MF radar scatter (1986/87) and the wind field (55–95 km): Saskatoon,Canada

The Saskatoon MF radar (2.2 MHz) at 52°N, 107°W, has been used to measure the heights of occurrence of radar scatter during four seasons, and twelve months of 1986/87. Mean winds, and gravity waves are also available, by the spaced antenna method and from the same radar echoes. Certain heights, called elsewhere ‘preferred heights’, are identified near 60km, 70km, 75km in summer, and 80–86 km. Several layers have seasonal and diurnal variations. Associations with electron density gradients (rocket data), mean wind shear in summer, and gravity wave amplitude-minima in the equinoxes are effectively demonstrated. Case studies, involving 3 h data sets of radar scatter and wind elaborate the comparison: gravity waves of long period (τ > 6 h) are shown to modulate the scattering process.     

Dynamic regime of the mesopause—lower thermosphere at mid-latitudes of the northern hemisphere by radio meteor observations

The coherent pulse Meteor Automatic Radar System (MARS) based at Kharkov (49°30′N, 36°51′E) was used to measure zonal winds in the altitude range 80–105 km in the period from November 1986 to December 1990. It was found that, for the greater part of the year, the zonal prevailing wind component was in the eastward direction. The change from eastward to westward direction begins in the lower thermosphere in February–March, propagating downwards to the mesosphere, and it remains there until June–July. The structure of semidiurnal tides has general regularities at different sites. Annual variations in the monthly mean values of semidiurnal vertical wavelengths are practically the same, both in the northern and southern hemispheres. Wavelengths are more than 100 km in summer months, whereas they are less than 60 km in winter months.Studies of internal gravity wave (IGW) parameters in the height range of 80–105 km have shown that the internal gravity wave amplitude does not exceed 30 m/s, the vertical wavelength is in the range of 10–30 km, the horizontal wavelengths are 100–800 km and the horizontal phase velocities are in the range 20–160 m/s. The propagation and breaking of upward and downward IGW at heights of 80–100 km have been recorded.     

HF Doppler observations of gravity waves during the 16 February 1980 solar eclipse

Observations by the HF Doppier technique of the ionospheric effects of the 16 February 1980 solar eclipse in Africa are presented. Some oscillations which are detected at two stations can be attributed to a travelling coherent structure. Its characteristics are consistent with a gravity wave generated by the eclipse.