A quartic dispersion equation for internal gravity waves in the thermosphere

A new quartic dispersion equation in the square of the complex vertical wave number is derived by employing the ‘shallow atmosphere’ approximation and an ion drag approximation. These approximations allow the coefficients of the quartic equation to be given in terms of the corresponding cubic equation, which neglects the Coriolis force and the zonal ion drag component, but modified to take into account these neglected effects. Coupling between the extraordinary viscosity wave mode and the other three wave modes is highlighted and numerical solutions are compared for this quartic equation, an exact eighth order equation and the cubic equation. For the first time the validity of using the ‘shallow atmosphere’ approximation to describe internal gravity wave motions is demonstrated.     

Large-scale TIDs and upper atmospheric gravity waves

Excitation of the guided acoustic-gravity waves in the upper thermosphere in response to enhanced auroral electrojets is calculated in the absence of dissipation under a fully ducted condition. It is shown that a model atmosphere terminated with an isothermal half-space supports a long-period, high-speed mode, which is the interface mode guided along the half-space termination of the atmosphere. The dispersion properties and the vertical distributions of the kinetic energy density of this mode are similar to those of the so called ‘gravity pseudomode’. The excitation of this mode is computed to show how the wave generation depends on the source mechanism (the Lorentz force and joule heating) and on the source altitude. Joule heating can generate the waves with appreciable amplitudes. On the other hand, the Lorentz force prevailing in the lower region cannot excite the waves with any observable amplitudes. The waves are intensified with increasing the heat source altitude. The gross features of the calculated waves indicate that the ducted thermospheric gravity waves are capable of producing observable thermospheric waves. It is therefore suggested that further examination of the excitation of the ducted acoustic-gravity waves undergoing partial reflections due to viscosity and thermal conduction should be useful for the theory of large-scale travelling ionospheric disturbances.     

Weak nonlinear theory of the ionospheric response to atmospheric gravity waves in the F-region

The nonlinear ionospheric response to atmospheric gravity waves is studied in an approximate fashion using a new approach. The concept of nonlinear travelling ionospheric disturbances (TIDs) is outlined, and the nonlinear behaviour of atmospheric gravity waves is calculated. A principal result is that harmonics are generated which cause the wave velocity perturbation to deform. The ionospheric response is investigated by solving the continuity equation for ionization in the F-region. The distortion of the TIDs waveform produced by the nonlinear interactions is depicted. The nonlinear TIDs depart seriously from a cosinusoidal wave described by previous linear TID theory. The distorted TIDs appear as ‘sharp peak’ and ‘sawtooth’ waveform shapes. The ‘peaks’ can be upward or downward, and the ‘sawteeth’ forward or backward, depending on the wave parameters. The nonlinearly distorted TIDs show a good agreement with various observed ionospheric irregularities produced by atmospheric gravity waves.     

A theoretical investigation of sources of large and medium scale atmospheric gravity waves in the auroral oval

Many papers have been published to devise models to describe the sources of large and medium scale atmospheric gravity waves (AGWs) in the auroral oval ionosphere. One of the models proposed by Chimonas and Hines [(1970) Planet. Space Sci.18, 565] calculated the relative importance of Lorentz force and Joule heating as sources of AGWs in the auroral regions based on certain assumptions. In this paper, we develop a general theory to describe the behavior of the AGW source terms. It has been found that the source terms which generate AGWs are closely related to the velocities and frequencies of AGWs, and that the Lorentz force is dominant in generating the vertical velocity perturbation of large scale AGWs. The formulas which determine the source term contributions are derived. This relationship gives us the possibility to predict what kind of AGW will be generated by observing the source terms, or conversely perhaps to deduce some of the source characteristics by measuring properties of the traveling ionospheric disturbances (TIDs).     

The generation and propagation of atmospheric gravity waves from activity in the auroral electrojet

EISCAT measurements of the electric field in the auroral electrojet are compared with the signature of TIDs propagating equatorward as observed by an HF-Doppler network. At night-time the onset of auroral activity is usually followed by the arrival of a TID at lower latitude. Cross-correlation of the time variations of the electric field measured by EISCAT and the frequency offset recorded by the HF-Doppler system confirms a relationship between the auroral activity and the gravity wave, indicating both the travel time and the periodicity of the wave. The relationship is especially close under quiet conditions when the cross-correlation coefficient is typically 60%, significant at 0.1%. When the observed electric field is used as input to a thermosphere-ionosphere coupled global model it predicts the time signature of the observed HF-Doppler variation reasonably well but seriously underestimates the amplitude of the disturbance. Examination of this discrepancy may lead to a better understanding of the mechanisms involved in the generation and propagation of atmospheric gravity waves.     

Equatorial spread-F by electric fields and atmospheric gravity waves generated by thunderstorms

It is assumed that atmospheric gravity waves, resulting in travelling ionospheric disturbances (TIDs), and electric fields, generated by convective thunderstorms, have a reasonable influence on the large-scale structure of premidnight equatorial spread-F irregularities. The responsible mechanisms, viz the superposition of thunderstorm generated electric fields on the ionospheric electric fields being the determining factor for irregularity generation and the steepening of TID structures due to spatial resonance, are briefly outlined. It is recalled that convective activity is most pronounced in the intertropical convergence zone over the African and South American continents. A model based on the typical features of seasonal and geographical variation of tropical convection generating the TIDs is presented which can explain seasonal and geographical variations of premidnight equatorial spread-F occurrence.     

The effects of neutral winds on the propagation of medium-scale atmospheric gravity waves at mid-latitudes

The influence of neutral winds on the propagation of medium-scale atmospheric gravity waves at mid-latitudes is investigated. A 3-dimensional neutral wind model is developed and used together with an atmospheric model in a gravity-wave ray-tracing analysis. It is demonstrated that the thermospheric wind can act as a filter for waves travelling at unfavorable angles to the mean flow, via the mechanisms of reflection and critical coupling. This wind filtering action rotates clockwise diurnally through 360° in the northern hemisphere. Observational evidence is presented which supports these predictions. Extensive modelling indicates that (a) faster and longer period waves are least affected by the neutral winds and (b) fixed-height (e.g. HF Doppler) observations of medium scale gravity waves is only likely to be possible for waves generated locally (within 500–1000 km). Waves generated at greater distances are probably dissipated before reaching the observation region.     

Measurement of vertical phase and group velocities of atmospheric gravity waves by VHF radar

A systematic method of deriving from MST radar data the group velocity and phase velocity of the atmospheric wave along the radar beam direction is proposed and verified by a series of numerical simulations. We apply the method to two data sets measured by Chung-Li radar under different background wind conditions. It is found that the vertical group velocity and phase velocity are mostly in the opposite direction when the background wind is weak. The energy source of downgoing wave packets was evidently related to the instability in the upper height range (10.5–11.7 km) where strong wind shear existed. When the background wind and wind shear are stronger, the vertical group and phase velocities may propagate in the same direction. We also found from numerical simulation and data analysis that the wave packet of gravity waves following power law spectrum are short-lived. A by-product of the group velocity measurement is that the horizontal wavelength may also be deduced from a vertical radar beam measurement from the dispersion relation if it is valid.     

Wind and temperature effects on F-region medium-scale gravity waves estimated using a multi-layer atmospheric model

Diurnal variations in the propagation direction of atmospheric gravity waves, and the travelling ionospheric disturbances to which they give rise, have been observed in many experimental observations and several modelling studies have demonstrated that this is primarily due to the corresponding diurnal rotation in the direction of the thermospheric wind. Other variations have been attributed to seasonal or other effects, but the effects of variations in the thermospheric temperature have not previously been analysed in detail. We present results from a study of the propagation of gravity waves through a layered atmosphere in which the thermospheric wind and temperature are derived from a three-dimensional time-dependent model. The analysis has been carried out for a range of wave speeds and periods, and for a range of times, seasons and propagation azimuths. Results suggest that a significant diurnal variation in the transmission coefficient for waves propagating through the thermosphere exists with seasonally dependent maxima. Transmission increases for increasing wave period up to about 50 min, after which it remains approximately constant. Maximum transmission occurs for wave phase speeds around 200–250 m/s and falls to zero for speeds less than about 100 m/s. An exception to this rule occurs for waves with periods less than 40 min and speeds less than 50 m/s for which significant transmission appears to be theoretically possible.     

The generation and propagation of atmospheric gravity waves observed during the Worldwide Atmospheric Gravity-wave Study (WAGS)

During the Worldwide Atmospheric Gravity-wave Study (WAGS) in October 1985, the EISCAT incoherent scatter radar was used to observe the generation of atmospheric gravity waves in the auroral zone in conjunction with a network of magnetometers and riometers. At the same time a chain of five ionosondes, an HF-Doppler system, a meteor radar and a radio telescope array were used to monitor any waves propagating southwards over the U.K.The EISCAT measurements indicated that in the evening sector both Joule heating and Lorentz forcing were sufficiently strong to generate waves, and both frequently showed an intrinsic periodicity caused by periodic variation in the magnetospheric electric field.Two occasions have been examined in detail where the onset of a source with intrinsic periodicity was followed by a propagating wave of the same period which was detected about an hour later, travelling southwards at speeds of over 300 m s⁻¹, by the ionosondes and the HF-Doppler radar. In both cases the delay in arrival was consistent with the observed velocity, which suggests a direct relationship between a source in the auroral zone and a wave observed at mid-latitude.     

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.     

Optical observations of gravity waves in the auroral zone

Night-time observations of O(¹D) λ630 nm and O(¹S) λ558 nm thermospheric emissions were made at Mawson, Antarctica (67.6°S, 62.9°E) from 1982 to 1989, using a three-field photometer. Crossspectral analysis of the data was used to extract frequencies and horizontal trace velocities of periodic structures. Structures in the λ630 nm emission were characteristic of large-scale waves, and those in the λ558 nm emission were characteristic of medium-scale waves. The results showed distinct polarisation of the propagation azimuths; waves in the λ630 nm emission propagated approximately northwestward throughout the 8 yr period, whilst propagation azimuths of waves in the λ558 nm emission appeared to be solar-cycle-dependent. It is suggested that waves observed in the λ630 nm emission were of predominantly auroral electrojet origin, whilst those observed in the λ558 nm emission were of both auroral and tropospheric origin.     

Generation of gravity waves by inhomogeneous heating of the atmosphere

Local variation of atmospheric heating which might occur in inhomogeneities of various constituents such as ozone or molecular oxygen may generate gravity waves. These perturbations are induced by the terminator crossing constituent inhomogeneities of short lifetime. The quasi-point heating model developed here shows that the largest amplitude must appear vertically above the source, where the perturbation frequency is close to the Vaisala-Brunt frequency. Numerical calculations not band limited in the frequency suggest several characteristics of the perturbation.     

A study of gravity waves in ionospheric electron content at L = 4

Using satellite radio beacon transmissions, travelling ionospheric disturbances have been observed in the electron content at L = 4. Waves are a common feature at this latitude, present for at least 98% of all daylight hours. The amplitude is usually 1–4% of the mean electron content and periods range between 15 and 90 minutes. Simultaneous observation of two satellite beacons, giving an effective east-west separation of 350 km, indicated apparent east-to-west velocities of 200–700 m/s.A search was made for a likely source of the waves, using data from magnetometers and riometers, from incoherent scatter radar measurements of Joule heating, and from orbiting satellite measurements of electron influx, but no definite source could be established.It is also shown that travelling disturbances are closely related to occurrences of spread-F on ionograms at high latitudes.     

Nonlinear disturbances in the ionosphere due to acoustic gravity waves

The influence of the higher harmonics of an internal gravity wave on the formation of nonlinear quasi-periodic disturbances in the F-region of the Earth's ionosphere is considered. It is shown that the Boussinesq approximation cannot be used in describing a plane nonlinear gravity wave as nonlinearities associated with the compressibility of the atmosphere have to be taken into account.     

Interactions between diurnal tides and gravity waves in the lower thermosphere

Recent progress on interactions between breaking gravity waves and the diurnal tide in the upper mesosphere and lower thermosphere is reviewed, mainly based on the recent results of our numerical models.     

The impact of gravity waves on nitric oxide in the lower thermosphere

Observations of nitric oxide (NO) by the Solar Mesosphere Explorer (SME) during equinox indicate a lower-thermosphere equatorial minimum which is at variance with theoretical predictions. To address this discrepancy a zonally averaged model of the thermosphere and upper mesosphere is used to evaluate the influence of a latitude variation in turbulence. Five numerical simulations were performed with different latitude structures of eddy diffusion (K_T), ranging from uniform in latitude, peaks at low, mid-, or high-latitude, to a hemispherically asymmetric distribution. A local increase in eddy diffusion causes the lower thermosphere to cool and induces a latitude pressure gradient that drives horizontal and vertical winds. The circulation, turbulent transport and temperature dependent chemistry act to change the distribution of species. Comparison of the model predictions of NO with SME data, and simulated wind and temperature structure with empirical climatology, indicates a preference for a midlatitude peak in K_T.     

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.     

Simultaneous optical observations of long-period gravity waves during AIDA '89

Ground-based optical instrumentation supported the AIDA '89 wind measurement comparisons by describing the gravity waves affecting the 80–100 km altitude region during clear dark hours over Puerto Rico. This study tabulates the characteristics of gravity waves with fractional column emission rate amplitudes up to 30% and with periods greater than 45 min as seen in the O₂ airglow layer by MORTI, a sensor of O₂ rotational temperature and column emission rate in twelve look directions. Data from seven other sensors operating at Guanica and the Arecibo Observatory are then compared with the MORTI data to check the consistency of the entire data set with the wave parameters, primarily velocities, deduced from MORTI. Nine nights of visually distinct crests and troughs were found, one of which was dominated by an evanescent wave and the rest by internal waves. The nights of 5/6 April and 4/5 May 1989 were selected for multi-sensor comparisons. The comparisons showed substantial agreement between the MORTI characterizations and the observations by others, and most differences were attributed to complexities introduced by higher frequency components with shorter coherence distances. Nightly summaries of the O₂ rotational temperature and column emission rate are also given.