Gravity Wave Theory Research Articles

Numerical simulations of the saturated gravity wave spectra in the atmosphere

A two dimensional numerical model is used to compute the saturation of small scale gravity waves in the region near the critical level. The vertical wave number spectrum of horizontal velocity fluctuations in the unstable region (USR) where shear instability develops is found to be governed by wave-shear interaction and follows a theoretical saturation spectrum ~ ω b 2/2 m 3. Wave-shear interaction is also found to be responsible for the observed fact that the variance of vertical velocity fluctuations is significantly lower than the level predicted by linear gravity wave theory. On the other hand, the corresponding spectrum in the stable region (SR) following a much shallower spectrum ~m −2 is found to result from the combined effects of wave-wave interactions and eddy diffusion. The key step in our simulation is the separate parameterization of horizontal and vertical eddy diffusion coefficients instead of a constant molecular viscosity coefficient.

Sources of Mesoscale Variability of Gravity Waves. Part I: Topographic Excitation

Abstract Aircraft measurements of winds and temperatures collected during the GASP program are used to study the effects of topography as a source of mesoscale variability. Variances of fluctuations at the mesoscale over rough terrain are enhanced up to nearly two orders of magnitude compared to nonsource regions in some cases and are frequently enhanced by an order of magnitude. The implications of these episodic enhancements of variances for the vertical transports of energy and momentum are considered in the framework of gravity wave theory. The observed flight data are used to estimate the momentum flux u′w′ on several flight segments. Results show that the flux is generally negative with mean value −0.26 m2 s−2 and with magnitudes ranging up to −1.5 m2 s−2. Spectral analysis shows that the largest contributions to the net flux come from horizontal scales of ∼25 < λx <60 km. Finally, the observed momentum fluxes are used to infer the anisotropy factor of gravity waves over rough terrain, which is foun...

Spectral analysis of temperature and Brunt‐Väisälä frequency fluctuations observed by radiosondes

We observed profiles of the temperature, T, and Brunt‐Väisälä frequency squared, N2, from 0 to 30 km in altitude using radiosondes with 150 m height resolution launched from the MU observatory, Japan (34°51′N, 136°06′), from September 27, 1986, to February 24, 1989. We analyzed vertical wavenumber spectra of the normalized temperature T/T and N2 fluctuations in the 2.0–8.5 km (troposphere) and 18.5–25.0 km (lower stratosphere) altitude ranges and compared them with model spectra based on saturated gravity wave theory. In the winter stratosphere the slope of the mean T/T spectra in the wavenumber range from 7.0×10−4 to 2.0×10−3 (cycles per meter) was very close to the −3 predicted by the model, and the spectral amplitudes were 1.3–1.9 times larger than the predicted values, which is within the possible range of variability of the model. On the other hand, in the summer stratosphere the spectral slope ranged from −2.2 to −2.4, which is more gradual than the model, and the spectral amplitudes were only 0.4 to 0.5 of the predictions. The spectral shape in the troposphere did not show a significant difference between summer and winter. The spectral amplitudes, however, exceeded the model values by factors of about 3.2 and 1.9 in winter and summer, respectively. The overall shape of the profile for fluctuations with vertical scales from 150 to 900 m was generally similar to the shape of the background value of N4, consistent with the saturated gravity wave model, but the details of the altitude variations were rather complicated. That is, just below the tropopause usually exceeded the model by a factor of 2 to 4, and it became significantly smaller than the model in the summer stratosphere and in a region above 25 km in winter.

Gravity waves and Rayleigh Taylor instability on a Jeffrey-fluid

A theory for linear surface gravity waves on a semi-infinite layer of viscoelastic fluid described by a Jeffrey model is presented. Results are given for the decay rate and the phase velocity as a function of the parameters of the fluid: a nondimensional time constant, and a ratio of the retardation time to the relaxation time. At small wave numbers the behavior is Newtonian. In other cases depending on the nondimensional parameters, a number of possible other behaviors exist. The influence of the non-dimensional parameters on the growth rate of Rayleigh-Taylor instability is also discussed.

Dispersion of fifth order Stoke waves: A numerical method

A computer program is described which can calculate the roots of the two coupled dispersion relations arising in Stokes' fifth order gravity wave theory. The numerical scheme involved is the solution of two nonlinear simultaneous equations by Newton-Raphson's method. A typical input and output are given.

Dispersion of fifth order Stoke waves: A numerical method

Abstract A computer program is described which can calculate the roots of the two coupled dispersion relations arising in Stokes' fifth order gravity wave theory. The numerical scheme involved is the solution of two nonlinear simultaneous equations by Newton-Raphson's method. A typical input and output are given.

Small-scale structure observed in-situ during MAC/EPSILON

We determine in this paper the level of turbulence activity in the middle atmosphere observed during the MAC/EPSILON campaign using different in-situ techniques. The observations show a minimum of turbulence in the height region 75–80 km, with increasing activity below and above. Based upon spectra of density fluctuations covering height intervals of typically 8 km, a unified spectral description is developed. It is shown that the buoyancy scale L B and inner scale l 0 of turbulence, as calculated from the power of fluctuations in the inertial subrange, agree with the visually observed breakpoints in the spectra. Spectra of ion density fluctuations are also seen to be consistent with spectral amplitudes predicted by linear saturation theory. The relationship between the level of turbulence in the middle atmosphere and the gravity wave environment in which the turbulence occurs is investigated in detail. Our results suggest that strong turbulence occurs preferentially in or near those phases of the wave motions predicted to be most unstable on the basis of linear gravity wave theory.

Gravity waves in the mesosphere observed with the middle and upper atmosphere radar

We have observed wind motions from 60 to 90 km altitudes with the middle and upper atmosphere (MU) radar during daylight hours (0800–1600 LT) from October 13 to 31, 1986. Gravity waves with fairly sinusoidal vertical structure were evident on 16 days of the 19 days of observations. They were characterized by a typical vertical wavelength of 5–15 km and intrinsic periods centered at about 8.6 hours. The propagation velocity of these waves was determined using the linear gravity wave theory. All of the waves propagated downward and had an equatorward component of the meridional propagation. The median direction of horizontal propagation was slightly east of south, and the mean horizontal phase speed was 35.3 m/s. The vertical wave number spectra of horizontal components of mesoscale wind fluctuations agree well with the theoretical spectrum of saturated gravity waves. At frequencies from 1 × 10−5 to about 4 × 10−5 c/s frequency spectra of vertical and radial wind components had logarithmic slopes of 1/3 and −5/3, respectively, which agree fairly well with a model gravity wave spectrum. The effects of Doppler shifting on frequency spectra are most obviously recognized at large frequencies near the Brunt Väisälä frequency. We have also determined the upward flux of horizontal momentum induced by waves with periods from 10 min to 8 hours and further estimated the westward and northward body force of 5.1 and 4.0 m/s/d, respectively.

Gravity wave spectra in the middle atmosphere as observed by Rayleigh lidar

Rayleigh lidar offers the unique ability to make routine measurements of temperature (or density) mesoscale fluctuations in the 30 to 75 km altitude range. Power spectra of density and temperature fluctuations, versus vertical wavenumber and (apparent) frequency, are derived from lidar measurements. These spectra are interpreted in the framework of the gravity wave theory. Power spectral density increases from the stratosphere to the mesosphere in the entire accessible spectral range. Comparison with vertical spectra obtained with various sounding systems indicates a dispersion of the temperature power spectra in the stratosphere as an increase with altitude of the ratio of potential to kinetic energy.

A Mixed-Layer Simulation of Daytime Boundary-Layer Variations within the Los Angeles Basin

Abstract The ability of an idealized mixed-layer model to predict mesoscale variations in boundary-layer (BL) properties is tested by simulating a case-study day in the Los Angeles Basin, a day typical of their summertime fair weather conditions. Large horizontal and temporal BL variations result from the strong land-sea thermal discontinuity, which primarily drives the flow, and the complex terrain with large terrain height differences, which primarily channels the flow. Rather than specifying an “undisturbed level” in the model, the parameterized interaction between the free atmosphere and the BL is derived from gravity wave theory and a representative horizontal length scale determined by the size of the basin. Predicted BL depths, velocities, and temperatures all show good agreement with observed values. Known convergence zones are predicted qualitatively; addition of an ad hoc detrainment increases model quantitative accuracy in those regions by allowing some of the converging air to exit the BL. How...

Further Study of Terrain Effects on the Mesoscale Spectrum of Atmospheric Motions

Wind and temperature data collected on commercial airliners are used to investigate the effects of underlying terrain on mesoscale variability. These results expand upon those of Nastrom et al., by including all available data from the Global Atmospheric Sampling Program (GASP) and by more closely focusing on the coupling of variance with the roughness of the underlying terrain over mountainous regions. The earlier results, showing that variances are larger over mountains than over oceans or plains, with greatest increases at wavelengths below about 80 km, are confirmed. Statistical tests are used to confirm that these differences are highly significant. Over mountainous regions the roughness of the underlying terrain was parameterized from topographic data and it was found that variances are highly correlated with roughness and, in the troposphere, with background windspeed. Average variances over the roughest terrain areas range up to about ten times larger than those over the oceans. These results are found to follow the scaling with stability predicted in the framework of linenar gravity wave theory. The implications of these results for vertical transports of momentum and energy, assuming they are due to gravity waves and considering the effects of intermittency and anisotroy, are also discussed.

Linear theory of gravity waves on a maxwell fluid

Surface gravity waves on a semi-infinite incompressible Maxwell fluid are studied by means of linear theory. A dimensionless (memory) time-number (Θ), different from the Deborah number, is introduced, together with a dimensionless wave-number and a dimensionless surface tension. A characteristic equation describing the waves is derived. This is an 8-degree complex polynomial which is solved to give the complex dispersion relation. Two critical time-numbers are found, Θ A = 0.321 and Θ c = 0.906. These are important for the number of pure decay solutions and propagating waves. The dispersion relation is shown for Θ in the range from 0 to 2. A similarity to gravity waves on inviscid fluids is seen for small wave numbers. For large wave numbers these are solutions of the Rayleigh wave type.

On the interaction between gravity waves and the OH Meinel (6‐2) and the O2 atmospheric (0‐1) bands in the polar night airglow

The effect of gravity waves on the OH (6–2) and O2 (0–1) airglow emissions was examined using spectroscopic airglow data from Longyearbyen, Svalbard (78°N), and Fairbanks, Alaska (64°N). The analysis was done by fitting a synthetic spectrum to the data to infer the rotational temperature as well as the band intensity of each of the emissions. Quasi‐periodic fluctuations in the band intensity and rotational temperature are assumed to be a result of modifications of a stable airglow layer by gravity waves. The relationship of the fluctuations in band intensity to rotational temperature may be expressed in terms of the parameters η, which is defined as the ratio of the amplitudes of the fluctuations in intensity and temperature, and θ, which is the phase angle between the fluctuations in intensity and temperature. These parameters were observed to vary with wave period for both the OH and O2 emissions. The variations in η(OH) and θ(OH) agreed fairly well with the most recent models for waves with periods of about 1 hour or longer. None of the models agree with the observed values of η(OH) and θ(OH) for short‐period waves. For the O2 emissions, the observed values of η(O2) range between 1 and 8 and do not agree with the model calculations, but θ(O2) is generally 180° which is expected from first‐order linear gravity wave theory.

Observations of Mesocale Wave Disturbances during the Genesis of Atlantic Lows Experiment

Abstract The Portable Automated Mesonet (PAM) data obtained during the Genesis of Atlantic Lows Fxperiment (GALE) are used to document mesoscale wave activity during the 3-day period from 4 to 6 February 1986. From the surface pressure analyses, four cases of wave activity are identified with wavelengths of 200–400 km, phase speeds of 20–40 m s−1 and trough-to-crest pressure amplitudes of 0.5–3.5 mb. Precipitation was associated with the waves in two of the four cases. Detailed analyses of the horizontal structure show that the waves do not have the pressure-wind relationship expected from linear gravity wave theory. The wind vectors are oriented from high to low pressure with a maximum amplitude between the high and low pressure areas. Low-level inversions were present in three of the four cases. In the raw without a low-level inversion, the amplitude rapidly decreased as the wave moved towards the east. In the case which lasted for the longest time period (at least 8 h). and had the largest pressure amp...

Modeling F region gravity waves observed during the WAGS campaign: 1. Special event

In the Worldwide Atmospheric Gravity Wave Study (WAGS) campaign, the source‐response relationship between the auroral activities and the gravity waves observed in the ionosphere was studied. Ionospheric parameters observed with the incoherent scatter radars at Sondrestrom and Millstone Hill were compared with predicted results based on gravity wave theory. In the observed data, usually two types of disturbances can be identified. One is the distinct, semiperiodic traveling ionospheric disturbance. The other is the ever present, semirandom perturbations. The first type will be classified as the “special event,” and in this paper, we shall concentrate on the “special event” which was observed on October 18, 1985 during a moderately magnetically active period. The observed parameters used in this study are the ionization density and the line‐of‐sight ion velocity. This provides more information than in most of the previous investigations of traveling ionospheric disturbances, in which only electron density perturbations were used. The data are analyzed and compared with theoretical models to yield information about the special gravity wave event, such as the vertical and horizontal wavelength, the horizontal phase and group speeds, and the kinetic energy density carried by the waves. The observed waves at the two radar sites are related to a possible source region in the auroral zone.

An Investigation of Terrain Effects on the Mesoscale Spectrum of Atmospheric Motions

Abstract Wind and temperature data collected on commercial aircraft during the Global Atmospheric Sampling Program (GASP) are used to investigate the effects of underlying terrain on mesoscale variability, and the observational results are interpreted within the theories of gravity wave motions and quasi-two-dimensional turbulence. The data show the variances are up to six times larger over mountainous terrain than over oceans or plains, with the most striking differences at horizontal scales from 4 to 80 km. Results were subdivided between the stratosphere and troposphere, and between high- and low-background wind speed cases, and show basically the same response to topography in all cases. The linear theory of gravity waves is found to predict correctly the scaling of wave amplitude with background stability in the case of low-background wind speeds, while the two-dimensional turbulence theory correctly predicts the shape of the variance spectrum and the observed amplitude scales with ϵ as required by t...

Short period fluctuations of the horizontal wind measured in the upper middle atmosphere and possible relationships to internal gravity waves

Horizontal wind fluctuations between heights of 61 and 105 km as obtained from the M.F. radar measurements at Saskatoon (52N, 107W) are analyzed with respect to their direction and intensity in two period ranges (about 10–60 min and 1–6 h). Frequency distributions of horizontal perturbation directions and monthly mean r.m.s. deviations of the horizontal wind are presented for both period ranges. Strong annual, semiannual and interannual variations of the wind variability dependent on height are evident. Wind perturbation directions exhibit pronounced anisotropies, especially a clear N-S maximum in the short period range which markedly varies with season. The observations are discussed in the framework of gravity wave theory. The tendency to a preferably north-southward orientation of wind fluctuation is attributed to directional filtering of transient gravity waves with phase velocities deviating from zero in the prevailing zonal wind below the height range of observation (below 60–70 km). Seasonal changes of gravity wave source strength and distribution are inferred from the Saskatoon direction statistics. Previously recognised mean meridional wind reversals with height appear to be consistent with the N-S polarization of the gravity wave field above the mesopause. The shorter and longer period fluctuation intensities show significant differences of their seasonal variation in the mesosphere. Eddy dissipation rates estimated from horizontal wind fluctuations also exhibit regular changes with height and season. They show a clear semiannual oscillation at heights below about 95 km and a dominant annual variation above with maximum values in the winter.

Polar mesopause gravity wave activity in the sodium and hydroxyl night airglow

The OH (6–2) band and the Na D lines in the night airglow have been observed from Spitsbergen (78°N latitude) during a 3‐day period in the end of November 1983. Regular and quasi‐regular variations in temperature and the OH and sodium intensity were observed and are here interpreted in terms of gravity wave theory. In particular, waves with periods in the range 90–120 min having overlying ripple structure, with periods of 5–15 min, were observed. From the phase difference between the waves in the OH and sodium layer a height difference between the centroid of the two emissions of less than 1 km could be deduced. A gravity wave induced vertical eddy diffusion coefficient in the range 8 × 106 to 8 × 107 cm²/s was estimated from OH‐enhanced intensities. No significant net heating or cooling was observed during gravity wave activity. The gravity wave activity was not associated with geomagnetic activity. Mean OH (6–2) band and sodium night airglow intensities were 1.9 kR and 75 R, respectively.

Zonal winds near Venus' cloud top level: A model study of the interaction between the zonal mean circulation and the semidiurnal tide

A primitive equation wave-mean flow interaction model, designed by J. R. Holton and used originally to study Earth's middle atmosphere, has been adapted to Venus in order to clarify our understanding of the interaction between the semidiurnal tide and the thermally driven mean meridional circulation near the cloud top level. With or without the tide the model produces midlatitude jets whose structure is insensitive to vertical shear of the background angular velocity above and below the cloud top level, but it is sensitive to background angular velocity at the cloud top level. When this background angular velocity is close to that of Venus, the latitudes and speeds of these jets are similar to the latitudes and speeds of jets at the Venus cloud top level as inferred from observed temperatures and the cyclostrophic balance condition. In agreement with the hypothesis of Fels and Lindzen, the model tide accelerates the equatorial zonal wind near the cloud top level and decelerates it at higher levels. The tidal vertical wavelength, maximum amplitude, dissipative decay length, and zonal flow accelerations are sensitive functions of background angular velocity, in agreement with elementary gravity wave theory. In the equatorial cloud top region, tidal acceleration is comparable in magnitude to the decelerative effects of vertical advection and the model's Rayleigh friction damping. For sufficiently rapid initial zonal flow near the cloud top level, the area-weighted global mean cloud top level zonal wind increases with time over a 50-day model run as a result of tidal acceleration. Agreement between the model tide and the observed tide, or the tide determined in the more detailed calculations of Pechmann and Ingersoll, is best when the background angular velocity at the jet level is about 30% larger than that observed.

Two classes of medium-scale traveling ionospheric disturbances observed by an HF Doppler array.

The daytime horizontal trace velocities (Vh) of medium-scale traveling ionospheric disturbances (TID) observed with a network of HF Doppler receivers in central Japan from 17 September to 11 October 1982 are analyzed. The TID with a specified wave period of 40min are found to fall into two separate classes not previously distinguished; i. e., the first class has Vh≤3×102ms-1 with the propagation azimuth in a confined range of about ±40° around the southeast direction, whereas the other has Vh≥4×102ms-1 with the omnidirectional features. The results are discussed in the light of atmospheric gravity wave theory. It is concluded that while the first class can be identified with the internal gravity waves, the second class may be explicable in terms of the quasi-evanescent gravity waves inherent to the dissipative thermosphere.