Gravity Wave Modes Research Articles

A Simple Nearly Analytic Model of a Gravity Wave Driven Middle Atmosphere Circulation

A nearby analytic model of a gravity wave driven middle atmosphere circulation is formulated. The simplified model represents the one-dimensional interaction of a single gravity wave mode with a zonal-mean flow. Solutions of this model are shown to agree very well with numerical results from a more complete mean-flow/gravity-wave model (essentially the model developed by Holton, 1982). A single nondimensional parameter, the ratio of a mean flow radiative forcing parameter, and the gravity wave momentum flux incident into the middle atmosphere from below largely determine the solution of the model. For typical middle atmosphere parameter values, an approximate solution can be obtained, and this solution permits the parameter dependence of the circulation to be characterized very simply. The gravity wave driven circulation extends downward from the level (the breaking level, approximately) where the momentum flux equals the mean flow radiative forcing.

A large‐amplitude traveling ionospheric disturbance excited by the space shuttle during launch

The ionosphere was monitored during the fourth space shuttle (STS 4) launch in June 1982 by the Arecibo incoherent scatter radar. A long‐lived, large‐amplitude, traveling ionospheric disturbance with dominant wave modes of ∼15 and 75 min was observed shortly after the launch. The disturbance wave train is likely the product of a variety of wave modes. The disturbance front traveled with an average group speed of >628 m/s. Such speeds are typical of fast moving shock waves and ducted gravity waves. Either one or both could be responsible for the signatures observed near the leading edge of the STS 4 wave train. Later arriving waves, with their inherently lower propagation speeds, are attributed to additional gravity wave modes. These waves, however, were not explicity identified in this study. Although atmospheric waves are excited along the entire flight path, the most intense region of excitation is located along a relatively short flight segment (∼70 km) near the launch site where all primary thrusters are firing and over 70% of the propellants are expended. Not since the nuclear bomb tests of the late 1950s and early 1960s has an artificial source of atmospheric gravity waves been more available for upper atmospheric studies. The routine launching of high thrust vehicles provides an excellent opportunity to observe the propogation characteristics of atmospheric waves under controlled conditions and to acquire information on the nature of the upper atmosphere.

VHF radar observations of mesoscale motions in the troposphere: Evidence for gravity wave Doppler shifting

A VHF radar at Adelaide (35°S, 138°E) has been used to study small‐scale horizontal velocity fluctuations in the troposphere. The measurements have been analyzed in the frequency domain and show that the motions are often “polarized,” such that they show a preference to be aligned along the direction of the mean background wind. This azimuthal anisotropy is especially apparent at high observed frequencies and becomes more pronounced as the wind speed increases. The cause of the polarization is analyzed in terms of both the gravity wave and vortical mode explanations of the mesoscale wind fluctuations. It is shown that the observed behavior is very consistent with the predicted effects of Doppler shifting on a spectrum of atmospheric gravity waves by non zero background winds. The results, however, are inconsistent with the predicted behavior of a spectrum of vortical modes advected past a ground‐based observer. It is concluded that internal gravity wave motions dominate the energy of the tropospheric mesoscale wind field in these observations. These findings have a number of implications for studies which use ground‐based techniques to study gravity wave wind fluctuations in the frequency domain because Doppler shifting of wave energy can produce significant biases, especially if narrow frequency bands are used. This problem and possible solutions are discussed.

The observable effects of gravity waves on airglow emissions

The influence of gravity waves on airglow emissions is explored with a view to elucidating the observable effects of such waves. The results obtained are applicable to ground-based photometric observations, where the total line-of-sight emission, at an arbitrary zenith angle, is measured. Explicit relations are developed for the dependence of the magnitude and phase of the observable parameter η, the ratio of brightness fluctuations to temperature fluctuations. Both magnitude and phase depend on dynamical parameters (wavelength and period), the zenith angle at which observations are made, and a chemical parameter which is specific to the reaction chemistry. Methods of (i) distinguishing between evanescent and internal gravity wave modes, and (ii) determining the vertical wavelength and sense of vertical propagation for internal modes, are proposed. The former may be of considerable importance observationally, since the effects of evanescent and internal modes on airglow are quite different. The latter is a measurement that is typically difficult to make directly. It is shown that, for an isothermal atmosphere, the dependence of η on the characteristics of the perturbing wave is partially separable from the dependence on the emission chemistry, making it possible to draw conclusions about the effects of gravity waves on airglow brightness and temperature that are independent of any specific emission mechanism, as well as conclusions that are independent of specific wave characteristics.

The assimilation of XBT data into a layer model of the tropical pacific ocean

Abstract Attempts have been made to initialize a one-layer reduced-gravity model of the tropical Pacific Ocean by updating it at regular intervals with expendable bathythermograph (XBT) observations of the 16°C isotherm collected as part of the TOGA ship-of-opportunity program. An interpolation procedure based upon the successive correction scheme was used to combine the new observations with the model first-guess each time the model was updated. The model was driven by the monthly mean winds of Legler and O'Brien, and when forced only with the wind field (i.e., no data assimilated), there were substantial differences between the model and the XBT observations. When data was assimilated, the model solution was substantially modified, particularly in the east Pacific. The length of time for which information imparted to the model by assimilation was retained varies geographically but is everywhere more than a month, implying that information was not projected heavily on to the gravity wave modes and dispersed. In fact, the result of data retention experiments (in which the model was initialized with part of the XBT data set and then forced with only the wind) indicate that away from the Equator in the west and central Pacific, the structure of any isotherm in the thermocline can be retained for up to 12 months. In the eastern equatorial Pacific, the improvements from data assimilation are lost more quickly because they are not balanced by the forcing. Planetary waves are excited on a time-scale of a month or two, which degrades the solution in the east. This deterioration then propagates westward eventually degrading the solution there too. The data-retention period of the model will therefore, in general, be a function of the model stratification and the forcing fields used to drive the model.

Solitons in a system of coupled Korteweg-de Vries equations

A system of two Korteweg-de Vries equations coupled by small linear and nonlinear terms, which is a model of a resonant interaction between two internal gravity-wave modes in a shallow stratified liquid, is considered. The present paper is a continuation of a preceding one, where only the linear coupling was dealt with. Various dynamical processes involving one-mode solitons are investigated. It is demonstrated that two solitons belonging to the different wave modes may form an oscillatory bound state (a bi-soliton) which provides an explanation for the numerical results of Gear & Grimshaw demonstrating leapfrogging motion of the two interacting solitons. In the framework of a perturbation theory based on the inverse scattering transform, the frequency of the bi-soliton's internal oscillations is found, and emission of radiation by a weakly excited bi-soliton is studied. Phase shifts and radiative energy losses accompnying a collision between two free solitons belonging to the different modes are calculated. In addition, a collision between a free soliton and a bi-soliton is considered, and it is demonstrated that the collision may result in break-up of the bi-soliton.

Gravity waves in the upper atmosphere of Venus

We present a spectral model in terms of spherical and Fourier harmonics to describe gravity waves in the thermosphere of Venus. This is an extension of a transfer function model for a dissipative multiconstituent atmosphere on Earth which describes quasi three‐dimensional perturbations on the globe, including acoustic‐gravity waves. Owing to the differences in the vertical temperature distributions on Earth and Venus, there are significant differences in the propagation characteristics of gravity waves. For example, the ducted wave mode that is excited in the Earth's thermosphere through reflections from the surface and the temperature minimum at the mesopause is absent on Venus. On Venus, as is the case on Earth, wave reflection from the surface can occur. For both planets, the most important gravity wave mode is propagating quasi horizontally, near the local speed of sound. The model is used to interpret density perturbations in CO2, O and He observed with the orbital neutral mass spectrometer on Pioneer Venus [Niemann, 1977; Kasprzak et al., this issue] which leads to the following conclusions: (1) For localized sources (2 km thick) in the lower atmosphere (at 80 km or below) and thermosphere (at 130 km), of the same magnitude day and night, the computed wave amplitudes at satellite altitudes are about a factor of three to five larger during the night than during the day; in substantial agreement with the observations. The difference is due to the large night to day increase in the thermospheric temperature. (2) Waves excited in the lower atmosphere propagate more obliquely, and geometric attenuation as well as dissipation are less important. Thus extended wave trains are produced that can simulate the data. (3) Waves excited in the thermosphere (at 130 km) are rapidly attenuated. Although such signatures are also observed in the data, they could also be produced by an impulsive perturbation propagating up from the lower atmosphere. (4) For the wavelengths observed, the wave periods are between 30 and 60 min. (5) Due to wind induced diffusion, the computed wave amplitudes for the three species are of comparable magnitude, that of CO2 being largest; and He varies out of phase with the heavier gases; reproducing the observed behavior.

Star-forming instabilities of a decelerating plane-parallel slab of finite thickness

In order to study how supernova blast waves might catalyze star formation, the stability of a slab of decelerating gas of finite thickness is explored. Previous analyses are extended by applying shock-like boundary conditions to the leading edge of the slab and by studying the effects of arbitrary deceleration. Contrary to some earlier claims, it is found that blast waves can indeed accelerate the rate of star formation in the interstellar medium by compressing the interstellar gas and enabling it to cool. Also, it is demonstrated that in an incompressible fluid, the symmetric and antisymmetric modes in the case of zero acceleration transform continuously into Rayleigh-Taylor and gravity-wave modes as acceleration grows more important. The dynamical overstability of an isothermal shock wave and its implications for star formation are discussed.

The modulation of short gravity waves by long waves or currents

AbstractThe modulation of short gravity waves by long waves or currents is described for the situation when the flow is irrotational and when the short waves are described by linearised equations. Two cases are distinguished depending on whether the basic flow can be characterised as a deep-water current, or a shallow-water current. In both cases the basic flow has a current which has finite amplitude, while in the first case the free surface slope of the basic flow can be finite, but in the second case is small. The modulation equations are the local dispersion relation of the short waves, the kinematic equation for conservation of wave crests and the wave action equation. The results incorporate and extend the earlier work of Longuet-Higgins and Stewart [10, 11].

Eigenstructure of eddy microfronts

Aircraft measurements of strong turbulence in a bora flow and in weak intermittent turbulence near the top of a nocturnal surface inversion layer are examined. An important feature of both types of turbulence are narrow zones of sharp gradients of velocity and temperature. These concentrated gradients, which are referred to as fronts in laboratory turbulence, are studied here by applying conditional sampling criteria and analyzing the eigenvectors of the resulting lagged multivariate covariance matrix. In addition, a new technique is developed which specifies a weighting function instead of specific selection criteria with cutoff values. The mathematics derived for the new technique leads to the usual eigenvalue problem for principal components except that the covariance matrix becomes transformed. The above analyses indicate that the eddy microfronts seem to be related to the relative horizontal motion of the drafts generated by vertical motions in shear flows. The horizontal gradients are sharpest at the upstream edge of the drafts where convergence occurs between the horizontal motion of the draft and the horizontal motion of the ambient air. For strong turbulence, the eigenstructures identify several stages of eddy transport consistent with shear-driven overturning and transverse vorticity. For intermittent turbulence in strongly stratified flow, the eigen structures indicate the predominance of two-dimensional modes which coexist with overturning eddies and gravity wave modes. DOI: 10.1111/j.1600-0870.1988.tb00410.x

Group Velocity and the Linear Response of Stratified Fluids to Internal Heat or Mass Sources

Abstract A steadily maintained line heat or mass source turned on in an unbounded, steadily moving, uniformly stratified flow will in general create ever-increasing vertical displacements of the fluid. Lin and Smith viewed a maintained heat source as a train of heat pulses. A pulse occurring a time T before the observation time creates a negative displacement proportional to T−1 at the heat source position when T is large. They pointed out that superposing the pulse responses leads to a displacement that grows logarithmically with time. This paper uses group velocity arguments to recreate the gravity wave field a time T after a heat pulse. The T−1 decay of the displacement is shown to be a geometrical consequence of dispersion in two dimensions. The growing response to a maintained source can be understood as the result of energy being pumped into the gravity wave modes, whose group velocity is near zero, faster than it can spread in physical space due to dispersion. A steady response is shown to be possi...

Gravitational and Dynamical Instabilities of a Decelerating Plane-Parallel Slab of Finite Thickness

AbstractIn order to explore how supernova blast waves might catalyze star formation, we investigate the stability of a slab of decelerating gas of finite thickness. We examine the early work in the field by Elmegreen and Lada and Elmegreen and Elmegreen and demonstrate that it is flawed. Contrary to their claims, blast waves can indeed accelerate the rate of star formation in the interstellar medium. Also, we demonstrate that in an incompressible fluid, the symmetric and antisymmetric modes in the case of zero acceleration transform continuously into Rayleigh-Taylor and gravity-wave modes as acceleration grows more important.

Global excitation of wave phenomena in a dissipative multiconstituent medium: 3. Response characteristics for different sources in the Earth's thermosphere

Using a transfer function model for the earth's thermosphere, we have previously discussed the properties of different wave modes and impulsive perturbations excited by Joule heating. The thermospheric response showed the expected propagating waves, but a significant part of the perturbation, the trapped component, remained confined to the source region. In the present paper we expand the analysis to include the electric field momentum source. We discuss the effects of these excitation mechanisms on the trapped component confined to the source region and on the propagating gravity waves emanating from the source. Our analysis leads to the following conclusions: (1) for Joule/particle heating, the temperature and density perturbations contain a relatively large trapped component which has the property of a low‐pass filter, with slow decay after the source is turned off. The decay time is sensitive to the altitude of energy deposition and is significantly reduced as one moves the source peak only from 125 to 150 km. (2) For electric field momentum coupling, the trapped components in the temperature and density perturbations are relatively small. In the curl field of the velocity, however, the trapped component dominates, but compared with the temperature (and density), its decay time is much shorter. (3) Outside the source region the form of excitation is of secondary importance for the generation of the various propagating gravity wave modes (direct, reflected, and ducted). Different atmospheric variables, however, respond differently. The model has been extended to allow for incoherence in the excitation sources, which is necessary to simulate the stochastic nature of auroral processes, and a numerical experiment is presented elucidating some salient features of the thermospheric response. Observations at times show long temperature and density decay times (order of days) in the source region, yet at other times the decay time is much shorter (order of hours). Differences in the excitation mechanism studied, e.g., the altitude of energy deposition, may be responsible for the apparent disparity.

Effects of atmospheric disturbances on polar mesopause airglow OH emissions

Temporal variations in the absolute intensity (I) and the rotational temperature (T) of the polar winter airglow OH(8, 3) bands were observed over Longyearbyen, Spitsbergen (78.2°N), in December 1984. The high latitude of the observatory places it in a continuous polar night around the winter solstice period, thereby permitting 24‐hour optical measurements. Spectral analyses of the I and T time series reveal a dominant semidiurnal component and a wave with a period of 3.7 hours. Other waves with shorter periods may be present for part of the total observing period, but the signal‐to‐noise ratios of their amplitudes averaged over a 24‐hour interval are too low to permit definitive identification. The ratio η of the correlated Fourier components of (I − Ī)/Ī to that of (an overbar signifies time average) has amplitude 3.2 ± 0.9 and 4.3 ± 1.3 for the 12‐ and 3.7‐hour waves, respectively, while the phase ϕ of η for these periods is 6° ± 16° and −12° ± 12°. The value of η for the 3.7‐hour wave can be compared with the theoretical prediction of η for gravity wave modulation of the OH emission. For an emission height of 87 km and an atomic oxygen scale height ℋ(O) of −2 km, theory gives |η| = 4.2 and ϕ = 0° for the 3.7‐hour wave, in good agreement with the observation. The theoretical interpretation of η at the 12‐hour period is complicated by the likelihood that the observed semidiurnal oscillation is not a simple tide. For tidal modulation of the OH nightglow, theory gives |η| between 2.6 and 0.9 and ϕ between 0° and 10° for high‐order semidiurnal modes and for the same values of emission height and ℋ(O) as above.

Linear theory of the urban heat island circulation

A linear time-dependent model of the urban heat island circulation is developed for use in situations with a marked inversion. It has the external and first-internal gravity wave modes as basic dynamic ingredients (the inversion is treated as a ‘free’ surface). The background wind field may vary with height and in time, and the Coriolis acceleration, though not important in most cases, is taken into account. The model equations are formulated in two-D (horizontal) Fourier space, permitting a fully implicit scheme to be used. Large time steps can then be employed, so that the external mode is implicitly in balance, while the internal mode slowly evolves. The value of the model lies in its efficiency: with 1600 two-D Fourier components and a 1-h time step, a 10-h integration typically takes 20 s of central processor time on a Cyber 175. The model is thus suitable for use in connection with operational air quality models running on smaller computers. Another advantage over more complete mesoscale atmospheric models is that initialization is very simple. Various examples are discussed to illustrate the performance of the model.

Horizontal and vertical winds and temperatures in the equatorial thermosphere: Measurements from Natal, Brazil during August–September 1982

Fabry-Perot interferometer measurements of Doppler shifts and widths of the 630.0 nm nightglow line have been used to determine the neutral winds and temperatures in the equatorial thermosphere over Natal, Brazil during August–September 1982. During this period, in the early night (2130 U.T.) the average value of the horizontal wind vector was 95 m s −1 at 100° azimuth, and the temperature varied from a low of 950 K during geomagnetically quiet conditions to a high of ~ 1400 K during a storm (6 September). The meridional winds were small, ≲, 50 m s −1, and the eastward zonal winds reached a maximum value 1–3 h after sunset, in qualitative agreement with TGCM predictions. On 26 August, an observed persistent convergence in the horizontal meridional flow was accompanied by a downward vertical velocity and an increase in the thermospheric temperature measured overhead. Oscillations with periods of 40–45 min in both the zonal and vertical wind velocities were observed during the geomagnetic storm of 6 September, suggesting gravity wave modulation of the equatorial thermospheric flow.

Multilayer Hydraulic Control with Application to the Alboran Sea Circulation

Abstract The flow of a single layer of fluid along a channel of variable dimensions is hydraulically controlled when long gravity waves can no longer propagate upstream at the cross-section of minimum area. For a multilayer fluid, it is shown that a controlled situation exists when there is a separate geometrical extremum for each of the gravity wave modes. The structure of each control section must be different, reflecting the different vertical structures of the internal modes. A channel with three layers of different density is studied in some detail as an analogue to the principal water masses in the Alboran Sea and Strait of Gibraltar. With the lowest layer at rest and the surface rigid, the control for the slowest second internal mode is primarily a width contraction while that for the first mode must also involve a reduction in bottom depth. The problem separates into control problems for each mode. That for the first mode is a classic lock exchange problem with just two layers (controlled at the S...

Comment on “On ‘potential’ well treatment for atmospheric gravity waves” by L. Yu et al. and “A dispersion formula for analyzing ‘modal interference’ among guided and free gravity wave modes and other phenomena in a realistic atmosphere” by T. F. Tuan and D. Tadic

Comment on “On ‘potential’ well treatment for atmospheric gravity waves” by L. Yu et al. and “A dispersion formula for analyzing ‘modal interference’ among guided and free gravity wave modes and other phenomena in a realistic atmosphere” by T. F. Tuan and D. Tadic

Reply [to “Comment on ‘On ‘potential’ well treatment for atmospheric gravity waves’ by L. Yu et al. and ‘A dispersion formula for analyzing ‘modal interference’ among guided and free gravity wave modes and other phenomena in a realistic atmosphere’ by T. F. Tuan and D. Tadic”

Reply [to “Comment on ‘On ‘potential’ well treatment for atmospheric gravity waves’ by L. Yu et al. and ‘A dispersion formula for analyzing ‘modal interference’ among guided and free gravity wave modes and other phenomena in a realistic atmosphere’ by T. F. Tuan and D. Tadic”

Instabilities in a Stratified Fluid Having One Critical Level. Part I: Results

We consider instabilities in a stratified Boussinesq fluid with basic velocity Uo(z). We initiate this study by considering the detailed stability properties of a profile where Uo(z) is constant in a top and bottom layer and varies linearly with z in an intermediate layer. For an infinite fluid, we find, in addition to Kelvin-Helmholtz instabilities similar to those found by Miles and Howard (1964), an unstable gravity wave mode propagating energy away from exactly one side of the shear zone if and only if the Richardson number in the shear zone is less than 0.1164±0.0001. With a lower boundary present, we find gravity wave instabilities propagating above as well as below the shear zone can exist only when the Richardson number is less than 0. 116. The ability of a shear zone to sustain instabilities propagating energy to infinity on one side is hence only present when the Richardson number is less than 0.116, whether or, not the ground is present. With a lower boundary present, we also find gravity wave instabilities evanescent above the shear zone for Richardson numbers up to 0.2499. After an exhaustive search involving varying the height of the shear zone above the ground and the wavenumber k, we conclude that, for any Richardson number less than ¼, the growth rates of gravity wave instabilities can be as much as, but not greater than, 26% of the maximal growth rates for Kelvin-Helmholtz instabilities having a critical level with the same Richardson number as the gravity wave instabilities have. Even though the relative importance of gravity wave instabilities can be significantly greater than found by other investigators (e.g., Davis and Peltier, 1976), the largest growth rates are still associated with Kelvin-Helmholtz instabilities. In order to understand the basis for this behavior we will analyze, in subsequent parts, both types of instability in terms of wave overreflection. This will enable us to show that the relative importance of Kelvin-Helmholtz and gravity wave instabilities is by no means universal.