Frequency Gravity Waves Research Articles

Homogeneous turbulence evolution in stably stratified flow—I. Internal gravity waves at low inverse Froude numbers

Abstract The evolution of homogeneous grid-generated turbulence in stratified fluid is investigated analytically. A small parameter decomposition on inverse Froude number is applied to the theory of nearly homogeneous turbulence developed earlier in refs. [1] and [2]. Applying the multiple scale method we calculate the frequency and amplitude of internal gravity waves and formulate differential system describing the wave-averaged behaviour of turbulence characteristics. The comparison with the numerical results published in [2] and with known experimental data shows a very good agreement as to internal waves as to small scale turbulence in collapsed state. The long-term turbulence evolution in weakly stratified media can be regarded as a singular perturbation problem permitting us to gain an insight into the interaction between gravity waves and active turbulence.

Angular Momentum Transport by Gravity Waves and Its Effect on the Rotation of the Solar Interior

We calculate the excitation of low frequency gravity waves by turbulent convection in the sun and the effect of the angular momentum carried by these waves on the rotation profile of the sun's radiative interior. We find that the gravity waves generated by convection in the sun provide a very efficient means of coupling the rotation in the radiative interior to that of the convection zone. In a differentially rotating star, waves of different azimuthal number have their frequencies in the local rest frame of the star Doppler shifted by different amounts. This leads to a difference in their local dissipation rate and hence a redistribution of angular momentum in the star. We find that the time scale for establishing uniform rotation throughout much of the radiative interior of the sun is $\sim 10^7$ years, which provides a possible explanation for the helioseismic observations that the solar interior is rotating as a solid body.

A reinterpretation of the data from the NASA Stratosphere‐Troposphere Exchange Project

Data obtained during the NASA Stratosphere Troposphere Exchange Project (STEP) Mid‐Latitude Field Experiment displayed laminae of ozone, water, and condensation nuclei in the stratosphere in association with a mid‐latitude stratosphere‐troposphere folding event. Danielsen et al. (1991) constructed cross sections of these observations, and interpreted these quasi‐horizontal laminae as evidence of ultra‐low frequency gravity waves. We use a new technique to show that these laminae could have resulted from differential advection, rather than transport by ultra‐low frequency gravity waves. This new technique uses reverse domain filling back trajectories on multiple isentropic surfaces in conjunction with modified potential vorticity to reveal the qualitative details of the constituent laminae.

Polar stratospheric clouds at the South Pole in 1990: Lidar observations and analysis

In December 1989 a Rayleigh/sodium lidar (589 nm) was installed at the Amundsen‐Scott South Pole station, and was used to measure stratospheric aerosol, temperature, and mesospheric sodium profiles through October 1990. Observations of stratospheric aerosol and temperature are presented in this paper. Polar stratospheric clouds (PSCs) were first observed in late May at about 20 km. As the lower stratosphere cooled further, PSCs were observed throughout the 12–27 km altitude region, and remained there from mid‐June until late August. Observations in early September detected no PSCs above 21 km. An isolated cloud was observed in mid‐October. Throughout the winter the clouds had small backscatter ratios (< 10). Observations made at two wavelengths in July show that the clouds are predominately composed of nitric acid trihydrate with associated Angstrom coefficients between 0.2 and 3.7. Comparison of the lidar data and balloon borne frost point measurements in late August indicate that the nitric acid mixing ratio was less than 1.5 ppbv. Observations over periods of several hours show downward motions in the cloud layers similar to the phase progressions of upwardly‐propagating gravity waves. The vertical phase velocities of these features (≈ 4 cm/s) are significantly faster than the expected settling velocities of the cloud particles. Both the backscatter ratio profiles and the radiosonde horizontal wind profiles show 1–4 km vertical structures. This suggests that the kilometer‐scale vertical structure of the PSCs is maintained by low frequency gravity waves propagating through the cloud layers.

Wave‐wave interactions in a compressible atmosphere: 1. A general formulation including rotation and wind shear

We present here a formulation of the resonant and nonresonant interactions among gravity waves, acoustic waves, and vortical modes in the atmosphere under the weak interaction approximation. This work generalizes previous studies by including the effects of rotation and wind shear. Rotation influences both wave and vortical mode structures, while wind shear is shown to influence the relative frequencies of gravity waves and vortical modes and thus may alter the conditions for gravity wave‐vortical mode interactions occurring in its absence. The theory is applied in the absence of rotation and is shown to permit interactions that depend in a complex manner on the gravity wave and vortical mode characteristics and relative orientation and on the mean wind shear. In a companion paper we apply this formalism in a study of the influences of variable stratification and inhomogeneity on resonant and nonresonant interactions.

Predictions and observations of seafloor noise generated by sea surface orbital motion.

A model is developed for the prediction of the seismo-acoustic noise spectrum in the microseism peak region (0.1 to 0.7 Hz). The model uses a theory developed by Cato [J. Acoust. Soc. Am. 89, 1096–1112 (1991)] for an infinite depth ocean in which the surface orbital motion caused by gravity waves may produce acoustic waves at twice the gravity wave frequency. Using directional wave spectra as inputs, acoustic source levels are computed and incorporated into a more realistic environment consisting of a horizontally stratified ocean with an elastic bottom. Noise predictions are made using directional wave spectra obtained from the SWADE surface buoys moored off the coast of Virginia and the SAFARI sound propagation code, with a bottom model derived using wave speeds measured in the EDGE deep seismic reflection survey. The predictions are analyzed for noise level variations with frequency, wave height, wind direction, and receiver depth. These predictions are compared to noise measurements made in ECONOMEX using near-bottom receivers located close to the surface buoys. Good agreement is found between the predictions and observations under a variety of environmental conditions. [Work supported by ONR.]

Wind shear rotary spectra in the atmosphere

In this paper we present the first rotary spectra of the horizontal wind shear measured in the stratosphere with a resolution of 25m. A low frequency gravity wave propagating upward with a vertical wavelength of ≈ 1000 m is clearly identified. This result is quite consistent with many previous observations and may explain why the horizontal velocity spectra may be biased and indicates a power variation law versus vertical wave number steeper than those of both temperature and vertical velocity. Nevertheless, around the small vertical wavelengths (100 m), the asymptotic slope of temperature and horizontal velocity spectra are both close to ‐3 and so in better agreement with the saturated model predictions.

Reconstruction of the vertical structure of internal waves in the troposphere from multifrequency measurements in the O2 lines

The observed frequencies of internnal gravity waves (IGWs) and their contribution to the variability of the brightness temperatures were determined on the basis of spectral analysis of the temporal dynamics of the thermal radio emission of the atmosphere at the frequencies 53.5, 54.0, 54.5, and 55.0 GHz. Methods for reconstructing from multifrequency measurements in the O2 lines the altitude distribution of the perturbation of the temperature of IGWs from the spectral amplitudes of their contribution to the brightness temperature were developed.

On the Anelastic Approximation for Deep Convection

Abstract A brief review of the scale analysis of Lipps and Hemler is given without any reference to the parameters G and B. The resulting anelastic equations conserve energy, in contrast to the modified anelastic set of equations analyzed by Durran. In addition, the present equations give an accurate solution for the frequency of gravity waves in an isothermal atmosphere. The present anelastic equations have these characteristics in common with the pseudo-incompressible equations introduced by Durran. The equations obtained from the scale analysis are appropriate for numerical integration of deep convection. The associated Poisson equation can be solved using standard procedures. For the pseudo-incompressible set of equations, the Poisson equation is more difficult to solve.

Stability Analysis of Inertio—Gravity Wave Structure in the Middle Atmosphere

We present a stability analysis of the environment due to a large-amplitude inertio—gravity wave. Our purpose is to examine the conditions under which the Kelvin-Helmholtz (KH) instability may be an effective wave saturation process in the middle atmosphere. The concurrence, range of wavenumber, and growth rate of the KH instability are shown to depend on the IGW frequency and the KH orientation within the wave field because of the influence of wave frequency on the shear and local stratification. Results of the analysis indicate that the KH instability is likely a preferred mode of instability for sufficiently low gravity wave frequencies, but that it cannot occur for high-frequency wave motions in the absence of a mean shear. Inertio—gravity waves are also most unstable to KH instabilities aligned transverse to the direction of large-scale wave propagation.

Low frequency gravity wave spectra generated by cosmic strings

Gravity wave spectra generated by populations of cosmic string loops are computed, showing that loop evolution and radiation properties have important effects at observable wavelengths. The spectra are compared with limits derived from various observations; bounds from millisecond pulsar timing are becoming severe for several string scenarios, but implied constraints on string parameters depend sensitively on details of the loop population and dynamics.

Postset beam steering and interferometer applications of VHF radars to study winds, waves, and turbulence in the lower and middle atmosphere

Spaced antenna VHF radar measurements are utilized for the postset beam steering technique and for interferometer applications to study winds, waves, and turbulence in the stratosphere and mesosphere. Following a brief description of the basic instrumental setup and the off‐line analysis method, some results are presented which demonstrate the consistency and applicability of these methods. Vertical velocity oscillations due to gravity waves are analyzed by means of the cross‐spectrum technique. It is shown that phase differences of gravity wave oscillations, measured between vertical and two opposite, off‐vertical postset beams, change their sign when the beam is swung back and forth. The same features of change of velocity sign are noticed when the mean wind is observed. The mean wind deduced with the postset beam steering technique is similar to the wind deduced with the spaced antenna drift technique and the independent radiosonde winds. Taking these results as justification for the applicability and feasibility of the postset beam steering method, the total wave vector and the intrinsic angular frequency of gravity waves in the stratosphere are deduced. Reasonable arguments are discussed to support the suggestion that these waves were generated in lower stratosphere wind shear regions and were attenuated little when propagating up to the middle stratosphere. Turbulence blobs in the mesosphere are tracked with the interferometer technique. It is shown that these blobs moved horizontally as well as vertically, a feature which cannot unequivocally be detected with conventional Doppler methods.

Some characteristics of internal gravity waves in the equatorial Pacific

One‐year moored current and temperature measurements made in the central equatorial Pacific Ocean at subthermocline depths display spectral characteristics at internal gravity wave frequencies which are distinct from those found at mid‐latitudes. These characteristics are meridional orientation of current ellipses, kinetic energy scaling proportional to (buoyancy frequency)1.2, and coherence of zonal current and temperature at phases significantly different then 0° or 180°. Characteristics vary over as little as 100 m vertically but not over 40 km horizontally. Low‐frequency flow is predominantly zonal and shares similar spatial structure, suggesting internal waves are influenced by it. Although horizontal internal wave fluxes cannot be calculated directly from the observations, models provide a framework in which to interpret internal wave spectral characteristics. Models of internal waves near the equator in a resting ocean, an ocean with a uniform zonal current, and an ocean with depth‐dependent zonal current all require wave flux to be horizontally anisotropic in order to obtain current ellipses and zonal current‐temperatures similar to those observed. The model with vertical shear is the most realistic of these three. Observed shears are sufficiently strong to allow the possibility of internal wave critical layers, which in turn are a likely source of both horizontal anisotropy and vertical asymmetry of wave fluxes.

経済的なエクスプリシット時間差分スキームの開発

An economical explicit scheme and its application to a primitive equation model is described. In the present scheme, the low-frequency advection terms are integrated by the leap-frog scheme with a time step interval Δta which is decided by a wind speed of meteorological waves, and not by a gravity wave phase speed. In order to get stable numerical solution, the high frequency gravity wave terms are integrated with a shorter time interval Δtb(≅Δta/M). Time integrations are carried out by combining low frequency terms which are assumed constant during 2Δta leap-frog time extrapolation interval with high frequency terms which are calculated at every Δtb interval. The scheme is three-time-level for low frequency terms. The present scheme is different from the splitting technique proposed by Marchuk (1965).The present economical explicit scheme has the advantage of the easiness in programming and the second order accuracy in the integration of low frequency terms.The present scheme has been applied to the 4L-NHM, operational 4-level northern hemispherical model used in 1978-81 in JMA. The results show that the economical explicit version model produces almost the same prediction as the original (explicit scheme) 4L-NHM. The present scheme saved the computation time as much as the semi-implicit version of 4L-NHM developed by Kudoh (1978) did.

Polygonal Eye Walls and Rainbands in Hurricanes

Abstract It was noted from analyses of radar data obtained in hurricanes that both the spiral bands and the inner boundary of the wall cloud frequently were composed of a series of straight line segments. Indeed, the eye of a strong hurricane is frequently polygonal rather than circular or elliptical. These features may have a possible kinematic explanation based an interference among differing wavenumbers and frequencies of internal gravity waves.

Nonlinear theory of acoustic-gravity waves 2. Frequency shifts

A nonlinear dispersion relation is derived for acoustic-gravity waves which includes nonlinear frequency shifts as well as nonlinear damping decrements (attenuations). The nonlinear damping decrement was derived in a previous paper. Here, a calculation is made of the nonlinear frequency shift. This calculation is based on the method of perturbed particle orbits (perturbed orbits). Explicit expressions are derived for the frequencies of gravity waves in terms of the mean square wave amplitude and wave spectrum. When the spectrum is narrow, it is found that nonlinearities can increase the frequency by as much as a factor of 2 for strong nonlinearities. It also is found that the qualitative features are not significantly changed by nonlinearities when the spectrum is narrow. These results confirm previous speculations by Hines that were based on heuristic arguments. It is also shown that nonlinear effects can be stronger when the spectrum is broad, in which case qualitative changes are possible.

On Resonant Interactions of Acoustic Gravity Waves

The method of averaging in the study of nonlinear oscillations is applied to the problem of resonant wave‐wave interaction of a nonlinear dispersive wave system. The simplicity and directness of the method make it possible to study rather general and complex systems. Two examples are treated, one is posed as an initial value problem and the other as a boundary value problem. The second example deals with the acoustic‐gravity wave system in the atmosphere. It is found that resonant condition can be satisfied for the three‐wave system for which one of the waves is the zero frequency gravity wave. Through resonant interaction, the other two waves become trapped. The trapping depth is plotted for typical atmospheric parameters.

Mass transport in rotatory tidal currents

A perturbation method is used to calculate steady non-linear effects in rotatory tidal currents. The inclusion of the Coriolis acceleration leads to a uniquely determined second order current system in the tidal stream. This is shown to be absent in high frequency gravity waves. It is found that particle drift, or mass transport, is critically dependent on this mean current, and consequently on the value off/σ,f being the Coriolis parameter, and σ the angular frequency of the oscillation.

Experiments on the frequency of finite-amplitude axisymmetric gravity waves in a circular cylinder : Fultz, D., and T. S. Murty, 1963. J. Geophys. Res., 68 (5): 1457–1462.

Experiments on the frequency of finite-amplitude axisymmetric gravity waves in a circular cylinder : Fultz, D., and T. S. Murty, 1963. J. Geophys. Res., 68 (5): 1457–1462.

Experiments on the frequency of finite-amplitude axisymmetric gravity waves in a circular cylinder

Experiments are reported which confirm Mack's prediction that the fundamental symmetric standing wave on a layer of liquid in a circular cylinder will increase in frequency as the amplitude increases for a shallow layer but decrease in frequency for deep layers. The depth-diameter ratio at which the frequency effect reversal occurs is found to be about 0.054. The predicted ratio is 0.111.