Gravity Wave Spectrum Research Articles

Seasonal Variation of Gravity Wave Spectrum Near the Polar Mesopause

使用MAP/WINE和MAC/SINE两次试验中测量的25 m高分辨率水平速度数据和1 km低分辨率温度数据,研究极区中层顶区域重力波谱的季节变化.温度的直接测量使计算的谱振幅和Richardson数更接近真实大气.结果显示,极区中层顶区域水平速度垂直波数谱的斜率和振幅存在相当大的变率,这些大的观测变率用各种饱和模式及普适垂直波数谱不能解释.然而平均垂直波数谱显示了明显的季节变化,在夏季,平均谱具有饱和特性;在冬季,平均谱具有非饱和特性.这意味着饱和过程存在于夏季而不是冬季.因此,夏季比冬季应有更强的湍流.这个结果与湍流季节变化的观测大致一致.从Brunt-Vaisala频率N和水平风切变计算的Richardson数Ri剖面也显示出季节差异,Ri＜1/4的动力不稳定区出现在夏季,而Ri＞0.4的稳定区出现在冬季.这些不稳定区与夏季谱结合很好,而稳定区则与冬季谱结合很好.

A mechanism of the effect of non-uniform current on the spectrum of short wind waves

A mechanism is suggested in this paper concerning the effect of non-uniform current on the spectrum of short wind waves. According to this mechanism, a non-uniform current brings changes to the breaking criteria of short wind waves through modulating the surface drift, and hence enhances or weakens wave breaking. Some modification is proposed to the source term, which represents the spectral rate of wave energy dissipation due to wave breaking so that the source term can incorporate this mechanism. In order to illustrate whether this mechanism is significant, a real case is studied, in which the wind waves propagate on a tidal current flowing over the sea bottom covered with sand waves. Finally, the effect of the new mechanism on the equilibrium spectrum of small scale gravity waves is discussed. Numerical estimates suggest that, for water depths less than 50 m and wavelengths less than 1 m, this current field may result in distinct spatial variations of the wave breaking criteria, the spectral rate of wave energy dissipation and the equilibrium spectrum of short gravity waves.

Gravity Wave Generation by a Three-Dimensional Thermal Forcing

Abstract Thermal forcing is one of the mechanisms of wave generation in convection. Although it does not account for all the wave generation mechanisms, thermal forcing is a good proxy for estimating the gravity wave spectrum forced by convection. This work presents a linear theory of gravity wave generation by a three-dimensional thermal forcing assuming constant mean wind conditions in the forcing region. Relationships are derived linking the amplitude and spectral characteristics of the generated gravity waves to the properties of the thermal forcing. It is shown that the three-dimensional problem can be viewed as a multiple two-dimensional problem by means of a squire transformation and that the gravity wave properties in a given azimuthal direction depend on the projection of the heating and environmental mean wind in that direction. Shown in detail is the sensitivity of the gravity wave characteristics in three dimensions to varying heating parameters, and it is concluded that the knowledge of both ...

Some inferences on turbulence generation by gravity waves

We analyze data from 17 high‐resolution thermosonde observations during a campaign near Adelaide, Australia, in 1998. We are able to explain the observed turbulence fractions by extending the turbulence model of Hines [1991], which explains turbulence by instabilities due to freely propagating independent gravity waves, from the hydrostatic wave regime toward lower frequencies. In a Monte Carlo simulation we show that the dependency of the observed gravity wave spectrum on vertical wave number is also consistent with the distribution of turbulent layer thickness as observed by the high‐resolution thermosondes.

Thermospheric responses to gravity waves arising from mesoscale convective complexes

We employ a linear model of the responses to local body forces to estimate the spectra of gravity waves arising due to vertical motions within mesoscale convective complexes (MCCs) at equatorial latitudes. Ray tracing methods are then used to propagate these spectra through model wind and temperature fields and to anticipate their thermospheric effects. We find that gravity wave forcing by MCCs is dominated by large vertical motions of limited horizontal extent, that individual convective cells within an MCC effectively act as independent sources of gravity waves if they are separated by two or more diameters, and that vertical body forces create higher-frequency gravity waves than comparable horizontal body forces. Ray tracing reveals that of the gravity waves excited by MCCs, only the high-frequency, long-vertical-wavelength portions of the refracted spectrum (above the shear) can penetrate to high altitudes, that variable winds impose significant anisotropy on the surviving gravity waves, that refraction and dissipation determine the portion of the MCC wave spectrum important in the lower thermosphere, and that large net momentum flux divergence may lead to strong local body forcing well into the thermosphere. Gravity waves excited by MCCs and having sufficiently large vertical wavelengths and group velocities above the shears at lower altitudes can penetrate to altitudes at which they may be expected to contribute to the seeding of equatorial spread F.

A search for mountain waves in MLS stratospheric limb radiances from the winter Northern Hemisphere: Data analysis and global mountain wave modeling

Despite evidence from ground‐based data that flow over mountains is a dominant source of gravity waves (GWs) for the Northern Hemisphere winter middle atmosphere, GW‐related signals in global limb radiances from the Microwave Limb Sounder (MLS) on the Upper Atmosphere Research Satellite (UARS) have shown little direct evidence of mountain waves. We address this issue by combining a renewed analysis of MLS limb‐track and limb‐scan radiances with global mountain wave modeling using the Naval Research Laboratory Mountain Wave Forecast Model (MWFM). MLS radiance variances show characteristics consistent with mountain waves, such as enhanced variance over specific mountain ranges and annual variations that peak strongly in winter. However, direct comparisons of MLS variance maps with MWFM‐simulated mountain wave climatologies reveal limited agreement. We further develop a detailed “MLS GW visibility function” that accurately specifies the three‐dimensional in‐orbit sensitivity of the MLS limb‐track radiance measurement to a spectrum of GWs with different wavelengths and horizontal propagation directions. On postprocessing MWFM‐generated mountain wave fields through these MLS visibility filters, we generate MWFM variance maps that agree substantially better with MLS radiance variances. This combined data analysis and MLS‐filtered MWFM modeling leads us to conclude that many MLS variance enhancements can be associated with mountain waves forced by flow over specific mountainous terrain. These include mountain ranges in Europe (e.g., Scandinavia; Alps; Scotland; Ural, Putoran, Altai, Hangay and Sayan Mountains; Yablonovyy, Stanovoy, Khingan, Verkhoyansk and Central Ranges), North America (e.g., Brooks Range, MacKenzie Mountains, Colorado Rockies), southeastern Greenland, and Iceland. Our results show that given careful consideration of the in‐orbit sensitivity of the instrument to GWs, middle atmospheric limb radiances measured from UARS MLS, as well as from the new MLS instrument on the Earth Observing System (EOS) satellite, can provide important global information on mountain waves in the extratropical Northern Hemisphere stratosphere and mesosphere.

A Method of Specifying the Gravity Wave Spectrum above Convection Based on Latent Heating Properties and Background Wind

Abstract The spectrum of convectively generated gravity waves is currently not resolved in general circulation models and must be parameterized. Due to the lack of understanding of the connection between convection properties and gravity waves, such parameterizations assume a source spectrum of gravity waves that is not linked to the forcing region. This paper introduces a method of specifying the gravity wave spectrum above convection based on the latent heating properties and background wind in the convective region that can be implemented in general circulation models. This method is based on linear calculations of momentum flux generated by a multifrequency thermal forcing and incorporates the effects of tropospheric mean wind in the convective environment. In the analysis, gravity waves that are generated by both the steady and the oscillatory component of the heating are included. It is shown that an accurate spectrum of convectively generated gravity waves can be deduced from the knowledge of appro...

A study of seasonal variations of gravity wave intensity in thelower thermosphere using LF D1 wind observations and a numerical model

Abstract. The data of the regular low-frequency D1 E-region observations at Collm, Germany (52°N, 15°E) in 1983–1999 are used for estimations of the intensity of short-period perturbations of the horizontal drift velocity at 85–110 km altitude. A simple half-hourly-difference numerical filter is used to extract perturbations with time scales of 0.7–3 h. The average monthly standard deviations of short-period perturbations of the zonal velocity near altitude 83 km have a main maximum in summer, a smaller maximum in winter, and minimum values at the equinoxes. At higher altitudes the summer maximum is shifted towards the spring months, and a second maximum of perturbation amplitudes appears in autumn at altitudes near and above 100 km. The seasonal changes in the standard deviations of meridional velocity show the maxima in spring and summer. A numerical model describing the propagation of a set of harmonics modeling a spectrum of internal gravity waves in the atmosphere is used for the interpretation of observed seasonal variations of wind perturbation intensity. Numerical modeling reveals that the observed altitude changes in the seasonal variations of the drift velocity standard deviations may be explained by a superposition of IGWs generated at different levels in the troposphere and middle atmosphere. IGWs generated in the stratospheric and mesospheric jet stream may have substantial amplitudes at altitudes near and above 100 km, where they may modify the seasonal variations, which are typical for IGWs propagating from the troposphere. Key words. Meteorology and atmospheric dynamics (middle atmosphere dynamics; waves and tides) – Ionosphere (ionospheric irregularities)

Gravity waves in the tropical middle atmosphere: Characteristics and wave-mean flow interaction

High-resolution Rayleigh lidar observations of temperature in the altitude region of 27–60 km over Gadanki (13.5°N, 79.2°E) during the period of January 18 to March 5 1999 and February 29 to March 31 2000 were used to study the gravity wave characteristics in the tropical middle atmosphere. The vertical wavenumber spectra of gravity waves and the altitude variation of the potential energy per unit mass (Ep) associated with gravity wave activity are found to be similar during both these years. Altitude profile of E p indicates that significant wave damping occurs in the stratosphere while nearly non-dissipating gravity wave growth is observed in the lower mesosphere. The slope of the vertical wave number spectra is observed to be about −2.1, which is less than that expected for saturated spectra (−3). The gravity wave activity in the stratosphere and lower mesosphere is found to undergo temporal variations, which are correlated with the temperature fluctuations in the middle atmosphere. A longer period wave with a mean vertical wavelength of about 12.8 km and wave period of about 8–14 hours is also observed on several nights.

Orographic Gravity Waves Close to the Nonhydrostatic Limit of Vertical Propagation

Orographic gravity waves excited by a narrow mountain ridge are investigated with the aid of numerical simulations. When the nondimensional mountain half-width Na/U is around 1—N, a, and U being the Brunt–Väisälä frequency, the dimensional half-width, and the ambient wind speed, respectively—only part of the gravity wave spectrum excited by the mountain is able to propagate vertically. In this case, linear theory, as well as numerical simulations with low mountains, show two wind maxima: one at the mountain crest and one in the lee of the mountain. As Na/U is reduced below 1, the wind maximum in the lee weakens and moves farther downstream, and the maximum at the crest intensifies rapidly with decreasing Na/U. Simulations in which a gap with a level axis is embedded in the mountain ridge demonstrate that the wind perturbations along the gap axis are qualitatively similar to those over the adjacent mountain ridge. However, their magnitude is substantially lower, and the tendency to form a wind maximum at the gap center (corresponding to a maximum at the mountaintop) is rather weak. When the mountain is high enough for nonlinear effects to become important, the flow structure changes substantially. Provided that Na/U is not below 1, there is a range of nondimensional mountain heights where gravity wave breaking establishes a flow structure very similar to that typical for wider mountains, including strong downslope winds in the lee of the mountain and a pressure drag well above the linear value. The results indicate that nonlinearity can shift the primary wind maximum from the mountain crest into the lee. For Na/U ≈ 0.75, gravity wave breaking no longer occurs, and the wind maximum is reached at the top of the mountain regardless of its height. Along a gap axis, however, there is a tendency for a pronounced wind maximum on the lee side even for narrow mountain ridges. In agreement with the results known for wider mountains, surface friction is found to reduce the wind speed close to the ground, to promote flow separation from the ground over the lee slope of the mountain and to reduce the tendency toward gravity wave breaking. For Na/U ≈ 1 and moderate surface friction, the formation of rotors becomes possible even for uniform large-scale flow.

Primordial Gravity Waves and Weak Lensing

Inflation produces a primordial spectrum of gravity waves in addition to the density perturbations which seed structure formation. We compute the signature of these gravity waves in the large scale shear field. The shear can be divided into a gradient mode (G or E) and a curl mode (C or B). The latter is produced only by gravity waves, so the observations of a nonzero curl mode could be seen as evidence for inflation. We find that the expected signal from inflation is small, peaking on the largest scales at l(l+1)C(l)/2pi<10(-11) at l=2 and falling rapidly thereafter. Even for an all-sky deep survey, this signal would be below noise at all multipoles.

On the development of large-scale cuspate features on a semi-reflective beach: Carchuna beach, Southern Spain

Carchuna beach, located on the southeast coast of Spain, has a series of natural permanent horns of time-dependent horizontal dimensions, which do not appear to be periodically spaced, and do not propagate alongshore. Until at present, it has been assumed that the permanency of these forms is related to the existence of bed rocks; nevertheless, analysis of the configuration of the depth contours and the bed sediment composition does not justify this hypothesis. This paper explores the formation of cuspate features by the effects of the wind wave dynamics and their development by nearshore circulation and infragravity waves, including edge waves. Three levels of wave energy flux conditions are considered. In all likelihood, wave refraction of severe storms on submerged fluvial valleys is the main cause for longshore variation of breaking wave height, which seems to be one of the initial conditions necessary for the cuspate to initiate. Moderate storms enhance the deepening of the embayments, whereas mild sea states are able to maintain the features by self-organization. The possibility of the occurrence of edge waves due to the non-linear interaction between the components of a gravity wave spectrum approaching the shore under moderate storm conditions is explored. Preliminary analysis of video images taken by an Argus station seems to confirm this hypothesis.

Nonlinear Four-Wave Interactions and Freak Waves

Four-wave interactions are shown to play an important role in the evolution of the spectrum of surface gravity waves. This fact follows from direct simulations of an ensemble of ocean waves using the Zakharov equation. The theory of homogeneous four-wave interactions, extended to include effects of nonresonant transfer, compares favorably with the ensemble-averaged results of the Monte Carlo simulations. In particular, there is good agreement regarding spectral shape. Also, the kurtosis of the surface elevation probability distribution is determined well by theory even for waves with a narrow spectrum and large steepness. These extreme conditions are favorable for the occurrence of freak waves.

High‐resolution profiling of layered structures in the lower stratosphere by GPS occultation

The back propagation method is applied to GPS occultation measurements of the lower stratosphere in order to reduce diffraction effects and to enhance the vertical resolution of the derived temperature profiles. The ionospheric bending angle correction should not be applied to small‐scale bending angle fluctuations (λz &lt; 1 km) of the GPS L1 and L2 signal, otherwise the retrieved profiles have enhanced artificial noise. Temperature profiles of two occultation events near to Japan on 4 and 5 February 1997 are discussed as examples for two different states of the lower stratosphere. One time the small‐scale fluctuations appear as sinusoidal wave trains. The other time the high‐resolution temperature profile has stairs which may result from atmospheric wave energy dissipation within a turbulence layer at each stair. The spectral energy distribution of the retrieved temperature fluctuations of both examples are well explained by the theoretical power spectra of saturated gravity waves at vertical wavelengths 0.1–2 km.

Evolution of a narrow-band spectrum of random surface gravity waves

Numerical simulations of the evolution of gravity wave spectra of fairly narrow bandwidth have been performed both for two and three dimensions. Simulations using the nonlinear Schrödinger (NLS) equation approximately verify the stability criteria of Alber (1978) in the two-dimensional but not in the three-dimensional case. Using a modified NLS equation (Trulsen et al. 2000) the spectra ‘relax’ towards a quasi-stationary state on a timescale (ε2ω0)−1. In this state the low-frequency face is steepened and the spectral peak is downshifted. The three-dimensional simulations show a power-law behaviour ω−4 on the high-frequency side of the (angularly integrated) spectrum.

Gravity wave dynamics and effects in the middle atmosphere

Atmospheric gravity waves have been a subject of intense research activity in recent years because of their myriad effects and their major contributions to atmospheric circulation, structure, and variability. Apart from occasionally strong lower‐atmospheric effects, the major wave influences occur in the middle atmosphere, between ∼ 10 and 110 km altitudes because of decreasing density and increasing wave amplitudes with altitude. Theoretical, numerical, and observational studies have advanced our understanding of gravity waves on many fronts since the review by Fritts [1984a]; the present review will focus on these more recent contributions. Progress includes a better appreciation of gravity wave sources and characteristics, the evolution of the gravity wave spectrum with altitude and with variations of wind and stability, the character and implications of observed climatologies, and the wave interaction and instability processes that constrain wave amplitudes and spectral shape. Recent studies have also expanded dramatically our understanding of gravity wave influences on the large‐scale circulation and the thermal and constituent structures of the middle atmosphere. These advances have led to a number of parameterizations of gravity wave effects which are enabling ever more realistic descriptions of gravity wave forcing in large‐scale models. There remain, nevertheless, a number of areas in which further progress is needed in refining our understanding of and our ability to describe and predict gravity wave influences in the middle atmosphere. Our view of these unknowns and needs is also offered.

Thermal effects of saturating gravity waves in the atmosphere

Breaking/saturating gravity waves (GWs) not only exert drag on the mean flow due to their momentum deposition but also affect the background thermally because of the associated energy flux divergence. We present a rigorous derivation of terms describing the thermal effects of GWs on the mean flow, based on the corresponding energy cycle for wave/mean flow interactions. The combined effect of saturating GWs is to produce both differential heating and cooling by inducing a downward wave heat flux, and an irreversible conversion of wave energy into heat. The former effect can also be represented as thermal diffusion acting on the mean potential temperature gradient. This rigorous theory for the thermal exchange between waves and the mean flow can be closed once the mechanism for GW dissipation is parameterized. To illustrate the procedure, we employ our recent nonlinear theory of GW spectra to derive expressions for the wave‐induced heating rates. This yields a parameterization of the thermal effects of GWs, which is suitable for use in general circulation models and requires the source GW spectrum as the only tunable parameter. We present results of numerical calculations of wave heating terms for typical wind and temperature profiles as well as simulations with the full‐scale Canadian Middle Atmosphere Model (CMAM).

Shoaling transformation of wave frequency‐directional spectra

A Boussinesq model for the nonlinear transformation of the frequency‐directional spectrum and bispectrum of surface gravity waves propagating over a gently sloping, alongshore uniform beach is compared with field and laboratory observations. Outside the surf zone the model predicts the observed spectral evolution, including energy transfers to harmonic components traveling in the direction of the dominant waves, and the cross‐interactions of waves traveling in different directions that transfer energy to components with the vector sum wavenumber. The sea surface elevation skewness and asymmetry, third‐order moments believed to be important for sediment transport, also are predicted well. Effects of surf zone wave breaking are incorporated with a heuristic frequency‐dependent dissipation term in the spectral energy balance equation and an empirical relaxation of the bispectrum to Gaussian statistics. The associated coefficients are calibrated with observations that span a wide range of surf zone conditions. With calibrated coefficients, the model predicts observed surf zone frequency spectra well and surf zone skewness and asymmetry fairly well. The observed directional spectra inside the surf zone are broader than the predicted spectra, suggesting that neglected scattering effects associated with the random onset of wave breaking or with higher‐order nonlinearity may be important.

The Treatment of Discontinuities in Computing the Nonlinear Energy Transfer for Finite-Depth Gravity Wave Spectra

Abstract The calculation of nonlinear energy transfer between interacting waves is one of the most computationally demanding tasks in understanding the dynamics of the growth and transformation of wind-generated surface waves. For shallow water in particular, existing schemes for computing the full Boltzmann integral representing the nonlinear energy transfer rate converge slowly with increasing spectral resolution. This means that it is difficult to build a spectral wave model with a treatment of nonlinear interactions that is sufficiently accurate without being computationally prohibitive for practical simulations. This paper examines the behavior of terms in the Boltzmann integral with a view to identifying potential improvements in numerical methods used in its solution. Discontinuities are identified in the variation of the nonlinear interaction coefficient where quadruplets of interacting wavenumbers include pairwise matches (k1 = k3, k2 = k4) or (k1 = k4, k2 = k3), a generalization of the specific ...

Relic backgrounds of gravitational waves from cosmic turbulence

Turbulence may have been produced in the early universe by several nonequilibrium processes. Periods of cosmic turbulence may have left a detectable relic under the form of stochastic backgrounds of gravitational waves. In this paper we derive general expressions for the power spectrum of the expected signal. Extending previous works on the subject, we take into account the effects of a continuous energy injection power and of magnetic fields. Both effects lead to relevant deviations from the Kolmogoroff turbulence spectrum. We apply our results to determine the spectrum of gravity waves which may have been produced by neutrino inhomogeneous diffusion and during a first order phase transition. We show that in both cases the expected signal may be in the sensitivity range of the interferometer LISA.