scholarly journals On the Momentum Flux of Vertically-Propagating Orographic Gravity Waves Excited in Nonhydrostatic Flow over Three-dimensional Orography

2021 ◽  
Author(s):  
Xin Xu ◽  
Runqiu Li ◽  
Miguel A. C. Teixeira ◽  
Yixiong Lu
Keyword(s):  
Gravity Waves ◽  
Wind Direction ◽  
Momentum Flux ◽  
Wave Spectrum ◽  
Three Dimensional ◽  
Horizontal Wind ◽  
Buoyancy Frequency ◽  
Minor Role ◽  
Linear Wave ◽  
Vertically Propagating

AbstractThis work studies nonhydrostatic effects (NHE) on the momentum flux of orographic gravity waves (OGWs) forced by isolated three-dimensional orography. Based on linear wave theory, an asymptotic expression for low horizonal Froude number ( where (U, V) is the mean horizontal wind, γ and a are the orography anisotropy and half-width and N is the buoyancy frequency) is derived for the gravity wave momentum flux (GWMF) of vertically-propagating waves. According to this asymptotic solution, which is quite accurate for any value of Fr, NHE can be divided into two terms (NHE1 and NHE2). The first term contains the high-frequency parts of the wave spectrum that are often mistaken as hydrostatic waves, and only depends on Fr. The second term arises from the difference between the dispersion relationships of hydrostatic and nonhydrostatic OGWs. Having an additional dependency on the horizontal wind direction and orography anisotropy, this term can change the GWMF direction. Examination of NHE for OGWs forced by both circular and elliptical orography reveals that the GWMF is reduced as Fr increases, at a faster rate than for two-dimensional OGWs forced by a ridge. At low Fr, the GWMF reduction is mostly attributed to the NHE2 term, whereas the NHE1 term starts to dominate above about Fr = 0.4. The behavior of NHE is mainly determined by Fr, while horizontal wind direction and orography anisotropy play a minor role. Implications of the asymptotic GWMF expression for the parameterization of nonhydrostatic OGWs in high-resolution and/or variable-resolution models are discussed.

scholarly journals Momentum Flux Spectrum of Convectively Forced Internal Gravity Waves and Its Application to Gravity Wave Drag Parameterization. Part I: Theory

2005 ◽  
Vol 62 (1) ◽  
pp. 107-124 ◽  
Author(s):  
In-Sun Song ◽  
Hye-Yeong Chun
Keyword(s):  
Gravity Waves ◽  
Momentum Flux ◽  
Three Dimensional ◽  
Internal Gravity Waves ◽  
Buoyancy Frequency ◽  
Spectral Structure ◽  
Two Dimensional ◽  
Resonance Factor ◽  
Flux Spectrum ◽  
Wave Momentum

Abstract The phase-speed spectrum of momentum flux by convectively forced internal gravity waves is analytically formulated in two- and three-dimensional frameworks. For this, a three-layer atmosphere that has a constant vertical wind shear in the lowest layer, a uniform wind above, and piecewise constant buoyancy frequency in a forcing region and above is considered. The wave momentum flux at cloud top is determined by the spectral combination of a wave-filtering and resonance factor and diabatic forcing. The wave-filtering and resonance factor that is determined by the basic-state wind and stability and the vertical configuration of forcing restricts the effectiveness of the forcing, and thus only a part of the forcing spectrum can be used for generating gravity waves that propagate above cumulus clouds. The spectral distribution of the wave momentum flux is largely determined by the wave-filtering and resonance factor, but the magnitude of the momentum flux varies significantly according to spatial and time scales and moving speed of the forcing. The wave momentum flux formulation in the two-dimensional framework is extended to the three-dimensional framework. The three-dimensional momentum flux formulation is similar to the two-dimensional one except that the wave propagation in various horizontal directions and the three-dimensionality of forcing are allowed. The wave momentum flux spectrum formulated in this study is validated using mesoscale numerical model results and can reproduce the overall spectral structure and magnitude of the wave momentum flux spectra induced by numerically simulated mesoscale convective systems reasonably well.

scholarly journals The Response of Parameterized Orographic Gravity Waves to Rapid Warming over the Tibetan Plateau

Atmosphere ◽  
2020 ◽  
Vol 11 (9) ◽  
pp. 1016
Author(s):  
Runqiu Li ◽  
Xin Xu ◽  
Yuan Wang ◽  
Miguel A. C. Teixeira ◽  
Jianping Tang ◽  
...  
Keyword(s):  
Tibetan Plateau ◽  
Gravity Waves ◽  
Horizontal Wind ◽  
Buoyancy Frequency ◽  
Minor Role ◽  
The Tibetan Plateau ◽  
A Minor ◽  
Increasing Trends ◽  
First Time

Using the ERA-Interim reanalysis during 1979–2017, this work for the first time investigates the climatology and long-term trend of orographic gravity waves (OGWs) in the Tibetan Plateau (TP). The linkage between the trends of OGWs and the rapid warming over the TP is also studied. Climatologically, the most prominent surface wave momentum flux (SWMF) of OGWs occurs in the western and southeastern TP, while it is weak in the central TP. The SWMF is stronger in winter and spring than in autumn and summer. Overall, the mean SWMF over the TP experienced a weak decreasing trend. The decrease of SWMF mainly took place in the western and southeastern TP in spring. However, increasing trends were found in the central TP in winter. Changes of SWMF are mainly caused by the changes of horizontal wind near the surface, while buoyancy frequency and air density play a minor role. In response to the inhomogeneous warming over the TP, the surface winds were adjusted through thermal wind balance. In spring (winter), the most remarkable warming occurred in the northern (southern) TP, which reduced (enhanced) the meridional temperature gradient across the plateau, and thus led to a deceleration (acceleration) of the horizontal wind.

scholarly journals Intercomparison of AIRS and HIRDLS stratospheric gravity wave observations

2018 ◽  
Vol 11 (1) ◽  
pp. 215-232 ◽  
Author(s):  
Catrin I. Meyer ◽  
Manfred Ern ◽  
Lars Hoffmann ◽  
Quang Thai Trinh ◽  
M. Joan Alexander
Keyword(s):  
High Resolution ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Momentum Flux ◽  
Wave Spectrum ◽  
Horizontal Resolution ◽  
Wave Activity ◽  
Large Variability ◽  
Wave Event ◽  
The Waves

Abstract. We investigate stratospheric gravity wave observations by the Atmospheric InfraRed Sounder (AIRS) aboard NASA's Aqua satellite and the High Resolution Dynamics Limb Sounder (HIRDLS) aboard NASA's Aura satellite. AIRS operational temperature retrievals are typically not used for studies of gravity waves, because their vertical and horizontal resolution is rather limited. This study uses data of a high-resolution retrieval which provides stratospheric temperature profiles for each individual satellite footprint. Therefore the horizontal sampling of the high-resolution retrieval is 9 times better than that of the operational retrieval. HIRDLS provides 2-D spectral information of observed gravity waves in terms of along-track and vertical wavelengths. AIRS as a nadir sounder is more sensitive to short-horizontal-wavelength gravity waves, and HIRDLS as a limb sounder is more sensitive to short-vertical-wavelength gravity waves. Therefore HIRDLS is ideally suited to complement AIRS observations. A calculated momentum flux factor indicates that the waves seen by AIRS contribute significantly to momentum flux, even if the AIRS temperature variance may be small compared to HIRDLS. The stratospheric wave structures observed by AIRS and HIRDLS often agree very well. Case studies of a mountain wave event and a non-orographic wave event demonstrate that the observed phase structures of AIRS and HIRDLS are also similar. AIRS has a coarser vertical resolution, which results in an attenuation of the amplitude and coarser vertical wavelengths than for HIRDLS. However, AIRS has a much higher horizontal resolution, and the propagation direction of the waves can be clearly identified in geographical maps. The horizontal orientation of the phase fronts can be deduced from AIRS 3-D temperature fields. This is a restricting factor for gravity wave analyses of limb measurements. Additionally, temperature variances with respect to stratospheric gravity wave activity are compared on a statistical basis. The complete HIRDLS measurement period from January 2005 to March 2008 is covered. The seasonal and latitudinal distributions of gravity wave activity as observed by AIRS and HIRDLS agree well. A strong annual cycle at mid- and high latitudes is found in time series of gravity wave variances at 42 km, which has its maxima during wintertime and its minima during summertime. The variability is largest during austral wintertime at 60∘ S. Variations in the zonal winds at 2.5 hPa are associated with large variability in gravity wave variances. Altogether, gravity wave variances of AIRS and HIRDLS are complementary to each other. Large parts of the gravity wave spectrum are covered by joint observations. This opens up fascinating vistas for future gravity wave research.

Multi-scale mountain waves observed with the ALIMA lidar during SOUTHTRAC-GW above the southern Andes

2021 ◽  
Author(s):  
Natalie Kaifler ◽  
Bernd Kaifler ◽  
Andreas Dörnbrack ◽  
Sonja Gisinger ◽  
Tyler Mixa ◽  
...  
Keyword(s):  
Wave Field ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Momentum Flux ◽  
Middle Atmosphere ◽  
Airborne Lidar ◽  
Horizontal Wind ◽  
Measured Temperature ◽  
Southern Andes ◽  
Mountain Waves

<p>During the SOUTHTRAC-GW (Southern hemisphere Transport, Dynamics and Chemistry – Gravity Waves) field campaign, gravity waves above the Southern Andes mountains, the Drake passage and the Antarctic Peninsula were probed with airborne instruments onboard the HALO research aircraft. The Airborne Lidar for Middle Atmosphere research (ALIMA) detected particularly strong mountain waves in excess of 25 K amplitude in cross-mountain legs above the Southern Andes of research flight ST08 on 12 September 2019. The mountain waves propagated well into the mesosphere up to 65 km altitude with possible generation of smaller-scale secondary waves during wave breaking above 65 km. A superposition of mountain waves with horizontal wavelengths in the range 15-200 km and vertical wavelengths 7-24 km dominated the wave field between 18 and 65 km altitude. Vertical wavelengths predicted by the hydrostatic equation and horizontal wind from the European Center for Medium-Range Weather Forecasts’ Integrated Forecasting System are in good agreement with observed vertical wavelengths. We apply wavelet analysis to the measured temperature field along the flight track in order to identify and separate dominant scales, and estimate their relative contributions to the total gravity wave momentum flux as well as the local and zonal-mean gravity wave drag. Furthermore, we compare our observations to results obtained by Fourier ray analysis of the terrain of the Southern Andes. The Fourier model allows the investigation of the 3d-wave field and trapped waves which are not well sampled by the ALIMA instrument because of the relative alignment between the wave fronts and the flight track. These sampling biases are quantified from virtual flights through the model domain at multiple angles and taken into account in the estimation of the total momentum flux derived from ALIMA observations. The combination of high-resolution observations and model data reveals the significance of this and similar mountain wave events in the Southern Andes region for the atmospheric dynamics at ~60° S.</p>

scholarly journals Regional variations of mesospheric gravity-wave momentum flux over Antarctica

2006 ◽  
Vol 24 (1) ◽  
pp. 81-88 ◽  
Author(s):  
P. J. Espy ◽  
R. E. Hibbins ◽  
G. R. Swenson ◽  
J. Tang ◽  
M. J. Taylor ◽  
...  
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Momentum Flux ◽  
Cross Correlation ◽  
Polar Vortex ◽  
Correlation Coefficients ◽  
Vertical Flux ◽  
Horizontal Wind ◽  
Wave Source ◽  
Horizontal Momentum

Abstract. Images of mesospheric airglow and radar-wind measurements have been combined to estimate the difference in the vertical flux of horizontal momentum carried by high-frequency gravity waves over two dissimilar Antarctic stations. Rothera (67° S, 68° W) is situated in the mountains of the Peninsula near the edge of the wintertime polar vortex. In contrast, Halley (76° S, 27° W), some 1658 km to the southeast, is located on an ice sheet at the edge of the Antarctic Plateau and deep within the polar vortex during winter. The cross-correlation coefficients between the vertical and horizontal wind perturbations were calculated from sodium (Na) airglow imager data collected during the austral winter seasons of 2002 and 2003 at Rothera for comparison with the 2000 and 2001 results from Halley reported previously (Espy et al., 2004). These cross-correlation coefficients were combined with wind-velocity variances from coincident radar measurements to estimate the daily averaged upper-limit of the vertical flux of horizontal momentum due to gravity waves near the peak emission altitude of the Na nightglow layer, 90km. The resulting momentum flux at both stations displayed a large day-to-day variability and showed a marked seasonal rotation from the northwest to the southwest throughout the winter. However, the magnitude of the flux at Rothera was about 4 times larger than that at Halley, suggesting that the differences in the gravity-wave source functions and filtering by the underlying winds at the two stations create significant regional differences in wave forcing on the scale of the station separation.

scholarly journals Short vertical-wavelength inertia-gravity waves generated by a jet–front system at Arctic latitudes – VHF radar, radiosondes and numerical modelling

2014 ◽  
Vol 14 (13) ◽  
pp. 6785-6799 ◽  
Author(s):  
A. Réchou ◽  
S. Kirkwood ◽  
J. Arnault ◽  
P. Dalin
Keyword(s):  
Gravity Waves ◽  
Potential Temperature ◽  
Wrf Model ◽  
Horizontal Wind ◽  
Buoyancy Frequency ◽  
Vertical Wavelength ◽  
Vhf Radar ◽  
The Waves ◽  
Inertia Gravity Waves ◽  
Good Agreement

Abstract. Inertia-gravity waves with very short vertical wavelength (λz≤1000 m) are a very common feature of the lowermost stratosphere as observed by the 52 MHz radar ESRAD (Esrange MST radar) in northern Scandinavia (67.88° N, 21.10° E). The waves are seen most clearly in radar-derived profiles of buoyancy frequency (N). Here, we present a case study of typical waves from 21 February to 22 February 2007. Good agreement between N2 derived from radiosondes and by radar shows the validity of the radar determination of N2. Large-amplitude wave signatures in N2 are clearly observed by the radar and the radiosondes in the lowermost stratosphere, from 9 km to 14–16 km height. Vertical profiles of horizontal wind components and potential temperature from the radiosondes show the same waves. Mesoscale simulations with the Weather Research and Forecasting (WRF) model are carried out to complement the analysis of the waves. Good agreement between the radar and radiosonde measurements and the model (except for the wave amplitude) shows that the model gives realistic results and that the waves are closely associated to the upper-level front in an upper-troposphere jet–front system. Hodographs of the wind fluctuations from the radiosondes and model data show that the waves propagate upward in the lower stratosphere confirming that the origin of the waves is in the troposphere. The observations and modelling all indicate vertical wavelengths of 700 ± 200 m. The radiosonde hodograms indicate horizontal wavelengths between 40 and 110 km and intrinsic periods between 6 and 9 h. The wave amplitudes indicated by the model are however an order of magnitude less than in the observations. Finally, we show that the profiles of N2 measured by the radar can be used to estimate wave amplitudes, horizontal wavelengths, intrinsic periods and momentum fluxes which are consistent with the estimates from the radiosondes.

Momentum Fluxes of Gravity Waves Generated by Variable Froude Number Flow over Three-Dimensional Obstacles

2010 ◽  
Vol 67 (7) ◽  
pp. 2260-2278 ◽  
Author(s):  
Stephen D. Eckermann ◽  
John Lindeman ◽  
Dave Broutman ◽  
Jun Ma ◽  
Zafer Boybeyi
Keyword(s):  
Froude Number ◽  
Gravity Waves ◽  
Momentum Flux ◽  
Mesoscale Model ◽  
Three Dimensional ◽  
Wave Drag ◽  
Analytical Relation ◽  
Far Field ◽  
Pressure Drag ◽  
Momentum Fluxes

Abstract Fully nonlinear mesoscale model simulations are used to investigate the momentum fluxes of gravity waves that emerge at a “far-field” height of 6 km from steady unsheared flow over both an axisymmetric and elliptical obstacle for nondimensional mountain heights ĥm = Fr−1 in the range 0.1–5, where Fr is the surface Froude number. Fourier- and Hilbert-transform diagnostics of model output yield local estimates of phase-averaged momentum flux, while area integrals of momentum flux quantify the amount of surface pressure drag that translates into far-field gravity waves, referred to here as the “wave drag” component. Estimates of surface and wave drag are compared to parameterization predictions and theory. Surface dynamics transition from linear to high-drag (wave breaking) states at critical inverse Froude numbers Frc−1 predicted to within 10% by transform relations. Wave drag peaks at Frc−1 < ĥm ≲ 2, where for the elliptical obstacle both surface and wave drag vacillate owing to cyclical buildup and breakdown of waves. For the axisymmetric obstacle, this occurs only at ĥm = 1.2. At ĥm ≳ 2–3 vacillation abates and normalized pressure drag assumes a common normalized form for both obstacles that varies approximately as ĥm−1.3. Wave drag in this range asymptotes to a constant absolute value that, despite its theoretical shortcomings, is predicted to within 10%–40% by an analytical relation based on linear clipped-obstacle drag for a Sheppard-based prediction of dividing streamline height. Constant wave drag at ĥm ∼ 2–5 arises despite large variations with ĥm in the three-dimensional morphology of the local wave momentum fluxes. Specific implications of these results for the parameterization of subgrid-scale orographic drag in global climate and weather models are discussed.

scholarly journals Linear Spectral Numerical Model for Internal Gravity Wave Propagation

2010 ◽  
Vol 67 (5) ◽  
pp. 1632-1642 ◽  
Author(s):  
J. Marty ◽  
F. Dalaudier
Keyword(s):  
Numerical Model ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Three Dimensional ◽  
Internal Gravity Wave ◽  
Temporal Variations ◽  
Buoyancy Frequency ◽  
Background Wind ◽  
First Order ◽  
Good Agreement

Abstract A three-dimensional linear spectral numerical model is proposed to simulate the propagation of internal gravity wave fluctuations in a stably stratified atmosphere. The model is developed to get first-order estimations of gravity wave fluctuations produced by identified sources. It is based on the solutions of the linearized fundamental fluid equations and uses the fully compressible dispersion relation for inertia–gravity waves. The spectral implementation excludes situations involving spatial variations of buoyancy frequency or background wind. However, density stratification variations are taken into account in the calculation of fluctuation amplitudes. In addition to gravity wave packet free propagation, the model handles both impulsive and continuous sources. It can account for spatial and temporal variations of the sources, encompassing a broad range of physical situations. The method is validated with a monochromatic pressure monopole, which is known to generate St. Andrew’s cross–shaped waves. It is then applied to the case of the ozone layer cooling during a total solar eclipse. The asymptotic response to a Gaussian thermal forcing traveling at constant velocity and the transient response to the 4 December 2002 eclipse show good agreement with previous numerical simulations. Further applications for the model are discussed.

scholarly journals Intercomparison of AIRS and HIRDLS stratospheric gravity wave observations

2017 ◽  
Author(s):  
Catrin I. Meyer ◽  
Manfred Ern ◽  
Lars Hoffmann ◽  
Quang Thai Trinh ◽  
M. Joan Alexander
Keyword(s):  
High Resolution ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Momentum Flux ◽  
Wave Spectrum ◽  
Horizontal Resolution ◽  
Wave Activity ◽  
Large Variability ◽  
Wave Event ◽  
The Waves

Abstract. We investigate stratospheric gravity wave observations by the Atmospheric InfraRed Sounder (AIRS) aboard NASA's Aqua satellite and the High Resolution Dynamics Limb Sounder (HIRDLS) aboard NASA's Aura satellite. AIRS operational temperature retrievals are typically not used for studies of gravity waves, because their horizontal resolution is rather limited. This study uses data of a high-resolution retrieval which provides stratospheric temperature profiles for each individual satellite footprint. Therefore the horizontal sampling of the high-resolution retrieval is nine times better than that of the operational retrieval. HIRDLS provides 2D spectral formation of observed gravity waves in terms of along-track and vertical wavelengths. AIRS as a nadir sounder is more sensitive to short horizontal wavelength gravity waves and HIRDLS as a limb sounder is more sensitive to short vertical wavelength gravity waves. Therefore HIRDLS is ideally suited to complement AIRS observations. A calculated momentum flux factor indicates that the waves seen by AIRS contribute significantly to momentum flux, even if the AIRS temperature variance may be small compared to HIRDLS. The stratospheric wave structures observed by AIRS and HIRDLS agree often very well. Case studies of a mountain wave event and a non-orographic wave event demonstrate that the observed phase structures of AIRS and HIRDLS are conform. AIRS has a coarser vertical resolution, which results in an attenuation of the amplitude and coarser vertical wavelengths compared to HIRDLS. However, AIRS has a much higher horizontal resolution and the propagation direction of the waves can be clearly identified in geographical maps. The horizontal orientation of the phase fronts can be deduced from AIRS 3D temperature fields. This is a restricting factor for gravity wave analyses of limb measurements. Additionally, temperature variances with respect to stratospheric gravity wave activity are compared on a statistical basis. The complete HIRDLS measurement period from January 2005 to March 2008 is covered. The seasonal and latitudinal distributions of gravity wave activity as observed by AIRS and HIRDLS fit well. A strong annual cycle at mid and high latitudes is found in time series of gravity wave variances at 42 km, which has during wintertime its maxima and during summertime its minima. During austral wintertime at 60° S the variability is largest. Variations in the zonal winds at 2.5 hPa are associated with large variability in gravity wave variances. Altogether, gravity wave variances of AIRS and HIRDLS are conform and complementary to each other. Thereby large parts of the gravity wave spectrum are covered by joint observations. This opens up fascinating vistas for future gravity wave research.

scholarly journals Gravity Waves Generated by Sheared Three-Dimensional Potential Vorticity Anomalies

2012 ◽  
Vol 69 (7) ◽  
pp. 2134-2151 ◽  
Author(s):  
François Lott ◽  
Riwal Plougonven ◽  
Jacques Vanneste
Keyword(s):  
Gravity Waves ◽  
Potential Vorticity ◽  
Richardson Number ◽  
Temporal Evolution ◽  
Three Dimensional ◽  
Vertical Shear ◽  
Flux Vector ◽  
Radiation Boundary Condition ◽  
Vertically Propagating ◽  
Radiation Boundary

Abstract The gravity waves (GWs) produced by three-dimensional potential vorticity (PV) anomalies are examined under the assumption of constant vertical shear, constant stratification, and unbounded domain. As in the two-dimensional case analyzed in an earlier paper, the disturbance near the PV anomaly is well modeled by quasigeostrophic theory. At larger distances the nature of the disturbance changes across the two inertial layers that are located above and below the anomaly, and it takes the form of a vertically propagating GW beyond these. For a horizontally monochromatic PV anomaly of infinitesimal depth, the disturbance is described analytically using both an exact solution and a WKB approximation; the latter includes an exponentially small term that captures the change of the solution near the PV anomaly induced by the radiation boundary condition in the far field. The analytical results reveal a strong sensitivity of the emission to the Richardson number and to the orientation of the horizontal wavenumber: the absorptive properties of the inertial layers are such that the emission is maximized in the Northern Hemisphere for wavenumbers at negative angles to the shear. For localized PV anomalies, numerical computations give the temporal evolution of the GW field. Analytical and numerical results are also used to establish an explicit form for the Eliassen–Palm flux that could be used to parameterize GW sources in GCMs. The properties of the Eliassen–Palm flux vector imply that in a westerly shear, the GWs exert a drag in a southwest direction in the upper inertial layer, and in a northwest direction at the altitudes where the GWs dissipate aloft.

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