On the nonlinear transfer of energy in the peak of a gravity-wave spectrum: a simplified model

1976 ◽  
Vol 347 (1650) ◽  
pp. 311-328 ◽  
Keyword(s):  
Energy Transfer ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Coupling Coefficient ◽  
Wave Packets ◽  
Wave Spectrum ◽  
Three Dimensions ◽  
Simplified Model ◽  
Narrow Spectrum ◽  
Nonlinear Transfer

An equation given by Davey & Stewartson (1974) for the evolution of wave packets in three dimensions is employed to discuss the resonant transfer of energy within the peak of a narrow spectrum of gravity waves. It is shown that the coupling coefficient G ( k 1 , k 2 , k 3 , k 4 ) between four nearly equal wavenumbers k 1 ,..., k 4 is not zero (as had been speculated) but is equal to 4π. This implies that the exchange of energy within the peak itself is of dominant importance, and leads to a simplified discussion of the energy transfer.

scholarly journals The nonlinear effects on the characteristics of gravity wave packets: dispersion and polarization relations

2000 ◽  
Vol 18 (10) ◽  
pp. 1316-1324 ◽  
Author(s):  
S.-D. Zhang ◽  
F. Yi ◽  
J.-F. Wang
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Middle Atmosphere ◽  
Wave Packets ◽  
Nonlinear Effects ◽  
Wave Theory ◽  
Nonlinear Propagation ◽  
Waves And Tides ◽  
Time Variations ◽  
Isothermal Atmosphere

Abstract. By analyzing the results of the numerical simulations of nonlinear propagation of three Gaussian gravity-wave packets in isothermal atmosphere individually, the nonlinear effects on the characteristics of gravity waves are studied quantitatively. The analyses show that during the nonlinear propagation of gravity wave packets the mean flows are accelerated and the vertical wavelengths show clear reduction due to nonlinearity. On the other hand, though nonlinear effects exist, the time variations of the frequencies of gravity wave packets are close to those derived from the dispersion relation and the amplitude and phase relations of wave-associated disturbance components are consistent with the predictions of the polarization relation of gravity waves. This indicates that the dispersion and polarization relations based on the linear gravity wave theory can be applied extensively in the nonlinear region.Key words: Meteorology and atmospheric dynamics (middle atmosphere dynamics; waves and tides)

scholarly journals Momentum and Energy Transport by Gravity Waves in Stochastically Driven Stratified Flows. Part I: Radiation of Gravity Waves from a Shear Layer

2007 ◽  
Vol 64 (5) ◽  
pp. 1509-1529 ◽  
Author(s):  
Nikolaos A. Bakas ◽  
Petros J. Ioannou
Keyword(s):  
Shear Flow ◽  
Shear Layer ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Wave Energy ◽  
Energy Transport ◽  
Wave Spectrum ◽  
Internal Gravity Waves ◽  
Wave Interference ◽  
Wide Range

Abstract In this paper, the emission of internal gravity waves from a local westerly shear layer is studied. Thermal and/or vorticity forcing of the shear layer with a wide range of frequencies and scales can lead to strong emission of gravity waves in the region exterior to the shear layer. The shear flow not only passively filters and refracts the emitted wave spectrum, but also actively participates in the gravity wave emission in conjunction with the distributed forcing. This interaction leads to enhanced radiated momentum fluxes but more importantly to enhanced gravity wave energy fluxes. This enhanced emission power can be traced to the nonnormal growth of the perturbations in the shear region, that is, to the transfer of the kinetic energy of the mean shear flow to the emitted gravity waves. The emitted wave energy flux increases with shear and can become as large as 30 times greater than the corresponding flux emitted in the absence of a localized shear region. Waves that have horizontal wavelengths larger than the depth of the shear layer radiate easterly momentum away, whereas the shorter waves are trapped in the shear region and deposit their momentum at their critical levels. The observed spectrum, as well as the physical mechanisms influencing the spectrum such as wave interference and Doppler shifting effects, is discussed. While for large Richardson numbers there is equipartition of momentum among a wide range of frequencies, most of the energy is found to be carried by waves having vertical wavelengths in a narrow band around the value of twice the depth of the region. It is shown that the waves that are emitted from the shear region have vertical wavelengths of the size of the shear region.

scholarly journals On the non-linear energy transfer in a gravity-wave spectrum. Part 3. Evaluation of the energy flux and swell-sea interaction for a Neumann spectrum

1963 ◽  
Vol 15 (3) ◽  
pp. 385-398 ◽  
Author(s):  
K. Hasselmann
Keyword(s):  
Energy Transfer ◽  
Gravity Wave ◽  
Wave Spectrum ◽  
Low Frequency ◽  
Low Frequencies ◽  
Frequency Peak ◽  
Non Linear ◽  
Gain Energy ◽  
Rate Of Decay ◽  
Linear Interactions

The energy transfer due to non-linear interactions between the components of a gravity-wave spectrum discussed in Parts 1 and 2 of this paper is evaluated for a fully and partially developed Neumann spectrum with various spreading factors. The characteristic time scales of the energy transfer are found to be typically of the order of a few hours. In all cases the high frequencies and the low-frequency peak are found to gain energy from an intermediate range of frequencies. The transfer of energy to very low frequencies and to waves travelling at large angles to the main propagation direction of the spectrum is negligible. Computations are presented also for the rate of decay of swell interacting with local wind-generated seas (represented by a Neumann spectrum). An appreciable decay is found only for swell frequencies in the same range as those of the local sea.

scholarly journals Simulation of Inertia–Gravity Waves in a Poleward-Breaking Rossby Wave

2006 ◽  
Vol 63 (12) ◽  
pp. 3253-3276 ◽  
Author(s):  
Christoph Zülicke ◽  
Dieter Peters
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Rossby Wave ◽  
Rossby Waves ◽  
Mesoscale Model ◽  
Wave Packets ◽  
The Impact ◽  
Jet Streak ◽  
Horizontal Wavelength ◽  
Inertia Gravity Waves

Poleward-breaking Rossby waves often induce an upper-level jet streak over northern Europe. Dominant inertia–gravity wave packets are observed downstream of this jet. The physical processes of their generation and propagation, in such a configuration, are investigated with a mesoscale model. The study is focused on an observational campaign from 17 to 19 December 1999 over northern Germany. Different simulations with the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) have been performed. For a high-resolution process study, three domains were set up that encompass the evolution of Rossby waves and that of inertia–gravity waves. To minimize the impact of model damping, the horizontal and vertical resolution has been adjusted appropriately. With a novel statistical approach, the properties of inertia–gravity wave packets have been estimated. This method uses the horizontal divergence field and takes into account the spatial extension of a wave packet. It avoids the explicit treatment of the background field and works for arbitrary wavelength. Two classes of inertia–gravity waves were found: subsynoptic waves with a horizontal wavelength of about 500 km and mesoscale waves with a horizontal wavelength of about 200 km. The subsynoptic structures were also detected in radiosonde observations during this campaign. The similarity between simulated and observed wavelengths and amplitudes suggests that the simulations can be considered as near realistic. Spontaneous radiation from unbalanced flow is an important process of inertia–gravity wave generation. Synoptic-scale imbalances in the exit region of the upper-tropospheric jet streak were identified with the smoothed cross-stream Lagrangian Rossby number. In a number of simulations with different physics, it was found that the inertia–gravity wave activity was related to the tropospheric jet, orography, and moist convection. The upward propagation of inertia–gravity waves was favored during this event of a poleward-breaking Rossby wave. The presence of the polar vortex induced background winds exceeding the critical line. Consequently, the activity of inertia–gravity waves in the lower stratosphere increased by an order of magnitude during the case study. The successful simulation of the complex processes of generation and propagation showed the important role of poleward Rossby wave breaking for the appearance of inertia–gravity waves in the midlatitudes.

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.

scholarly journals On the origin of mesoscale TIDs at midlatitudes

2011 ◽  
Vol 29 (2) ◽  
pp. 361-366 ◽  
Author(s):  
M. C. Kelley
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Wave Spectrum ◽  
Wave Interaction ◽  
Magnetic Activity ◽  
Auroral Zone ◽  
Ionospheric Disturbances ◽  
F Region ◽  
Perkins Instability ◽  
Classical Gravity

Abstract. A recent breakthrough experiment by Ogawa et al. (2009) showed that Mesoscale Traveling Ionospheric Disturbances (MSTIDs), a common phenomenon at midlatitudes, originate in the auroral zone as gravity waves. Curiously, however, the latter do not seem to be related to magnetic activity. These atmospheric waves are common at high latitudes (Bristow and Greenwald, 1996; Bristow et al., 1996), and we argue here that, as they propagate to lower latitudes, Joule damping reduces the gravity wave spectrum to waves suffering the weakest damping. The direction of weakest damping corresponds to the direction predicted by the Perkins instability (Perkins, 1973) for nighttime MSTIDs. The daytime features reported by Ogawa et al. (2009) are very likely due to classical gravity wave interaction with the F-region ionosphere.

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