Articles de revues : « Gravity waves »

1

Naciri, Mamoun, and Chiang C. Mei. "Evolution of short gravity waves on long gravity waves." Physics of Fluids A: Fluid Dynamics 5, no. 8 (August 1993): 1869–78. http://dx.doi.org/10.1063/1.858812.

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Dias, Frédéric, and Christian Kharif. "NONLINEAR GRAVITY AND CAPILLARY-GRAVITY WAVES." Annual Review of Fluid Mechanics 31, no. 1 (January 1999): 301–46. http://dx.doi.org/10.1146/annurev.fluid.31.1.301.

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Akers, Benjamin F., David M. Ambrose, and J. Douglas Wright. "Gravity perturbed Crapper waves." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2161 (January 8, 2014): 20130526. http://dx.doi.org/10.1098/rspa.2013.0526.

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Crapper waves are a family of exact periodic travelling wave solutions of the free-surface irrotational incompressible Euler equations; these are pure capillary waves, meaning that surface tension is accounted for, but gravity is neglected. For certain parameter values, Crapper waves are known to have multi-valued height. Using the implicit function theorem, we prove that any of the Crapper waves can be perturbed by the effect of gravity, yielding the existence of gravity–capillary waves nearby to the Crapper waves. This result implies the existence of travelling gravity–capillary waves with multi-valued height. The solutions we prove to exist include waves with both positive and negative values of the gravity coefficient. We also compute these gravity perturbed Crapper waves by means of a quasi-Newton iterative scheme (again, using both positive and negative values of the gravity coefficient). A phase diagram is generated, which depicts the existence of single-valued and multi-valued travelling waves in the gravity–amplitude plane. A new largest water wave is computed, which is composed of a string of bubbles at the interface.

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Gnevyshev, Vladimir, and Sergei Badulin. "Wave Patterns of Gravity–Capillary Waves from Moving Localized Sources." Fluids 5, no. 4 (November 24, 2020): 219. http://dx.doi.org/10.3390/fluids5040219.

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We study wave patterns of gravity–capillary waves from moving localized sources within the classic setup of the problem of ship wakes. The focus is on the co-existence of two wave systems with opposite signatures of group velocity relative to the localized source. It leads to the problem of choice of signs for phase functions of the gravity (“slow”) and capillary (“fast”) branches of the dispersion relation: the question generally ignored when constructing phase patterns of the solutions. We detail characteristic angles of the wake patterns: (i) angle of demarcation of gravity and capillary waves—“the phase Mach” cone, (ii) angle of the minimal group velocity of gravity–capillary waves—“the group Mach” cone, (iii, iv) angles of cusps of isophases that appear after a threshold current speed. The outer cusp cone is naturally associated with the classic cone of Kelvin for pure gravity waves. The inner one results from the effect of capillarity and tends to the “group Mach” pattern at high speeds of current. Amplitudes of the wave patterns are estimated within the recently proposed approach of reference functions for the problem of propagation of packets of linear dispersive waves. The effect of shape is discussed for elliptic reference sources.

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Naeser, Harald. "The Capillary Waves’ Contribution to Wind-Wave Generation." Fluids 7, no. 2 (February 10, 2022): 73. http://dx.doi.org/10.3390/fluids7020073.

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Published theories and observations have shown that dissipation of gravity waves implies frequency downshifting of wave energy. Hence, for wind-waves, the wind energy input to the highest frequencies is of special interest. Here it is shown that this input is vital, because the direct wind energy input obtained by the air-pressure’s work on most gravity waves is slightly less than what the waves need to grow. Further, the wind’s input of the angular momentum that waves need to grow is found to be absent at most gravity wave frequencies. The capillary waves that appear at the surface of the sea when the wind is blowing solve these problems. To demonstrate this, an extension of linear wave theory is established to study possibilities and limitations for transfer of energy and angular momentum from the wind to waves through these frequencies. The theory describes regular, gravity–capillary waves with constant amplitude under laminar conditions. It includes surface tensions, viscosity, gravity and a wind-generated shear current, and shows that these waves—contrary to most gravity waves—receive more energy from the wind than they dissipate and angular momentum they cannot keep. Hence, the problem of the missing input of energy and angular momentum from wind to gravity waves is solved by transfers through the capillary waves. This implies that capillary waves are vital to obtain growing gravity waves.

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Wang, Xiujuan, Lingkun Ran, Yanbin Qi, Zhongbao Jiang, Tian Yun, and Baofeng Jiao. "Analysis of Gravity Wave Characteristics during a Hailstone Event in the Cold Vortex of Northeast China." Atmosphere 14, no. 2 (February 20, 2023): 412. http://dx.doi.org/10.3390/atmos14020412.

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Based on high-resolution pressure data collected by a microbarograph and Fourier transform (FFT) data processing, a detailed analysis of the frequency spectra characteristics of gravity waves during a hailstone event in the cold vortex of Northeast China (NECV) on 9 September 2021 is presented. The results show that the deep NECV served as the large-scale circulation background for the hailstone event. The development of hailstones was closely related to gravity waves. In different hail stages, the frequency spectra characteristics of gravity waves were obviously different. One and a half hours before hailfall, there were gravity wave precursors with periods of 50–180 min and corresponding amplitudes ranging from 30 to 60 Pa. During hailfall, the center amplitudes of the gravity waves were approximately 50 Pa and 60 Pa, with the corresponding period ranges expanding to 60–70 min and 160–240 min. Simultaneously, hailstones initiated shorter periods (26–34 min) of gravity waves, with the amplitudes increasing to approximately 12–18 Pa. The relationship between hailstones and gravity waves was positive. After hailfall, gravity waves weakened and dissipated rapidly. As shown by the reconstructed gravity waves, key periods of gravity wave precursors ranged from 50–180 min, which preceded hailstones by several hours. When convection developed, there was thunderstorm high pressure and an outflow boundary. The airflow converged and diverged downstream, resulting in the formation of gravity waves and finally triggering hailfall. Gravity wave predecessors are significant for hail warnings and artificial hail suppression.

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Kenyon, Kern E. "Frictionless Surface Gravity Waves." Natural Science 12, no. 04 (2020): 199–201. http://dx.doi.org/10.4236/ns.2020.124017.

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SUN, TIEN-YU, and KAI-HUI CHEN. "ON INTERNAL GRAVITY WAVES." Tamkang Journal of Mathematics 29, no. 4 (December 1, 1998): 249–69. http://dx.doi.org/10.5556/j.tkjm.29.1998.4254.

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   We are concerned with the steady wave motions in a 2-fluid system with constant densities. This is a free boundary problem in which the lighter fluid is bounded above by a free surface and is separated from the heavier one down below by an interface. By using a contractive mapping principle type argument. a constructive proof to the existence of some of these exact periodic internal gravity waves is proveded.   

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Vikulin, A. V., A. A. Dolgaya, and S. A. Vikulina. "Geodynamic waves and gravity." Geodynamics & Tectonophysics 5, no. 1 (2014): 291–303. http://dx.doi.org/10.5800/gt-2014-5-1-0128.

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Longuet-Higgins, M. S. "Bifurcation in gravity waves." Journal of Fluid Mechanics 151, no. -1 (February 1985): 457. http://dx.doi.org/10.1017/s0022112085001057.

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Pizzo, Nick E. "Surfing surface gravity waves." Journal of Fluid Mechanics 823 (June 16, 2017): 316–28. http://dx.doi.org/10.1017/jfm.2017.314.

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A simple criterion for water particles to surf an underlying surface gravity wave is presented. It is found that particles travelling near the phase speed of the wave, in a geometrically confined region on the forward face of the crest, increase in speed. The criterion is derived using the equation of John (Commun. Pure Appl. Maths, vol. 6, 1953, pp. 497–503) for the motion of a zero-stress free surface under the action of gravity. As an example, a breaking water wave is theoretically and numerically examined. Implications for upper-ocean processes, for both shallow- and deep-water waves, are discussed.

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STENFLO, L., and P. K. SHUKLA. "Nonlinear acoustic–gravity waves." Journal of Plasma Physics 75, no. 6 (March 11, 2009): 841–47. http://dx.doi.org/10.1017/s0022377809007892.

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AbstractPrevious results on nonlinear acoustic–gravity waves are reconsidered. It turns out that the mathematical techniques used are somewhat similar to those already adopted by the plasma physics community. Consequently, a future interaction between physicists in different fields, e.g. in meteorology and plasma physics, can be very fruitful.

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13

Miles, Alan J., and B. Roberts. "Magnetoacoustic-gravity surface waves." Solar Physics 141, no. 2 (October 1992): 205–34. http://dx.doi.org/10.1007/bf00155176.

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Miles, Alan J., H. R. Allen, and B. Roberts. "Magnetoacoustic-gravity surface waves." Solar Physics 141, no. 2 (October 1992): 235–51. http://dx.doi.org/10.1007/bf00155177.

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Lomnitz, Cinna. "Gravity waves in earthquakes?" Engineering Geology 29, no. 1 (June 1990): 95–97. http://dx.doi.org/10.1016/0013-7952(90)90084-e.

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Hassler, Donald M. "Drowning in Gravity Waves." Academic Questions 30, no. 3 (July 15, 2017): 342. http://dx.doi.org/10.1007/s12129-017-9644-6.

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Gonz�lez, Alejandro G., and Julio Gratton. "Magnetoacoustic surface gravity waves." Solar Physics 134, no. 2 (August 1991): 211–32. http://dx.doi.org/10.1007/bf00152645.

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Hara, Tetsu, Kurt A. Hanson, Erik J. Bock, and B. Mete Uz. "Observation of hydrodynamic modulation of gravity-capillary waves by dominant gravity waves." Journal of Geophysical Research: Oceans 108, no. C2 (February 2003): n/a. http://dx.doi.org/10.1029/2001jc001100.

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19

Hankinson, Mai C. N., M. J. Reeder, and T. P. Lane. "Gravity waves generated by convection during TWP-ICE: I. Inertia-gravity waves." Journal of Geophysical Research: Atmospheres 119, no. 9 (May 13, 2014): 5269–82. http://dx.doi.org/10.1002/2013jd020724.

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Beya, Jose, William Peirson, and Michael Banner. "ATTENUATION OF GRAVITY WAVES BY TURBULENCE." Coastal Engineering Proceedings 1, no. 32 (February 2, 2011): 3. http://dx.doi.org/10.9753/icce.v32.waves.3.

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We report new laboratory measurements of the interaction between mechanically-generated gravity waves and turbulence generated by simulated rain. Wave attenuation coefficients and vertical profiles of turbulent velocity fluctuations were measured. Observations are in broad agreement with Teixeira and Belcher (2002) despite substantial differences between assumed and measured turbulence profiles. Wave attenuation due to surface turbulence appears to be stronger than theoretical estimates. These finding could have significant implications for the next generation of spectral wave models and the understanding of wave dissipation processes.

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Yasui, Ryosuke, Kaoru Sato, and Yasunobu Miyoshi. "The Momentum Budget in the Stratosphere, Mesosphere, and Lower Thermosphere. Part II: The In Situ Generation of Gravity Waves." Journal of the Atmospheric Sciences 75, no. 10 (October 2018): 3635–51. http://dx.doi.org/10.1175/jas-d-17-0337.1.

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The contributions of gravity waves to the momentum budget in the mesosphere and lower thermosphere (MLT) is examined using simulation data from the Ground-to-Topside Model of Atmosphere and Ionosphere for Aeronomy (GAIA) whole-atmosphere model. Regardless of the relatively coarse model resolution, gravity waves appear in the MLT region. The resolved gravity waves largely contribute to the MLT momentum budget. A pair of positive and negative Eliassen–Palm flux divergences of the resolved gravity waves are observed in the summer MLT region, suggesting that the resolved gravity waves are likely in situ generated in the MLT region. In the summer MLT region, the mean zonal winds have a strong vertical shear that is likely formed by parameterized gravity wave forcing. The Richardson number sometimes becomes less than a quarter in the strong-shear region, suggesting that the resolved gravity waves are generated by shear instability. In addition, shear instability occurs in the low (middle) latitudes of the summer (winter) MLT region and is associated with diurnal (semidiurnal) migrating tides. Resolved gravity waves are also radiated from these regions. In Part I of this paper, it was shown that Rossby waves in the MLT region are also radiated by the barotropic and/or baroclinic instability formed by parameterized gravity wave forcing. These results strongly suggest that the forcing by gravity waves originating from the lower atmosphere causes the barotropic/baroclinic and shear instabilities in the mesosphere that, respectively, generate Rossby and gravity waves and suggest that the in situ generation and dissipation of these waves play important roles in the momentum budget of the MLT region.

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Christodoulides, P., and F. Dias. "Resonant capillary–gravity interfacial waves." Journal of Fluid Mechanics 265 (April 25, 1994): 303–43. http://dx.doi.org/10.1017/s0022112094000856.

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Two-dimensional space-periodic cabillary–gravity waves at the interface between two fluids of different densities are considered when the second harmonic and the fundamental mode are near resonance. A weakly nonlinear analysis provides the equations (normal form), correct to third order, that relate the wave frequency with the amplitudes of the fundamental mode and of the second harmonic for all waves with small energy. A study of the normal form for waves which are also periodic in time reveals three possible types of space- and time-periodic waves: the well-known travelling and standing waves as well as an unusual class of three-mode mixed waves. Mixed waves are found to provide a connection between standing and travelling waves. The branching behaviour of all types of waves is shown to depend strongly on the density ratio. For travelling waves the weakly nonlinear results are confirmed numerically and extended to finite-amplitude waves. When slow modulations in time of the amplitudes are considered, a powerful geometrical method is used to study the resulting normal form. Finally a discussion on modulational stability suggests that increasing the density ratio has a stabilizing effect.

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Subba Reddy, I. V., D. Narayana Rao, A. Narendra Babu, M. Venkat Ratnam, P. Kishore, and S. Vijaya Bhaskara Rao. "Studies on atmospheric gravity wave activity in the troposphere and lower stratosphere over a tropical station at Gadanki." Annales Geophysicae 23, no. 10 (November 30, 2005): 3237–60. http://dx.doi.org/10.5194/angeo-23-3237-2005.

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Abstract. MST radars are powerful tools to study the mesosphere, stratosphere and troposphere and have made considerable contributions to the studies of the dynamics of the upper, middle and lower atmosphere. Atmospheric gravity waves play a significant role in controlling middle and upper atmospheric dynamics. To date, frontal systems, convection, wind shear and topography have been thought to be the sources of gravity waves in the troposphere. All these studies pointed out that it is very essential to understand the generation, propagation and climatology of gravity waves. In this regard, several campaigns using Indian MST Radar observations have been carried out to explore the gravity wave activity over Gadanki in the troposphere and the lower stratosphere. The signatures of the gravity waves in the wind fields have been studied in four seasons viz., summer, monsoon, post-monsoon and winter. The large wind fluctuations were more prominent above 10 km during the summer and monsoon seasons. The wave periods are ranging from 10 min-175 min. The power spectral densities of gravity waves are found to be maximum in the stratospheric region. The vertical wavelength and the propagation direction of gravity waves were determined using hodograph analysis. The results show both down ward and upward propagating waves with a maximum vertical wave length of 3.3 km. The gravity wave associated momentum fluxes show that long period gravity waves carry more momentum flux than the short period waves and this is presented.

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Mehta, Dhvanit, Andrew J. Gerrard, Yusuke Ebihara, Allan T. Weatherwax, and Louis J. Lanzerotti. "Short-period mesospheric gravity waves and their sources at the South Pole." Atmospheric Chemistry and Physics 17, no. 2 (January 20, 2017): 911–19. http://dx.doi.org/10.5194/acp-17-911-2017.

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Abstract. The sourcing locations and mechanisms for short-period, upward-propagating gravity waves at high polar latitudes remain largely unknown. Using all-sky imager data from the Amundsen–Scott South Pole Station, we determine the spatial and temporal characteristics of 94 observed small-scale waves in 3 austral winter months in 2003 and 2004. These data, together with background atmospheres from synoptic and/or climatological empirical models, are used to model gravity wave propagation from the polar mesosphere to each wave's source using a ray-tracing model. Our results provide a compelling case that a significant proportion of the observed waves are launched in several discrete layers in the tropopause and/or stratosphere. Analyses of synoptic geopotentials and temperatures indicate that wave formation is a result of baroclinic instability processes in the stratosphere and the interaction of planetary waves with the background wind fields in the tropopause. These results are significant for defining the influences of the polar vortex on the production of these small-scale, upward-propagating gravity waves at the highest polar latitudes.

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Williams, Paul D., Thomas W. N. Haine, and Peter L. Read. "Inertia–Gravity Waves Emitted from Balanced Flow: Observations, Properties, and Consequences." Journal of the Atmospheric Sciences 65, no. 11 (November 1, 2008): 3543–56. http://dx.doi.org/10.1175/2008jas2480.1.

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Abstract This paper describes laboratory observations of inertia–gravity waves emitted from balanced fluid flow. In a rotating two-layer annulus experiment, the wavelength of the inertia–gravity waves is very close to the deformation radius. Their amplitude varies linearly with Rossby number in the range 0.05–0.14, at constant Burger number (or rotational Froude number). This linear scaling challenges the notion, suggested by several dynamical theories, that inertia–gravity waves generated by balanced motion will be exponentially small. It is estimated that the balanced flow leaks roughly 1% of its energy each rotation period into the inertia–gravity waves at the peak of their generation. The findings of this study imply an inevitable emission of inertia–gravity waves at Rossby numbers similar to those of the large-scale atmospheric and oceanic flow. Extrapolation of the results suggests that inertia–gravity waves might make a significant contribution to the energy budgets of the atmosphere and ocean. In particular, emission of inertia–gravity waves from mesoscale eddies may be an important source of energy for deep interior mixing in the ocean.

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Melville, W. Kendall, and Alexey V. Fedorov. "The equilibrium dynamics and statistics of gravity–capillary waves." Journal of Fluid Mechanics 767 (February 18, 2015): 449–66. http://dx.doi.org/10.1017/jfm.2014.740.

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AbstractRecent field observations and modelling of breaking surface gravity waves suggest that air-entraining breaking is not sufficiently dissipative of surface gravity waves to balance the dynamics of wind-wave growth and nonlinear interactions with dissipation for the shorter gravity waves of $O(10)$ cm wavelength. Theories of parasitic capillary waves that form at the crest and forward face of shorter steep gravity waves have shown that the dissipative effects of these waves may be one to two orders of magnitude greater than the viscous dissipation of the underlying gravity waves. Thus the parasitic capillaries may provide the required dissipation of the short wind-generated gravity waves. This has been the subject of speculation and conjecture in the literature. Using the nonlinear theory of Fedorov & Melville (J. Fluid Mech., vol. 354, 1998, pp. 1–42), we show that the dissipation due to the parasitic capillaries is sufficient to balance the wind input to the short gravity waves over some range of wave ages and wave slopes. The range of gravity wave lengths on which these parasitic capillary waves are dynamically significant approximately corresponds to the range of short gravity waves that Cox & Munk (J. Mar. Res., vol. 13, 1954, pp. 198–227) found contributed significantly to the mean square slope of the ocean surface, which they measured to be proportional to the wind speed. Here we show that the mean square slope predicted by the theory is proportional to the square of the friction velocity of the wind, ${u_{\ast }}^{2}$, for small wave slopes, and approximately $u_{\ast }$ for larger slopes.

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Lingevitch, Joseph F., Michael D. Collins, and William L. Siegmann. "Parabolic equations for gravity and acousto-gravity waves." Journal of the Acoustical Society of America 105, no. 6 (June 1999): 3049–56. http://dx.doi.org/10.1121/1.424634.

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Laxague, Nathan J. M., Milan Curcic, Jan-Victor Bjorkqvist, and Brian K. Haus. "Gravity-Capillary Wave Spectral Modulation by Gravity Waves." IEEE Transactions on Geoscience and Remote Sensing 55, no. 5 (May 2017): 2477–85. http://dx.doi.org/10.1109/tgrs.2016.2645539.

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Lane, Todd P., and Jason C. Knievel. "Some Effects of Model Resolution on Simulated Gravity Waves Generated by Deep, Mesoscale Convection." Journal of the Atmospheric Sciences 62, no. 9 (September 1, 2005): 3408–19. http://dx.doi.org/10.1175/jas3513.1.

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Abstract Over the past decade, numerous numerical modeling studies have shown that deep convective clouds can produce gravity waves that induce a significant vertical flux of horizontal momentum. Such studies used models with horizontal grid spacings of O(1 km) and produced strong gravity waves with horizontal wavelengths greater than about 20 km. This paper is an examination of how simulated gravity waves and their momentum flux are sensitive to model resolution. It is shown that increases in horizontal resolution produce more power in waves with shorter horizontal wavelengths. This change in the gravity waves’ spectra influences their vertical propagation. In some cases, gravity waves that were vertically propagating in coarse simulations become vertically trapped in fine simulations, which strongly influences the vertical flux of horizontal momentum.

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Khan, Mehtab A., Simon J. Watson, Dries J. N. Allaerts, and Matthew Churchfield. "Recommendations on setup in simulating atmospheric gravity waves under conventionally neutral boundary layer conditions." Journal of Physics: Conference Series 2767, no. 9 (June 1, 2024): 092042. http://dx.doi.org/10.1088/1742-6596/2767/9/092042.

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Abstract Wind farm-induced atmospheric gravity waves have been the subject of recent research as they can impact wind farm performance. Pressure variations associated with gravity waves can contribute to the global blockage effect and wind farm wake recovery. Therefore, accurate numerical simulation of flow fields, where wind-farm-induced gravity waves may be produced, is important. Three main considerations in such simulations are the overall domain size, the use of Rayleigh damping near domain boundaries to dampen gravity waves, and advection damping at the inlet to prevent spurious oscillations. Often these considerations are treated ad hoc rather than systematically. This work aims to test and extend the systematic modelling of internal gravity waves proposed in a preliminary investigation to modelling of both internal and trapped gravity waves. The preliminary study identifies the length scales to set the domain and damping layer sizes and the time scale to configure the Rayleigh damping coefficient but under linearly stratified conditions. Large eddy simulations of flow through a wind farm canopy are performed under conventionally neutral boundary layer (CNBL) conditions to test the validity of proposed setups for CNBL conditions. Background atmospheric parameters, such as Froude number (Fr), inversion height (Hi ), and inversion layer Froude number (Fri ) control most of the atmospheric gravity wave characteristics. We validated for CBNL conditions that the effective wavelengths of the internal gravity waves are the correct length scale to configure the domain size and damping layer thickness. Likewise, the optimum damping coefficient to dampen the internal gravity waves relates to the free atmosphere’s buoyancy frequency or buoyant perturbations’ time scale. We infer that the damping coefficient in the inversion layer may relate to the inversion buoyancy frequency to effectively dampen the trapped gravity waves. Moreover, the advection damping length is linked to the horizontal wavelength of the trapped gravity waves in the inversion layer to prevent spurious waves at the inlet by retaining wave energy accumulation.

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Hankinson, Mai C. N., M. J. Reeder, and T. P. Lane. "Gravity waves generated by convection during TWP-ICE: 2. High-frequency gravity waves." Journal of Geophysical Research: Atmospheres 119, no. 9 (May 13, 2014): 5257–68. http://dx.doi.org/10.1002/2013jd020726.

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Voisin, Bruno. "Internal wave generation in uniformly stratified fluids. Part 1. Green's function and point sources." Journal of Fluid Mechanics 231 (October 1991): 439–80. http://dx.doi.org/10.1017/s0022112091003464.

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In both Boussinesq and non-Boussinesq cases the Green's function of internal gravity waves is calculated, exactly for monochromatic waves and asymptotically for impulsive waves. From its differentiation the pressure and velocity fields generated by a point source are deduced. by the same method the Boussinesq monochromatic and impulsive waves radiated by a pulsating sphere are investigated.Boussinesq monochromatic waves of frequency ω < N are confined between characteristic cones θ = arccos(ω/N) tangent to the source region (N being the buoyancy frequency and θ the observation angle from the vertical). In that zone the point source model is inadequate. For the sphere an explicit form is given for the waves, which describes their conical 1/r½ radial decay and their transverse phase variations.Impulsive waves comprise gravity and buoyancy waves, whose separation process is non-Boussinesq and follows the arrival of an Airy wave. As time t elapses, inside the torus of vertical axis and horizontal radius 2Nt/β for gravity waves and inside the circumscribing cylinder for buoyancy waves, both components become Boussinesq and have wavelengths negligible compared with the scale height 2/β of the stratification. Then, gravity waves are plane propagating waves of frequency N cos θ, and buoyancy waves are radial oscillations of the fluid at frequency N; for the latter, initially propagating waves comparable with gravity waves, the horizontal phase variations have vanished and the amplitude has become insignificant as the Boussinesq zone has been entered. In this zone, outside the torus of vertical axis and horizontal radius Nta, a sphere of radius a [Lt ] 2/β is compact compared with the wavelength of the dominant gravity waves. Inside the torus gravity waves vanish by destructive interference. For the remaining buoyancy oscillations the sphere is compact outside the vertical cylinder circumscribing it, whereas the fluid is quiescent inside this cylinder.

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Salmon, Rick. "Variational treatment of inertia–gravity waves interacting with a quasi-geostrophic mean flow." Journal of Fluid Mechanics 809 (November 14, 2016): 502–29. http://dx.doi.org/10.1017/jfm.2016.693.

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The equations for three-dimensional hydrostatic Boussinesq dynamics are equivalent to a variational principle that is closely analogous to the variational principle for classical electrodynamics. Inertia–gravity waves are analogous to electromagnetic waves, and available potential vorticity (i.e. the amount by which the potential vorticity exceeds the potential vorticity of the rest state) is analogous to electric charge. The Lagrangian can be expressed as the sum of three parts. The first part corresponds to quasi-geostrophic dynamics in the absence of inertia–gravity waves. The second part corresponds to inertia–gravity waves in the absence of quasi-geostrophic flow. The third part represents a coupling between the inertia–gravity waves and quasi-geostrophic motion. This formulation provides the basis for a general theory of inertia–gravity waves interacting with a quasi-geostrophic mean flow.

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WU, XUESONG, and JING ZHANG. "Instability of a stratified boundary layer and its coupling with internal gravity waves. Part 2. Coupling with internal gravity waves via topography." Journal of Fluid Mechanics 595 (January 8, 2008): 409–33. http://dx.doi.org/10.1017/s0022112007009391.

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The aim of this paper is to show that the viscous shear instability identified in Part 1 is intrinsically coupled with internal gravity waves when a localized surface topography is present within a boundary layer. The coupling involves two aspects: receptivity and radiation. The former refers to excitation of shear instability modes by gravity waves, and the latter to emission of gravity waves by instability modes. Both physical processes are studied using triple-deck theory. In particular, the radiated gravity waves are found to produce a leading-order back action on the source, and this feedback effect, completely ignored in the acoustic analogy type of approach, is naturally taken into account by the triple-deck formalism. A by-product is that for certain incident angles, gravity waves are over-reflected by the boundary layer, i.e. the reflected waves are stronger than the incident waves.

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Bakas, Nikolaos A., and Brian F. Farrell. "Gravity Waves in a Horizontal Shear Flow. Part II: Interaction between Gravity Waves and Potential Vorticity Perturbations." Journal of Physical Oceanography 39, no. 3 (March 1, 2009): 497–511. http://dx.doi.org/10.1175/2008jpo3837.1.

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Abstract Interaction among potential vorticity perturbations and propagating internal gravity waves in a horizontally sheared zonal flow is investigated. In the strong stratification limit, an initial vorticity perturbation weakly excites two propagating gravity waves while the density component of the potential vorticity perturbation is significantly amplified, potentially leading to convective collapse. If stratification is sufficiently weak, a strong coupling between vorticity perturbations and gravity waves is found and spontaneous gravity wave generation occurs. This coupling can be traced to the nonnormal interaction between the potential vorticity and gravity wave manifolds in the weak stratification limit. Vorticity perturbations amplify in energy due to downgradient Reynolds stress when their phase lines tilt against the shear and the large growth attained is transferred to propagating gravity waves. When the flow geometry is such that the excited gravity waves are confined in the vicinity of the vorticity perturbation by their trapping levels, an overall convective collapse of this region can be anticipated. On the other hand, when the flow geometry permits wave propagation, significant gravity wave emission occurs.

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Zülicke, Christoph, and Dieter Peters. "Parameterization of Strong Stratospheric Inertia–Gravity Waves Forced by Poleward-Breaking Rossby Waves." Monthly Weather Review 136, no. 1 (January 1, 2008): 98–119. http://dx.doi.org/10.1175/2007mwr2060.1.

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Abstract The link between poleward-breaking Rossby waves and stratospheric inertia–gravity waves is examined. With a visual inspection of Ertel’s potential vorticity maps based on ECMWF analyses it was found that Rossby wave–breaking events occurred over northern Europe in about 40% of the winter days in 1999–2003. The majority of them were breaking poleward downstream. A total of 10 field campaigns were performed in the winters of 1999–2002 at Kühlungsborn, Germany (54°N, 12°E). They are related to such events and can be considered as representative for poleward-breaking Rossby waves. Inertia–gravity wave properties are diagnosed from radiosonde observations. They appeared to be shallower, slower, and stronger than the climatological mean for the north German lowlands. Hence, Rossby wave–breaking events are linked with strong stratospheric inertia–gravity wave activity. A novel parameterization of inertia–gravity wave generation and propagation is proposed. The stratospheric inertia–gravity wave action in the 16–20-km height range was parameterized with the synoptic-scale cross-stream ageostrophic wind, which accounts for imbalances in the upper-tropospheric jet streak. This empirical relationship is supported with quasigeostrophic theory. Effects of damping and critical level absorption are taken into account with Wentzel–Kramers–Brillouin theory. For verification of the parameterization with homogeneous meteorological fields in space and time, the 10 field campaigns were hindcasted with the nonhydrostatic fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model. About 80% of the variance in inertia–gravity wave action was found to be explained. For the 10 campaigns a close link was found between the poleward-breaking Rossby waves and the strong stratospheric inertia–gravity waves. The role of the polar vortex was twofold: first, it forced the poleward-oriented Rossby waves to break downstream and to form strong tropospheric jet streaks generating inertia–gravity waves. Second, the strong winds in the stratosphere favored the upward propagation of the inertia–gravity waves. The proposed new parameterization of inertia–gravity wave generation and propagation was validated and can be used to deduce mesoscale wave intensity from synoptic flow characteristics during poleward Rossby wave–breaking events.

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Lecoanet, D., G. M. Vasil, J. Fuller, M. Cantiello, and K. J. Burns. "Conversion of internal gravity waves into magnetic waves." Monthly Notices of the Royal Astronomical Society 466, no. 2 (December 15, 2016): 2181–93. http://dx.doi.org/10.1093/mnras/stw3273.

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Henderson, Stephen M., R. T. Guza, Steve Elgar, and T. H. C. Herbers. "Refraction of Surface Gravity Waves by Shear Waves." Journal of Physical Oceanography 36, no. 4 (April 1, 2006): 629–35. http://dx.doi.org/10.1175/jpo2890.1.

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Abstract Previous field observations indicate that the directional spread of swell-frequency (nominally 0.1 Hz) surface gravity waves increases during shoreward propagation across the surf zone. This directional broadening contrasts with the narrowing observed seaward of the surf zone and predicted by Snell’s law for bathymetric refraction. Field-observed broadening was predicted by a new model for refraction of swell by lower-frequency (nominally 0.01 Hz) current and elevation fluctuations. The observations and the model suggest that refraction by the cross-shore currents of energetic shear waves contributed substantially to the observed broadening.

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Yih, Chia-Shun, and Songping Zhu. "Patterns of ship waves. II. Gravity-capillary waves." Quarterly of Applied Mathematics 47, no. 1 (March 1, 1989): 35–44. http://dx.doi.org/10.1090/qam/987893.

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Mukherjee, Animesh, P. R. Sengupta, and Lokenath Debnath. "Surface waves in higher order visco-elastic media under the influence of gravity." Journal of Applied Mathematics and Stochastic Analysis 4, no. 1 (January 1, 1991): 71–82. http://dx.doi.org/10.1155/s1048953391000047.

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Based upon Biot's [1965] theory of initial stresses of hydrostatic nature produced by the effect of gravity, a study is made of surface waves in higher order visco-elastic media under the influence of gravity. The equation for the wave velocity of Stonely waves in the presence of viscous and gravitational effects is obtained. This is followed by particular cases of surface waves including Rayleigh waves and Love waves in the presence of viscous and gravity effects. In all cases the wave-velocity equations are found to be in perfect agreement with the corresponding classical results when the effects of gravity and viscosity are neglected.

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Wang, Shuguang, and Fuqing Zhang. "Sensitivity of Mesoscale Gravity Waves to the Baroclinicity of Jet-Front Systems." Monthly Weather Review 135, no. 2 (February 1, 2007): 670–88. http://dx.doi.org/10.1175/mwr3314.1.

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Abstract This study investigates the sensitivity of mesoscale gravity waves to the baroclinicity of the background jet-front systems by simulating different life cycles of baroclinic waves with a high-resolution mesoscale model. Four simulations are made starting from two-dimensional baroclinic jets having different static stability and wind shear in order to obtain baroclinic waves with significantly different growth rates. In all experiments, vertically propagating mesoscale gravity waves are simulated in the exit region of upper-tropospheric jet streaks. A two-dimensional spectral analysis demonstrates that these gravity waves have multiple components with different wave characteristics. The short-scale wave components that are preserved by a high-pass filter with a cutoff wavelength of 200 km have horizontal wavelengths of 85–161 km and intrinsic frequencies of 3–11 times the Coriolis parameter. The medium-scale waves that are preserved by a bandpass filter (with 200- and 600-km cutoff wavelengths) have horizontal wavelengths of 250–350 km and intrinsic frequencies less than 3 times the Coriolis parameter. The intrinsic frequencies of these gravity waves tend to increase with the growth rate of the baroclinic waves; gravity waves with similar frequency are found in the experiments with similar average baroclinic wave growth rate but with significantly different initial tropospheric static stability and tropopause geometry. The residuals of the nonlinear balance equation are used to assess the flow imbalance. In all experiments, the developing background baroclinic waves evolve from an initially balanced state to the strongly unbalanced state especially near the exit region of upper-level jet fronts before mature mesoscale gravity waves are generated. It is found that the growth rate of flow imbalance also correlates well to the growth rate of baroclinic waves and thus correlates to the frequency of gravity waves.

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Perez, Iael, and Dragani Walter. "Spectral variability in high frequency in sea level and atmospheric pressure on Buenos Aires Coast, Argentina." Brazilian Journal of Oceanography 65, no. 1 (March 2017): 69–78. http://dx.doi.org/10.1590/s1679-87592017130506501.

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Abstract There are some observational evidences which support that atmospheric gravity waves constitute an efficient forcing for meteorological tsunamis (meteotsunamis) along the coast of Buenos Aires, Argentina. Meteotsunamis and atmospheric gravity waves, which propagate simultaneously on the sea surface and the atmosphere, respectively, are typical examples of non-stationary geophysical signals. The variability of meteotsunamis and atmospheric gravity waves recorded at Mar del Plata was investigated in this paper. Results obtained in this work reinforce the idea of a cause (atmospheric gravity waves) effect (meteotsunami) relationship, because wavelet spectra obtained from both signals resulted quite similar. However, several very short episodes of mod-erate/low activity of atmospheric gravity waves were detected without detecting meteotsunami activity. On the other hand, it was found that atmospheric gravity wave spectral energy can appear in the wavelets as a single or multiple burst as relatively long and irregular events or as regular wave packets. Results obtained in this paper provide original spectral data about atmospheric gravity waves along the coast of Buenos Aires. This information is useful to be included in realistic numerical models in order to investigate the genesis of this complex atmosphere-ocean interaction.

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Alexander, M. Joan, David A. Ortland, Alison W. Grimsdell, and Ji-Eun Kim. "Sensitivity of Gravity Wave Fluxes to Interannual Variations in Tropical Convection and Zonal Wind." Journal of the Atmospheric Sciences 74, no. 9 (August 15, 2017): 2701–16. http://dx.doi.org/10.1175/jas-d-17-0044.1.

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Abstract Using an idealized model framework with high-frequency tropical latent heating variability derived from global satellite observations of precipitation and clouds, the authors examine the properties and effects of gravity waves in the lower stratosphere, contrasting conditions in an El Niño year and a La Niña year. The model generates a broad spectrum of tropical waves including planetary-scale waves through mesoscale gravity waves. The authors compare modeled monthly mean regional variations in wind and temperature with reanalyses and validate the modeled gravity waves using satellite- and balloon-based estimates of gravity wave momentum flux. Some interesting changes in the gravity spectrum of momentum flux are found in the model, which are discussed in terms of the interannual variations in clouds, precipitation, and large-scale winds. While regional variations in clouds, precipitation, and winds are dramatic, the mean gravity wave zonal momentum fluxes entering the stratosphere differ by only 11%. The modeled intermittency in gravity wave momentum flux is shown to be very realistic compared to observations, and the largest-amplitude waves are related to significant gravity wave drag forces in the lowermost stratosphere. This strong intermittency is generally absent or weak in climate models because of deficiencies in parameterizations of gravity wave intermittency. These results suggest a way forward to improve model representations of the lowermost stratospheric quasi-biennial oscillation winds and teleconnections.

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Longuet-Higgins, Michael S. "Parasitic capillary waves: a direct calculation." Journal of Fluid Mechanics 301 (October 25, 1995): 79–107. http://dx.doi.org/10.1017/s0022112095003818.

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As in a previous theory (Longuet-Higgins 1963) parasitic capillary waves are considered as a perturbation due to the local action of surface tension forces on an otherwise pure progressive gravity wave. Here the theory is improved by: (i) making use of our more accurate knowledge of the profile of a steep Stokes wave; (ii) taking account of the influence of gravity on the capillary waves themselves, through the effective gravitational acceleration g* for short waves riding on longer waves.Nonlinearity in the capillary waves themselves is not included, and certain other approximations are made. Nevertheless, the theory is shown to be in essential agreement with experiments by Cox (1958), Ebuchi, Kawamura & Toba (1987) and Perlin, Lin & Ting (1993).A principal result is that for gravity waves of a given length L > 5 cm there is a critical steepness parameter (AK)c at which the surface velocity (in a frame of reference moving with the phase-speed) equals the minimum (local) speed of capillary-gravity waves. On subcritical gravity waves, with steepness AK < (AK)c, capillary waves may be generated at all points of the wave surface. On supercritical waves, with AK > (AK)c, capillary waves can only be generated in the wave troughs; they are trapped between two caustics near the crests. Generally, the amplitude of the parasitic capillaries is greatest on gravity waves of near critical (but not maximum) steepness.

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Yu, Shiwang, Lifeng Zhang, Ming Zhang, and Yuan Wang. "Dynamics of Mechanical Oscillator Mechanism for Stratospheric Gravity Waves Generated by Convection." Atmosphere 11, no. 9 (September 3, 2020): 942. http://dx.doi.org/10.3390/atmos11090942.

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The mechanical oscillator mechanism (MOM) for stratospheric gravity waves generated by convection is investigated with a dynamics model using the two-dimensional, nonhydrostatic and linear governing equations based on the Boussinesq approximation. The model is solved analytically with a fixed buoyancy oscillation (BO) at the tropopause as the boundary conditions. Results show that this BO is the source of stratospheric gravity waves and the MOM is the generation mechanism. The characteristics of the stratospheric gravity waves not only depend on the BO, but also rely on the stratospheric state, such as the background wind and the buoyancy frequency. When the vertical wavenumbers of the stratospheric gravity waves are close to those of the intrinsic characteristic waves (ICWs), which are the model solution without BO forcing at the tropopause, resonance occurs. Under the resonance conditions, the amplitudes of the stratospheric gravity waves increase significantly, even for low BO intensity. The background wind in the stratosphere has a large effect on wave resonance. Finally, numerical simulation results of a low-vortex system also verify that the MOM is the generation mechanism of stratospheric gravity waves generated by convection.

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Fabris, Júlio C., Marcelo H. Alvarenga, Mahamadou Hamani Daouda, and Hermano Velten. "Nonconservative Unimodular Gravity: Gravitational Waves." Symmetry 14, no. 1 (January 6, 2022): 87. http://dx.doi.org/10.3390/sym14010087.

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Unimodular gravity is characterized by an extra condition with respect to general relativity, i.e., the determinant of the metric is constant. This extra condition leads to a more restricted class of invariance by coordinate transformation: The symmetry properties of unimodular gravity are governed by the transverse diffeomorphisms. Nevertheless, if the conservation of the energy–momentum tensor is imposed in unimodular gravity, the general relativity theory is recovered with an additional integration constant which is associated to the cosmological term Λ. However, if the energy–momentum tensor is not conserved separately, a new geometric structure appears with potentially observational signatures. In this text, we consider the evolution of gravitational waves in a nonconservative unimodular gravity, showing how it differs from the usual signatures in the standard model. As our main result, we verify that gravitational waves in the nonconservative version of unimodular gravity are strongly amplified during the evolution of the universe.

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Dörnbrack, Andreas, Stephen D. Eckermann, Bifford P. Williams, and Julie Haggerty. "Stratospheric Gravity Waves Excited by a Propagating Rossby Wave Train—A DEEPWAVE Case Study." Journal of the Atmospheric Sciences 79, no. 2 (February 2022): 567–91. http://dx.doi.org/10.1175/jas-d-21-0057.1.

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Abstract Stratospheric gravity waves observed during the DEEPWAVE research flight RF25 over the Southern Ocean are analyzed and compared with numerical weather prediction (NWP) model results. The quantitative agreement of the NWP model output and the tropospheric and lower-stratospheric observations is remarkable. The high-resolution NWP models are even able to reproduce qualitatively the observed upper-stratospheric gravity waves detected by an airborne Rayleigh lidar. The usage of high-resolution ERA5 data—partially capturing the long internal gravity waves—enabled a thorough interpretation of the particular event. Here, the observed and modeled gravity waves are excited by the stratospheric flow past a deep tropopause depression belonging to an eastward-propagating Rossby wave train. In the reference frame of the propagating Rossby wave, vertically propagating hydrostatic gravity waves appear stationary; in reality, of course, they are transient and propagate horizontally at the phase speed of the Rossby wave. The subsequent refraction of these transient gravity waves into the polar night jet explains their observed and modeled patchy stratospheric occurrence near 60°S. The combination of both unique airborne observations and high-resolution NWP output provides evidence for the one case investigated in this paper. As the excitation of such gravity waves persists during the quasi-linear propagation phase of the Rossby wave’s life cycle, a hypothesis is formulated that parts of the stratospheric gravity wave belt over the Southern Ocean might be generated by such Rossby wave trains propagating along the midlatitude waveguide.

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Milewski, Paul A., and Zhan Wang. "Transversally periodic solitary gravity–capillary waves." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2161 (January 8, 2014): 20130537. http://dx.doi.org/10.1098/rspa.2013.0537.

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When both gravity and surface tension effects are present, surface solitary water waves are known to exist in both two- and three-dimensional infinitely deep fluids. We describe here solutions bridging these two cases: travelling waves which are localized in the propagation direction and periodic in the transverse direction. These transversally periodic gravity–capillary solitary waves are found to be of either elevation or depression type, tend to plane waves below a critical transverse period and tend to solitary lumps as the transverse period tends to infinity. The waves are found numerically in a Hamiltonian system for water waves simplified by a cubic truncation of the Dirichlet-to-Neumann operator. This approximation has been proved to be very accurate for both two- and three-dimensional computations of fully localized gravity–capillary solitary waves. The stability properties of these waves are then investigated via the time evolution of perturbed wave profiles.

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Stober, Gunter, Sharon L. Vadas, Erich Becker, Alan Liu, Alexander Kozlovsky, Diego Janches, Zishun Qiao, et al. "Gravity waves generated by the Hunga Tonga–Hunga Ha′apai volcanic eruption and their global propagation in the mesosphere/lower thermosphere observed by meteor radars and modeled with the High-Altitude general Mechanistic Circulation Model." Atmospheric Chemistry and Physics 24, no. 8 (April 24, 2024): 4851–73. http://dx.doi.org/10.5194/acp-24-4851-2024.

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Abstract. The Hunga Tonga–Hunga Ha′apai volcano erupted on 15 January 2022, launching Lamb waves and gravity waves into the atmosphere. In this study, we present results using 13 globally distributed meteor radars and identify the volcanogenic gravity waves in the mesospheric/lower thermospheric winds. Leveraging the High-Altitude Mechanistic general Circulation Model (HIAMCM), we compare the global propagation of these gravity waves. We observed an eastward-propagating gravity wave packet with an observed phase speed of 240 ± 5.7 m s−1 and a westward-propagating gravity wave with an observed phase speed of 166.5 ± 6.4 m s−1. We identified these waves in HIAMCM and obtained very good agreement of the observed phase speeds of 239.5 ± 4.3 and 162.2 ± 6.1 m s−1 for the eastward the westward waves, respectively. Considering that HIAMCM perturbations in the mesosphere/lower thermosphere were the result of the secondary waves generated by the dissipation of the primary gravity waves from the volcanic eruption, this affirms the importance of higher-order wave generation. Furthermore, based on meteor radar observations of the gravity wave propagation around the globe, we estimate the eruption time to be within 6 min of the nominal value of 15 January 2022 04:15 UTC, and we localized the volcanic eruption to be within 78 km relative to the World Geodetic System 84 coordinates of the volcano, confirming our estimates to be realistic.

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Murashige, Sunao, and Wooyoung Choi. "Parasitic Capillary Waves on Small-Amplitude Gravity Waves with a Linear Shear Current." Journal of Marine Science and Engineering 9, no. 11 (November 4, 2021): 1217. http://dx.doi.org/10.3390/jmse9111217.

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This paper describes a numerical investigation of ripples generated on the front face of deep-water gravity waves progressing on a vertically sheared current with the linearly changing horizontal velocity distribution, namely parasitic capillary waves with a linear shear current. A method of fully nonlinear computation using conformal mapping of the flow domain onto the lower half of a complex plane enables us to obtain highly accurate solutions for this phenomenon with the wide range of parameters. Numerical examples demonstrated that, in the presence of a linear shear current, the curvature of surface of underlying gravity waves depends on the shear strength, the wave energy can be transferred from gravity waves to capillary waves and parasitic capillary waves can be generated even if the wave amplitude is very small. In addition, it is shown that an approximate model valid for small-amplitude gravity waves in a linear shear current can reasonably well reproduce the generation of parasitic capillary waves.

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