scholarly journals Inertia–gravity-wave radiation by a sheared vortex

2008 ◽  
Vol 596 ◽  
pp. 169-189 ◽  
Author(s):  
E. I. ÓLAFSDÓTTIR ◽  
A. B. OLDE DAALHUIS ◽  
J. VANNESTE
Keyword(s):  
Gravity Wave ◽  
Couette Flow ◽  
Gravity Waves ◽  
Dimensional Structure ◽  
Analytic Description ◽  
Wave Radiation ◽  
Rossby Number ◽  
Spontaneous Radiation ◽  
Initial State ◽  
Inertia Gravity Waves

We consider the linear evolution of a localized vortex with Gaussian potential vorticity that is superposed on a horizontal Couette flow in a rapidly rotating strongly stratified fluid. The Rossby number, defined as the ratio of the shear of the Couette flow to the Coriolis frequency, is assumed small. Our focus is on the inertia–gravity waves that are generated spontaneously during the evolution of the vortex. These are exponentially small in the Rossby number and hence are neglected in balanced models such as the quasi-geostrophic model and its higher-order generalizations. We develop an exponential-asymptotic approach, based on an expansion in sheared modes, to give an analytic description of the three-dimensional structure of the inertia–gravity waves emitted by the vortex. This provides an explicit example of the spontaneous radiation of inertia–gravity waves by localized balanced motion in the small-Rossby-number regime.The inertia–gravity waves are emitted as a burst of four wavepackets propagating downstream of the vortex. The approach employed reduces the computation of inertia–gravity-wave fields to a single quadrature, carried out numerically, for each spatial location and each time. This makes it possible to unambiguously define an initial state that is entirely free of inertia–gravity waves, and circumvents the difficulties generally associated with the separation between balanced motion and inertia–gravity waves.

scholarly journals Exponential Smallness of Inertia–Gravity Wave Generation at Small Rossby Number

2008 ◽  
Vol 65 (5) ◽  
pp. 1622-1637 ◽  
Author(s):  
J. Vanneste
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Initial Conditions ◽  
Wave Generation ◽  
Rossby Number ◽  
Spontaneous Generation ◽  
Steady Flows ◽  
Generation Mechanisms ◽  
Inertia Gravity Waves ◽  
Exponentially Small

Abstract This paper discusses some of the mechanisms whereby fast inertia–gravity waves can be generated spontaneously by slow, balanced atmospheric and oceanic flows. In the small Rossby number regime relevant to midlatitude dynamics, high-accuracy balanced models, which filter out inertia–gravity waves completely, can in principle describe the evolution of suitably initialized flows up to terms that are exponentially small in the Rossby number ɛ, that is, of the form exp(−α/ɛ) for some α > 0. This suggests that the mechanisms of inertia–gravity wave generation, which are not captured by these balanced models, are also exponentially weak. This has been confirmed by explicit analytical results obtained for a few highly simplified models. These results are reviewed, and some of the exponential-asymptotic techniques that have been used in their derivation are presented. Two types of mechanisms are examined: spontaneous-generation mechanisms, which generate exponentially small waves from perfectly balanced initial conditions, and unbalanced instability mechanisms, which amplify unbalanced initial perturbations of steady flows. The relevance of the results to realistic flows is discussed.

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.

Ageostrophic dynamics of an intense localized vortex on a β-plane

2001 ◽  
Vol 443 ◽  
pp. 351-376 ◽  
Author(s):  
G. M. REZNIK ◽  
R. GRIMSHAW
Keyword(s):  
Gravity Waves ◽  
Potential Vorticity ◽  
Rapid Development ◽  
Water Model ◽  
Wave Radiation ◽  
Main Role ◽  
Fast Time ◽  
Translation Speed ◽  
Continuous Potential ◽  
Inertia Gravity Waves

We consider the non-stationary dynamics of an intense localized vortex on a β-plane using a shallow-water model. An asymptotic theory for a vortex with piecewise-continuous potential vorticity is developed assuming the Rossby number to be small and the free surface elevation to be small but finite. Analogously to the well-known quasi-geostrophic model, the vortex translation is produced by a secondary dipole circulation (β-gyres) developed in the vortex vicinity and consisting of two parts. The first part (geostrophic β-gyres) coincides with the β-gyres in the geostrophic model, and the second (ageostrophic β-gyres) is due to ageostrophic terms in the governing equations. The time evolution of the ageostrophic β-gyres consists of fast and slow stages. During the fast stage the radiation of inertia–gravity waves results in the rapid development of the β-gyres from zero to a dipole field independent of the fast time variable. Correspondingly, the vortex accelerates practically instantaneously (compared to the typical swirling time) to some finite value of the translation speed. At the next slow stage the inertia–gravity wave radiation is insignificant and the β-gyres evolve with the typical swirling time. The total zonal translation speed induced by the geostrophic and ageostrophic β-gyres tends with increasing time to the speed of a steadily translating monopole exceeding (not exceeding) the drift velocity of Rossby waves for anticyclones (cyclones). This cyclone/anticyclone asymmetry generalizes the well-known finding about the greater longevity of anticyclones compared to cyclones to the case of non-stationary evolving monopoles. The influence of inertia–gravity waves upon the vortex evolution is analysed. The main role of these waves is to provide a ‘fast’ adjustment to the ‘slow’ vortex evolution. The energy of inertia–gravity waves is negligible compare to the energy of the geostrophic β-gyres. Yet another feature of the ageostrophic vortex evolution is that the area of the potential vorticity patch changes in the course of time, the cyclonic patch contracting and the anticyclonic one expanding.

scholarly journals Atmospheric inertia-gravity waves retrieved from level-2 data of the satellite microwave limb sounder Aura/MLS

2016 ◽  
Vol 34 (9) ◽  
pp. 781-788
Author(s):  
Klemens Hocke ◽  
Martin Lainer ◽  
Lorena Moreira ◽  
Jonas Hagen ◽  
Susana Fernandez Vidal ◽  
...  
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Deep Convection ◽  
Satellite Orbit ◽  
Wave Activity ◽  
Strong Wind ◽  
Wave Maps ◽  
Tropical Deep Convection ◽  
Level 2 ◽  
Inertia Gravity Waves

Abstract. The temperature profiles of the satellite experiment Aura/MLS are horizontally spaced by 1.5° or 165 km along the satellite orbit. These level-2 data contain valuable information about horizontal fluctuations in temperature, which are mainly induced by inertia-gravity waves. Wave periods of 2–12 h, horizontal wavelengths of 200–1500 km, and vertical wavelengths of 6–30 km efficiently contribute to the standard deviation of the horizontal temperature fluctuations. The study retrieves and discusses the global distributions of inertia-gravity waves in the stratosphere and mesosphere during July 2015 and January 2016. We find many patterns that were previously present in data of TIMED/SABER, Aura/HIRDLS, and ECMWF analysis. However, it seems that Aura/MLS achieves a higher vertical resolution in the gravity wave maps since the maps are derived from the analysis of horizontal fluctuations along the orbit of the sounding volume. The zonal mean of the inertia-gravity wave distribution shows vertical modulations with scales of 10–20 km. Enhanced wave amplitudes occur in regions of increased zonal wind or in the vicinity of strong wind gradients. Further, we find a banana-like shape of enhanced inertia-gravity waves above the Andes in the winter mesosphere. We find areas of enhanced inertia-gravity wave activity above tropical deep convection zones at 100 hPa (z ∼ 13 km). Finally, we study the temporal evolution of inertia-gravity wave activity at 100 hPa in the African longitude sector from December 2015 to February 2016.

Generation and Propagation of Inertia–Gravity Waves from Vortex Dipoles and Jets

2009 ◽  
Vol 66 (5) ◽  
pp. 1294-1314 ◽  
Author(s):  
Shuguang Wang ◽  
Fuqing Zhang ◽  
Chris Snyder
Keyword(s):  
Ray Tracing ◽  
Gravity Waves ◽  
Mesoscale Model ◽  
Rossby Number ◽  
Small Range ◽  
Grid Spacing ◽  
Coriolis Parameter ◽  
Vortex Dipoles ◽  
Horizontal Variations ◽  
Inertia Gravity Waves

Abstract This study investigates gravity wave generation and propagation from jets within idealized vortex dipoles using a nonhydrostatic mesoscale model. Two types of initially balanced and localized jets induced by vortex dipoles are examined here. These jets have their maximum strength either at the surface or in the middle levels of a uniformly stratified atmosphere. Within these dipoles, inertia–gravity waves with intrinsic frequencies 1–2 times the Coriolis parameter are simulated in the jet exit region. These gravity waves are nearly phase locked with the jets as shown in previous studies, suggesting spontaneous emission of the waves by the localized jets. A ray tracing technique is further employed to investigate the propagation effects of gravity waves. The ray tracing analysis reveals strong variation of wave characteristics along ray paths due to variations (particularly horizontal variations) in the propagating environment. The dependence of wave amplitude on the jet strength (and thus on the Rossby number of the flow) is examined through experiments in which the two vortices are initially separated by a large distance but subsequently approach each other and form a vortex dipole with an associated amplifying localized jet. The amplitude of the stationary gravity waves in the simulations with 90-km grid spacing increases as the square of the Rossby number (Ro), when Ro falls in a small range of 0.05–0.15, but does so significantly more rapidly when a smaller grid spacing is used.

scholarly journals Generation of gravity waves from thermal tides in the Venus atmosphere

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Norihiko Sugimoto ◽  
Yukiko Fujisawa ◽  
Hiroki Kashimura ◽  
Katsuyuki Noguchi ◽  
Takeshi Kuroda ◽  
...  
Keyword(s):  
Gravity Waves ◽  
General Circulation ◽  
Three Dimensional ◽  
Circulation Model ◽  
Cloud Layer ◽  
Dimensional Structure ◽  
Wave Radiation ◽  
Small Scale ◽  
Thermal Tides ◽  
Venus Atmosphere

AbstractGravity waves play essential roles in the terrestrial atmosphere because they propagate far from source regions and transport momentum and energy globally. Gravity waves are also observed in the Venus atmosphere, but their characteristics have been poorly understood. Here we demonstrate activities of small-scale gravity waves using a high-resolution Venus general circulation model with less than 20 and 0.25 km in the horizontal and vertical grid intervals, respectively. We find spontaneous gravity wave radiation from nearly balanced flows. In the upper cloud layer (~70 km), the thermal tides in the super-rotation are primary sources of small-scale gravity waves in the low-latitudes. Baroclinic/barotropic waves are also essential sources in the mid- and high-latitudes. The small-scale gravity waves affect the three-dimensional structure of the super-rotation and contribute to material mixing through their breaking processes. They propagate vertically and transport momentum globally, which decelerates the super-rotation in the upper cloud layer (~70 km) and accelerates it above ~80 km.

scholarly journals The merger of geophysical vortices at finite Rossby and Froude number

2018 ◽  
Vol 848 ◽  
pp. 388-410 ◽  
Author(s):  
Jean N. Reinaud ◽  
David G. Dritschel
Keyword(s):  
Froude Number ◽  
Gravity Wave ◽  
Potential Vorticity ◽  
Initial Conditions ◽  
The Other ◽  
Vertical Shear ◽  
Wave Radiation ◽  
Rossby Number ◽  
Other Hand ◽  
Vorticity Anomaly

We investigate the merger of two co-rotating geophysical vortices at finite Rossby and Froude number. The initial conditions consist of two uniform potential vorticity vortices in near-equilibrium and in a nearly ‘balanced’ state (i.e. with negligible emission of inertia–gravity wave radiation). We determine the critical merger distance between the two vortices. This distance is found to increase with the magnitude of the Rossby number: intense cyclones or intense anticyclones are able to merge from further apart compared to weaker cyclones and anticyclones. Note that the Froude number is proportional to the Rossby number for the near-equilibrium initial conditions considered. The critical merging distance also depends on the sign of the potential vorticity anomaly, which is positive for ‘cyclones’ and negative for ‘anticyclones’. We show that ageostrophic motions occurring at finite Rossby number tend to draw cyclones together but draw anticyclones apart. On the other hand, we show that anticyclones tend to deform more, in particular when subject to vertical shear (as when the vortices are vertically offset). These two effects compete. Overall, nearly aligned cyclones tend to merge from further apart than their anticyclonic counterparts, while vertically offset anticyclones merge from further apart than cyclones.

How white is the sky? 

2021 ◽  
Author(s):  
Nedjeljka Žagar ◽  
Žiga Zaplotnik ◽  
Valentino Neduhal
Keyword(s):  
Kinetic Energy ◽  
Gravity Wave ◽  
Power Law ◽  
Gravity Waves ◽  
Global Analysis ◽  
Vertical Motion ◽  
Energy Spectra ◽  
Horizontal Wind ◽  
Unified Framework ◽  
Inertia Gravity Waves

<p>The energy spectrum of atmospheric horizontal motions has been extensively studied in observations and numerical simulations. Its canonical shape includes a transition from the -3 power law at synoptic scale to -5/3 power law at mesoscale. The transition is taking place at scales around 500 km that can be seen as the scale where energy associated with quasi-linear inertia-gravity waves exceeds the balanced (or Rossby wave) energy. In contrast to the horizontal spectrum, the spectrum of kinetic energy of vertical motions is poorly known since the vertical motion is not an observed quantity of the global observing system and vertical kinetic energy spectra from non-hydrostatic models are difficult to validate.</p> <p>Traditionally, vertical velocities associated with the Rossby and gravity waves have been treated separately using the quasi-geostrophic omega equations and polarization relations for the stratified Boussinesq fluid in the (x,z) plane, respectively. In the tropics, the Rossby and gravity  wave regimes are difficult to separate and their frequency gap, present in the extra-tropics, is filled with the Kelvin and mixed Rossby-gravity waves. A separate treatment of the Rossby and gravity wave regimes makes it challenging to quantify energies of their vertical motions and vertical momentum fluxes. A unified treatment and wave interactions is performed by high-resolution non-hydrostatic models but their understanding requires the toolkit of theory. </p> <p>This contribution presents a unified framework for the derivation of vertical velocities of the Rossby and inertia-gravity waves and associated kinetic energy spectra. Expressions for the Rossby and gravity wave vertical velocities are derived using the normal-mode framework in the hydrostatic atmosphere that can be considered applicable up to the scale around 10 km. The derivation involves the analytical evaluation of divergence of the horizontal wind associated with the Rossby and inertia-gravity eigensolutions of the linearized primitive equations. The new framework is applied to the global analysis data of the ECMWF system. Results confirm that the tropical vertical kinetic energy spectra associated with inertia-gravity waves are on average indeed white. Deviations from the white spectrum are discussed for latitude and altitude bands.</p>

scholarly journals Quasi-12 h inertia–gravity waves in the lower mesosphere observed by the PANSY radar at Syowa Station (39.6° E, 69.0° S)

2017 ◽  
Vol 17 (10) ◽  
pp. 6455-6476 ◽  
Author(s):  
Ryosuke Shibuya ◽  
Kaoru Sato ◽  
Masaki Tsutsumi ◽  
Toru Sato ◽  
Yoshihiro Tomikawa ◽  
...  
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Spontaneous Radiation ◽  
Jet Streams ◽  
Radiation Mechanism ◽  
Syowa Station ◽  
Wave Parameters ◽  
Meridional Cross Section ◽  
Relationship Of ◽  
Inertia Gravity Waves

Abstract. The first observations made by a complete PANSY radar system (Program of the Antarctic Syowa MST/IS Radar) installed at Syowa Station (39.6° E, 69.0° S) were successfully performed from 16 to 24 March 2015. Over this period, quasi-half-day period (12 h) disturbances in the lower mesosphere at heights of 70 to 80 km were observed. Estimated vertical wavelengths, wave periods and vertical phase velocities of the disturbances were approximately 13.7 km, 12.3 h and −0.3 m s−1, respectively. Under the working hypothesis that such disturbances are attributable to inertia–gravity waves, wave parameters are estimated using a hodograph analysis. The estimated horizontal wavelengths are longer than 1100 km, and the wavenumber vectors tend to point northeastward or southwestward. Using the nonhydrostatic numerical model with a model top of 87 km, quasi-12 h disturbances in the mesosphere were successfully simulated. We show that quasi-12 h disturbances are due to wave-like disturbances with horizontal wavelengths longer than 1400 km and are not due to semidiurnal migrating tides. Wave parameters, such as horizontal wavelengths, vertical wavelengths and wave periods, simulated by the model agree well with those estimated by the PANSY radar observations under the abovementioned assumption. The parameters of the simulated waves are consistent with the dispersion relationship of the inertia–gravity wave. These results indicate that the quasi-12 h disturbances observed by the PANSY radar are attributable to large-scale inertia–gravity waves. By examining a residual of the nonlinear balance equation, it is inferred that the inertia–gravity waves are likely generated by the spontaneous radiation mechanism of two different jet streams. One is the midlatitude tropospheric jet around the tropopause while the other is the polar night jet. Large vertical fluxes of zonal and meridional momentum associated with large-scale inertia–gravity waves are distributed across a slanted region from the midlatitude lower stratosphere to the polar mesosphere in the meridional cross section. Moreover, the vertical flux of the zonal momentum has a strong negative peak in the mesosphere, suggesting that some large-scale inertia–gravity waves originate in the upper stratosphere.

Cyclone–anticyclone asymmetry in gravity wave radiation from a co-rotating vortex pair in rotating shallow water

2015 ◽  
Vol 772 ◽  
pp. 80-106 ◽  
Author(s):  
Norihiko Sugimoto ◽  
K. Ishioka ◽  
H. Kobayashi ◽  
Y. Shimomura
Keyword(s):  
Shallow Water ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Water System ◽  
Local Maximum ◽  
Vortex Pair ◽  
Wave Radiation ◽  
Earth’S Rotation ◽  
Far Field ◽  
Earth's Rotation

Cyclone–anticyclone asymmetry in spontaneous gravity wave radiation from a co-rotating vortex pair is investigated in an $f$-plane shallow water system. The far field of gravity waves is derived analytically by analogy with the theory of aeroacoustic sound wave radiation (Lighthill theory). In the derived form, the Earth’s rotation affects not only the propagation of gravity waves but also their source. While the results correspond to the theory of vortex sound in the limit of $f\rightarrow 0$, there is an asymmetry in gravity wave radiation between cyclone pairs and anticyclone pairs for finite values of $f$. Anticyclone pairs radiate gravity waves more intensely than cyclone pairs due to the effect of the Earth’s rotation. In addition, there is a local maximum of intensity of gravity waves from anticyclone pairs at an intermediate $f$. To verify the analytical solution, a numerical simulation is also performed with a newly developed spectral method in an unbounded domain. The novelty of this method is the absence of wave reflection at the boundary due to a conformal mapping and a pseudo-hyperviscosity that acts like a sponge layer in the far field of waves. The numerical results are in excellent agreement with the analytical results even for finite values of $f$ for both cyclone pairs and anticyclone pairs.

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