scholarly journals Inertia–Gravity Waves Emitted from Balanced Flow: Observations, Properties, and Consequences

2008 ◽  
Vol 65 (11) ◽  
pp. 3543-3556 ◽  
Author(s):  
Paul D. Williams ◽  
Thomas W. N. Haine ◽  
Peter L. Read
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Significant Contribution ◽  
Rotation Period ◽  
Mesoscale Eddies ◽  
Energy Budgets ◽  
Linear Scaling ◽  
Deep Interior ◽  
Balanced Flow ◽  
Inertia Gravity Waves

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.

scholarly journals Transition from geostrophic flows to inertia-gravity waves in the spectrum of a differentially heated rotating annulus experiment.

2020 ◽  
Author(s):  
Costanza Rodda ◽  
Uwe Harlander
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Small Scale ◽  
Turbulent Regime ◽  
Weakly Nonlinear ◽  
Geostrophic Flows ◽  
Balanced Flow ◽  
Energy And Momentum ◽  
Open Question ◽  
Inertia Gravity Waves

<p>Inertia-gravity waves (IGWs) are known to play an essential role in the terrestrial atmospheric dynamics as they can lead to energy and momentum flux when they propagate upwards. An open question is to which extent nearly linear IGWs contribute to the total energy and to flattening of the energy spectrum observed at the mesoscale.<br>In this work, we present an experimental investigation of the energy distribution between the large-scale balanced flow and the small-scale imbalanced flow. Weakly nonlinear IGWs emitted from baroclinic jets are observed in the differentially heated rotating annulus experiment. Similar to the atmospheric spectra, the experimental kinetic energy spectra reveal the typical subdivision into two distinct regimes with slopes <em>k</em><sup>-3</sup> for the large scales and <em>k<sup>-</sup></em><sup>5/3</sup> for smaller scales. By separating the spectra into a vortex and wave part, it emerges that at the largest scales in the mesoscale range the gravity waves observed in the experiment cause a flattening of the spectra and provide most of the energy. At smaller scales, our data analysis suggests a transition towards a turbulent regime with a forward energy cascade up to where dissipation by diffusive processes occurs.</p>

scholarly journals Transition from Geostrophic Flows to Inertia–Gravity Waves in the Spectrum of a Differentially Heated Rotating Annulus Experiment

2020 ◽  
Vol 77 (8) ◽  
pp. 2793-2806
Author(s):  
Costanza Rodda ◽  
Uwe Harlander
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Small Scale ◽  
Turbulent Regime ◽  
Weakly Nonlinear ◽  
Geostrophic Flows ◽  
Balanced Flow ◽  
Energy And Momentum ◽  
Open Question ◽  
Inertia Gravity Waves

Abstract Inertia–gravity waves (IGWs) play an essential role in the terrestrial atmospheric dynamics as they can lead to energy and momentum flux when propagating upward. An open question is to what extent IGWs contribute to the total energy and to the flattening of the energy spectrum observed at the mesoscale. In this work, we present an experimental investigation of the energy distribution between the large-scale balanced flow and the small-scale imbalanced flow. Weakly nonlinear IGWs emitted from baroclinic jets are observed in the differentially heated rotating annulus experiment. Similar to the atmospheric spectra, the experimental kinetic energy spectra reveal the typical subdivision into two distinct regimes with slopes k−3 for the large scales and k−5/3 for the small scales. By separating the spectra into the vortex and wave components, it emerges that at the large-scale end of the mesoscale the gravity waves observed in the experiment cause a flattening of the spectra and provide most of the energy. At smaller scales, our data analysis suggests a transition toward a turbulent regime with a forward energy cascade up to where dissipation by diffusive processes occurs.

Geophysical turbulence dominated by inertia–gravity waves

2019 ◽  
Vol 875 ◽  
pp. 71-100 ◽  
Author(s):  
Jim Thomas ◽  
Ray Yamada
Keyword(s):  
Gravity Waves ◽  
Boussinesq Equations ◽  
Tidal Energy ◽  
Ocean Model ◽  
Small Scale ◽  
Baroclinic Mode ◽  
Transfer Energy ◽  
Geophysical Turbulence ◽  
Balanced Flow ◽  
Inertia Gravity Waves

Recent evidence from both oceanic observations and global-scale ocean model simulations indicate the existence of regions where low-mode internal tidal energy dominates over that of the geostrophic balanced flow. Inspired by these findings, we examine the effect of the first vertical mode inertia–gravity waves on the dynamics of balanced flow using an idealized model obtained by truncating the hydrostatic Boussinesq equations on to the barotropic and the first baroclinic mode. On investigating the wave–balance turbulence phenomenology using freely evolving numerical simulations, we find that the waves continuously transfer energy to the balanced flow in regimes where the balanced-to-wave energy ratio is small, thereby generating small-scale features in the balanced fields. We examine the detailed energy transfer pathways in wave-dominated flows and thereby develop a generalized small Rossby number geophysical turbulence phenomenology, with the two-mode (barotropic and one baroclinic mode) quasi-geostrophic turbulence phenomenology being a subset of it. The present work therefore shows that inertia–gravity waves would form an integral part of the geophysical turbulence phenomenology in regions where balanced flow is weaker than gravity waves.

On the Forcing of Inertia–Gravity Waves by Synoptic-Scale Flows

2007 ◽  
Vol 64 (5) ◽  
pp. 1737-1742 ◽  
Author(s):  
Riwal Plougonven ◽  
Fuqing Zhang
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Present Note ◽  
Quantitative Relation ◽  
Synoptic Scale ◽  
Linear Dynamics ◽  
Large Scale Flow ◽  
The Right ◽  
Scaling Arguments ◽  
Inertia Gravity Waves

Abstract Studies on the spontaneous emission of gravity waves from jets, both observational and numerical, have emphasized that excitation of gravity waves occurred preferentially near regions of imbalance. Yet a quantitative relation between the several large-scale diagnostics of imbalance and the excited waves is still lacking. The purpose of the present note is to investigate one possible way to relate quantitatively the gravity waves to diagnostics of the large-scale flow that is exciting them. Scaling arguments are used to determine how the large-scale flow may provide a forcing on the right-hand side of a wave equation describing the linear dynamics of the excited waves. The residual of the nonlinear balance equation plays an important role in this forcing.

Spontaneous Imbalance and Hybrid Vortex–Gravity Structures

2009 ◽  
Vol 66 (5) ◽  
pp. 1315-1326 ◽  
Author(s):  
Michael E. McIntyre
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Large Scale ◽  
General Rule ◽  
Radiation Reaction ◽  
Water Dynamics ◽  
Small Scale ◽  
Wave Source ◽  
Vortical Motion ◽  
Inertia Gravity Waves

Abstract After reviewing the background, this article discusses the recently discovered examples of hybrid propagating structures consisting of vortex dipoles and comoving gravity waves undergoing wave capture. It is shown how these examples fall outside the scope of the Lighthill theory of spontaneous imbalance and, concomitantly, outside the scope of shallow-water dynamics. Besides the fact that going from shallow-water to continuous stratification allows disparate vertical scales—small for inertia–gravity waves and large for vortical motion—the key points are 1) that by contrast with cases covered by the Lighthill theory, the wave source feels a substantial radiation reaction when Rossby numbers R ≳ 1, so that the source cannot be prescribed in advance; 2) that examples of this sort may supply exceptions to the general rule that spontaneous imbalance is exponentially small in R; and 3) that unsteady vortical motion in continuous stratification can stay close to balance thanks to three quite separate mechanisms. These are as follows: first, the near-suppression, by the Lighthill mechanism, of large-scale imbalance (inertia–gravity waves of large horizontal scale), where “large” means large relative to a Rossby deformation length LD characterizing the vortical motion; second, the flaccidity, and hence near-steadiness, of LD-wide jets that meander and form loops, Gulf-Stream-like, on streamwise scales ≫ LD; and third, the dissipation of small-scale imbalance by wave capture leading to wave breaking, which is generically probable in an environment of random shear and straining. Shallow-water models include the first two mechanisms but exclude the third.

scholarly journals A Theoretical Study on the Spontaneous Radiation of Inertia–Gravity Waves Using the Renormalization Group Method. Part I: Derivation of the Renormalization Group Equations

2015 ◽  
Vol 72 (3) ◽  
pp. 957-983 ◽  
Author(s):  
Yuki Yasuda ◽  
Kaoru Sato ◽  
Norihiko Sugimoto
Keyword(s):  
Renormalization Group ◽  
Time Scales ◽  
Gravity Waves ◽  
Radiation Reaction ◽  
Vortical Flow ◽  
Group Method ◽  
Linear Potential ◽  
Slow Time ◽  
Balanced Flow ◽  
Inertia Gravity Waves

Abstract By using the renormalization group (RG) method, the interaction between balanced flows and Doppler-shifted inertia–gravity waves (GWs) is formulated for the hydrostatic Boussinesq equations on the f plane. The derived time-evolution equations [RG equations (RGEs)] describe the spontaneous GW radiation from the components slaved to the vortical flow through the quasi resonance, together with the GW radiation reaction on the large-scale flow. The quasi resonance occurs when the space–time scales of GWs are partially comparable to those of slaved components. This theory treats a coexistence system with slow time scales composed of GWs significantly Doppler-shifted by the vortical flow and the balanced flow that interact with each other. The theory includes five dependent variables having slow time scales: one slow variable (linear potential vorticity), two Doppler-shifted fast ones (GW components), and two diagnostic fast ones. Each fast component consists of horizontal divergence and ageostrophic vorticity. The spontaneously radiated GWs are regarded as superpositions of the GW components obtained as low-frequency eigenmodes of the fast variables in a given vortical flow. Slowly varying nonlinear terms of the fast variables are included as the diagnostic components, which are the sum of the slaved components and the GW radiation reactions. A comparison of the balanced adjustment equation (BAE) by Plougonven and Zhang with the linearized RGE shows that the RGE is formally reduced to the BAE by ignoring the GW radiation reaction, although the interpretation on the GW radiation mechanism is significantly different; GWs are radiated through the quasi resonance with a balanced flow because of the time-scale matching.

scholarly journals Impact of upper-level jet-generated inertia-gravity waves on surface wind and precipitation

2007 ◽  
Vol 7 (6) ◽  
pp. 15873-15909 ◽  
Author(s):  
C. Zülicke ◽  
D. H. W. Peters
Keyword(s):  
Baltic Sea ◽  
Gravity Waves ◽  
Large Scale ◽  
Surface Wind ◽  
Synoptic Situation ◽  
Strong Wind ◽  
The Baltic Sea ◽  
The Baltic ◽  
The Impact ◽  
Inertia Gravity Waves

Abstract. A meteorological case study for the impact of inertia-gravity waves on surface meteorology is presented. The large-scale environment from 17 to 19 December 1999 was dominated by a poleward breaking Rossby wave transporting subtropical air over the North Atlantic Ocean upward and north-eastward. The synoptic situation was characterized with an upper tropospheric jet streak passing Northern Europe. The unbalanced jet spontaneously radiated inertia-gravity waves from its exit region. Near-inertial waves appeared with a horizontal wavelength of about 200 km and an apparent period of about 12 h. These waves transported energy downwards and interacted with large-scale convection. This configuration is simulated with the nonhydrostatic Fifth-Generation Mesoscale Model. Together with simplified runs without orography and moisture it is demonstrated that the imbalance of the jet (detected with the cross-stream ageostrophic wind) and the deep convection (quantified with the latent heat release) are forcing inertia-gravity waves. This interaction is especially pronounced when the upper tropospheric jet is located above a cold front at the surface and supports deep frontal convection. Weak indication was found for triggering post-frontal convection by inertia-gravity waves. The realism of model simulations was studied in an extended validation study for the Baltic Sea region. It included observations from radar (DWDPI, BALTRAD), satellite (GFZGPS), weather stations (DWDMI) and assimilated products (ELDAS, MESAN). The detected spatio-temporal patterns show wind pulsations and precipitation events at scales corresponding to those of inertia-gravity waves. In particular, the robust features of strong wind and enhanced precipitation near the front appeared with nearly the same amplitudes as in the model. In some datasets we found indication for periodic variations in the post-frontal region. These findings demonstrate the impact of upper tropospheric jet-generated inertia-gravity waves on the dynamics of the boundary layer. It also gives confidence to models, observations and assimilation products for covering such processes. In an application for the Gotland Basin in the Baltic Sea, the implications of such mesoscale events on air-sea interaction and energy and water budgets are discussed.

scholarly journals Inertia–gravity waves generated by near balanced flow in 2-layer shallow water turbulence on the β-plane

2013 ◽  
Vol 20 (1) ◽  
pp. 25-34 ◽  
Author(s):  
A. Wirth
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Shallow Water Equations ◽  
Continuous Emission ◽  
Coriolis Parameter ◽  
Balanced Flow ◽  
Grid Points ◽  
Fine Resolution ◽  
Enstrophy Cascade ◽  
Inertia Gravity Waves

Abstract. Using a fine resolution numerical model (40002 × 2 grid-points) of the two-layer shallow-water equations of the mid-latitude β-plane dynamics, it is shown that there is no sudden breakdown of balance in the turbulent enstrophy cascade but a faint and continuous emission of inertia–gravity waves. The wave energy accumulates in the equator-ward region of the domain due to the Coriolis parameter depending on the latitude and dispersion relation of inertia–gravity waves.

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.

Primitive Equations Model

2018 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Tangent Plane ◽  
Primitive Equations ◽  
Vertical Coordinate ◽  
Rotating Sphere ◽  
Beta Plane ◽  
Key Concepts ◽  
Judicious Choice ◽  
Inertia Gravity Waves

The chapter gives the foundations of modelling of large-scale atmospheric and oceanic motions and presents the ‘primitive equations’ (PE) model. After a concise reminder on general fluid mechanics, the main hypotheses leading to the PE model are explained, together with the tangent-plane (so-called f and beta plane) approximations, and ‘traditional’ approximation to the hydrodynamical equations on the rotating sphere. PE are derived in parallel for the ocean and for the atmosphere. It is then shown that, with a judicious choice of the vertical coordinate, the ‘pseudo-height’, in the atmosphere, these two sets of equations are practically equivalent. The main properties of PE are derived and the key concepts of wave–vortex dichotomy, and of slow and fast motions, are explained. The essential notion of potential vorticity is introduced and its conservation by fluid masses is demonstrated. Inertia–gravity waves are explained and their properties presented. Limitations of the hydrostatic hypothesis are demonstrated.

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