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 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>

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.

scholarly journals A Theoretical Study on the Spontaneous Radiation of Inertia–Gravity Waves Using the Renormalization Group Method. Part II: Verification of the Theoretical Equations by Numerical Simulation

2015 ◽  
Vol 72 (3) ◽  
pp. 984-1009 ◽  
Author(s):  
Yuki Yasuda ◽  
Kaoru Sato ◽  
Norihiko Sugimoto
Keyword(s):  
Renormalization Group ◽  
Numerical Simulations ◽  
Large Scale ◽  
Companion Paper ◽  
Vortical Flow ◽  
Japan Meteorological Agency ◽  
Velocity Variation ◽  
Group Method ◽  
Spontaneous Radiation ◽  
Momentum Fluxes

Abstract The renormalization group equations (RGEs) describing spontaneous inertia–gravity wave (GW) radiation from part of a balanced flow through a quasi resonance that were derived in a companion paper by Yasuda et al. are validated through numerical simulations of the vortex dipole using the Japan Meteorological Agency nonhydrostatic model (JMA-NHM). The RGEs are integrated for two vortical flow fields: the first is the initial condition that does not contain GWs used for the JMA-NHM simulations, and the second is the simulated thirtieth-day field by the JMA-NHM. The theoretically obtained GW distributions in both RGE integrations are consistent with the numerical simulations using the JMA-NHM. This result supports the validity of the RGE theory. GW radiation in the dipole is physically interpreted either as the mountain-wave-like mechanism proposed by McIntyre or as the velocity-variation mechanism proposed by Viúdez. The shear of the large-scale flow likely determines which mechanism is dominant. In addition, the distribution of GW momentum fluxes is examined based on the JMA-NHM simulation data. The GWs propagating upward from the jet have negative momentum fluxes, while those propagating downward have positive ones. The magnitude of momentum fluxes is approximately proportional to the sixth power of the Rossby number between 0.15 and 0.4.

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 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 ◽  
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.

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.

Mechanisms for Spontaneous Gravity Wave Generation within a Dipole Vortex

2009 ◽  
Vol 66 (11) ◽  
pp. 3464-3478 ◽  
Author(s):  
Chris Snyder ◽  
Riwal Plougonven ◽  
David J. Muraki
Keyword(s):  
Gravity Waves ◽  
Linear Equations ◽  
Leading Edge ◽  
Wave Generation ◽  
Small Scale ◽  
Homogeneous Solutions ◽  
Dipole Vortex ◽  
Balanced Flow ◽  
The Waves ◽  
Inertia Gravity Waves

Abstract Previous simulations of dipole vortices propagating through rotating, stratified fluid have revealed small-scale inertia–gravity waves that are embedded within the dipole near its leading edge and are approximately stationary relative to the dipole. The mechanism by which these waves are generated is investigated, beginning from the observation that the dipole can be reasonably approximated by a balanced quasigeostrophic (QG) solution. The deviations from the QG solution (including the waves) then satisfy linear equations that come from linearization of the governing equations about the QG dipole and are forced by the residual tendency of the QG dipole (i.e., the difference between the time tendency of the QG solution and that of the full primitive equations initialized with the QG fields). The waves do not appear to be generated by an instability of the balanced dipole, as homogeneous solutions of the linear equations amplify little over the time scale for which the linear equations are valid. Linear solutions forced by the residual tendency capture the scale, location, and pattern of the inertia–gravity waves, although they overpredict the wave amplitude by a factor of 2. There is thus strong evidence that the waves are generated as a forced linear response to the balanced flow. The relation to and differences from other theories for wave generation by balanced flows, including those of Lighthill and Ford et al., are discussed.

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