Generation and stability of inertia–gravity waves

2016 ◽  
Vol 808 ◽  
pp. 539-561 ◽  
Author(s):  
P. Maurer ◽  
S. Joubaud ◽  
P. Odier
Keyword(s):  
Gravity Waves ◽  
Finite Size ◽  
Deep Ocean ◽  
Wave Frequency ◽  
Secondary Wave ◽  
Infinite Plane ◽  
Coriolis Parameter ◽  
Ocean Stratification ◽  
Set Up ◽  
Inertia Gravity Waves

In the ocean, stratification and rotation allow for the existence of inertia–gravity waves. Instabilities of these waves, such as triadic resonant instability (TRI), may play a key role in the mixing process of the deep ocean. In an experimental set-up, we generate inertia–gravity waves which may become unstable depending on the background rotation and wave frequency. The instability produces secondary waves that match the spatial and temporal resonance conditions of TRI. The effect of rotation is introduced in a pre-existing theory and results in a prediction of the growth rate of TRI in the case of an infinite plane wave. The issue of finite size of the beam is then addressed using a simple model in which we show that the instability is enhanced in a given range of Coriolis parameter. Finally, we compare the experimental threshold of the instability with the model, and find good agreement except at higher rotation rate. At constant primary wave frequency, we analyse the evolution of the secondary wave characteristics with rotation. The appearance of unexpected sub-inertial secondary waves may be related to the discrepancy observed between predicted and experimental thresholds at higher rotation.

Inertia-gravity waves beyond the inertial latitude. Part 1. Inviscid singular focusing

2010 ◽  
Vol 664 ◽  
pp. 478-509 ◽  
Author(s):  
VICTOR I. SHRIRA ◽  
WILLIAM A. TOWNSEND
Keyword(s):  
Wave Field ◽  
Internal Waves ◽  
Gravity Waves ◽  
Deep Ocean ◽  
Vertical Shear ◽  
Buoyancy Frequency ◽  
Local Minima ◽  
Wave Evolution ◽  
Vertical Scales ◽  
Inertia Gravity Waves

The paper is concerned with analytical study of inertia-gravity waves in rotating density-stratified ideal fluid confined in a spherical shell. It primarily aims at clarifying the possible role of these motions in deep ocean mixing. Recently, it was found that on the ‘non-traditional’ β-plane inertia-gravity internal waves can propagate polewards beyond their inertial latitude, where the wave frequency equals the local Coriolis parameter, by turning into subinertial modes trapped in the narrowing waveguides around the local minima of buoyancy frequency N. The behaviour of characteristics was established: wave horizontal and vertical scales decrease as the wave advances polewards and tend to zero at a latitude corresponding to an attractor of characteristics. However, the basic questions about wave evolution, its quantitative description and the possibility of its reflection from the critical latitude remain open. The present work addresses these issues by studying the linear inviscid evolution of finite bandwidth wavepackets on the ‘non-traditional’ β-plane past the inertial latitude for generic oceanic stratification. Beyond the inertial latitude, the wave field is confined in narrowing waveguides of three distinct generic types around different local minima of the buoyancy frequency. In the oceanic context, the widest is adjacent to the flat bottom, the thinnest is the upper mixed layer, and the middle one is located between the seasonal and main thermocline. We find explicit asymptotic solutions describing the wave field in the WKB approximation. As a byproduct, the conservation of wave action principle is explicitly formulated for all types of internal waves on the ‘non-traditional’ β-plane. The wave velocities and vertical shear tend to infinity and become singular at the attractor latitude or its vicinity for both monochromatic and finite bandwidth packets. We call this phenomenon singular focusing. These WKB solutions are shown to remain valid up to singularity for the bottom and mid-ocean waveguides. The main conclusion is that even in the inviscid setting the wave evolution towards smaller and smaller horizontal and vertical scales is irreversible: there is no reflection. For situations typical of deep ocean, a simultaneous increase in wave amplitude and decrease of vertical scale causes a sharp increase of vertical shear, which may lead to wave breaking and increased mixing.

Inertia–Gravity Waves Generated within a Dipole Vortex

2007 ◽  
Vol 64 (12) ◽  
pp. 4417-4431 ◽  
Author(s):  
Chris Snyder ◽  
David J. Muraki ◽  
Riwal Plougonven ◽  
Fuqing Zhang
Keyword(s):  
Gravity Waves ◽  
Initial Conditions ◽  
Initial Period ◽  
Potential Temperature ◽  
Leading Edge ◽  
Vertical Shear ◽  
Coriolis Parameter ◽  
Dipole Vortex ◽  
The Waves ◽  
Inertia Gravity Waves

Abstract Vortex dipoles provide a simple representation of localized atmospheric jets. Numerical simulations of a synoptic-scale dipole in surface potential temperature are considered in a rotating, stratified fluid with approximately uniform potential vorticity. Following an initial period of adjustment, the dipole propagates along a slightly curved trajectory at a nearly steady rate and with a nearly fixed structure for more than 50 days. Downstream from the jet maximum, the flow also contains smaller-scale, upward-propagating inertia–gravity waves that are embedded within and stationary relative to the dipole. The waves form elongated bows along the leading edge of the dipole. Consistent with propagation in horizontal deformation and vertical shear, the waves’ horizontal scale shrinks and the vertical slope varies as they approach the leading stagnation point in the dipole’s flow. Because the waves persist for tens of days despite explicit dissipation in the numerical model that would otherwise damp the waves on a time scale of a few hours, they must be inherent features of the dipole itself, rather than remnants of imbalances in the initial conditions. The wave amplitude varies with the strength of the dipole, with waves becoming obvious once the maximum vertical vorticity in the dipole is roughly half the Coriolis parameter. Possible mechanisms for the wave generation are spontaneous wave emission and the instability of the underlying balanced dipole.

scholarly journals Deep ocean inertia-gravity waves simulated in a high-resolution global coupled atmosphere–ocean GCM

2008 ◽  
Vol 35 (4) ◽  
Author(s):  
Nobumasa Komori ◽  
Wataru Ohfuchi ◽  
Bunmei Taguchi ◽  
Hideharu Sasaki ◽  
Patrice Klein
Keyword(s):  
High Resolution ◽  
Gravity Waves ◽  
Deep Ocean ◽  
Inertia Gravity Waves

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 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.

Inertio-gravity waves under the non-traditional -plane approximation: singularity in the large-scale limit

2016 ◽  
Vol 810 ◽  
pp. 475-488 ◽  
Author(s):  
Jun-Ichi Yano
Keyword(s):  
Gravity Waves ◽  
Taylor Expansion ◽  
Large Scale ◽  
Rotation Axis ◽  
Vertical Direction ◽  
Wave Frequency ◽  
Coriolis Parameter ◽  
Higher Order Terms ◽  
Solution Behaviour ◽  
Scale Limit

The low horizontal wavenumber limit of waves on a plane under a constant rotation rate (the so-called $f$-plane) is degenerate: all wave frequencies asymptotically approach the inertial frequency. This degeneracy has no serious consequence when the rotation axis is perpendicular to the plane (traditional $f$-plane approximation). However, when the rotation axis is tilted from the vertical direction (non-traditional $f$-plane approximation), we encounter a type of ‘singularity’ in the sense that each term of the Taylor expansion of the wave frequency in the horizontal Coriolis parameter diverges in the limit of low horizontal wavenumber. Such a drastic change of the solution behaviour by adding the horizontal Coriolis parameter in the low horizontal wavenumber limit is rather counter-intuitive, because the conventional scale analysis suggests that the horizontal Coriolis effect is negligible in this limit. However, the degeneracy of the system makes this effect critical with a need for considering higher-order terms. Two possible asymptotic limits are proposed for resolving this degeneracy. One of them, as it turns out, amounts to a representation of the wave frequency by a Taylor expansion in the horizontal wavenumber.

scholarly journals Properties of inertia-gravity waves in the lowermost stratosphere as observed by the PANSY radar over Syowa Station in the Antarctic

2016 ◽  
Vol 34 (5) ◽  
pp. 543-555 ◽  
Author(s):  
Maria Mihalikova ◽  
Kaoru Sato ◽  
Masaki Tsutsumi ◽  
Toru Sato
Keyword(s):  
Gravity Waves ◽  
Middle Atmosphere ◽  
Winter Season ◽  
Radiosonde Data ◽  
Coriolis Parameter ◽  
Antarctic Region ◽  
Height Range ◽  
Hodograph Method ◽  
The Antarctic ◽  
Inertia Gravity Waves

Abstract. Inertia-gravity waves (IGWs) are an important component for the dynamics of the middle atmosphere. However, observational studies needed to constrain their forcing are still insufficient especially in the remote areas of the Antarctic region. One year of observational data (January to December 2013) by the PANSY radar of the wind components (vertical resolution of 150 m and temporal resolution of 30 min) are used to derive statistical analysis of the properties of IGWs with short vertical wavelengths ( ≤ 4 km) and ground-based periods longer than 4 h in the lowermost stratosphere (height range 10 to 12 km) with the help of the hodograph method. The annual change of the IGWs parameters are inspected but no pronounced year cycle is found. The year is divided into two seasons (summer and winter) based on the most prominent difference in the ratio of Coriolis parameter (f) to intrinsic frequency (ω^) distribution. Average of f∕ω^  for the winter season is 0.40 and for the summer season 0.45 and the average horizontal wavelengths are 140 and 160 km respectively. Vertical wavelengths have an average of 1.85 km through the year. For both seasons the properties of IGWs with upward and downward propagation of the energy are also derived and compared. The percentage of downward propagating waves is 10.7 and 18.4 % in the summer and winter season respectively. This seasonal change is more than the one previously reported in the studies from mid-latitudes and model-based studies. It is in agreement with the findings of past radiosonde data-based studies from the Antarctic region. In addition, using the so-called dual-beam technique, vertical momentum flux and the variance of the horizontal perturbation velocities of IGWs are examined. Tropospheric disturbances of synoptic-scale are suggested as a source of episodes of IGWs with large variance of horizontal perturbation velocities, and this is shown in a number of cases.

Wave Turbulence

2018 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Gravity Waves ◽  
Random Phase ◽  
Kinetic Equations ◽  
Finite Size ◽  
Approximate Solutions ◽  
Collision Integral ◽  
Turbulence Theory ◽  
Energy Spectra ◽  
Random Waves ◽  
Inertia Gravity Waves

Main notions and ideas of wave (weak) turbulence theory are explained with the help of Hamiltonian approach to wave dynamics, and are applied to waves in RSW model. Derivation of kinetic equations under random-phase approximation is explained. Short inertia–gravity waves on the f plane, short equatorial inertia–gravity waves, and Rossby waves on the beta plane are then considered along these lines. In all of these cases, approximate solutions of kinetic equation, annihilating the collision integral, can be obtained by scaling arguments, giving power-law energy spectra. The predictions of turbulence of inertia–gravity waves on the f plane are compared with numerical simulations initialised by ensembles of random waves. Energy spectra much steeper than theoretical are observed. Finite-size effects, which prevent energy transfer from large to short scales, provide a plausible explanation. Long waves thus evolve towards breaking and shock formation, yet the number of shocks is insufficient to produce shock turbulence.

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