scholarly journals Dynamics of Mechanical Oscillator Mechanism for Stratospheric Gravity Waves Generated by Convection

Atmosphere ◽  
2020 ◽  
Vol 11 (9) ◽  
pp. 942
Author(s):  
Shiwang Yu ◽  
Lifeng Zhang ◽  
Ming Zhang ◽  
Yuan Wang
Keyword(s):  
Gravity Waves ◽  
Boussinesq Approximation ◽  
Generation Mechanism ◽  
Buoyancy Frequency ◽  
Background Wind ◽  
Dynamics Model ◽  
Mechanical Oscillator ◽  
Vortex System ◽  
Wave Resonance ◽  
Intrinsic Characteristic

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.

scholarly journals Linear Spectral Numerical Model for Internal Gravity Wave Propagation

2010 ◽  
Vol 67 (5) ◽  
pp. 1632-1642 ◽  
Author(s):  
J. Marty ◽  
F. Dalaudier
Keyword(s):  
Numerical Model ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Three Dimensional ◽  
Internal Gravity Wave ◽  
Temporal Variations ◽  
Buoyancy Frequency ◽  
Background Wind ◽  
First Order ◽  
Good Agreement

Abstract A three-dimensional linear spectral numerical model is proposed to simulate the propagation of internal gravity wave fluctuations in a stably stratified atmosphere. The model is developed to get first-order estimations of gravity wave fluctuations produced by identified sources. It is based on the solutions of the linearized fundamental fluid equations and uses the fully compressible dispersion relation for inertia–gravity waves. The spectral implementation excludes situations involving spatial variations of buoyancy frequency or background wind. However, density stratification variations are taken into account in the calculation of fluctuation amplitudes. In addition to gravity wave packet free propagation, the model handles both impulsive and continuous sources. It can account for spatial and temporal variations of the sources, encompassing a broad range of physical situations. The method is validated with a monochromatic pressure monopole, which is known to generate St. Andrew’s cross–shaped waves. It is then applied to the case of the ozone layer cooling during a total solar eclipse. The asymptotic response to a Gaussian thermal forcing traveling at constant velocity and the transient response to the 4 December 2002 eclipse show good agreement with previous numerical simulations. Further applications for the model are discussed.

Radiation of internal waves from groups of surface gravity waves

2017 ◽  
Vol 829 ◽  
pp. 280-303 ◽  
Author(s):  
S. Haney ◽  
W. R. Young
Keyword(s):  
Internal Waves ◽  
Energy Flux ◽  
Gravity Waves ◽  
Three Dimensions ◽  
Stokes Drift ◽  
Surface Gravity ◽  
Fourth Power ◽  
Buoyancy Frequency ◽  
Surface Gravity Waves ◽  
Short Period

Groups of surface gravity waves induce horizontally varying Stokes drift that drives convergence of water ahead of the group and divergence behind. The mass flux divergence associated with spatially variable Stokes drift pumps water downwards in front of the group and upwards in the rear. This ‘Stokes pumping’ creates a deep Eulerian return flow that sets the isopycnals below the wave group in motion and generates a trailing wake of internal gravity waves. We compute the energy flux from surface to internal waves by finding solutions of the wave-averaged Boussinesq equations in two and three dimensions forced by Stokes pumping at the surface. The two-dimensional (2-D) case is distinct from the 3-D case in that the stratification must be very strong, or the surface waves very slow for any internal wave (IW) radiation at all. On the other hand, in three dimensions, IW radiation always occurs, but with a larger energy flux as the stratification and surface wave (SW) amplitude increase or as the SW period is shorter. Specifically, the energy flux from SWs to IWs varies as the fourth power of the SW amplitude and of the buoyancy frequency, and is inversely proportional to the fifth power of the SW period. Using parameters typical of short period swell (e.g. 8 s SW period with 1 m amplitude) we find that the energy flux is small compared to both the total energy in a typical SW group and compared to the total IW energy. Therefore this coupling between SWs and IWs is not a significant sink of energy for the SWs nor a source for IWs. In an extreme case (e.g. 4 m amplitude 20 s period SWs) this coupling is a significant source of energy for IWs with frequency close to the buoyancy frequency.

scholarly journals The semiannual oscillation (SAO) in the tropical middle atmosphere and its gravity wave driving in reanalyses and satellite observations

2021 ◽  
Vol 21 (18) ◽  
pp. 13763-13795
Author(s):  
Manfred Ern ◽  
Mohamadou Diallo ◽  
Peter Preusse ◽  
Martin G. Mlynczak ◽  
Michael J. Schwartz ◽  
...  
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Wave Drag ◽  
Satellite Observations ◽  
Absolute Gravity ◽  
Data Sets ◽  
Background Wind ◽  
Wind Climatology ◽  
Basic Features ◽  
Semiannual Oscillation

Abstract. Gravity waves play a significant role in driving the semiannual oscillation (SAO) of the zonal wind in the tropics. However, detailed knowledge of this forcing is missing, and direct estimates from global observations of gravity waves are sparse. For the period 2002–2018, we investigate the SAO in four different reanalyses: ERA-Interim, JRA-55, ERA-5, and MERRA-2. Comparison with the SPARC zonal wind climatology and quasi-geostrophic winds derived from Microwave Limb Sounder (MLS) and Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) satellite observations show that the reanalyses reproduce some basic features of the SAO. However, there are also large differences, depending on the model setup. Particularly, MERRA-2 seems to benefit from dedicated tuning of the gravity wave drag parameterization and assimilation of MLS observations. To study the interaction of gravity waves with the background wind, absolute values of gravity wave momentum fluxes and a proxy for absolute gravity wave drag derived from SABER satellite observations are compared with different wind data sets: the SPARC wind climatology; data sets combining ERA-Interim at low altitudes and MLS or SABER quasi-geostrophic winds at high altitudes; and data sets that combine ERA-Interim, SABER quasi-geostrophic winds, and direct wind observations by the TIMED Doppler Interferometer (TIDI). In the lower and middle mesosphere the SABER absolute gravity wave drag proxy correlates well with positive vertical gradients of the background wind, indicating that gravity waves contribute mainly to the driving of the SAO eastward wind phases and their downward propagation with time. At altitudes 75–85 km, the SABER absolute gravity wave drag proxy correlates better with absolute values of the background wind, suggesting a more direct forcing of the SAO winds by gravity wave amplitude saturation. Above about 80 km SABER gravity wave drag is mainly governed by tides rather than by the SAO. The reanalyses reproduce some basic features of the SAO gravity wave driving: all reanalyses show stronger gravity wave driving of the SAO eastward phase in the stratopause region. For the higher-top models ERA-5 and MERRA-2, this is also the case in the lower mesosphere. However, all reanalyses are limited by model-inherent damping in the upper model levels, leading to unrealistic features near the model top. Our analysis of the SABER and reanalysis gravity wave drag suggests that the magnitude of SAO gravity wave forcing is often too weak in the free-running general circulation models; therefore, a more realistic representation is needed.

scholarly journals Observation and a numerical study of gravity waves during tropical cyclone Ivan~(2008)

2013 ◽  
Vol 13 (4) ◽  
pp. 10757-10807 ◽  
Author(s):  
F. Chane Ming ◽  
C. Ibrahim ◽  
S. Jolivet ◽  
P. Keckhut ◽  
Y.-A. Liou ◽  
...  
Keyword(s):  
Tropical Cyclone ◽  
Gravity Waves ◽  
High Frequency ◽  
Lower Stratosphere ◽  
Numerical Study ◽  
Wide Spectrum ◽  
Spectral Characteristics ◽  
Background Wind ◽  
Quasi Biennial Oscillation ◽  
North East

Abstract. Activity and spectral characteristics of gravity-waves (GWs) are analyzed during tropical cyclone (TC) Ivan (2008) in the troposphere and lower stratosphere using radiosonde and GPS radio occultation data, ECMWF outputs and simulations of French numerical model Meso-NH with vertical resolution varying between 150 m near the surface and 500 m in the lower stratosphere. Conventional methods for GW analysis and signal and image processing tools provide information on a wide spectrum of GWs with horizontal wavelengths of 40–1800 km and short vertical wavelengths of 0.6–10 km respectively and periods of 20 min–2 days. MesoNH model, initialized with Aladin-Réunion analyses, produces realistic and detailed description of TC dynamics, GWs, variability of the tropospheric and stratospheric background wind and TC rainband characteristics at different stages of TC Ivan. In particular a dominant eastward propagating TC-related quasi-inertia GW is present during intensification of TC Ivan with horizontal and vertical wavelengths of 400–600 km and 1.5–3.5 km respectively during intensification. A wavenumber-1 vortex Rossby wave is identified as a source of this medium-scale mode while short-scale modes located at north-east and south-east of the TC could be attributed to strong localized convection in spiral bands resulting from wavenumber-2 vortex Rossby waves. Meso-NH simulations also reveal high-frequency GWs with horizontal wavelengths of 20–80 km near the TC eye and high-frequency GWs-related clouds behind TC Ivan. In addition, GWs produced during landfall are likely to strongly contribute to background wind in the middle and upper troposphere as well as the stratospheric quasi-biennial oscillation.

Impact of Vertical Wind Shear on Gravity Wave Propagation in the Land–Sea-Breeze Circulation at the Equator

2019 ◽  
Vol 76 (10) ◽  
pp. 3247-3265
Author(s):  
Yu Du ◽  
Richard Rotunno ◽  
Fuqing Zhang
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Wind Shear ◽  
Vertical Wind Shear ◽  
Sea Breeze ◽  
Vertical Wind ◽  
Background Wind ◽  
Breeze Circulation ◽  
Attenuation Level ◽  
Ray Path

Abstract The impact of vertical wind shear on the land–sea-breeze circulation at the equator is explored using idealized 2D numerical simulations and a simple 2D linear analytical model. Both the idealized and linear analytical models indicate Doppler shifting and attenuation effects coexist under the effect of vertical wind shear for the propagation of gravity waves that characterize the land–sea-breeze circulation. Without a background wind, the idealized sea breeze has two ray paths of gravity waves that extend outward and upward from the coast. A uniform background wind causes a tilting of the two ray paths due to Doppler shifting. With vertical shear in the background wind, the downstream ray path of wave propagation can be rapidly attenuated near a certain level, whereas the upstream ray path is not attenuated and the amplitudes even increase with height. The downstream attenuation level is found to descend with increasing linear wind shear. The present analytical model establishes that the attenuation level corresponds to the critical level where the background wind is equal to the horizontal gravity wave phase speed. The upstream gravity wave ray path can propagate upward without attenuation as there is no critical level there.

Hopf Bifurcation in the Double-Glazing Problem With Conducting Boundaries

1987 ◽  
Vol 109 (4) ◽  
pp. 894-898 ◽  
Author(s):  
K. H. Winters
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Gravity Waves ◽  
Traveling Waves ◽  
Critical Rayleigh Number ◽  
Boussinesq Approximation ◽  
Time Dependent ◽  
Oscillatory Convection ◽  
Extended System ◽  
State Equations

Oscillatory convection has been observed in recent experiments in a square, air-filled cavity with differentially heated sidewalls and conducting horizontal surfaces. We show that the onset of the oscillatory convection occurs at a Hopf bifurcation in the steady-state equations for free convection in the Boussinesq approximation. The location of the bifurcation point is found by solving an extended system of steady-state equations. The predicted critical Rayleigh number and frequency at the onset of oscillations are in excellent agreement with the values measured recently and with those of a time-dependent simulation. Four other Hopf bifurcation points are found near the critical point and their presence supports a conjectured resonance between traveling waves in the boundary layers and interior gravity waves in the stratified core.

Reflection properties of internal gravity waves incident upon a hyperbolic tangent shear layer

1982 ◽  
Vol 120 ◽  
pp. 505-521 ◽  
Author(s):  
Cornelis A. Van Duin ◽  
Hennie Kelder
Keyword(s):  
Shear Layer ◽  
Gravity Waves ◽  
Critical Level ◽  
Boussinesq Approximation ◽  
Internal Gravity Waves ◽  
Hyperbolic Tangent ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Heun’S Equation ◽  
Stable Flow

The properties of reflection and transmission of internal gravity waves incident upon a shear layer containing a critical level are investigated. The shear layer is modelled by a hyperbolic tangent profile. In the Boussinesq approximation, the differential equation governing the propagation of these waves can then be transformed into Heun's equation. For large Richardson numbers this equation can be approximated by an equation that has solutions in terms of hypergeometric functions. For these values of the Richardson number the reflection coefficient proves to be strongly dependent on the place of the critical level in the shear flow. If the Doppler-shifted frequency is an odd function of the height difference with respect to the critical level, the reflection and transmission coefficients can be evaluated in closed form.Over-reflection is possible for sufficiently small wavenumbers and Richardson numbers. It is pointed out that over-reflection and over-transmission cannot occur in a stable flow and that resonant over-reflection is not possible in our model.

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.

scholarly journals An Improved Weak Pressure Gradient Scheme for Single-Column Modeling

2014 ◽  
Vol 71 (7) ◽  
pp. 2415-2429 ◽  
Author(s):  
Jacob P. Edman ◽  
David M. Romps
Keyword(s):  
Pressure Gradient ◽  
Gravity Waves ◽  
Large Scale ◽  
Atmospheric Models ◽  
Wave Resonance ◽  
Single Column ◽  
The One ◽  
New Formulation ◽  
Weak Pressure Gradient ◽  
Steady State Solutions

Abstract A new formulation of the weak pressure gradient approximation (WPG) is introduced for parameterizing large-scale dynamics in limited-domain atmospheric models. This new WPG is developed in the context of the one-dimensional, linearized, damped, shallow-water equations and then extended to Boussinesq and compressible fluids. Unlike previous supradomain-scale parameterizations, this formulation of WPG correctly reproduces both steady-state solutions and first baroclinic gravity waves. In so doing, this scheme eliminates the undesirable gravity wave resonance in previous versions of WPG. In addition, this scheme can be extended to accurately model the emission of gravity waves with arbitrary vertical wavenumber.

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