scholarly journals Large-Scale Modes in a Rotating Atmosphere with Radiative–Convective Instability and WISHE

2005 ◽  
Vol 62 (11) ◽  
pp. 4084-4094 ◽  
Author(s):  
Zeljka Fuchs ◽  
David J. Raymond
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Normal Modes ◽  
Moist Convection ◽  
Mean Flow ◽  
Beta Plane ◽  
Additional Mode ◽  
Diabatic Processes ◽  
Relaxation Time Scale ◽  
The One

Abstract A highly simplified parameterization of diabatic processes is applied to linearized equations on a equatorial beta plane. The diabatic processes include moist convection, cloud–radiation interactions (CRI), and wind-induced surface heat exchange (WISHE). The precipitation rate is assumed to increase linearly as the vertically averaged saturation deficit decreases. The modeled modes are Matsuno’s normal modes, that is, Kelvin waves, mixed Rossby–gravity waves, Rossby waves, and inertio–gravity waves, and an additional mode called here a slow moisture mode. All of the Matsuno modes are damped and remain stable even when CRI and WISHE are turned on. Their phase speeds do not vary much from Matsuno’s adiabatic values except for very long wavelength Kelvin and Rossby modes, for which the phase speeds are reduced compared to the adiabatic values. The slow moisture modes are stationary and unstable under CRI, while WISHE causes them to propagate. Under CRI and WISHE together the slow moisture modes are unstable and eastward propagating for long wavelengths and slowly moving relative to the mean flow for short wavelengths. The dispersion relations of the slow moisture modes are one of nearly constant or decreasing frequency with increasing wavenumber. The most important model parameter is the tropospheric moisture relaxation time scale, which is chosen to be 1 day. The model failed to explain the observed phase speeds of convectively coupled Matsuno modes. Following Mapes, the authors suggest that other dynamics, more realistic than the one including only the first baroclinic mode, may be responsible for these modes.

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.

scholarly journals Rossby waves and two-dimensional turbulence in a large-scale zonal jet

1987 ◽  
Vol 183 ◽  
pp. 467-509 ◽  
Author(s):  
Theodore G. Shepherd
Keyword(s):  
Large Scale ◽  
Zonal Flow ◽  
Order Effect ◽  
Spatial Inhomogeneity ◽  
Mean Flow ◽  
Scale Separation ◽  
Zonal Flows ◽  
Beta Plane ◽  
Zonal Wavenumber ◽  
Scale Shear

The theory of homogeneous barotropic beta-plane turbulence is here extended to include effects arising from spatial inhomogeneity in the form of a zonal shear flow. Attention is restricted to the geophysically important case of zonal flows that are barotropically stable and are of larger scale than the resulting transient eddy field.Because of the presumed scale separation, the disturbance enstrophy is approximately conserved in a fully nonlinear sense, and the (nonlinear) wave-mean-flow interaction may be characterized as a shear-induced spectral transfer of disturbance enstrophy along lines of constant zonal wavenumber k. In this transfer the disturbance energy is generally not conserved. The nonlinear interactions between different disturbance components are turbulent for scales smaller than the inverse of Rhines's cascade-arrest scale κβ≡ (β0/2urms)½ and in this regime their leading-order effect may be characterized as a tendency to spread the enstrophy (and energy) along contours of constant total wavenumber κ ≡ (k2 + l2)½. Insofar as this process of turbulent isotropization involves spectral transfer of disturbance enstrophy across lines of constant zonal wavenumber k, it can be readily distinguished from the shear-induced transfer which proceeds along them. However, an analysis in terms of total wavenumber K alone, which would be justified if the flow were homogeneous, would tend to mask the differences.The foregoing theoretical ideas are tested by performing direct numerical simulation experiments. It is found that the picture of classical beta-plane turbulence is altered, through the effect of the large-scale zonal flow, in the following ways: (i) while the turbulence is still confined to KKβ, the disturbance field penetrates to the largest scales of motion; (ii) the larger disturbance scales K < Kβ exhibit a tendency to meridional rather than zonal anisotropy, namely towards v2 > u2 rather than vice versa; (iii) the initial spectral transfer rate away from an isotropic intermediate-scale source is significantly enhanced by the shear-induced transfer associated with straining by the zonal flow. This last effect occurs even when the large-scale shear appears weak to the energy-containing eddies, in the sense that dU/dy [Lt ] κ for typical eddy length and velocity scales.

scholarly journals Mesospheric gravity wave activity estimated via airglow imagery, multistatic meteor radar, and SABER data taken during the SIMONe–2018 campaign

2020 ◽  
Author(s):  
Fabio Vargas ◽  
Jorge L. Chau ◽  
Harikrishnan Charuvil Asokan ◽  
Michael Gerding
Keyword(s):  
Gravity Waves ◽  
Momentum Flux ◽  
Large Scale ◽  
Lower Thermosphere ◽  
Small Scale ◽  
Meteor Radar ◽  
Mean Flow ◽  
Horizontal Scale ◽  
Momentum Fluxes ◽  
Mesosphere And Lower Thermosphere

Abstract. We describe in this study the analysis of small and large horizontal scale gravity waves from datasets composed of images from multiple mesospheric nightglow emissions as well as multistatic specular meteor radar (MSMR) winds collected in early November 2018, during the SIMONe–2018 campaign. These ground-based measurements are supported by temperature and neutral density profiles from TIMED/SABER satellite in orbits near Kühlungsborn, northern Germany (54.1° N, 11.8° E). The scientific goals here include the characterization of gravity waves and their interaction with the mean flow in the mesosphere and lower thermosphere and their relationship to dynamical conditions in the lower and upper atmosphere. We obtain intrinsic parameters of small and large horizontal scale gravity waves and characterize their impact in the mesosphere region via momentum flux and flux divergence estimations. We have verified that a small percent of the detected wave events are responsible for most of the momentum flux measured during the campaign from oscillations seen in the airglow brightness and MSMR winds. From the analysis of small-scale gravity waves in airglow images, we have found wave momentum fluxes ranging from 0.38 to 24.74 m2/s2 (0.88 ± 0.73 m2/s2 on average), with a total of 586.96 m2/s2 (sum over all 362 detected waves). However, small horizontal scale waves with flux > 3 m2/s2 (11 % of the events) transport 50 % of the total measured flux. Likewise, wave events having flux > 10 m2/s2 (2 % of the events) transport 20 % of the total flux. The examination of two large-scale waves seen simultaneously in airglow keograms and MSMR winds revealed relative amplitudes > 35 %, which translates into momentum fluxes of 21.2–29.6 m/s. In terms of gravity wave–mean flow interactions, these high momentum flux waves could cause decelerations of 22–41 m/s/day (small-scale waves) and 38–43 m/s/day (large-scale waves) if breaking or dissipating within short distances in the mesosphere and lower thermosphere region. The dominant large-scale waves might be the result of secondary gravity excited from imbalanced flow in the stratosphere caused by primary wave breaking.

Inertia–gravity waves in a liquid-filled, differentially heated, rotating annulus

2015 ◽  
Vol 782 ◽  
pp. 144-177 ◽  
Author(s):  
Anthony Randriamampianina ◽  
Emilia Crespo del Arco
Keyword(s):  
Prandtl Number ◽  
Gravity Waves ◽  
Large Scale ◽  
Baroclinic Instability ◽  
Zonal Flow ◽  
Small Scale ◽  
Mean Flow ◽  
Baroclinic Waves ◽  
Fluid Properties ◽  
Spatio Temporal

Direct numerical simulations based on high-resolution pseudospectral methods are carried out for detailed investigation into the instabilities arising in a differentially heated, rotating annulus, the baroclinic cavity. Following previous works using air (Randriamampianina et al., J. Fluid Mech., vol. 561, 2006, pp. 359–389), a liquid defined by Prandtl number $Pr=16$ is considered in order to better understand, via the Prandtl number, the effects of fluid properties on the onset of gravity waves. The computations are particularly aimed at identifying and characterizing the spontaneously emitted small-scale fluctuations occurring simultaneously with the baroclinic waves. These features have been observed as soon as the baroclinic instability sets in. A three-term decomposition is introduced to isolate the fluctuation field from the large-scale baroclinic waves and the time-averaged mean flow. Even though these fluctuations are found to propagate as packets, they remain attached to the background baroclinic waves, locally triggering spatio-temporal chaos, a behaviour not observed with the air-filled cavity. The properties of these features are analysed and discussed in the context of linear theory. Based on the Richardson number criterion, the characteristics of the generation mechanism are consistent with a localized instability of the shear zonal flow, invoking resonant over-reflection.

scholarly journals Squall Lines and Convectively Coupled Gravity Waves in the Tropics: Why Do Most Cloud Systems Propagate Westward?

2012 ◽  
Vol 69 (10) ◽  
pp. 2995-3012 ◽  
Author(s):  
Stefan N. Tulich ◽  
George N. Kiladis
Keyword(s):  
Gravity Waves ◽  
Wrf Model ◽  
Zonal Flow ◽  
Mean Flow ◽  
Wave Speeds ◽  
Squall Lines ◽  
Beta Plane ◽  
Pure Gravity ◽  
The Tropics ◽  
Inertia Gravity Waves

Abstract The coupling between tropical convection and zonally propagating gravity waves is assessed through Fourier analysis of high-resolution (3-hourly, 0.5°) satellite rainfall data. Results show the familiar enhancement in power along the dispersion curves of equatorially trapped inertia–gravity waves with implied equivalent depths in the range 15–40 m (i.e., pure gravity wave speeds in the range 12–20 m s−1). Here, such wave signals are seen to extend all the way down to zonal wavelengths of around 500 km and periods of around 8 h, suggesting that convection–wave coupling may be important even in the context of mesoscale squall lines. This idea is supported by an objective wave-tracking algorithm, which shows that many previously studied squall lines, in addition to “2-day waves,” can be classified as convectively coupled inertia–gravity waves with the dispersion properties of shallow-water gravity waves. Most of these disturbances propagate westward at speeds faster than the background flow. To understand why, the Weather Research and Forecast (WRF) Model is used to perform some near-cloud-resolving simulations of convection on an equatorial beta plane. Results indicate that low-level easterly shear of the background zonal flow, as opposed to steering by any mean flow, is essential for explaining the observed westward-propagation bias.

scholarly journals Statistical State Dynamics of Jet–Wave Coexistence in Barotropic Beta-Plane Turbulence

2016 ◽  
Vol 73 (5) ◽  
pp. 2229-2253 ◽  
Author(s):  
Navid C. Constantinou ◽  
Brian F. Farrell ◽  
Petros J. Ioannou
Keyword(s):  
Large Scale ◽  
Cooperative Interaction ◽  
Small Scale ◽  
Mean Flow ◽  
Theoretical Understanding ◽  
Laminar Jet ◽  
Planetary Scale ◽  
Statistical State ◽  
Beta Plane ◽  
Scale Turbulence

Abstract Jets coexist with planetary-scale waves in the turbulence of planetary atmospheres. The coherent component of these structures arises from cooperative interaction between the coherent structures and the incoherent small-scale turbulence in which they are embedded. It follows that theoretical understanding of the dynamics of jets and planetary-scale waves requires adopting the perspective of statistical state dynamics (SSD), which comprises the dynamics of the interaction between coherent and incoherent components in the turbulent state. In this work, the stochastic structural stability theory (S3T) implementation of SSD for barotropic beta-plane turbulence is used to develop a theory for the jet–wave coexistence regime by separating the coherent motions consisting of the zonal jets together with a selection of large-scale waves from the smaller-scale motions that constitute the incoherent component. It is found that mean flow–turbulence interaction gives rise to jets that coexist with large-scale coherent waves in a synergistic manner. Large-scale waves that would exist only as damped modes in the laminar jet are found to be transformed into exponentially growing waves by interaction with the incoherent small-scale turbulence, which results in a change in the mode structure, allowing the mode to tap the energy of the mean jet. This mechanism of destabilization differs fundamentally and serves to augment the more familiar S3T instabilities in which jets and waves arise from homogeneous turbulence with the energy source exclusively from the incoherent eddy field and provides further insight into the cooperative dynamics of the jet–wave coexistence regime in planetary turbulence.

On the vorticity transport due to dissipating or breaking waves in shallow-water flow

2000 ◽  
Vol 407 ◽  
pp. 235-263 ◽  
Author(s):  
OLIVER BÜHLER
Keyword(s):  
Numerical Simulations ◽  
Shallow Water ◽  
Gravity Waves ◽  
Large Scale ◽  
Bottom Topography ◽  
Breaking Waves ◽  
Small Scale ◽  
Practical Consideration ◽  
Mean Flow ◽  
Vorticity Transport

Theoretical and numerical results are presented on the transport of vorticity (or potential vorticity) due to dissipating gravity waves in a shallow-water system with background rotation and bottom topography. The results are obtained under the assumption that the flow can be decomposed into small-scale gravity waves and a large-scale mean flow. The particle-following formalism of ‘generalized Lagrangian-mean’ theory is then used to derive an ‘effective mean force’ that captures the vorticity transport due to the dissipating waves. This can be achieved without neglecting other, non-dissipative, effects which is an important practical consideration. It is then shown that the effective mean force obeys the so-called ‘pseudomomentum rule’, i.e. the force is approximately equal to minus the local dissipation rate of the wave's pseudomomentum. However, it is also shown that this holds only if the underlying dissipation mechanism is momentum-conserving. This requirement has important implications for numerical simulations, and these are discussed.The novelty of the results presented here is that they have been derived within a uniform theoretical framework, that they are not restricted to small wave amplitude, ray-tracing or JWKB-type approximations, and that they also include wave dissipation by breaking, or shock formation. The theory is tested carefully against shock-capturing nonlinear numerical simulations, which includes the detailed study of a wavetrain subject to slowly varying bottom topography. The theory is also cross-checked in the appropriate asymptotic limit against recently formulated weakly nonlinear theories. In addition to the general finite-amplitude theory, detailed small-amplitude expressions for the main results are provided in which the explicit appearance of Lagrangian fields can be avoided. The motivation for this work stems partly from an on-going study of high-altitude breaking of internal gravity waves in the atmosphere, and some preliminary remarks on atmospheric applications and on three-dimensional stratified versions of these results are given.

Simulation of Direct Contact Condensation Using Large Scale Interface Multifluid Model

2016 ◽  
Author(s):  
Vinesh H. Gada ◽  
Mohit P. Tandon ◽  
Jebin Elias ◽  
Andrew Splawski ◽  
Simon Lo
Keyword(s):  
Direct Contact ◽  
Large Scale ◽  
Cold Water ◽  
Cooling System ◽  
Euler Method ◽  
Two Phase ◽  
Relaxation Time Scale ◽  
The One ◽  
Core Cooling ◽  
Contact Condensation

The Large Scale Interface (LSI) model of the Euler-Euler method in STAR-CCM+ is extended to simulate two-phase flow with phase change. This extended methodology is used to simulate direct contact condensation (DCC) of steam in a hot leg when cold water is injected by emergency core cooling system to remove the residual heat. The case corresponds an experimental study conducted at Hungarian Atomic Energy Research Institute KFKI using the PMK-2 device. Out of the several experiments reported for this scenario, the one experiment considered in this work corresponds to a case without the water hammer phenomena. It was found that the LSI model is able to capture core physics of direct contact condensation during steam-water counter-current flow in a pipe. The model could capture entrapment of steam between the interface and its subsequent rapid condensation. The role of the relaxation time-scale of the large interface drag and the turbulence damping at interface is also studied.

scholarly journals Eastward-moving convection-enhanced modons in shallow water in the equatorial tangent plane

2019 ◽  
Author(s):  
M. Rostami
Keyword(s):  
Shallow Water ◽  
Numerical Scheme ◽  
Large Scale ◽  
Tangent Plane ◽  
Water Model ◽  
Moist Convection ◽  
Shallow Water Model ◽  
Beta Plane ◽  
Vapour Condensation ◽  
Velocity Approximation

We report a discovery of steady long-living slowly eastward moving large-scale coherent twin cyclones, the equatorial modons, in the shallow water model in the equatorial beta-plane, the archetype model of the ocean and atmosphere dynamics in tropics. We start by constructing analytical asymptotic modon solutions in the non-divergent velocity approximation and then show by simulations with a high-resolution numerical scheme that such configurations evolve into steady dipolar solutions of the full model. In the atmospheric context, the modons persist in the presence of moist convection, being accompanied and enhanced by specific patterns of water-vapour condensation.

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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