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.

scholarly journals Improved moist-convective rotating shallow water model and its application to instabilities of hurricane-like vortices

2018 ◽  
Author(s):  
LMD
Keyword(s):  
Tropical Cyclone ◽  
Shallow Water ◽  
Water Vapour ◽  
Large Scale ◽  
Precipitable Water ◽  
Water Model ◽  
Moist Convection ◽  
Shallow Water Model ◽  
Atmospheric Motions ◽  
Rotating Shallow Water

We show how the two-layer moist-convective rotating shallow water model (mcRSW), which proved to be a simple and robust tool for studying effects of moist convection on large-scale atmospheric motions, can be improved by including, in addition to the water vapour, precipitable water, and the effects of vaporisation, entrainment, and precipitation. Thus improved mcRSW becomes cloud-resolving. It is applied, as an illustration, to model the development of instabilities of tropical cyclone-like vortices.

scholarly journals A Shallow Water Model for Convective Self-Aggregation

2020 ◽  
Author(s):  
Da Yang
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Large Scale ◽  
Wave Pattern ◽  
Water Model ◽  
Shallow Water Model ◽  
Modeling Framework ◽  
Convective Storms ◽  
Wide Range ◽  
Self Aggregation

AbstractRandomly distributed convective storms can self-aggregate in the absence of large-scale forcings. Here we present a 1D shallow water model to study the convective self-aggregation. This model simulates the dynamics of the planetary boundary layer and represents convection as a triggered process. Once triggered, convection lasts for finite time and occupies finite length. We show that the model can successfully simulate self-aggregation, and that the results are robust to a wide range of parameter values. In the simulations, convection excites gravity waves. The gravity waves then form a standing wave pattern, separating the domain into convectively active and inactive regions. We analyze the available potential energy (APE) budget and show that convection generates APE, providing energy for self-aggregation. By performing dimensional analysis, we develop a scaling theory for the size of convective aggregation, which is set by the gravity wave speed, damping timescale, and number density of convective storms. This paper provides a simple modeling framework to further study convective self-aggregation.

scholarly journals Influence of condensation and latent heat release upon barotropic and baroclinic instabilities of vortices in rotating shallow water f -plane model

2018 ◽  
Author(s):  
LMD
Keyword(s):  
Heat Release ◽  
Shallow Water ◽  
Latent Heat ◽  
Large Scale ◽  
Lower Layer ◽  
Passive Scalar ◽  
Water Model ◽  
Moist Convection ◽  
Latent Heat Release ◽  
Rotating Shallow Water

Analysis of the influence of condensation and related latent heat release upon developing barotropic and baroclinic instabilities of large-scale low Rossby-number shielded vortices on the f - plane is performed within the moist-convective rotating shallow water model, in its barotropic (one-layer) and baroclinic (two-layer) versions. Numerical simulations with a high-resolution well-balanced finite-volume code, using a relaxation parameterisation for condensation, are made. Evolution of the instability in four different environments, with humidity (i) behaving as passive scalar, (ii) subject to condensation beyond a saturation threshold, (iii) sub-ject to condensation and evaporation, with two different parameterisations of the latter, are inter-ompared.The simulations are initialised with unstable modes determined from the detailed linear stability analysis in the “dry” version of the model. In a configuration corresponding to low-level mid-latitude atmospheric vortices, it is shown that the known scenario of evolution of barotropically unstable vortices, consisting information of a pair of dipoles (“dipolar breakdown”) is substantially modified by condensation and related moist convection, especially in the presence of surface evaporation. No enhancement of the instability due to precipitation was detected in this case. Cyclone-anticyclone asymmetry with respect to sensitivity tothe moist effects is evidenced. It is shown that inertia-gravity wave emission during the vortex evolution is enhanced by the moist effects. In the baroclinic configuration corresponding to idealised cut-off lows in the atmosphere, it is shown that the azimuthal structure of the leading unstable mode is sensitive to the details of stratification. Scenarios of evolution are completely different for different azimuthal structures, one leading to dipolar breaking, and another to tripole formation. The effects of moisture considerably enhance the perturbations in the lower layer, especially in the tripole formation scenario.

Simplifying Primitive Equations: Rotating Shallow-Water Models and their Properties

2018 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Conservation Laws ◽  
Shallow Water ◽  
Variational Principles ◽  
Mean Field ◽  
Tangent Plane ◽  
Primitive Equations ◽  
Water Model ◽  
Shallow Water Model ◽  
Shallow Water Models ◽  
Rotating Shallow Water

In this chapter, one- and two-layer versions of the rotating shallow-water model on the tangent plane to the rotating, and on the whole rotating sphere, are derived from primitive equations by vertical averaging and columnar motion (mean-field) hypothesis. Main properties of the models including conservation laws and wave-vortex dichotomy are established. Potential vorticity conservation is derived, and the properties of inertia–gravity waves are exhibited. The model is then reformulated in Lagrangian coordinates, variational principles for its one- and two-layer version are established, and conservation laws are reinterpreted in these terms.

scholarly journals Triggered Convection, Gravity Waves, and the MJO: A Shallow-Water Model

2013 ◽  
Vol 70 (8) ◽  
pp. 2476-2486 ◽  
Author(s):  
Da Yang ◽  
Andrew P. Ingersoll
Keyword(s):  
Shallow Water ◽  
Large Scale ◽  
Low Frequency ◽  
Propagation Speed ◽  
Water Model ◽  
Shallow Water Model ◽  
Horizontal Scale ◽  
Frequency Wave ◽  
Large Scale Structures ◽  
Scale Structures

Abstract The Madden–Julian oscillation (MJO) is the dominant mode of intraseasonal variability in the tropics. Despite its primary importance, a generally accepted theory that accounts for fundamental features of the MJO, including its propagation speed, planetary horizontal scale, multiscale features, and quadrupole structures, remains elusive. In this study, the authors use a shallow-water model to simulate the MJO. In this model, convection is parameterized as a short-duration localized mass source and is triggered when the layer thickness falls below a critical value. Radiation is parameterized as a steady uniform mass sink. The following MJO-like signals are observed in the simulations: 1) slow eastward-propagating large-scale disturbances, which show up as low-frequency, low-wavenumber features with eastward propagation in the spectral domain, 2) multiscale structures in the time–longitude (Hovmöller) domain, and 3) quadrupole vortex structures in the longitude–latitude (map view) domain. The authors propose that the simulated MJO signal is an interference pattern of westward and eastward inertia–gravity (WIG and EIG) waves. Its propagation speed is half of the speed difference between the WIG and EIG waves. The horizontal scale of its large-scale envelope is determined by the bandwidth of the excited waves, and the bandwidth is controlled by the number density of convection events. In this model, convection events trigger other convection events, thereby aggregating into large-scale structures, but there is no feedback of the large-scale structures onto the convection events. The results suggest that the MJO is not so much a low-frequency wave, in which convection acts as a quasi-equilibrium adjustment, but is more a pattern of high-frequency waves that interact directly with the convection.

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