Numerical Simulations of Forced Shallow-Water Turbulence: Effects of Moist Convection on the Large-Scale Circulation of Jupiter and Saturn

2007 ◽  
Vol 64 (9) ◽  
pp. 3132-3157 ◽  
Author(s):  
Adam P. Showman
Keyword(s):  
Numerical Simulations ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Large Scale ◽  
Spherical Geometry ◽  
Small Deformation ◽  
Moist Convection ◽  
Zonal Jets ◽  
Strong Control ◽  
Water Turbulence

Abstract To test the hypothesis that the zonal jets on Jupiter and Saturn result from energy injected by thunderstorms into the cloud layer, forced-dissipative numerical simulations of the shallow-water equations in spherical geometry are presented. The forcing consists of sporadic, isolated circular mass pulses intended to represent thunderstorms; the damping, representing radiation, removes mass evenly from the layer. These results show that the deformation radius provides strong control over the behavior. At deformation radii <2000 km (0.03 Jupiter radii), the simulations produce broad jets near the equator, but regions poleward of 15°–30° latitude instead become dominated by vortices. However, simulations at deformation radii >4000 km (0.06 Jupiter radii) become dominated by barotropically stable zonal jets with only weak vortices. The lack of midlatitude jets at a small deformation radii results from the suppression of the beta effect by column stretching; this effect has been previously documented in the quasigeostrophic system but never before in the full shallow-water system. In agreement with decaying shallow-water turbulence simulations, but in disagreement with Jupiter and Saturn, the equatorial flows in these forced simulations are always westward. In analogy with purely two-dimensional turbulence, the size of the coherent structures (jets and vortices) depends on the relative strengths of forcing and damping; stronger damping removes energy faster as it cascades upscale, leading to smaller vortices and more closely spaced jets in the equilibrated state. Forcing and damping parameters relevant to Jupiter produce flows with speeds up to 50–200 m s−1 and a predominance of anticyclones over cyclones, both in agreement with observations. However, the dominance of vortices over jets at deformation radii thought to be relevant to Jupiter (1000–3000 km) suggests that either the actual deformation radius is larger than previously believed or that three-dimensional effects, not included in the shallow-water equations, alter the dynamics in a fundamental manner.

Waves, jets and vortices: Regime transitions in shallow water turbulence

2021 ◽  
Author(s):  
Nikos Bakas
Keyword(s):  
Shallow Water ◽  
Large Scale ◽  
Rossby Waves ◽  
Phase Speed ◽  
Critical Value ◽  
Turbulent Regime ◽  
Wave Regime ◽  
Frequency Spectra ◽  
Spectra Analysis ◽  
Zonal Jets

<p>Forced-dissipative beta-plane turbulence in a single-layer shallow-water fluid has been widely considered as a simplified model of planetary turbulence as it exhibits turbulence self-organization into large-scale structures such as robust zonal jets and strong vortices. In this study we perform a series of numerical simulations to analyze the characteristics of the emerging structures as a function of the planetary vorticity gradient and the deformation radius. We report four regimes that appear as the energy input rate ε of the random stirring that supports turbulence in the flow increases. A homogeneous turbulent regime for low values of ε, a regime in which large scale Rossby waves form abruptly when ε passes a critical value, a regime in which robust zonal jets coexist with weaker Rossby waves when ε passes a second critical value and a regime of strong materially coherent propagating vortices for large values of ε. The wave regime which is not predicted by standard cascade theories of turbulence anisotropization and the vortex regime are studied thoroughly. Wavenumber-frequency spectra analysis shows that the Rossby waves in the second regime remain phase coherent over long times. The coherent vortices are identified using the Lagrangian Averaged Deviation (LAVD) method. The statistics of the vortices (lifetime, radius, strength and speed) are reported as a function of the large scale parameters. We find that the strong vortices propagate zonally with a phase speed that is equal or larger than the long Rossby wave speed and advect the background turbulence leading to a non-dispersive line in the wavenumber-frequency spectra.</p>

Predicting mesh density for adaptive modelling of the global atmosphere

2009 ◽  
Vol 367 (1907) ◽  
pp. 4523-4542 ◽  
Author(s):  
Hilary Weller
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Large Scale ◽  
Mesh Adaptation ◽  
Similar Proportion ◽  
Test Case ◽  
Uniform Mesh ◽  
Coarse Mesh ◽  
Mesh Density ◽  
The Cost

The shallow water equations are solved using a mesh of polygons on the sphere, which adapts infrequently to the predicted future solution. Infrequent mesh adaptation reduces the cost of adaptation and load-balancing and will thus allow for more accurate mapping on adaptation. We simulate the growth of a barotropically unstable jet adapting the mesh every 12 h. Using an adaptation criterion based largely on the gradient of the vorticity leads to a mesh with around 20 per cent of the cells of a uniform mesh that gives equivalent results. This is a similar proportion to previous studies of the same test case with mesh adaptation every 1–20 min. The prediction of the mesh density involves solving the shallow water equations on a coarse mesh in advance of the locally refined mesh in order to estimate where features requiring higher resolution will grow, decay or move to. The adaptation criterion consists of two parts: that resolved on the coarse mesh, and that which is not resolved and so is passively advected on the coarse mesh. This combination leads to a balance between resolving features controlled by the large-scale dynamics and maintaining fine-scale features.

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 Can the Impact of Aerosols on Deep Convection be Isolated from Meteorological Effects in Atmospheric Observations?

2018 ◽  
Vol 75 (10) ◽  
pp. 3347-3363 ◽  
Author(s):  
Wojciech W. Grabowski
Keyword(s):  
Numerical Simulations ◽  
Large Scale ◽  
Cloud Condensation Nuclei ◽  
Deep Convection ◽  
Surface Fluxes ◽  
Phase Iii ◽  
Moist Convection ◽  
Atmospheric Measurements ◽  
The Impact ◽  
Meteorological Effects

Influence of pollution on dynamics of deep convection continues to be a controversial topic. Arguably, only carefully designed numerical simulations can clearly separate the impact of aerosols from the effects of meteorological factors that affect moist convection. This paper argues that such a separation is virtually impossible using observations because of the insufficient accuracy of atmospheric measurements and the fundamental nature of the interaction between deep convection and its environment. To support this conjecture, results from numerical simulations are presented that apply modeling methodology previously developed by the author. The simulations consider small modifications, difficult to detect in observations, of the initial sounding, surface fluxes, and large-scale forcing tendencies. All these represent variations of meteorological conditions that affect deep convective dynamics independently of aerosols. The setup follows the case of daytime convective development over land based on observations during the Large-Scale Biosphere–Atmosphere (LBA) field project in Amazonia. The simulated observable macroscopic changes of convection, such as the surface precipitation and upper-tropospheric cloudiness, are similar to or larger than those resulting from changes of cloud condensation nuclei from pristine to polluted conditions studied previously using the same modeling case. Observations from Phase III of the Global Atmospheric Research Program Atlantic Tropical Experiment (GATE) are also used to support the argument concerning the impact of the large-scale forcing. The simulations suggest that the aerosol impacts on dynamics of deep convection cannot be isolated from meteorological effects, at least for the daytime development of unorganized deep convection considered in this study.

scholarly journals Zonostrophic Beta-plumes, Breaking Waves and Zonal Jets in Locally-forced, Large-Scale Shallow Water Experiments

2021 ◽  
Author(s):  
Peter Read ◽  
Roland Young ◽  
Hélène Scolan ◽  
Enrico Ferrero ◽  
Boris Galperin ◽  
...  
Keyword(s):  
Shallow Water ◽  
Large Scale ◽  
Breaking Waves ◽  
Zonal Jets

scholarly journals Jets and Orography: Idealized Experiments with Tip Jets and Lighthill Blocking

2007 ◽  
Vol 64 (10) ◽  
pp. 3627-3639 ◽  
Author(s):  
P. B. Rhines
Keyword(s):  
Numerical Simulations ◽  
Shallow Water ◽  
Rossby Wave ◽  
Potential Vorticity ◽  
Rossby Waves ◽  
Zonal Flow ◽  
Flow Acceleration ◽  
Westerly Flow ◽  
The Mean ◽  
Strong Control

Abstract This paper describes qualitative features of the generation of jetlike concentrated circulations, wakes, and blocks by simple mountainlike orography, both from idealized laboratory experiments and shallow-water numerical simulations on a sphere. The experiments are unstratified with barotropic lee Rossby waves, and jets induced by mountain orography. A persistent pattern of lee jet formation and lee cyclogenesis owes its origins to arrested topographic Rossby waves above the mountain and potential vorticity (PV) advection through them. The wake jet occurs on the equatorward, eastern flank of the topography. A strong upstream blocking of the westerly flow occurs in a Lighthill mode of long Rossby wave propagation, which depends on βa2/U, the ratio of Rossby wave speed based on the scale of the mountain, to zonal advection speed, U (β is the meridional potential vorticity gradient, f is the Coriolis frequency, and a is the diameter of the mountain). Mountains wider (north–south) than the east–west length scale of stationary Rossby waves will tend to block the oncoming westerly flow. These blocks are essentially β plumes, which are illustrated by their linear Green function. For large βa2/U, upwind blocking is strong; the mountain wake can be unstable, filling the fluid with transient Rossby waves as in the numerical simulations of Polvani et al. For small values, βa2/U ≪ 1 classic lee Rossby waves with large wavelength compared to the mountain diameter are the dominant process. The mountain height, δh, relative to the mean fluid depth, H, affects these transitions as well. Simple lee Rossby waves occur only for such small heights, δh/h ≪ aβ/f, that the f/h contours are not greatly distorted by the mountain. Nongeostrophic dynamics are seen in inertial waves generated by geostrophic shear, and ducted by it, and also in a texture of finescale, inadvertent convection. Weakly damped circulations induced in a shallow-water numerical model on a sphere by a lone mountain in an initially simple westerly wind are also described. Here, with βa2/U ∼1, potential vorticity stirring and transient Rossby waves dominate, and drive zonal flow acceleration. Low-latitude critical layers, when present, exert strong control on the high-latitude waves, and with no restorative damping of the mean zonal flow, they migrate poleward toward the source of waves. While these experiments with homogeneous fluid are very simplified, the baroclinic atmosphere and ocean have many tall or equivalent barotropic eddy structures owing to the barotropization process of geostrophic turbulence.

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.

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