The emergence of zonal jets in forced rotating shallow water turbulence: A laboratory study

2010 ◽  
Vol 92 (3) ◽  
pp. 34006 ◽  
Author(s):  
S. Espa ◽  
G. Di Nitto ◽  
A. Cenedese
Keyword(s):  
Shallow Water ◽  
Laboratory Study ◽  
Zonal Jets ◽  
Rotating Shallow Water ◽  
Water Turbulence

scholarly journals Laboratory study of forced rotating shallow water turbulence

2011 ◽  
Vol 318 (8) ◽  
pp. 082020 ◽  
Author(s):  
Stefania Espa ◽  
Gabriella Di Nitto ◽  
Antonio Cenedese
Keyword(s):  
Shallow Water ◽  
Laboratory Study ◽  
Rotating Shallow Water ◽  
Water Turbulence

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.

Rotating shallow water turbulence: Experiments with altimetry

2013 ◽  
Vol 25 (10) ◽  
pp. 106603 ◽  
Author(s):  
Y. D. Afanasyev ◽  
J. D. C. Craig
Keyword(s):  
Shallow Water ◽  
Rotating Shallow Water ◽  
Water Turbulence

scholarly journals Rotating shallow water dynamics: Extra invariant and the formation of zonal jets

2011 ◽  
Vol 83 (4) ◽  
Author(s):  
Alexander M. Balk ◽  
Francois van Heerden ◽  
Peter B. Weichman
Keyword(s):  
Shallow Water ◽  
Water Dynamics ◽  
Zonal Jets ◽  
Shallow Water Dynamics ◽  
Rotating Shallow Water

Instabilities of coupled density fronts and their nonlinear evolution in the two-layer rotating shallow-water model: influence of the lower layer and of the topography

2013 ◽  
Vol 716 ◽  
pp. 528-565 ◽  
Author(s):  
Bruno Ribstein ◽  
Vladimir Zeitlin
Keyword(s):  
Shallow Water ◽  
Nonlinear Evolution ◽  
Lower Layer ◽  
Phase Locking ◽  
Water Model ◽  
Shallow Water Model ◽  
Wave Instability ◽  
Rotating Shallow Water ◽  
New Generation ◽  
Rotating Shallow Water Equations

AbstractWe undertake a detailed analysis of linear stability of geostrophically balanced double density fronts in the framework of the two-layer rotating shallow-water model on the $f$-plane with topography, the latter being represented by an escarpment beneath the fronts. We use the pseudospectral collocation method to identify and quantify different kinds of instabilities resulting from phase locking and resonances of frontal, Rossby, Poincaré and topographic waves. A swap in the leading long-wave instability from the classical barotropic form, resulting from the resonance of two frontal waves, to a baroclinic form, resulting from the resonance of Rossby and frontal waves, takes place with decreasing depth of the lower layer. Nonlinear development and saturation of these instabilities, and of an instability of topographic origin, resulting from the resonance of frontal and topographic waves, are studied and compared with the help of a new-generation well-balanced finite-volume code for multilayer rotating shallow-water equations. The results of the saturation for different instabilities are shown to produce very different secondary coherent structures. The influence of the topography on these processes is highlighted.

Spontaneous formation of equatorial jets in freely decaying shallow water turbulence

1999 ◽  
Vol 11 (5) ◽  
pp. 1272-1274 ◽  
Author(s):  
R. Iacono ◽  
M. V. Struglia ◽  
C. Ronchi
Keyword(s):  
Shallow Water ◽  
Spontaneous Formation ◽  
Water Turbulence

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>

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