scholarly journals The emergence of jets and vortices in freely evolving, shallow‐water turbulence on a sphere

1996 ◽  
Vol 8 (6) ◽  
pp. 1531-1552 ◽  
Author(s):  
James Y‐K. Cho ◽  
Lorenzo M. Polvani
Keyword(s):  
Shallow Water ◽  
Water Turbulence

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

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.

scholarly journals Equatorial Jets in Decaying Shallow-Water Turbulence on a Rotating Sphere

2007 ◽  
Vol 64 (9) ◽  
pp. 3340-3353 ◽  
Author(s):  
Yuji Kitamura ◽  
Keiichi Ishioka
Keyword(s):  
Wave Packet ◽  
Shallow Water ◽  
Equatorial Region ◽  
Equatorial Waves ◽  
Mean Flow ◽  
Wave Interactions ◽  
Rotating Sphere ◽  
Flow Acceleration ◽  
Water Turbulence ◽  
Ensemble Experiments

Abstract Ensemble experiments of decaying shallow-water turbulence on a rotating sphere are performed to confirm the robustness of the emergence of an equatorial jet. While previous studies have reported that the equatorial jets emerging in shallow-water turbulence are always retrograde, predominance of a prograde jet, although less likely, was also found in the present ensemble experiments. Furthermore, a zonal-mean flow induced by wave–wave interactions was examined using a weak nonlinear model to investigate the acceleration mechanisms of the equatorial jet. The second-order acceleration is induced by the Rossby and mixed Rossby–gravity waves and its mechanisms can be categorized into two types. First, the local meridional wavenumber of a Rossby wave packet propagating toward the equator increases because of meridional variation of the Rossby deformation radius and/or the retrograde zonal-mean flow, resulting in a dissipation of the wave packet in the equatorial region. This mechanism always contributes to retrograde acceleration of an equatorial jet. Another mechanism is derived from the tilting of equatorial waves due to meridional shear of the zonal-mean flow. In this case, zonal-mean flow acceleration contributes to the intensification of a given basic flow.

scholarly journals Mechanism for the Formation of Equatorial Superrotation in Forced Shallow-Water Turbulence with Newtonian Cooling

2015 ◽  
Vol 72 (4) ◽  
pp. 1466-1483 ◽  
Author(s):  
Izumi Saito ◽  
Keiichi Ishioka
Keyword(s):  
Statistical Analysis ◽  
Structural Change ◽  
Shallow Water ◽  
Nonlinear Theory ◽  
Mean Flow ◽  
Rotating Sphere ◽  
Absolute Value ◽  
Acceleration Mechanism ◽  
Numerical Studies ◽  
Water Turbulence

Abstract Forced shallow-water turbulence on a rotating sphere with Newtonian cooling is examined with the aim of elucidating the mechanism of the robust formation of equatorial superrotation reported by R. K. Scott and L. M. Polvani. It is shown that the Newtonian cooling term distorts the structure of the Hough modes. This distortion can be visualized as either the westward or eastward tilting of the equiphase line with increasing absolute value of latitude; the structural change of the Hough modes leads to the acceleration of the zonal-mean flow. A statistical analysis based on a weak-nonlinear theory predicts that stochastically excited Hough modes generate a prograde equatorial jet, the profile of which is quantitatively consistent with that of the ensemble-averaged zonal-mean flow obtained in nonlinear time evolutions. The predicted prograde equatorial jet originates mainly from the acceleration produced by Rossby modes, the equiphase line of which is tilted westward by the Newtonian cooling term. This tilt of the equiphase line of the Hough modes is clarified and a comparison between the acceleration mechanism presented in the present paper and that in other numerical studies in which equatorial superrotation emerges is made.

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