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Yuji Kitamura and Keiichi Ishioka

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.

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Izumi Saito and Keiichi Ishioka

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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Norihiko Sugimoto, Keiichi Ishioka, and Katsuya Ishii

Abstract

Inertial gravity wave radiation from an unsteady rotational flow (spontaneous radiation) is investigated numerically in an f-plane shallow water system for a wide range of Rossby numbers, 1 ≤ Ro ≤ 1000, and Froude numbers, 0.1 ≤ Fr ≤ 0.8. A barotropically unstable jet flow is initially balanced and maintained by forcing so that spontaneous gravity wave radiation is generated continuously. The amount of gravity wave flux is proportional to Fr for large Ro(≥30), which is consistent with the power law of the aeroacoustic sound wave radiation theory (the Lighthill theory). In contrast, for small Ro(≤10) this power law does not hold because of the vortex stabilization due to the small deformation radius. In the case of fixed Fr, gravity wave flux is almost constant for larger Ro(>30) and decreases rapidly for smaller Ro(<5). There is a local maximum value between these Ro(∼10). Spectral frequency analysis of the gravity wave source shows that for Ro = 10, while the source term related to the earth’s rotation is larger than that related to unsteady rotational flow, the inertial cutoff frequency is still lower than the peak frequency of the dominant source. The results suggest that the effect of the earth’s rotation may intensify spontaneous gravity wave radiation for Ro ∼ 10.

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Keiichi Ishioka, Jitsuko Hasegawa, and Shigeo Yoden

Abstract

In a previous paper, asymmetry was found in jet profiles between eastward and westward jets, which appear spontaneously in two-dimensional β-plane decaying turbulence. That is, westward jets are narrower and more intense than eastward jets. In this paper, the dependence of the asymmetry on the order of hyperviscosity is examined. It is shown that the dependence is not as strong as expected in the previous paper. A revised theoretical scenario to explain the weak dependence is also given.

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Yoshi-Yuki Hayashi, Seiya Nishizawa, Shin-ichi Takehiro, Michio Yamada, Keiichi Ishioka, and Shigeo Yoden

Abstract

Jet formation in decaying two-dimensional turbulence on a rotating sphere is reviewed from the viewpoint of Rossby waves. A series of calculations are performed to confirm the behavior of zonal mean flow generation on the parameter space of the rotation rate Ω and Froude number Fr. When the flow is nondivergent and Ω is large, intense easterly circumpolar jets tend to emerge in addition to the appearance of a banded structure of zonal mean flows with alternating flow directions. When the system allows surface elevation, circumpolar jets disappear and an equatorial easterly jet emerges with increasing Fr. The appearance of the intense easterly jets can be understood by the angular-momentum transport associated with the generation, propagation, and absorption of Rossby waves. When the flow is nondivergent, long Rossby waves tend to be absorbed near the poles. In contrast, when Fr is large, Rossby waves can hardly propagate poleward and tend to be absorbed near the equator.

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Shigeo Yoden, Keiichi Ishioka, Dale Durran, Takeshi Enomoto, Yoshi-Yuki Hayashi, Takemasa Miyoshi, and Michio Yamada
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