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Michio Yamada and Kanefusa Gotoh

Abstract

The reflection of the Rossby wave by the shear zone of the basic flow with hyperbolic tangent profile is investigated by examining the eigenfunction of the disturbance equation. The reflection coefficient is evaluated for various values of wavenumbers and Coriolis parameter. The overreflection is found in some narrow range of the wavenumber.

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Michio Yamada and Makoto Okamura

Abstract

The reflection and transmission of Rossby waves by zonal shear is investigated for the cases U(y)=tanhy and −sech2 y. The coefficients of reflection and transmission are evaluated numerically and some asymptotic properties are obtained analytically. Overtransmission together with overreflection is found for an easterly jet profile.

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Shigeo Yoden and Michio Yamada

Abstract

A series of numerical experiments on the decaying two dimensional turbulence is performed for a nondivergent barotropic fluid on a rotating sphere by using a high-resolution spectral model with a triangular truncation of T85. Temporal variations of the total kinetic energy, the total enstrophy, and the enstrophy dissipation rate are found to be influenced by both the spherical geometry and the rotation rate. The energy spectrum is different from that in the β-plane experiments with Cartesian geometry.

Morphology of streamfunction and vorticity fields is investigated for several rotation rates. In nonrotational cases, isolated coherent vortices emerge in the course of time development as in the planar 2D turbulence. As the rotation rate increases, however, the temporal evolution of the flow field changes drastically, and an easterly circumpolar vortex appears in high latitudes. The flow field is then anisotropic in all the latitudes and elongated in the longitudinal direction. Temporal evolution of the flow field is characterized by Rossby wave motions.

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Shin Takehiro, Michio Yamada, and Yoshi-Yuki Hayashi

Abstract

A series of numerical experiments on two-dimensional decaying turbulence is performed for a barotropic fluid on a rotating sphere. Numerical calculations have confirmed two important asymptotic features: emergence of the banded structure of zonal flows and their extreme latitudinal inhomogeneities in which kinetic energy is accumulated into the easterly circumpolar jets. The banded structure of zonal flows is established relatively early on in the initial stage. Later, after extended periods of time integration, only the circumpolar jets are intensified gradually, while there is no further evolution in the banded structure in the low and midlatitudes. Wave activity flux analysis illustrates that the initial vortices in the low and midlatitudes propagate poleward as Rossby waves and converge to produce easterly circumpolar flows. In association with this convergence, accumulation of the mean zonal component of kinetic energy proceeds. The tendency for the accumulation becomes strong as the rotation rate is increased, and nearly all of the kinetic energy is concentrated to the circumpolar flows in cases of rapid rotation.

A theoretical model is constructed under the assumption that a circumpolar jet emerges around the latitude where the local Rhines scale is equal to the distance from the Pole, and that initial vortices at the lower latitudes contribute to the generation of the jets. The model describes the mean zonal component of kinetic energy and the averaged speed and width of the circumpolar jets as functions of the rotation rate, which agree satisfactorily with the numerical results.

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Jun-Ichi Yano, Mitchell W. Moncrieff, Xiaoqing Wu, and Michio Yamada

Abstract

A wavelet analysis of a three-dimensional 7-day explicit simulation of the tropical cloud systems in the Global Atmosphere Research Programme (GARP) Atlantic Tropical Experiment Phase III is performed. Three physically distinct regimes (squall line, nonsquall cloud cluster, and scattered convection) in a doubly periodic domain are analyzed using discrete Meyer wavelets. These wavelets are complete and facilitate the inversion of the decomposed modes.

The full wavelet spectra well characterize the spatial localization of each physical variable, in particular, the vertical velocity and the condensate fields. The probability distribution of the wavelet coefficients is non-Gaussian despite the horizontal winds, the temperature, and humidity being closely Gaussian in physical space. This demonstrates the effectiveness of the wavelet basis for analyzing cloud system organization. The full wavelet spectrum also selects a preferred spatial orientation of the convective organization in physical space.

A pseudospectrum is defined by taking the maximum absolute value of the wavelet coefficients for a given horizontal wavenumber vector as the spectrum coefficient. Unlike the conventional spectrum, this pseudospectrum objectively selects the observed convective-scale and mesoscale structure characteristic of observed mesoscale convective systems.

The results demonstrate the broad utility of discrete Meyer wavelet analysis for objectively characterizing the structure and organization of multiscale convective cloud systems in an objective way.

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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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