Keiichi Ishioka

Parameter Sweep Experiments on Spontaneous Gravity Wave Radiation from Unsteady Rotational Flow in an f-Plane Shallow Water System

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 r...

Emergence of Circumpolar Vortex in Two Dimensional Turbulence on a Rotating Sphere

Characteristics of the decaying non-divergent two dimensional turbulence on a rotating sphere is considered. The spontaneous appearance of circumpolar easterly vortices reported in the previous study (Yo-den and Yamada, 1993) is interpreted by the Rossby wave property from the framework of weak-nonlinear theory. The resolution of the numerical model utilized by Yoden and Yamada (1993) T85 is not high enough to represent the upward energy cascade of two dimensional turbulence. The initial energy spectral peak adapted there is located almost in the range of wave regime especially when the rotation rate is large, which justifies the explanation of angular momentum redistribution by Rossby waves. A series of new experiments with the higher resolution T341 and new sets of initial energy spectral distributions are performed to confirm that the circumpolar vortices appear even after the full nonlinear upward cascade of turbulent energy and that the band structure of angular momentum emerges even when the rotation rate of the system is large.

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

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 contribute...

Rossby Waves and Jets in Two-Dimensional Decaying Turbulence on a Rotating Sphere

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.

Asymmetrization Mechanism of Jet Profiles in Decaying β-Plane Turbulence

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.

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

AbstractForced 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. Thi...

A Spectral Method for Unbounded Domains and Its Application to Wave Equations in Geophysical Fluid Dynamics

A spectral method for wave equations on 1D or 2D unbounded domain is proposed. It uses a mapping from a closed domain to an unbounded domain with a standard spectral method for the closed domain. Although the idea to use the mapping is not brand-new, two new ideas are introduced into the spectral method. One is “pseudo-hyper-viscosity”, which prevents spurious wavy errors from growing. The other is a variational formulation of the spectral discretization, which leads to enstrophy conservation so that it can avoid numerical instability. Several application examples for GFD wave equations are shown.

Angular distribution of energy spectrum in two-dimensional β-plane turbulence in the long-wave limit

The time-evolution of two-dimensional decaying turbulence governed by the long-wave limit, in which LD/L → 0, of the quasi-geostrophic equation is investigated numerically. Here, LD is the Rossby radius of deformation, and L is the characteristic length scale of the flow. In this system, the ratio of the linear term that originates from the β-term to the nonlinear terms is estimated by a dimensionless number, γ=βLD2/U, where β is the latitudinal gradient of the Coriolis parameter, and U is the characteristic velocity scale. As the value of γ increases, the inverse energy cascade becomes more anisotropic. When γ ⩾ 1, the anisotropy becomes significant and energy accumulates in a wedge-shaped region where |l|>3|k| in the two-dimensional wavenumber space. Here, k and l are the longitudinal and latitudinal wavenumbers, respectively. When γ is increased further, the energy concentration on the lines of l=±3k is clearly observed. These results are interpreted based on the conservation of zonostrophy, which is a...

Theoretical Aspects of Variability and Predictability in Weather and Climate Systems

Weather and Climate Systems Author(s) Yoden, Shigeo; Ishioka, Keiichi; Durran, Dale; Enomoto, Takeshi; Hayashi, Yoshi-Yuki; Miyoshi, Takemasa; Yamada, Michio Citation Bulletin of the American Meteorological Society (2014), 95(7): 1101-1104 Issue Date 2014-07 URL http://hdl.handle.net/2433/202107 Right

Interaction between thermal convection and mean flow in a rotating system with a tilted axis

Thermal convection in a sine-type horizontal shear flow in a rotating system with the rotation axis tilted from the vertical direction is investigated, sweeping three parameters: Taylor number, tilt angle of the rotation axis (i.e. latitude) and Rayleigh number. Nonlinear time evolutions show that there is not only a regime in which roll convections of a herringbone pattern accelerate a mean flow but also a regime in which a large-scale east?west roll convection accelerates the mean flow strongly. The parameter region in which this type of stable steady two-dimensional (2D) roll solution exists is determined by linear stability analyses. Even when the 2D steady solution is not linearly stable, unsteady quasi-periodic solutions oscillating around the steady solution can be found in the nonlinear time evolutions. Finally, a simple mechanism for the acceleration of the mean flow by the large-scale east?west roll convection is described in detail, in which both the tilt of the rotation axis and the sine-type horizontal shear of the flow are important.