文献一覧: Hirotada KANEHISA (著者)

2 0 0 0 OA Analytical Solutions of Vortex Rossby Waves Associated with Vortex Resiliency of Tropical Cyclones

著者: Shusuke NISHIMOTO Hirotada KANEHISA
出版者: Meteorological Society of Japan
雑誌: 気象集誌. 第2輯 (ISSN:00261165)
巻号頁・発行日: vol.96, no.1, pp.5-24, 2018 (Released:2018-02-08)
参考文献数: 17
被引用文献数: 1

We analytically solve a forced linear problem of vortex Rossby waves (VRWs) associated with the vortex resiliency of tropical cyclones. We consider VRWs on a basic barotropic axisymmetric vortex. VRWs, which are initially absent, are successively forced by a vertically sheared unidirectional environmental flow. The problem is formulated in the quasigeostrophic equations, linearized about the basic vortex. The basic potential vorticity (PV) is assumed to be piecewise constant in the radial direction so that the problem can be analytically solved. The obtained solutions show the following. When the vertical interaction (VI) between the VRWs is weak, a stationary mode (called the pseudo mode) is selectively forced and grows linearly in time, and the vortex is eventually destroyed by the environmental vertical shear. When the VI is moderate, an almost form-preserving quasi-mode (simply called the quasi mode) of the VRWs appears and precesses about a downshear-left tilt equilibrium (DSLTE). The precession does not grow and the vortex maintains vertical coherence. In particular, in the presence of the inward radial gradient of the basic PV at the critical radius, the precession damps and the quasi mode eventually approaches the DSLTE. When the VI is strong, the VRWs are simply advected by the basic angular velocity at each radius to be axisymmetrized to some extent about the DSLTE, and the vortex maintains vertical coherence. To examine the diabatic effect near the eyewall, the solution with the basic buoyancy frequency being small in the central region and large in the outer region is also obtained. The small and large buoyancy frequencies imply strong and weak VIs, respectively. The central VRWs are simply advected by the basic vortex flow. While, the outer VRWs precess about the DSLTE just like a quasi mode, and the vortex maintains vertical coherence.

2018-02-09 12:16:35
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1 0 0 0 OA Analytical Solutions of Vertically Propagating Gravity Waves—from the Perspective of Buoyancy-Vorticity Thinking

著者: Mayuko ODA Hirotada KANEHISA
出版者: Meteorological Society of Japan
雑誌: 気象集誌. 第2輯 (ISSN:00261165)
巻号頁・発行日: vol.88, no.2, pp.227-238, 2010 (Released:2010-05-22)
参考文献数: 12

On the basis of buoyancy-vorticity (BV) formulation of Harnik et al. (2008), the initial value problem of vertically propagating gravity waves is analytically solved in a zonal-vertical two-dimensional system. The analytical solutions provide an example of the visualization of BV thinking. Further, the analytical solutions enable a qualitative understanding of the growth of gravity waves in a vertically sheared zonal flow (so-called shear instability of gravity waves) by BV thinking. To this end, the basic buoyancy (i.e., basic potential temperature) is assumed to be piecewise uniform in the vertical direction, and the Green function method is employed. The obtained analytical solutions show the following. In a vertically uniform basic zonal flow, the gravity wave, which is initially at the lowest level, propagates vertically upwards, gets reflected from the highest level back to the lowest level and again from the lowest level to the highest level, and so on. In a vertically sheared basic zonal flow, the behavior of the gravity waves depends on the horizontal wave number. This is caused by the dependence of horizontal propagation velocity on the horizontal wave number. Here, horizontal propagation is defined relative to the fluid. If the horizontal propagation and advection by the basic zonal flow are successfully balanced so that the lower and upper phase velocities are nearly equal, then the gravity wave propagates vertically, and the upper and lower disturbances are phase-locked to each other; this results in an effective interaction between them and in growth as an exponential function of time. On the other hand, if the horizontal propagation and advection by the basic zonal flow are out of balance so that the lower and upper phase velocities are different from each other, then the gravity wave hardly propagates vertically, and the upper and lower disturbances horizontally flow away from each other resulting in an absence of interaction between them and in the oscillation (i.e., no growth). At the marginal points between oscillation and growth, the gravity wave grows as a linear function of time. The behavior of analytical solutions can be qualitatively explained by the BV thinking of Harnik et al. (2008).

2019-07-17 17:14:25
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1 0 0 0 Analytical Solutions of Vortex Rossby Waves in a Discrete Barotropic Model

著者: Takahiro ITO Hirotada KANEHISA
出版者: Meteorological Society of Japan
雑誌: 気象集誌. 第2輯 (ISSN:00261165)
巻号頁・発行日: vol.91, no.6, pp.775-788, 2013
被引用文献数: 4

The initial value problem of vortex Rossby waves (VRWs) is analytically solved in a linearized barotropic system on an f plane. The basic axisymmetric vorticity q is assumed to be piecewise uniform in the radial direction so that the radial gradient dq/dr and the disturbance vorticity q are expressed in terms of Dirac delta functions. After Fourier transformation in the azimuthal direction with the wavenumber m, the linearized vorticity equation becomes a system of ordinary differential equations with respect to time; these can be analytically solved to give a closed-form solution with a prescribed initial value. For a monopolar q, the solution of q starting from the innermost radius exhibits the outward propagation of VRWs. As the outer disturbances are generated, the inner disturbance is diminished. On the other hand, in the case of a solution forced at the innermost radius, the inner disturbance is not diminished, and the outward propagation of VRWs forms a distribution of spiral-shaped disturbance vorticity. For a basic vorticity q with a moat, and if the radial distribution of q satisfies a certain additional condition, the solution of q with |m| ≠ 1 grows exponentially or linearly in time as a result of the interaction of counterpropagating VRWs near the moat. Although the solution of q with |m| = 1 cannot grow exponentially for any q, it can grow as a linear function of time. This linear growth may be regarded as a result of resonance between two internal modes of the system.

2015-10-04 19:33:47
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