著者

ITO Takahiro NISHIMOTO Shusuke KANEHISA Hirotada

出版者

Meteorological Society of Japan

雑誌

気象集誌. 第2輯 (ISSN:00261165)

巻号頁・発行日

pp.2018-055, (Released:2018-09-07)

被引用文献数

1

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In this study, we show analytically that vortex Rossby waves (VRWs) with azimuthal wavenumber m =1 in a basic axisymmetric vortex can grow exponentially in a quasi-geostrophic system, although they cannot do so in a barotropic system. VRWs grow exponentially if Rayleigh’s condition and Fjørtoft’s condition are satisfied. Satisfying Rayleigh’s condition means that two horizontally aligned VRWs at two different radii propagate (here and hereafter “propagate” refers to propagation relative to the fluid) azimuthally counter to each other. Satisfying Fjørtoft’s condition means that the cyclonic advective angular velocity of the basic vortex is distributed radially so as to enable the VRWs to be phase-locked with each other. Under these conditions, a strong mutual interaction between the VRWs becomes possible, and thus they grow exponentially. In a barotropic system, even if Rayleigh’s condition is satisfied, the azimuthal counter propagation of VRWs with azimuthal wavenumber m =1 is so strong that phase-locking between them cannot occur, and thus they cannot grow exponentially. In a quasi-geostrophic system, however, the upper and lower VRWs of the first baroclinic vertical mode are equal in magnitude and have opposite signs. Because of this baroclinic structure, the azimuthal counter propagation of the horizontally aligned VRWs is suppressed by the vertical interactions between the upper and lower VRWs. Consequently, horizontally aligned VRWs with azimuthal wavenumber m =1 may become phase-locked, and hence they may grow exponentially. By analytically solving the linear problem of VRWs in a quasi-geostrophic system, we show that this is indeed the case.

著者

ODA Mayuko KANEHISA Hirotada

出版者

Meteorological Society of Japan

雑誌

気象集誌. 第2輯 (ISSN:00261165)

巻号頁・発行日

pp.2019-006, (Released:2018-10-29)

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A simple conceptual model of the resonant interaction in a typhoon-like vortex between vortex Rossby waves (VRWs) and gravity waves (GWs), which are caused by the VRWs, is presented. It is well known that the VRWs in the central region of the vortex can grow by the interaction with the GWs in the outer region, but a simple conceptual model for their interaction has not yet been proposed. The proposed conceptual model is based on the buoyancy-vorticity formulation (BV-thinking), and is different from that for the barotropic and baroclinic instabilities based on PV interactions (PV- thinking). We consider disturbances of the first baroclinic mode on a basic barotropic vortex. The disturbance vertical vorticity ζ of the VRW in the central region has a large amplitude on the upper and lower levels. While, the disturbance buoyancy b and radial vorticity η of the GW have a large amplitude on the middle level. The central VRW propagates (relative to the fluid) anticy-clonically, but moves cyclonically because of the strong cyclonic advection by the vortex. The outer cyclonically propagating GW is weakly advected also cyclonically by the vortex. As a result, the counter-propagating VRW and GW (satisfying Rayleigh's condition) may be phase-locked with each other (satisfying Fjørtoft's condition). By the counter-propagation and phase-lock, the circulation around ζ of the VRW enhances b of the GW, which in turn enhances η. At the same time, the circulation around η of the GW enhances ζ of the VRW. As a result, the VRW and GW grow simultaneously. We analytically show the possibility of the resonant interaction, and numerically obtain the growing solution in the system linearized about the basic vortex.