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On the Negative Vorticity in a Typhoon* S. Syono, Y. Ogura, K. Gambo and A. Kasahara

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On the Negative Vorticity in a Typhoon* S. Syono, Y. Ogura, K. Gambo and A. Kasahara ˜_•¶ Memoirs On the Negative Vorticity in a Typhoon* S. Syono, Y. Ogura, K. Gambo and A. Kasahara (GeophysicalInstitute, Tokyo University) - Abstract - In this paper, an attempt has been made to show the important role of negative vortioity, that was introduced through theoretical considerations, by the analysis of actual data obtained of the typhoons " Kitty " and " Jane ". The fine structure of a tyhoon, that some small vortical cells of about 50-100 km in diameter and of signs of vorticity + and - are embedded in a large vortex, was elucidated by the following observational facts: the distributions of wind velocity and of horizontal convergence and divergence, the intensity of rainfall and the changes of pressure distribution with time. The schematic diagram of the vertical cross section of a typhoon is set forth, based on these new observational features. In addition to these problems, the oscillation of a vortical cell in a typhoon is discussed. •˜ 1. Introduction The theoretical studies of the structure of atmospheric vortices have been developed by many authors since the end of the 1.9 th century (for example, C. M. Guldberg and H. Mohn (1876), A. Oberbeck (18118), D. Kitao (1887) and others) from purely mathematical stand points. But owing to the scarcity of appropriate data, it has been hardly possible to elucidate the actual structure of atmospheric vortices, especially of hurricanes and typhoons. Recently, numerous aerological data at up to the heights 20 km have been obtained. Based on these materials, studies of the atmospheric vortices have made a considerable progress, and some models of hurricane and tropical cyclone have come to be discussed. (for example, J. S. Sawyer (1949), C. E. Deppermann (1947) and H. Riehl (1950)). While one of the present authors (Syono (1948, 1951)) suggested the existence of a region of negative relative vorti city (anticyclonic v orticity) around' that of the positive one (cyclonic vorticity) as shown in Fig. 1. This region was at first introduced from a theoretical point of view, to avoid the divergence of the integrals of the kinetic energy and pre ssure difference which appear in using the RankinPs combined Fig. 1 Schematic distri vortex as a model of tropical cyclone. And the existence of bution of relative vorti this region was shown also by him from the wind velocity city in a typhoon * Division of Meteorology, Contribution No. 35. - 1- 398 Journ. Met. Soc. Japan, Vol. 29, No. 12, 1951 distribution of Typhoon "Okinawa ". Such a model of cyclone was first noticed by Luighi di Marchi (1893) from a different standpoint. Afterwards Syono (1950) put forward the concept of " vortical rain " in, addition to the convective, frontal and orographic rains. For a semi-infinite air column of unit cross sec tion, the intensity of vortical rain is proportional to the horizontal mass convergence in it. The horizontal mass convergence in the frictional layer is proportional to the vorticity of gradient wind. Thus the intensity of rainfall is proportional to that of the vorticity in a typhoon. Since the region of negative relative vorticity is that of horizontal divergence, we cannot expect any rainfall in it. This idea was verified by him using the data of Typhoon " Okinawa ". One of the authors (A. Kasahara (1950 a)) also studied theoretically the distribution of the intensity of rainfall in Typhoon "Kitty". According to his previous study (A. Kasahara (1949)), the speed of filling-up of a typhoon is also proportional to the horizontal mass convergence. This result was supported by the agreement between the time change of the pressure depth at the centre and the filling-up index in the case of Typhoon "Kitty" (A. Kasahara (1950a)), This fact tells us that the filling-up does not take place in the whole region of a typhoon (see •˜ 5). Thus the horizontal mass convergence and divergence are very , important in explaining the distribution of rainfall intensities and the filling-up as well as the relative vorticity of a typhoon. It is the purpose of this paper to show synoptically the physical meaning of the nega tive vorticity which has been introduced from the purely theoretical standpoint and to propose the schematic diagram of the structure of a typhoon along the line of above men tioned arguments. Lastly, in addition to these problems, the oscillation of a vortical cell in a typhoon is discussed. It would appear to be reasonable from this point of view that the vortical cells are embedded , in a typhoon (see •˜ 6). •˜ 2. Observations of negative vorticity in typhoons (I) By synoptic studies of the vorticity distribution in typhoons, the existence of negative vorticity regions has been made known by some authors as will be shown later. Its important meaning, however, was not discussed in these studies owing to the lack of theory concerning the negative vorticity in a typhoon. (i) Typhoons which appeared during August-November, 1931 T. Ootani and H. Hatakeyama (1932) studied statistically the vorticity distribution in typhoons which appeared in the neighbourhood of Japan during August-November in 1931, using the data of upper air currents obtained by the pibal observations at 51 stations in Japan. In that study they regarded that all observations made at the equal distance and azimuth from the centres of typhoons are equivalent, disregarding the time of observations and the position of every typhoon. - 2 - On the Negative Vorticity in a Typhoon 399 Fig. 2 shows the vorticity* distributions at each level obtained from the distribution of wind velocity. Corresponding to these vorticity distri butions, we may expect that convergence is ac companied with positive vorticity, and divergence with negative. Fig. 3 shows the distribution of calculated horizontal convergence and divergence from the observed data of winds. In these figures, Fig. 3 The distribution of calculated horizontal convergence and divergen ce (unit : m3 sec--1 km-2) Fig. 4 The mean distribution of wind velocity in typhoons Fig. 2 The vorticity distributions at each level obtained from the dist ribution of wind velocity (unit : m3 sec-1 km-2) * Hereafter, this term means the relative vorticity as far as not otherweise provided. - 3 - 400 Journ. Met. Soc. Japan, Vol. 29, No. 12, 1951 we can see the alternate distribution of convergence and divergence as well as the negative and positive vorticities. Fig. 4 shows the distribution of calculated vertical wind velocity which is obtained under the assumption that the horizontal mass convergence below is canceled by the hori zontal mass divergence aloft, so that the state is maintained stationary. Within the distance 600 km from the centre, there exist ascending currents. On the other hand, there exist descending currents beyond 600 km. This fact may be a very remarkable feature concerning the structure of typhoons. (ii) Typhoon "Muroto " (which attacked the Kansai district on Sept. 20, 1934) T. Yamamoto and K. Takeda (Central Meteo rological Observatory (1935)) computed the vorticity distribution in Typhoon "Muroto " from the gra dient wind distribution at 500 in level. Fig. 5 shows the vorticity distribution. From this we may find also the region of negative vorticity around that of the positive one. •˜ 3. Observation of negative vorticity in typhoons (II) -General comments of negative vorticity - Fig. 5 The distribution of vorticity (i) The radial distribution of meteorological in Tyhoon Muroto (unit : 10-5 C. G. S.) elements in a typhoon It may seem reasonable to compute the distribution of meteorological elements, for example, wind velocity, pressure, etc. in a typhoon from the weather charts at each map time. We are puzzled, however, where we should choose the radial cross section of a, typhoon in order to get the representative distribution of meteorological elements, by reason. that isobars in a typhoon are scarcely circular As a rule, the time section based on meteorological elements which are observed at one station, is used instead of the above procedurefor the sake of convenience. But this time cross section of a typhoon may not be considered as a space cross section, since the moving speed of a typhoon is not uniform and the more remote the station is from the centre of typhoon, the more markedly this effect may arise. Then, in order to get a correct space cross section, it is necessary to rearrange the time axis of the time cross section to the axis of the radial distance of the station fromm the centre of typhoon because the distance may be measured on the weather chart. By this procedure it becomes possible not only to get the radial distribution of meteorological: elements, but also to compute that of horizontal convergence and divergence as well as that of vorticity in a typhoon. The change of successive space cross section obtained at each, station may be considered as the time change of the distribution of meteorological elements. - 4 - On the Negative Vorticity in a Typhoon 401 In order to get the information about the distribution of meteorological elements near the centre of a typhoon, it is desirable to use the space cross section referred to the station, where the centre of the typhoon passed by . In this paper, only the space cross sections ahead of the centre of a typhoon are analyzed. The typhoons which are the objects of analysis hereafter are mainly Typhoons "Kitty" and "Jane ". The former attacked the Kanto district, the latter the Kansai district in Japan, and they caused serious damages. Typhoon "Kitty" appeared on August 27 , 1949 and was named "Kitty" at 9 a. M. on the 28 th. On the other hand, Typhoon "Jane" appeared on August 28, 1950 and was named "Jane" on the 1st of September . The tracks of these typhoons and the names and locations of meteorological stations are shown in Fig.
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