1 INTRODUCTION

In the past decades of years, thanks to the unceasing progress of observational technique (especially satellite and dropsonde observation (Soden et al., 2001 ; Tuleya and Lord, 1997 ; Aberson and Franklin, 1999 ) ), numerical model (Emanuel and Ivkovic-Rothman, 1999 ) and theoretical knowledge (Chan and Gray, 1982 ; McAdie and Lawrence, 2000 ; Wu and Wang, 2000 ), the track of TC (tropical cyclone) can be forecasted with a stably improved accuracy; but the ability to forecast TC intensity is not distinctly improved by the complicated numerical model and advanced satellite detection (McAdie and Lawrence, 2000 ) technique. Therefore, research on physical mechanism of structure and intensity change had always been the focus of the global tropical cyclones research in consideration of the fact that the structure and intensity of a tropical cyclone are remarkably impacted by complicated physical movements such as air-sea interaction and typhoon-environment interaction (Zeng et al., 2008 ; Ying and Zhang, 2012 ; Wang, 2002a, 2002b ; Zhang et al., 2005 ; Houze et al., 2007 ; Qiu et al., 2010 ; Sun et al., 2014, 2015a, 2015b ). Furthermore, more and more researches are centralized on the convection belt in TC, especially on how the structure and change of eye wall and spiral rain impact the TC structure and intensity change. The deep and thick convection belt in TC is distributed in a roller shape and mesoscale belt, the triggering and developing mechanism of belt convection is a key topic in TC structure and intensity change. The mesoscale circulating system generated in the internal atmosphere course is restricted by the instable aerodynamic force, the mesoscale instability includes Kelvin-Helmholtz instability, symmetry instability and EKman instability which are all correlated to vertical wind shear (VMS), therefore, TC structure and intensity change are correlated to the interaction of complicated environment on one hand, especially the interaction with VWS, and are also correlated to the convection development in inner TC on the other hand.

It is proved that TC intensity change is significantly impacted by VWS, and according to the research of Frank and Ritchie (1999, 2001 ), the increasing (or decreasing) value of VWS is correlated to the rapid fading (or growing) of TC. Some researches have revealed that the level of VWS is inversely correlated to the intensity change of TC, a higher VWS has a negative effect on the intensifying of TC which is the principal reason (DeMaria and Kaplan, 1994 ; Zeng et al., 2007, 2008 ) that TC cannot reach the potential intensity. The physical mechanism of TC intensity impacted by VWS may include: the ventilating effect in the high warm center (Frank and Ritchie, 2001 ; Wong and Chan, 2004 ;), the increasing stability of troposphere (DeMaria, 1996 ), the effect of eddy kinetic energy flux, the infringing of low entropy air on the eye wall area (Riemer et al., 2010 ) and the middle layer ventilating effect in the low entropy air (Tang and Emanuel, 2010 ). These researches have revealed the impact of thermal effect on the TC development under the effect of VWS, but few analyze the momentum effect of VWS. Zeng et al.(2009) had preliminarily studied and pointed the impact of the nonhomogeneity of VWS level, magnitude and direction on TC intensity, e.g. the impact of eastern wind shear on TC intensity change is smaller than that of western wind shear, VWS of deep layer impacts the intensity of TC, while the VWS of middle-low level in the weak TC troposphere had an obvious impact on it. Zhang and Chen (2012) suggested that more attention should be paid to the high layer VWS besides the VWS change at 200∼850 hPa. It is obvious that TC is significantly impacted by nonhomogeneity of VWS, but the physical process that how the TC intensity variation is impacted by the nonhomogeneous distribution is still unclear.

Another important effect of VWS is to change the asymmetrical convection distribution in TC, Frank and Ritchie (1999) considered that the VWS was closely related to the kernel structure of TC, but there are few researches on how the VWS impacts the generation and development of rain belts inside and outside the eye wall, especially very few analyses on the interaction between VWS and the whirling movement in inner TC.

Past researches on VWS always focused on the vertical distribution of environmental wind of low resolution, i.e. the VWS in the whole layer was represented by the wind vector difference between 200 hPa and 850 hPa, however, VWS distribution is nonhomogeneous in consideration that the atmospheric system changes with TC movement and the relative position change of TC in the deep and thick TC convection area, and such nonhomogeneity is significant to study the impact of TC intensity and the structure change. Therefore, this paper studies the development of typhoon Fitow based on the observational data, simulates with the WRF (V3.4) mode so that the modeled atmospheric data can recreate the features of observational data, based on which we can divide the typhoon Fitow into three stages: enhanced developing, continuously intensifying, and rapidly fading, by analyzing the environmental average wind of typhoon Fitow and the wave-like space-time evolving characteristics of VWS, it is revealed that how VWS wave-like space-time evolving characteristics impact the symmetrical structure change of typhoon Fitow and strongly maintain its long life.

2 COURSE OF TYPHOON FITOW AND NUMERICAL SIMULATION 2.1 Course of Fitow

At 12:00 on September 30th, 2013 (world time, the same in the following), No.13 typhoon Fitow was formed above the ocean east to the Philippines; it intensified into a strong tropical storm above the northwest Pacific Ocean at 09:00 on October 1st, further into a typhoon at 21:00 on 2nd, and a strong typhoon at 12:00 on 4th; it landed on the coast of Shacheng Town, Fuding City, Fujian Province at 17:15 on 6th, and the maximum wind scale near the center was 14(42 m·s^-1) and the minimum air pressure at the center was 955 hPa when landing; it was weakened into a typhoon at 19:00 on 6th, into a strong tropical storm at 20:00, and into a tropical storm at 21:00; it was further weakened into a tropical depression in Jian'ou City, Fujian Province at 01:00 on 7th and lasted for 95 hours totally during which a 54-hour long strong typhoon was lasted from 12:00 on 4th to 18:00 on 6th. The change of minimum air pressure over time was different from the “V” shape change of any common typhoon, shown as a “U” shape change and it was an uncommon long life strong typhoon. During the period, No.14 typhoon Danas in 2013 intensified into a tropical storm at 06:00 on October 4th and moved northwestwards together with typhoon Fitow, it developed into a strong tropical storm at 06:00 on 5th, into a typhoon at 18:00 on 5th, and a strong typhoon at 06:00 on 6th; when it developed into a strong typhoon at 00:00 on 7th, the track of which gradually turned northwards. The satellite cloud figures (omitted) showed that the Fitow cloud system turned from the discrete and asymmetrical state during the enhanced developing stage into the compact and symmetrical state during the strong typhoon stage. After it was landed, the cloud system structure gradually turned into the discrete and asymmetrical state, and the intense rainfall was mainly centralized in the north of the typhoon.

Synoptic scale analysis showed that the impacting system of environmental field changes during the movement of Fitow, when typhoon Fitow developed and moved westwards, the subtropical high pressure above the western Pacific also kept intensifying and extending westwards, and as typhoon Fitow approached and landed, the subtropical high pressure distinctly extended westwards and confronted the ridge movement in the mid-high latitude circulation near N36δ. The typhoon Fitow weakened after landing, and the subtropical high pressure also became weak and faded eastwards gradually, at this time, the mid-high latitude ridge movement distinctly pressed southwards and connected with the residual vortex of Fitow and formed into an inverted trough from northeast to southwest, and the western continental high pressure also blocked the western movement of Fitow. There was a strong wind area followed between the north of typhoon Danas and the subtropical high pressure, the eastward airflow of which was brought to the strong wind area of Fitow along the south edge of the subtropical high; as the intensifying of typhoon Danas, the west-to-north movement of the subtropical high also intensified in southwest, and it is favorable for the northward lifting of the subtropical high in west and the strengthening of the south circulation in the west-extended subtropical high. As a result, typhoon Fitow was generally led by the eastward airflow between itself and the southwest of the subtropical high above the west Pacific after it moved westward, it kept moving to the west until landed and faded away. During the development, typhoon Fitow interacted with the subtropical high, mid-high latitude ridge, western continental high and Danas at the southeast in multiple systems, because of the interactions, the environmental wind field of typhoon Fitow was nonhomogeneous in the vertical spatial distribution over time, and this paper studies the effect of such nonhomogeneity on the variation of intensity and structure of typhoon.

2.2 Numerical Test

WRF (v3.4) was applied in the paper, NCE P1° ×1° reanalyzed data was regarded as the initial field and border condition, the area was dually nested, the center of the area was at 130°E, 30°N, there were 488×365 grid points at the horizontal direction of the coarse grid, and the grid spacing was 18 km; there were 702×558 grid points at the horizontal direction on the fine grid, and the grid spacing was 6 km; it was divided into 50 layers vertically, the top layer was 50 hPa, and the time step was 36 s. The micro-physical plan adopts the Thompson Hail Plan, long wave radiation adopts RRTMG Plan, short wave radiation adopts RRTMG Plan, cumulus convection adopts shallow convection Kain-Fritsch Plan, side border adopts YSU, near ground adopts MM5 Monin-Obukhov Plan, and ground course adopts Unified Noah; all plans were the same in both internal layer and external layer except that the cumulus convection layer does not use the parameterized plan. During this simulation, the initial time was selected to be 12:00 on October 3rd, 2013, 84 hours were accumulated, and the simulated result was output for the first time every 3 h for the external layer and for the second time every 1 h for the internal layer.

The model result showed that the observed track was generally expressed by the moving track of the modeled air, in other words, the observed track consists well with the simulated track, especially in the early and middle typhoon stages when the simulated track was only dozens of kilometers away from the observed track, while the deviation was about a hundred kilometers after landing; their moving tracks also changed in good consistency and the model successfully expressed the variation of typhoon which moved northward in the beginning, from west to north after turned westward, and southwestward after landed (Fig. 1a ). The intensity change of typhoon (minimum air pressure and maximum wind speed) simulated by the model was basically consistent with the observed data, which means that the changing curve of intensity and maximum wind speed basically complied with the observation. The air pressure changing curve showed that there was subtle difference of intensity between the simulation and the observation in the beginning which was the deviation in the initial adjusting period, and deviation also existed at landing due to the impact of landform, however, the general variation trend of air pressure basically matched the observed data, the 54-hour continuous intensifying was also favorably reflected, the “U” shape variation trend was also completely reproduced (Fig. 1b ), and the high resolution data were thus provided for analyzing the long life maintenance mechanism by modeled air. Meanwhile the high resolution data from mesoscale analysis were provided by modeled air for studying the typhoon structure and intensity change. The simulation of Fitow was divided into three stages: enhanced developing stage (24 hours totally) : 12:00 on 3rd-12:00 on 4th; continuously intensifying stage (48 hours totally) : 12:00 on 4th-12:00 on 6th; and rapidly fading stage (18 hours) : 12:00 on 6th-6:00 on 7th.

3 EVOLVING CHARACTERISTICS OF ENVIRONMENTAL AVERAGE WIND AND ITS VERTICAL SHEAR 3.1 Calculation and Evolving Characteristics of Environmental Average Wind

VWS indicates the change of average horizontal wind with altitude in the macroscale circulation background field for TC, strictly speaking, it is the measurement of vertical gradient for the environmental average wind, and usually the unit is m·s^-1. The definition for VWS is basically consistent in common researches, but the horizontal areas and vertical selected layers in calculation are different, generally, the VWS is the difference of average wind at 200 hPa minus the average wind at 850 hPa, the wind vector obtained is used as the vertical shear of environmental wind of the whole layer, and the environmental average wind is usually the average wind in the area of 300∼800 km extended from the cyclone center. Because of the complexity of environmental wind field changing with altitude and in consideration of the deficiency in past middle and high resolution researches, this paper took a square of 10°×10° originated from the cyclone center and vertically extended from 950 hPa to 50 hPa as the horizontal area to comply with the scale of typhoon Fitow and satisfy the requirement for research. Four high resolution plans with spacing of 50 hPa, 100 hPa, 150 hPa, and 200 hPa, respectively, were used to calculate the vertical gradient of average wind, i.e. the VWS in different vertical resolutions were calculated, and a suitable vertical layer spacing was chosen to express the nonhomogeneity of average wind vertical distribution.

As shown in Fig. 2a, the environmental average wind in the low layer (850∼950 hPa) during the three developing stages of typhoon was mainly the eastern wind whose waveform varied with altitude in different developing stages.(1) In the enhanced developing stage (at 18:00 on 3rd typically), the wind mainly changed clockwise with altitude, and in this paper the waveform wind changing with altitude was defined as a single mode.(2) In the late stage of enhanced developing, i.e. from 06:00 on 4th, the wind changed with altitude clockwise at 450∼950 hPa, in a thick enough layer, the environmental wind scale and direction were relatively stable, and it turned counterclockwise from 450 hPa. In this paper, such waveform change was defined as bimodal, and it was 6 hours earlier than the starting time of the continuously intensifying stage of typhoon.(3) In the continuously intensifying stage (at 18:00 on 5th typically), the wind turned from clockwise to counterclockwise from the low layer to the high layer. In connection with the vertical direction change starting from 06:00 on 4th, the bimodal distribution lasted for 48 hours.(4) From 06:00 on 6th in the late continuously intensifying stage, counterclockwise turning at high layer changed to clockwise, and thus the whole layer changed to clockwise and it entered the rapidly fading stage (at 18:00 on 6th typically). To express the time-space changing characteristics of environmental average wind in different typhoon developing stages, wind outline projections (Fig. 2b, 2c, 2d) at the typical time were mapped for each of the three developing stages to clarify the characteristics of average wind changing with altitude. The first was that the wind changed with altitude in different wave forms from single mode (e.g. at 18:00 on 03rd) to bimodal (e.g. at 18:00 on 05th) and then back to single mode (e.g. at 18:00 on 06th) during the three stages; the second was that the vertical distribution of environmental wind scale and direction were relatively stable in a thick enough layer especially there was a 48-hour uninterrupted relatively stable stage in the continuously intensifying stage; the third was that the typhoon intensity changed about 6 hours later after the mode change.

3.2 Evolving characteristics of vertical wind shear

The environmental average wind of typhoon Fitow changed in a waveform in time-space distribution, so the actual VWS characteristics cannot be exactly described and it is difficult to analyze the impact of VWS waveform change on the intensity and structure change of TC in the mesoscale convection belt only by expressing the VWS in the whole layer with the difference of 850 hPa minus 200 hPa. Analysis in 3.1 showed the vertical distribution of environmental wind changed in a waveform and also kept stable relatively in a certain thickness, and thus it is necessary to select a suitable vertical resolution to express the characteristics of waveform change. In this paper, four plans with spacing of 50 hPa, 100 hPa, 150 hPa, and 200 hPa were used to calculate the environmental VWS so that a resolution suitable for both expressing the actual atmosphere and calculating the VWS could be found.

The characteristics of VWS changing with time obtained from four high vertical resolution plans were basically the same (charts omitted), as they precisely expressed the distribution of VWS, and spacing of 100 hPa was a suitable plan (Fig. 3 ) for calculation in this paper. Analysis showed that the time-space distribution of VWS had the same waveform as the change of environment wind, in other words, during the enhanced developing stage, the vertical distribution of VWS turned clockwise in a single mode; from 06:00 on 4th in the late enhanced developing stage, counterclockwise turning occurred with altitude change, i.e. a bimodal state occurred, which lasted for 48 hours; and a single mode of turning clockwise occurred again in the rapidly fading stage. The mode change of VWS was also 6 hours in advance of the transition of typhoon developing stages. In addition to the mode change, the intensity of VWS also varied with altitude in different developing stages, the main characteristic was that there was a long life western wind shear maintained in the middle layer (700∼500 hPa) of troposphere, especially there were three peak value centers in different developing stages, and they were 5.4 m·s^-1, 6.5 m·s^-1 and 4.6 m·s^-1 respectively, but the western wind shear thickness in the continuously intensifying stage was thinner than that in any of the other stages, and the peak value area of high layer eastern wind shear in the continuously intensifying stage was maintained for 48 hours, and the maximum value was as high as 6.3 m·s^-1. These nonhomogeneous characteristics significantly impacted on the nonhomogeneous maintenance, development and structure of mesoscale convection and the asymmetrical change of TC.

In order to compare the impact of VWS in different layers, the degrees of VWS in different altitudes were analyzed (Fig. 4 ), the figure showed the changing trend of typhoon Fitow in different developing stages varied in the high layer (200∼450 hPa), middle layer (450∼650 hPa) and low layer (650∼950 hPa), where, the changing trends of VWS in the middle layer was most similar to that in the whole layer, but there was a great difference of shear intensity, it was less similar in the high layer, the VWS in the low layer changed a little with time, and it became weaker and weaker generally. The VWS intensity in the whole layer reached above 8 m·s^-1, and the maximum value was nearly 15 m·s^-1; the VWS in the middle layer also reached 8 m·s^-1, the maximum value was as high as 20 m·s^-1, and the VWS changed in a reversed phase with the whole layer at 850∼200 hPa in the continuously intensifying stage, and thus it is necessary to analyze the momentum effect of VWS in different altitudes. Therefore, the waveform change of typhoon in different developing stages can be more exactly expressed by calculating the VWS with a high vertical resolution; and it will be pertinent to analyze the momentum effect according to the relative stability of change in different layers during a same developing stage.

4 IMPACT OF VERTICAL WIND SHEAR ON TYPHOON FITOW 4.1 Impact of Vertical Wind Shear on the Structure and Intensity Change of Typhoon Fitow in the Mesoscale Convection Belt

VWS has a significant impact on the structure distribution and intensity change of the convection belt of typhoon, and it is at the right of the down shear typhoon center of the environmental wind for the environmental field of linear change of VWS vertical distribution, i.e. the asymmetrical uprising movement was arising from the “down shear left”(Wong and Chen, 2004 ). The basic principle is shown as Fig. 5a, when there is a linear vertical shear of environmental wind in the western airflow, a secondary circulation rotating clockwise will be generated on the vertical section, this circulation is overlapped with the vertical circulation of TC, thus the uprising movement of TC at the down wind right (left) is enhanced (weakened), and it further influences the asymmetry of TC convection belt. When the vortex of TC in the continuously intensifying stage is enhanced, such asymmetrical distribution gradually becomes symmetrical with the enhanced rotating. When VWS changes in a waveform with altitude, the secondary circulation caused by VWS will be nonhomogeneous in vertical distribution, and thus the secondary circulation and vertical circulation of typhoon will not be matched any more. For example in Fig. 5b, when the environmental wind speed of western airflow changes in a waveform, the secondary circulation in the vertical direction will also change complicatedly.

This paper adopts the sectional distribution characteristics of south-to-north and east-to-west radar reflectivity and vertical circulation across the typhoon eye at seven time points during the three developing stages of enhanced developing, continuously intensifying and rapidly fading to analyze the impact of the characteristics of VWS waveform change on the structure and intensity change of typhoon Fitow.

4.1.1 Impact of vertical wind shear on the structure and intensity change of TC in the enhanced developing stage

(1) The vertical wind shear (Fig. 3 ) analyzed with a vertical resolution of 100 hPa showed that the vertical distribution of VWS at 18:00 on 3rd during the enhanced developing stage was characterized as below: There was a weak east wind shear at the low layer in the troposphere, the shear vector was a south wind at 850∼750 hPa and a western wind at 750∼400 hPa with a speed increasing with altitude, and it was a east wind at 300∼200 hPa with a speed also increasing with altitude. According to the principle that the secondary circulation caused by wind shear is overlapped with the vertical movement of TC at the east and west, and as shown in Fig. 6a, a counterclockwise enhancing circulation ring (A) was overlapped onto the low layer in the west of TC, a clockwise weakening circulation ring (B) was overlapped onto the middle layer, and a counterclockwise enhancing circulation ring (C) was overlapped onto the high layer. As a result, two enhancing vertical movement centers were generated at the low layer and high layer in the west of TC; the action at the east of TC was opposite to the action at the west, by the enhancing circulation ring (D) at the middle layer, the vertical movement can be continuously extended from the middle and low layers to the high layer, however, the strong convection was at the middle layer. The radar reflectivity at east and west showed that the west had two peak value centers at the low and high layers of the troposphere, and in the east because of the strong convection in the east, the extending continuity of convection in the low, middle and high layers was given a characteristic of deep convection in the whole layer. Therefore, VWS not only impacted the nonhomogeneity of east and west convections of TC in the vertical direction, i.e. it was strong in the high and low layers and weak in the middle layer at west, and was opposite at east, and it also impacted the asymmetry of east and west convections, however, it was strong at east and weak at west generally. Similarly, the VWS at south and north was also nonhomogeneous in the vertical direction, i.e. it was weak in the low layer and strong in the middle and high layers at south, and was opposite at north; for the asymmetry of south and north, it was weak in south and strong in north (Fig. 6b ).

(2) It was not in the continuously intensive stage at 06:00 on 4th when the distribution characteristics of VWS was different from that at 18:00 on 3rd and it entered the bimodal state of waveform change (figure omitted) and the shear intensity also changed, for example, the east wind was enlarged in the low layer and high layer of troposphere, and it was increased from 0.6 m·s^-1 to 1.4 m·s^-1 and from 2m·s^-1 to 5.8 m·s^-1 respectively. It enhanced the convection of TC in the low layer and high layer at west and also enlarged the radar echo intensity, so it meant the secondary circulation overlapping effect was modified by the direction of VWS, and the secondary circulation overlapping degree was also impacted by the degree of VWS.

The nonhomogeneity of convection belt in the vertical direction caused by VWS was also expressed by the asymmetry of horizontal distribution (Fig. 7a, 7b, 7c), the radar reflectivity intensity distribution showed that because of the differences of VWS effect between east-to-west and south-to-north at different altitudes, the strong echo belt was at the southwest and northeast areas in the low layer (800 hPa) of troposphere, at the east area in the middle layer (500 hPa), and at the southwest and northeast areas in the high layer (200 hPa). It also showed that the rotation change of horizontally asymmetrical convection belt with altitude favorably complied with the rotation of VWS with altitude.

4.1.2 Impact of vertical wind shear on the structure and intensity change of TC in the continuously intensifying stage

The continuously intensifying stage of TC lasted for 48 hours, VWS was distributed in a similar mode in the vertical direction before 06:00 on 6th, and it was the most distinct at 18:00 on 5th, so the state at 18:00 on 5th is chosen to analyze the impact of VWS on the structure and intensity change of TC in the continuously intensifying stage. The bimodal distribution of VWS at 18:00 on 5th was: it was a southeast wind at 950 hPa and southwest wind at 850∼700 hPa in the low layer, it was a high west wind at 650∼450 hPa in the middle layer, and the peak value of west wind shear 6.8 m·s^-1 appeared at 500 hPa; it was a southwest wind at 400∼300 hPa and a high northeast wind at above 300 hPa in the high layer, and the wind shear reached 7 m·s^-1. The inflection point of VWS appeared at 500 hPa, i.e. the wind changed clockwise with altitude below 500 hPa and counterclockwise above this altitude. Because of such bimodal distribution of VWS, the nonhomogeneity of vertical convection at east and west was clearer in vertical distribution, and the radar echo intensity distribution (Fig. 8a ) showed that the convection was enhanced in the low layer and high layer and weakened in the middle layer at west, and was opposite at east; it showed an asymmetry as strong at east and weak at west generally. The same principle was used to analyze the situation at south and north (Fig. 8b ), it was weakened in the middle and low layers (950∼600 hPa) and enhanced in the high layer (500∼200 hPa) at south, and was opposite at north; it also showed an asymmetry as weak at south and strong at north, the vertical wind shear had a long lasting northeast wind shear in the high layer (300∼200 hPa) during the continuously intensifying stage, because of the secondary circulation ring, the convection of TC in the high layer at west and south developed higher and more intensively than that at east and north; there was a long lasting western wind shear in the middle layer (650∼500 hPa), and TC in the middle layer at east was enhanced by the secondary circulation ring generated, it promoted the convection development and long life maintenance in the whole layer at east.

Table 1 showed the maximum values of east-to-west and south-to-north sectional vorticity and vertical speed of typhoon across the eye center at typical time points during three different developing stages. Analysis showed that the vorticity and divergence in the continuously intensifying stage were distinctly higher than those in the enhanced developing stage, and in this stage, the vortex motion (4.2×10^-3s^-1) at 18:00 on 5th was nearly 1.5 times that at 18:00 on 3rd, and thus the enhanced vortex motion made the horizontal asymmetrical distribution of convection belt symmetrical (Fig. 9a, 9b), but in the high layer at 200 hPa, there was still some asymmetry consistent with VWS (Fig. 9c ). Therefore, the long lasting high value vertical wind shear in the middle and high layers played an important part in the symmetry, nonhomogeneity and long life maintenance of typhoon Fitow during the enhanced developing stage. VWS turned into the single mode from 06:00 on 6th which was 6 hours ahead of the starting time of rapidly fading stage.

4.1.3 Impact of vertical wind shear on the structure and intensity change of TC in the rapidly fading stage

The distribution of VWS at 12:00 on 6th was almost the same as that at 06:00 on 6th, it was also changed in a single mode but the intensity is a little stronger. The uprising effect in the low layer and high layer of TC at east (west) arising from the secondary circulation caused by VWS was weakened (enhanced), and in the middle layer at east (west) it was enhanced (weakened) (Fig. 10 ). Furthermore, the vortex motion was distinctly weakened (Table 1 ), and the asymmetrical distribution caused by VWS was revealed again (Fig. 11 ).

The above analysis showed that the time-space asymmetry had a significant impact on the structure and intensity of TC. Because of the dynamic secondary circulation of VWS in the enhanced developing stage and rapidly fading stage, the convection of TC at east-west sides and south-north sides in different altitudes was asymmetrically distributed, as it was respectively enhanced or weakened, the structure of convection belt was distributed asymmetrically, and the change of such asymmetry with altitude was consistent with the change of VWS with altitude. The two long lasting VWS peak value areas in the middle and high layers during the continuously intensifying stage played an important part in the nonhomogeneity, asymmetry and long life maintenance of typhoon Fitow. Furthermore, because of the vortex, the horizontal distribution structure of typhoon Fitow in the middle and low layers was asymmetrical in the continuously intensifying stage. The mode change of VWS was favorably anand temporally correlated to the change of typhoon Fitow in the three life stages, as it was in advance of 6 hours.

4.2 Impact of Waveform Changing of Vertical Wind Shear on the Instability and Development of Mesoscale Typhoon Convection Belt

Observation and simulation showed that the eye wall and spiral rain belt of typhoon consisted of mesoscale convection belts, i.e. the eye wall area and external spiral rain belt consisted of convection units, the functioning convection belt was about 10 km wide and 5∼7 km long vertically, the complete spiral rain belt was characterized by a roller circulation, i.e. it had a 2D single circulation on the vertical plane, and for the formation of 2D single convection, the secondary circulation arising from the dynamic instability in Ekman layer was used by Faller (1963) , Faller and Kaylor (1966) and Brown (1970), et al. Willoughby (1979) discussed the formation and development of 3D roller in typhoon with the forced secondary circulation theory of balance equation.

Kuettner (1971) introduced a new theory and then the secondary circulation development caused by the momentum effect of VWS attracted an extensive attention, in the theoretical work of Kuettner, vorticity force (the acting force connected to the vertical outline curvature of wind speed) was brought into the convection generation mechanism, and the unbalance of floating force, viscous force and vorticity force was comprehensively taken into the consideration at the occurrence of convection. The basic principle of Kuettner's theory is as follows: imagine there is a basic parallel airflow along axis X in the planet border layer, and it is involved with a vertical wind speed shear and vorticity along axis Y. As shown in Fig. 12, there is a curved bimodal vertical wind speed outline in the border layer, the vorticity along axis Y in the low layer is larger than that in the top layer above altitude H₁, the vertical gradient of vorticity is negative, if there is an air unit moving upwards from the bottom layer below the maximum wind speed layer, because of the vorticity conservation, an overbalance vorticity is generated in the new environment, and a “relative vorticity” is formed. As a result the basic vorticity field is destructed, the environmental vorticity is redistributed, and further, the vortex moves down acceleratively, and the unit is recovered to the original position. The acting force by which the unit is recovered to the original position is called as vorticity force. The acceleration of “vortex” under such vorticity force can be given by the equation below (Lin, 1955 ) :

(1)

where Γ^-1 is the vortex intensity, η'(z) is the vertical vorticity gradient of basic airflow, i.e. η'(z) = $\frac{\partial }{\partial z}\left( \frac{\partial \bar{u}}{\partial z} \right)$ or η'(z) = $\frac{\partial }{\partial z}\left( \frac{\partial \bar{u}}{\partial z} \right)$, and v' is the horizontal air motion speed in relation to the vortex. The equation above showed that in the air layer where the vorticity increases with altitude (below altitude H1), i.e. when the vorticity gradient η'(z) is larger than zero, the vorticity force is upwards, the unit will move upwards acceleratively, and some instability appears. H₁ is the inflexion point of vertical wind speed outline, and is the altitude symbolizing the change of vorticity gradient force, in other words, the vertical acceleration turns negative from positive at this altitude, and it is the altitude where the vertical speed is the maximum. Obviously, when VWS changes in a waveform, the impact on the instability of mesoscale convection belt and the development of convection of TC will also change with altitude. One of Kuettner's view points is that distinct VWS can cause the formation of roller circulation, and data analysis showed that VWS of typhoon Fitow was also significant in free air, this paper tried to apply Keuttner's theory on the free air. To describe the impact of the environmental wind waveform changing with altitude in detail, the projection outline of environmental average wind V (composition of horizontal wind speed u and v) in Figs. 2b, 2c and 2d were decomposed into the vertical distributions of u (Fig. 13 ) and v (Fig. 14 ) to discuss the impact of nonhomogeneous vorticity force on the convection stability at different altitude.

(1) In the enhanced developing stage, the inflection point of vertical environmental wind outline for component u was at about 450 hPa (Fig. 13 (a, b) ), the vorticity force generated by VWS was larger than zero and the convection acceleration was generated below this altitude; the vorticity force was smaller than zero and convection development was inhibited above this altitude. On the corresponding east-to-west section, the peak value centers of two vertical speeds at east and west were 7 m·s^-1 and 1.4 m·s^-1 respectively, and both of them were above 450 hPa. Radar echo intensities at east and west were also gradually weakened upwards in the layer of altitude corresponding to the inflection points. The inflection point of vertical environmental wind outline was at about 300 hPa for component v (Fig. 14 (a, b) ), and the vorticity force caused by VWS was larger than zero and the convection acceleration was generated below this altitude. The peak value centers (2.6 m·s^-1 and 6.5 m·s^-1) of vertical speed corresponding to the radar echo on the south-to-north section were also at 300 hPa in the layer of inflection point. The key point of Kuettner's theory is to determine the impact of vorticity force on the convection instability, the acceleration caused by VWS is an important mechanism to determine the starting of convection, and thus it is meaningful to analyze the instability in the enhanced developing stage.(2) For the continuously intensifying stage, the same principle could be used to analyze the distribution of acceleration in the convection belt, as shown in Fig. 13c and 13d, the convection belt was distributed symmetrically in this stage, for example on the east-west section, the inflection point of environmental wind outline functioned at 550 hPa, and according to the vorticity force, both the peak value centers of vertical speed at east and west were 3.5 m·s^-1 at 550 hPa above in the altitude of the inflection point. The vertical environmental wind outline for component v (Fig. 14 (c, d) ) showed that the vorticity force of the whole layer was larger than zero except it was smaller than zero at 400 hPa around, so the promotion for convection and the complicated change of component v were the main cause of the bimodal character of vertical wind shear in this stage.(3) Similarly in the rapidly fading stage (Fig. 13 (e, f) ), for example on the east-to-west section, the inflection point of environmental wind outline was at 550 hPa, and the peak value center (3.5 m·s^-1) of the two vertical speeds at west was also in the layer of inflection point. The two radar echo column intensities were also gradually weakened upwards in the layer corresponding to the inflection points. In respect of the vertical environmental wind outline of component v (Fig. 14 (e, f) ), comparing with that in the enhanced developing stage, there was further an inhibiting layer where the vorticity force was negative, the wind speed of the whole layer was high, and it was relatively higher in the layers where the vorticity gradients were positive. Therefore, the outline was adverse to the development of convection comparing with that in the enhanced developing stage.

The above analysis showed that in the three stages of typhoon Fitow, the vorticity force with nonhomogeneous vertical distribution generated by VWS on component u was in favor of the generation and development of convection, it started to inhibit the development of convection at 550∼450 hPa, and the peak value center of vertical speed at each time point occurred at the same altitude with the inflection point of vertical environmental wind outline. The vertical speed was the highest as 7 m·s^-1 in the enhanced developing stage and 3.5 m·s^-1, and there was still vertical motion maintained in the initial stage of rapid fading. The impact of vorticity force arising from the component v varied in the three stages: in the enhanced developing stage, the vorticity force of the whole layer at 300 hPa below was larger than zero and it played a promoting and enhancing part; in the continuously intensifying stage, the wind outline was distributed in multiple steps, the vorticity was larger than zero except around 400 hPa, and it also played a promoting and enhancing part; in the rapidly fading stage, the vorticity force was smaller than zero and it inhibited the convection development in the lower layer, and the vorticity was higher than zero and it promoted the convection development in the upper layer.

5 CONCLUSION AND DISCUSSIONS

According to the analysis of the data observed, the mesoscale structure of typhoon Fitow showed the characteristics of asymmetry-symmetry-asymmetry in the roller belt strong convection area during the enhanced developing, continuously intensifying and rapidly fading stages; but during the 95-hour long life of typhoon Fitow, there was a 54-hour long continuously intensifying stage, in other words, the minimum air pressure varied in a “U” shape. These characteristics were correlated to the waveform distribution of VWS with altitude, continuous delivery of vapor and the multi-system interaction. In this paper, air data in WRF (v3.4) mode was used to indicate the image of physical impact of VWS waveform distribution with altitude on the mesoscale convection belt structure and intensity change of typhoon by sufficiently expressing the observation with numerical tests.

(1) During the movement of long-life typhoon Fitow, the time-space distribution of VWS changed in a waveform due to the modification of environmental system, i.e. data analysis with high vertical resolution showed that the vertical distribution from the low layer to the high layer turned clockwise in the troposphere, and in this altitude layer, VWS changed uninterruptedly, in other words, it had relatively stable change in a relative thick layer; however, it turned counterclockwise in the high layer of troposphere, and thus waveform characteristics of bimodal distribution were formed in the vertical direction; such waveform characteristics had different modes in different developing stages, and it was distributed in a bimodal wave during the continuously intensifying stage.

(2) According to the basic principle that the vertical wind shear had an impact on the convection distribution and intensity change of typhoon, the impact of waveform time-space distribution of VWS on the mesoscale convection belt and intensity change of typhoon Fitow was analyzed, and it was found that: the vertical wind shear in the middle layer of troposphere was the major part of vertical wind shear in the whole layer, the intensity change of typhoon lagged 6 hours after the vertical wind shear; the coupling degree of secondary vertical circulation and typhoon circulation caused by the time-space waveform distribution of vertical wind shear in different developing stages of typhoon was analyzed in details, and it was found that the impact of secondary circulation on the vertical uprising motion varied in the low, middle and high layers of the eye wall areas at both sides of the typhoon center, and thus the vertical distribution of convection belt in the eye wall area was nonhomogeneous; furthermore, the secondary circulation arising from vertical wind shear also played an important part in the asymmetrical-symmetrical-asymmetrical change of the strong convection belt of typhoon; the combined effect of vortex divergence distribution and vertical wind shear on the mesoscale structure during different developing stages of typhoon was analyzed, and it was found that the vortex motion was enhanced during the continuously intensifying stage, as a result, the strong convection belt turned to be symmetrically distributed, but it was still obviously asymmetrical in the high layer.

(3) According to the principle that the nonhomogeneous distribution of vorticity force in the vertical direction arising from the waveform distribution of vertical wind shear with altitude would cause instable development of mesoscale roller convection belt, the vorticity force distribution of typhoon Fitow in the vertical direction arising from the waveform distribution of vertical wind shear was analyzed, and it was found that the vorticity force in the middle and low layers of troposphere could enhance the convection instability during the three developing stages of typhoon, the maximum value of vertical speed was at the same altitude with the inflection point of vertical wind outline, the maximum vertical speed was the highest as 7 m·s^-1 in the enhanced developing stage, and the convection accelerating area and maximum vertical speed distribution given by the theoretical model were basically complying with those given by the air model. Therefore, it is analyzed and suggested that the waveform distribution of vertical wind shear not only has an impact on the mesoscale structure change of strong convection belt but also plays an important role in the continuously intensifying of convection belt in a typhoon; in addition, it might be the initializing mechanism for the instability of roller convection belt in a typhoon.

ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China (41675058, 41175054, 41275002, 41230421).