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Figure 10. Synoptic maps at 850 hPa analyzed using ECMWF gridded data every 6h from (a) 1200 UTC 7 to (d) 0600 UTC 8 June 1998. Geopotential heights (gpm, contour) are analyzed at 10 gpm intervals. Full and half barbs represent 5 and 2.5ms"1, respectively, and areas with wind speed >10 ms"1 are shaded (gray scale shown at lower right corner). Heavy solid (dotted) lines indicate a Meiyu front as defined by the maximum 0e gradient (relative vorticity), and asterisks (★) mark the location of Ishigakijima station (from G. Chen et al., 2006).

Figure 10. Synoptic maps at 850 hPa analyzed using ECMWF gridded data every 6h from (a) 1200 UTC 7 to (d) 0600 UTC 8 June 1998. Geopotential heights (gpm, contour) are analyzed at 10 gpm intervals. Full and half barbs represent 5 and 2.5ms"1, respectively, and areas with wind speed >10 ms"1 are shaded (gray scale shown at lower right corner). Heavy solid (dotted) lines indicate a Meiyu front as defined by the maximum 0e gradient (relative vorticity), and asterisks (★) mark the location of Ishigakijima station (from G. Chen et al., 2006).

Figure 11. Nonlinearly balanced fields of geopotential height (gpm) and wind (m s"1) associated with the ms component at 850 hPa for (a) 1200 UTC 7 June and (b) 0000 UTC 8 June, 1998. Geopotential heights are analyzed at 5 gpm intervals. The pennant, full barb, and half barb represent 5, 1, and 0.5 ms"1, respectively, and areas with winds >5ms_1 are gray-shaded (scale shown on right hand side). The dotted lines indicate frontal position (from G. Chen et al., 2006).

Figure 11. Nonlinearly balanced fields of geopotential height (gpm) and wind (m s"1) associated with the ms component at 850 hPa for (a) 1200 UTC 7 June and (b) 0000 UTC 8 June, 1998. Geopotential heights are analyzed at 5 gpm intervals. The pennant, full barb, and half barb represent 5, 1, and 0.5 ms"1, respectively, and areas with winds >5ms_1 are gray-shaded (scale shown on right hand side). The dotted lines indicate frontal position (from G. Chen et al., 2006).

Figure 12. Time variations of vorticity budget terms (a) local rate of change (dZ/dt), (b) horizontal advection • V(Z + f)], (c) divergence [-(Z + f)V • Vw], and (d) vertical advection [-u(dZ/dp), all in 10"5 s"1 (6h)" ] across the front at 850 hPa during 0000 UTC 7-0600 UTC 8 June 1998 (abscissa). Values were averaged along the front from 5.5° south (negative, ordinate) to 5.5 north (positive). Isolines are analyzed at 1 x 10"5 s"1 (6h)_1, and heavy dashed lines indicate frontal position (from G. Chen et al., 2006).

Figure 12. Time variations of vorticity budget terms (a) local rate of change (dZ/dt), (b) horizontal advection • V(Z + f)], (c) divergence [-(Z + f)V • Vw], and (d) vertical advection [-u(dZ/dp), all in 10"5 s"1 (6h)" ] across the front at 850 hPa during 0000 UTC 7-0600 UTC 8 June 1998 (abscissa). Values were averaged along the front from 5.5° south (negative, ordinate) to 5.5 north (positive). Isolines are analyzed at 1 x 10"5 s"1 (6h)_1, and heavy dashed lines indicate frontal position (from G. Chen et al., 2006).

of the front. Based on the overall diagnoses, they suggested the vital role of the vorticity advection process associated with LLJ in causing the northward retreat of the Meiyu front in this case.

4. Low-Level Jet (LLJ) Formation

The frequency distribution of the 850 hPa migratory LLJ's which affect northern Taiwan in the Meiyu season is presented in Fig. 13 (G. Chen et al., 2005). The LLJ's tended to form over southern China between 20° and

30°N [Fig. 13(a)], with the highest frequency (near 23°N, 109°E) just to the east of the Tibetan Plateau. The main axis of the jets was oriented from southwest to northeast, also roughly parallel to the terrain. As the LLJ's migrated eastward at t-24 and t-12, their overall shape became much more elongated, with the area of high frequency extending farther downstream [Figs. 13(b) and 13(c)]. In addition, the orientation of the maximum axis also turned slightly from west-southwest to east-northeast. From t-12 to t0, the LLJ's moved

Figure 13. Geographical distribution of frequencies of wind speed reaching 10 m s~1 at 850 hPa associated with a total of 30 migratory LLJ cases in May—June, 1985—1994, at (a) the time of LLJ formation, (b) 24 h before (t = —24), (c) 12 h before (t = —12), and (d) at the synoptic time (t = 0) when the LLJ moved over northern Taiwan (inside the area of 24°-26°N, 120.5°-122.5°E). Regions with a terrain higher than 0.5km are shaded (from G. Chen et al.., 2005).

Figure 13. Geographical distribution of frequencies of wind speed reaching 10 m s~1 at 850 hPa associated with a total of 30 migratory LLJ cases in May—June, 1985—1994, at (a) the time of LLJ formation, (b) 24 h before (t = —24), (c) 12 h before (t = —12), and (d) at the synoptic time (t = 0) when the LLJ moved over northern Taiwan (inside the area of 24°-26°N, 120.5°-122.5°E). Regions with a terrain higher than 0.5km are shaded (from G. Chen et al.., 2005).

southward significantly, and the frequency converged toward the main axis passing through northern Taiwan [Fig. 13(d)].

Observational study by G. Chen and Yu (1988) suggested that an LLJ might form to the south of the heavy rainfall area. They proposed that the reversed secondary circulation to the south of the Meiyu front as observed in the composite by G. Chen and Chi (1978), presumably driven by convective latent heating, was a possible formation mechanism for an LLJ. This mechanism was also suggested by both theoretical study (Chen, 1982) and numerical experiments (Chen et al., 1998; Chen et al., 2000; Chou et al., 1990). Results of Chen's theoretical study (1982) suggested that the existence of an unstable inertiogravity wave in the ascending motion region caused a thermally direct circulation beneath the upper-level jet. Latent heating in the area of ascending motion accelerated the thermally direct circulation to the north and induced a reversed circulation to the south through the geostrophic adjustment process. It was concluded that the LLJ formed through the Coriolis acceleration of northward flow in the lower branch of this reversed circulation. Numerical study by Chou et al. (1990) using a two-dimensional frontogenesis model simulated the formation of an LLJ to the south of the area of strong convection and suggested the importance of cumulus convection, especially a slantwise structure, in developing the reversed circulation and the LLJ.

A weak thermally indirect circulation was observed to the south of the Meiyu front for TAMEX IOP 5 case, as presented in Fig. 14(a) (Chen et al., 1994). In that case, the LLJ was observed to the south of the Meiyu front within the lower return branch of the secondary circulation and the thermally direct circulation across the front was observed similar to that of G. Chen and Chi (1978) and G. Chen and Chang (1980). Numerical study by Chen et al. (1997) of this LLJ case revealed that the LLJ developed through the Coriolis force acting on the cross contour ageostrophic winds in response to the increased pressure gradients related to the development of the cyclone, and was enhanced by latent heating. A recent case study using momentum budget computations of numerical simulation by Zhang et al. (2003) also suggested that the pressure gradient force and the horizontal advection are the main contributors to the development of mesoscale LLJ's. Numerical simulation study of a Meiyu frontal case by Chen et al. (1998) suggested that the existence of an upper-level jet will induce the development of the thermally direct circulation, as illustrated in Fig. 14(b). It was also suggested that the southward branch of the thermally

Mei Front Structure

Figure 14. Schematic diagram delineating the secondary circulations across the Meiyu front (a) from Chen et al. (1994), (b) the upper-level jet, and (c) the vertical and slantwise convection in the development of the LLJ from Chen et al. (1998). In (a), thin solid and dashed lines depict the strong direct (D) and the weak indirect (I) circulations, respectively. The heavy solid line with triangles shows the frontal position. The J indicates the upper-level and low-level jet positions, and the boldness of the J represents the jet strength in (b) and (c). Thick heavy lines show the positions of the tropopause boundary. The dashed line depicts the weaker circulation and the thin solid line represents the stronger circulation. Regions with relative humidity greater than 70% are shaded.

Figure 14. Schematic diagram delineating the secondary circulations across the Meiyu front (a) from Chen et al. (1994), (b) the upper-level jet, and (c) the vertical and slantwise convection in the development of the LLJ from Chen et al. (1998). In (a), thin solid and dashed lines depict the strong direct (D) and the weak indirect (I) circulations, respectively. The heavy solid line with triangles shows the frontal position. The J indicates the upper-level and low-level jet positions, and the boldness of the J represents the jet strength in (b) and (c). Thick heavy lines show the positions of the tropopause boundary. The dashed line depicts the weaker circulation and the thin solid line represents the stronger circulation. Regions with relative humidity greater than 70% are shaded.

indirect circulation, with its rising motion in the frontal region and equatorward sinking motion, is driven by the frontal vertical deep convection, as presented in Fig. 14(c). The return flow of this circulation at low level can produce an LLJ through geostrophic adjustment. Observational case studies (Lin and Chiou, 1985; G. Chen et al., 1986; Lin, 1988; Lin and Tsai, 1989; Pu and G. Chen, 1988; Qian et al., 2004) also showed that an LLJ tended to form or to intensify to the south of an MCS in South China. A numerical study of a TAMEX case by Hsu and Sun (1994), on the other hand, suggested that cumulus heating may not have played a critical role in the LLJ formation and the latent heat release by stratiform clouds contributed to the development of the LLJ.

In a recent case study of a retreating Meiyu front (Fig. 10), G. Chen et al. (2006) observed that diabatic latent heating from the MCS, large enough in scale, generated positive PV and height fall at low levels. The enhanced height gradient induced northwestward-directed ageostrophic wind toward the area of the MCS (Fig. 15) and the LLJ formed to the southeast of the MCS through Coriolis torque. The piecewise PV inversion contributions from different components to the LLJ at 850 hPa in this case are presented in Fig. 16. Apparently, the formation and intensification of the LLJ in this case could be largely attributed to the latent heating effects of the organized MCS, superimposed upon a background southwesterly monsoonal flow of about 6ms~1. Similar results were obtained for a Meiyu system over South China by G. Chen, Wang, and Chang (2007) using piecewise PV inversion and ageostrophic wind analysis techniques.

In summary, results of observational, theoretical, and numerical studies all suggested that a thermally indirect circulation with rising motion in the frontal region and equatorward sinking motion is driven by the latent heat release associated with frontal deep convection. The LLJ

could then form to the south of the convective heavy rainfall area through the Coriolis acceleration of the lower branch of an induced thermally indirect secondary circulation.

5. Development of the Frontal

Cyclone

A theoretical study by Du and Cho (1996) proposed that the growth rate of the most unstable wave along the Meiyu front depends on the intensity of cumulus heating. Their results suggested that when the cumulus heating parameter is below a critical value, the wavelength is about 8-15 times the cross-front width scale of the PV anomaly, and the structure of the wave is of the barotropic type but modified by convection. When the heating parameter is above the critical value, the disturbance draws its energy almost entirely from heating and the structure of the wave resembles a system driven purely by cumulus heating. The wavelength of the most unstable wave is about 1700-2100 km and bears little relationship to the width of the background PV anomaly.

Observationally, one kind of low-level vortex during the Meiyu season is the intermediate-scale cyclone (1000-3000 km), which forms along the Meiyu front, and the latent heat release was found to play a major role in its development (Chang and Chen, 2000; Zhao et al., 1982). It was also found that the vertical coupling processes compounded the diabatic heating effect, and could lead to the strong intensification of the Meiyu frontal cyclone (Chang et al., 1998). In a recent study, Takahashi (2003) also found that the coupling of the upper-level migratory trough and the lower-level shear line can be important for the evolution of the Meiyu frontal disturbances. Lee et al. (2006) examined 20 tropical cyclone formations in the South China Sea in May and June of 1972-2002 and found that 11 of them were associated with the weak baroclinic environment of a Meiyu front, while the remaining 9 were nonfrontal. They also

Figure 15. Ageostrophic wind component (arrow, ms 1) perpendicular to geopotential height contours and local tendency of the wind component along the geopotential height contours (shaded, ms"1 per 12 h, gray scale shown at bottom) at 850 hPa at 6 h intervals from (a) 1200 UTC 7 to (d) 0600 UTC 8 June, 1998. The 850-hPa LLJ is depicted by isotachs (thick solid) analyzed at intervals of 2ms"1, starting from 10ms"1 (from G. Chen et al., 2006).

Figure 15. Ageostrophic wind component (arrow, ms 1) perpendicular to geopotential height contours and local tendency of the wind component along the geopotential height contours (shaded, ms"1 per 12 h, gray scale shown at bottom) at 850 hPa at 6 h intervals from (a) 1200 UTC 7 to (d) 0600 UTC 8 June, 1998. The 850-hPa LLJ is depicted by isotachs (thick solid) analyzed at intervals of 2ms"1, starting from 10ms"1 (from G. Chen et al., 2006).

Figure 16. Wind vectors averaged over a hexagonal domain centered along the axis of the LLJ from different components at 0000 UTC 8 June 1998. "EC" depicts the observed wind of ECMWF gridded analysis, and "Total" and "Mean" represent balanced total wind and time mean wind (15 May-15 June 1998), respectively. See text for the definition of other terms (from G. Chen et al., 2006).

Figure 16. Wind vectors averaged over a hexagonal domain centered along the axis of the LLJ from different components at 0000 UTC 8 June 1998. "EC" depicts the observed wind of ECMWF gridded analysis, and "Total" and "Mean" represent balanced total wind and time mean wind (15 May-15 June 1998), respectively. See text for the definition of other terms (from G. Chen et al., 2006).

found that the strengthening of northeasterlies to the north of the Meiyu front was important for increased cyclonic vorticity of the frontal cyclone, and finally caused the detachment of the cyclone from the Meiyu front to become a tropical storm.

A recent diagnostic case study by G. Chen, Wang, and Chang (2007) suggested that the growth of frontal disturbances was a result of the nonlinear mechanism similar to the CISK, in which the frontal PV centers and cumulus convection reinforce each other through a positive feedback process. Figure 17 presents 850 hPa analyses of that case. At 1200 UTC 6 June [Fig. 17(a)], the Meiyu front had developed

Figure 17. 850-hPa ECMWF analysis of geopotential height (solid, gpm), temperature (dashed, ° C), and horizontal wind (ms"1) at (a) 1200 UTC, (b) 1800 UTC 6 June, and (c) 0000 UTC 7 June, 2003. Geopotential heights and temperatures are analyzed at intervals of 10 gpm and 1°C, respectively. For winds, full (half) barbs are 5 (2.5) ms"1, and wind speed > 12.5 ms"1 is shaded. Thick wind flags in (a) and (c) are sounding data, and thick dashed lines indicate the position of the Meiyu front at 850 hPa (from G. Chen, Wang, and Chang, 2007).

Figure 17. 850-hPa ECMWF analysis of geopotential height (solid, gpm), temperature (dashed, ° C), and horizontal wind (ms"1) at (a) 1200 UTC, (b) 1800 UTC 6 June, and (c) 0000 UTC 7 June, 2003. Geopotential heights and temperatures are analyzed at intervals of 10 gpm and 1°C, respectively. For winds, full (half) barbs are 5 (2.5) ms"1, and wind speed > 12.5 ms"1 is shaded. Thick wind flags in (a) and (c) are sounding data, and thick dashed lines indicate the position of the Meiyu front at 850 hPa (from G. Chen, Wang, and Chang, 2007).

along 24°N with the deepening of a frontal cyclone and the eastward extension of its trough.

The development of the frontal cyclone was also evident at 1800 UTC 6 June [Fig. 17(b)]. At 0000 UTC 7 June, three individual vortices could be seen near 115°, 119°, and 122° E as the Meiyu front reached 125°E while moving slowly southward [Fig. 17(c)]. Figure 18 presents the nonlinear balanced 850 hPa height, wind, and Z fields from the component of latent heat release "ms." From 1800 UTC 6 June to 0000 UTC

105E 110E 115E 120E 125E

Figure 18. 850-hPa nonlinear balanced geopotential height (gpm, contour), horizontal wind (m s"1), and Z(10"5 s"1, shading) inverted from the low- to mid-level q' related to latent heat release (ms) at 6 h intervals at (a) 1800 UTC 6 June and (b) 0000 UTC 7 June, 2003. Contour intervals are 5 gpm and dashed lines are used for negative values, while full (half) barbs in wind flags correspond to 2 (1)ms"1, respectively (from G. Chen, Wang, and Chang, 2007).

105E 110E 115E 120E 125E

Figure 18. 850-hPa nonlinear balanced geopotential height (gpm, contour), horizontal wind (m s"1), and Z(10"5 s"1, shading) inverted from the low- to mid-level q' related to latent heat release (ms) at 6 h intervals at (a) 1800 UTC 6 June and (b) 0000 UTC 7 June, 2003. Contour intervals are 5 gpm and dashed lines are used for negative values, while full (half) barbs in wind flags correspond to 2 (1)ms"1, respectively (from G. Chen, Wang, and Chang, 2007).

7 June, the distribution of Z from "ms" was very similar to that derived from the observed wind field (not shown). The frontal cyclonic circulation grew stronger at 0000 UTC 7 June [Fig. 17(b)], with a pattern and an evolution very similar to those appearing in Fig. 17.

In summary, it is evident that the latent heat release from the MCS's played a vital role in the strengthening and maintenance of the frontal disturbances in this case. However, whether the Meiyu frontal cyclogenesis is driven by a CISK process or not is still an open question. Further research efforts are needed to shed some light on the mechanism of the Meiyu cyclogenesis.

6. Concluding Remarks

The Meiyu frontal system is the key synoptic feature responsible for the seasonal rainfall maximum occurring during mid-May to mid-June over South China and Taiwan. The important components of the Meiyu frontal system include the Meiyu front, LLJ, and frontal cyclone. Recently, numerous studies have been focused on various aspects of these components, particularly on the role of cumulus heating in the development and evolution of the Meiyu frontal system from a PV perspective. What we have learned about the Meiyu frontal system recently can be summarized as follows.

Diagnoses for weak baroclinic Meiyu front cases using the piecewise PV inversion technique all revealed that the cumulus heating played a major role in frontogenesis. Whereas the diagnosis of the frontogenetical function for the relatively strong baroclinic Meiyu front case indicated that the frontogenesis and the maintenance of the front were due to both horizontal convergence and deformation similar to what would be expected from the classical frontal theory. Based on the piecewise PV inversion technique and vorticity budget analyses, it was also suggested that the cumulus heating was the cause of the formation and intensification of the LLJ, and the subsequent northward retreat of the Meiyu front was caused by the vorticity advection processes associated with the LLJ. Diagnosis of the frontogenetical function indicated that the Meiyu frontal movement was caused by the southward frontal propagation due to frontogenetical processes in addition to the advection of the postfrontal cold air.

Case studies of the formation of LLJ's using the piecewise PV inversion technique all suggested that the formation and intensification of LLJ's could be attributed to the cumulus heating effects of the organized MCS over a heavy rainfall area through the Coriolis acceleration of the lower branch of an induced secondary circulation superimposed upon the background southwesterly monsoonal flows. Using a similar technique, it was also found that the growth of the frontal cyclone was a result of a nonlinear mechanism similar to the CISK, in which the frontal PV centers and cumulus convection reinforce each other through the positive feedback process.

In this paper, we have attempted to give an overview of the recent research results on the role of cumulus heating in the development and evolution of the Meiyu frontal system, particularly from a PV perspective. It is clear that our knowledge is far from complete. More research efforts will be needed to conduct observational, theoretical, and modeling studies in order to improve our understanding of the Meiyu frontal system including the Meiyu front, LLJ, and frontal cyclone. Particularly, the role of latent heat release in the Meiyu frontogenesis for the strong baroclinic Meiyu fronts deserves further studies in both theoretical and numerical simulation aspects. Also, more studies are needed to shed some more light on the role of the nonlinear positive feedback mechanism between the frontal PV center and the cumulus convection in the cyclogenesis process along the Meiyu front.

Acknowledgements

Thanks are due to Miss Man-Chun Chiu and Mr. Chih-Sheng Chang for preparing this manuscript. This article is partially supported by NSC 96-2111-M-002-011 and NSC 96-2111-M-002-010-MY3.

[Received 12 January 2007; Revised 31 May 2007; Accepted 5 June 2007.]

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Advance in the Dynamics and Targeted Observations of Tropical Cyclone Movement

Chun-Chieh Wu

Department of Atmospheric Sciences, National Taiwan University, Taipei,, Taiwan [email protected] as. ntu. edu. tw

The advance in the dynamics and targeted observations of hurricane movement is reviewed in this article. In celebration of the 50th anniversary of the Department of Atmospheric Sciences, National Taiwan University, special emphasis is put on the author's major scientific contributions to the following issues: the baroclinic effect on tropical cyclone motion, the potential vorticity diagnosis of the tropical cyclone motion, and the targeted observations from DOTSTAR (Dropwindsonde Observations for Typhoon Surveillance near the Taiwan Region) in understanding and improving the tropical cyclone track predictability.

1. Introduction

The dynamics of tropical cyclone (TC) motion are rather complex. As pointed out by Holland (1984), a complete description would require at least detailed knowledge of the interactions between the cyclone circulation, the environmental wind field, the underlying surface, and the distribution of moist convection. It has generally been proposed that TC motion is governed by the tropospheric average steering flow and a drift caused by the presence of a background potential vorticity gradient. However, there are many other factors that can affect the cyclone's motion. Thanks to scientific advances in the past few decades, the understanding of the dynamics of TC motion is rather comprehensive, along with the improvement of observations (Aberson, 2003; Wu et al., 2005) and numerical models (Kurihara et al., 1998); the forecasting of TC motion has also been in steady progress.

Some reviews on this issue have been well conducted, by Wang et al. (1998) and Chan (2005). To celebrate the 50th anniversary of the Department of Atmospheric Sciences, National Taiwan University, this article reviews the author's major contributions to the current understanding of the dynamics and targeted observations of TC movement. The following topics are covered: the baroclinic effect on TC motion (Wu and Emanuel, 1993, 1994), the potential vorticity perspective of the TC motion (Wu and Emanuel, 1995a,b; Wu and Kurihara, 1996; Wu et al., 2003, 2004), and the targeted observations in improving TC track prediction (Wu et al., 2005, 2006, 2007a,b). In Sec. 2, the baroclinic effect on TC motion is shown. The potential vorticity perspective of the TC motion and the targeted observations from DOTSTAR (Dropwindsonde Observations for Typhoon Surveillance near the Taiwan Region) in improving the forecasting of TC motion are discussed in Sees. 3 and 4, respectively. Finally, a summary appears in Sec. 5.

2. Baroclinic Effect on TC Motion

(Wu and Emanuel, 1993, 1994)

2.1. Background

Studies of TC motion have focused mainly on steering by the mean flow and the effect of background potential vorticity gradients, i.e. the evolution of barotropic vortices in a barotropic flow. These effects, taken together, suggest that TCs should follow the mean large scale (steering) flow (George and Gray, 1976), but with a westward and poleward relative drift (Fiorino and Elsberry, 1989). Other, minor factors may also affect TC motion, such as the asymmetric convection (Willoughby, 1988) and the vortex interaction (Holland and Dietachmayer, 1993).

However, observations have shown that real TCs are strongly baroclinic, with broad anticyclones aloft, and the distribution of the large-scale potential vorticity gradient in the tropical atmosphere is very nonuniform. As indicated by Wu and Emanuel (1993), these properties may substantially influence the movement of storms. The upper anticyclone, though weak in terms of wind velocity relative to the lower-layer cyclonic circulation, can be very extensive. Slight displacements of the upper region of anticyclonic flow from the low-level cyclone can conceivably lead to large mutual interaction, and the potential vorticity gradient may act on these two flows in very different ways.

Based on the concepts of vortex interaction, Wu and Emanuel (1993) proposed that a baroclinic TC, which is structured like a vertically distributed pair of vortices of opposite signs, would experience a mutual propagation if the vortex dipole is tilted (Fig. 1). In other words, the background vertical wind shear can tilt the vortex pair by blowing the upper potential vorticity anomaly downshear. As members of the vortex pair are displaced, they begin to interact with each other and thus move at right angles to the axis connecting them. On this basis, it is hypothesized that Northern Hemispheric (Southern Hemispheric) TCs should drift with respect to the mean winds in a direction to the left (right) of the background vertical shear vector.

2.2. Methodology

The intention is to isolate the effect of background vertical shear. The hurricane is represented in a two-layer quasi-geostrophic model as a point source of mass and zero potential vor-ticity air in the upper layer, collocated with a point cyclone in the lower layer. The model is integrated by the method of contour dynamics and contour surgery. The contour dynamics is a

Figure 1. The vertical shear (black arrows) of the environmental flow results differential advection of the potential vorticity associated with a storm. Black and gray ellipses indicate the lower- and upper-level storm circulations, respectively. The upper layer is tilted due to the presence of vertical shear, and its projection (dashed gray ellipse) results in the storm drift to the left (Northern Hemisphere) of the shear vector (gray arrow).

Figure 1. The vertical shear (black arrows) of the environmental flow results differential advection of the potential vorticity associated with a storm. Black and gray ellipses indicate the lower- and upper-level storm circulations, respectively. The upper layer is tilted due to the presence of vertical shear, and its projection (dashed gray ellipse) results in the storm drift to the left (Northern Hemisphere) of the shear vector (gray arrow).

Lagrangian computational method used to integrate flows associated with patches of piecewise constant potential vorticity. This method leads to a closed dynamical system within which the evolution of the flow can be uniquely determined by the contours bounding the patches. The method of contour surgery improves the resolution of the contour by adding nodes (called node adjustment) in regions of high curvature or small node velocity. It is also more efficient and prevents unlimited enstrophy cascades to a small scale by removing contour features (called contour adjustment) thinner than some prescribed tolerance. A detailed description of the methods of contour dynamics and contour surgery can be found in Dritschel (1989).

In this work, the simplest analog of a mature TC is considered to be a diabatically, fric-tionally maintained point vortex of constant strength in the lower layer, and a patch of uniform, zero potential vorticity air in the upper layer, surrounded by an infinite region of constant potential vorticity (it is assumed that the mean meridional gradient of potential vor-ticity associated with the coriolis parameter can be canceled out by introducing upper and lower boundaries with gentle meridional slopes in the two-layer model). The diabatic sink of potential vorticity in the upper layer is represented as the expansion of the upper potential vorticity anomaly, owing to a radial outward potential (irrotational) flow emanating from a point mass source collocated with the lower vortex. According to the principle of mass continuity, the potential flow can be calculated from the lower boundary frictionally driven mass influx.

The case of a vanishing ambient potential vorticity gradient is explored as well. Therefore, the upper vortex patch is advected by the rotational flows (associated with both the upper-layer contour itself and the lower-layer vortex), the divergent flow (associated with the mass source), and the mean shear flow. The work of Wu and Emanuel (1993, 1994) is meant to describe the first-order effects of vertical shear, given the approximation inherent in the model.

2.3. Results

For the case with no vertical shear, it is found that, as expected, the upper patch expands with time and remains circularly symmetric with no lower vortex movement. The wind distributions in each layer show that the upper flow is anticy-clonic and outward, similar to a real hurricane outflow, and the lower layer flow is symmetric around the vortex center, so that no vortex drift is induced.

For the case with shear, the vortex patch expands and is advected downshear. Also, roll-up of the vortex patch occurs on the downshear side, essentially due to barotropic instability. For cases with larger shear, the patch is advected rapidly downshear and becomes zonally elongated. The low potential vorticity anomaly behaves like a passive plume.

The trajectories of the lower vortex in three experiments with westerly shear of various magnitudes are shown in Fig. 2. In all cases,

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