YAMEI XU YUQING WANG. (Manuscript received 8 December 2012, in final form 14 June 2013) ABSTRACT

Transcription

1 NOVEMBER 2013 X U A N D W A N G 3471 On the Initial Development of Asymmetric Vertical Motion and Horizontal Relative Flow in a Mature Tropical Cyclone Embedded in Environmental Vertical Shear YAMEI XU Department of Geosciences, Zhejiang University, Hangzhou, China, and International Pacific Research Center, and Department of Meteorology, School of Ocean and Earth Science and Technology, University of Hawai i at Manoa, Honolulu, Hawaii YUQING WANG International Pacific Research Center, and Department of Meteorology, School of Ocean and Earth Science and Technology, University of Hawai i at Manoa, Honolulu, Hawaii (Manuscript received 8 December 2012, in final form 14 June 2013) ABSTRACT In this paper, the authors focus on the initial development of asymmetric vertical motion and horizontal relative flow in a mature tropical cyclone (TC) embedded in an environmental vertical shear. The fully compressible, nonhydrostatic TC model was used to perform a series of numerical experiments with a mature TC with different intensities embedded in shear with different magnitudes and different vertical profiles. Results show that the development of both the wavenumber-1 asymmetric vertical motion and horizontal relative flow for a TC embedded in vertical shear is quite sensitive to both the magnitude and the vertical profile of wind shear, as well as the intensity of the TC itself. Diagnostic analysis based on the quasi-balanced potential vorticity inversion indicates that the balanced dynamics can only explain a small portion of the asymmetric vertical motion and relative flow. The unbalanced processes contribute predominantly to the development of the asymmetric flow in the simulations. It is shown that the eyewall of a mature TC plays a role somewhat like a material cylinder embedded in an environmental flow with vertical shear. The interaction between the environmental shear and the eyewall produces vertical gradient of convergence/divergence of horizontal wind around the lateral edge of the eyewall. This forces much stronger asymmetric vertical motion than the balanced processes do and drives significant horizontal relative divergent flow over the storm core, which opposes vertical shear and reduces the vertical tilt of the storm axis. In addition, the budget analysis for the axisymmetric tangential wind demonstrates that the asymmetric flow plays a dominant role in weakening the storm top down. 1. Introduction Environmental vertical shear has long been recognized as a negative factor for the genesis and intensification of tropical cyclones (TCs) (Gray 1968; McBride and Zehr 1981; DeMaria and Kaplan 1994; Elsberry and Jeffries 1996). The vertical shear weakens tropical cyclones by ventilating the warm core above the low-level storm center (Gray 1968) by triggering the development of asymmetric structure in the inner-core region (Jones 1995; Wang and Holland 1996; DeMaria 1996; Frank Corresponding author address: Dr. Yamei Xu, Department of Geosciences, Zhejiang University, 38 Zheda Road, Hangzhou, China. xuyamei@zju.edu.cn and Ritchie 2001; Rogers et al. 2003; Wu and Braun 2004) or by midlevel dry-air intrusion that either directly dilutes the eyewall s warm, moist air (Tang and Emanuel 2010, 2012) or induces downdrafts that bring low equivalent potential temperature air into the inflow boundary layer (Riemer et al. 2010), or their combination. Previous studies suggest that under the influence of vertical shear, a TC would develop a quasi-steady wavenumber-1 asymmetry in the core region with downdraft (updraft) in upshear (downshear) side and enhanced convection and rainfall downshear left of the shear vector (Wang and Holland 1996; Bender 1997; Frank and Ritchie 1999, 2001; Rogers et al. 2003; Heymsfield et al. 2006; Molinari et al. 2004, 2006). How the quasi-steady wavenumber-1 asymmetric structure develops for a TC embedded in vertical shear DOI: /JAS-D Ó 2013 American Meteorological Society

2 3472 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 70 is an important issue and has been studied extensively in the literature. Jones (1995, 2004) conducted numerical experiments for TC-like vortices embedded in vertically sheared environmental flow using a dry, primitive equation model and demonstrated that the shear caused a dry vortex to tilt downshear initially and develop a wavenumber-1 vertical motion couplet with weak ascent downshear and descent upshear in the inner-core region. Jones (1995) explained the formation of this asymmetric vertical motion as being required for the rising/lowering isentropic surface in response to the tilted cyclonic circulation. She found that after this initial adjustment, the cyclonic flow around the eyewall would follow the isentropic surface, resulting in a quasi-balanced ascent (descent) to the right (left) of the vertical shear vector, which is 908 out of phase with the potential temperature anomalies. Although the above dry dynamics can explain reasonably well the initial development of asymmetric vertical motion in the inner core to a TC embedded in vertical shear, the subsequent evolution can become much more complicated when diabatic and moist processes are considered (Wang and Holland 1996; Frank and Ritchie 1999, 2001). With moist and diabatic processes, vertical shear induced adiabatic vertical motion may result in the development of convective asymmetry. Wang and Holland (1996) and Bender (1997) attributed the development of such convective asymmetries in the inner-core region to the relative flow across the elevated cyclonic relative vorticity core. They showed that both upward motion and convection were enhanced to the downshear left of the TC center but suppressed to the upshear right when facing downshear. In both dry and moist simulations, Wang and Holland (1996) found a quasi-steady tilt of the TC circulation center with height to the left of the shear. This was later further confirmed and conceptualized by Reasor et al. (2004). This distribution of asymmetry in eyewall convection due to the effect of vertical shear was also found later by Frank and Ritchie (1999, 2001) using a more sophisticated high-resolution model and by Corbosiero and Molinari (2002, 2003) and Black et al. (2002) from observations. Frank and Ritchie (1999) performed both dry and moist numerical simulations for TCs embedded in vertical shear using the fifth-generation Pennsylvania State University National Center for Atmospheric Research Mesoscale Model (MM5). They found that latent heating associated with eyewall convection greatly reduced the tilt of the TC vortex. They showed that early in their simulation, the adiabatic processes proposed by Jones (1995) dominantly produced maximum upward motion and convection downshear right of the shear vector. Enhanced convection then shifted downshear left after some initial adjustment. In a later study, Frank and Ritchie (2001) found that both the development of the asymmetric structure in the inner core and the subsequent weakening of the storm occurred without significant vertical tilt of the storm s axis. They also found that latent heating generally balances the downtilt temperature anomaly since the motion is no longer adiabatic. In a simulation study for Hurricane Bonnie (1998), Braun et al. (2006) examined the relationship between the vortex tilt and wavenumber-1 vertical motion as well as the role of shear-induced relative flow. They found that the vertical motion asymmetry was qualitatively consistent with an assumed balance between horizontal vorticity advection by the relative flow and the vertical stretching term in the vorticity budget as suggested by Wang and Holland (1996) and Bender (1997). Zhang and Kieu (2005) obtained the balanced response of the secondary circulation to vertical shear, latent heating, and friction based on piecewise potential vorticity (PV) inversion and quasi-balanced vertical motion equation. Their results indicated that the dry dynamical processes produced the secondary circulation in the inner-core region with rising motion downshear and the vertically sheared horizontal relative flows opposing the environmental vertical shear. They suggested that the environmental shear induced secondary circulation acts to resist the downshear tilt of the storm and reduces the influence of the environmental shear in the inner core by as much as 30% 40%. Although many efforts have been made to understand how the asymmetric vertical motion in the inner core develops for a TC embedded in an environmental vertical shear, some questions still remain. For instance, according to Jones (1995) s mechanisms based on vortex tilt and adiabatic balanced dynamics, the maximum upward motion should appear downshear initially and then downshear right of the shear vector. However, not only does the asymmetric vertical motion develop before any resolvable tilt of the storm s vertical axis occurs, but also the maximum upward motion occurs downshear left, not downshear right (Wang and Holland 1996; Frank and Ritchie 2001; Zhang and Kieu 2005). Diagnostics based on the piecewise PV inversion and quasi-balanced vertical motion equation (Zhang and Kieu 2005) suggested that about 30% 40% of the shear-induced asymmetric vertical motion and horizontal relative flow could be explained by balanced dynamics. This seems to suggest that about 60% 70% of the shear-induced vertical motion is related to the unbalanced dynamics, but the way to achieve this has not been well understood. Furthermore, most previous studies (Jones 1995, 2004; Wang and Holland 1996; Frank and Ritchie 1999, 2001; Wong and Chan 2004) studied the vertical shear effect

3 NOVEMBER 2013 X U A N D W A N G 3473 FIG. 1. Vertical wind shear (a) with different magnitudes and (b) with different vertical profiles used in numerical experiments. based on numerical experiments with a given vertical profile of the sheared flow between 850 and 200 hpa, even though observational study by Elsberry and Jeffries (1996) indicated differences in the vertical shear profile and suggested that the response of TC intensity depends on the shear profile. How the shear profile and magnitude matter to the development of asymmetric structure for a TC remains unknown. In addition, the possible dependence of the shear-induced asymmetries on the intensity of the TC itself has not been previously examined. In this paper, the fully compressible, nonhydrostatic TC model (TCM4) was used to conduct a series of idealized experiments to examine the initial development of the asymmetric vertical motion and horizontal relative flow for a TC embedded in vertical shear. The experiments include environmental wind shear with different magnitude and different vertical profiles imposed onto a TC or a shear imposed onto TCs with different initial intensities. The piecewise PV inversion method used in Zhang and Kieu (2005) was utilized to obtain the associated quasi-balanced asymmetric motion and asymmetric flow and thus the unbalanced flow. This allows us to examine how important the unbalanced dynamics are to the initial development of asymmetric flow and how the shear-induced asymmetric flow depends on the vertical profile and magnitude of the shear and the TC intensity. The rest of the paper is organized as follows. In the next section, a brief description of the model used in the study and the numerical experiments are presented. The initial development of asymmetric vertical motion and horizontal relative flow are discussed in sections 3 and 4, respectively. Conclusions are given in the last section. 2. Model description and numerical experiments A full description of TCM4 can be found in Wang (2007). In this study, four interactive nested domains have their grid spacings of 67.5, 22.5, 7.5, and 2.5 km, with , , , and grid points, respectively. All three inner meshes automatically move to follow the model TC so that the model TC is always located near the mesh centers. The model has 32 levels in the vertical with unperturbed surface pressure of 1010 hpa and a top at about 41 km, with relatively high resolution both in the lower troposphere and near the tropopause. The model physics include an E «turbulence closure scheme for subgrid-scale vertical turbulent mixing (Langland and Liou 1996), a modified Monin Obukhov scheme for the surface flux calculations (Fairall et al. 2003), an explicit treatment of mixed-phase cloud microphysics (Wang 2001), a nonlinear fourth-order horizontal diffusion for all prognostic variables except for that related to mass conservation equation, a simple Newtonian cooling term that is added to the perturbation potential temperature equation to mimic the radiative cooling in the model (Rotunno and Emanuel 1987), and the dissipative heating due to molecular friction related to the turbulent kinetic energy dissipation rate «directly from the prognostic turbulent closure scheme. The same model physics are used in all meshes. The model domain is on an f plane of 188N over the ocean with a constant SST of 298N. The first experiment is conducted as the control experiment, referred to as the no-shear experiment (NOSH), in which the environment is quiescent with no vertical shear (Fig. 1). The initial thermodynamic structure of the unperturbed model atmosphere is defined as the western

4 3474 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 70 FIG. 2. Time series of minimum sea level pressure (hpa) in numerical experiments with (a) different vertical shear magnitudes and (b) different vertical profile of shear and different initial storm intensity when the shear was imposed; E100_W and E100_S denote the experiments with the same vertical shear as E100, but the shear is imposed when the storm is weaker (E100_W) or stronger (E100_S) than in E100. Pacific clear-sky environment given in Gray (1975). The initial cyclonic vortex has the maximum tangential wind speed of 20 m s 21 at a radius of 80 km near the surface and decreases sinusoidally with pressure to vanish at 100 hpa (Wang 2007). The mass and thermodynamic fields are obtained by solving the nonlinear balance equation as shown in Wang (2001). Figure 2 shows the intensity evolution of the simulated TC in experiment NOSH. Note that the first 72 h of model integration is considered as the spinup of a mature TC in the simulation without any vertical shear. As a result, we assigned the time as 0 h after the 72 h spinup (from 272 to 0 h in Fig. 2) before the vertical shear was introduced in all sensitivity experiments. We can see that after an initial 24 h adjustment, the model storm intensified steadily in the first 72 h of integration, which was followed by a slower deepening for another 48 h and reached a quasi-steady intensity with the central sea level pressure of 899 hpa and the maximum 10-m wind speed of 76 m s 21 after 96 h in the noshear experiment. Six sensitivity experiments were conducted with easterly vertical shear of magnitudes of 2.5, 5, 10, 15, 17.5, and 20 m s 21 imposed onto the spunup TC at 0 h. In these experiments, environmental easterly wind is a cosine function from about 1.5 to 11.5 km in height. These experiments are hereafter referred to as E025, E050, E100, E150, E175, and E200 (Fig. 1a). To understand the influence of different vertical profiles of vertical shear on the storm evolution, two other sensitivity experiments, referred to as E10L and E10U, are designed, in which the wind shears are of similar magnitude to that in E100 (10 m s 21 ), but the shears are imposed between 1.5 and 5.5 km (E10L, lower-level shear) and between 5.5 and 11.5 km (E10U, upper-level shear), instead of in a deep layer between 1.5 and 11.5 km in E100. Figure 1b shows the environmental wind profiles in NOSH, E100, E10L, and E10U. In all the above sensitivity experiments, the vertical shear was introduced to the spunup TC vortex and integrated from 0 for 96 h. In two other experiments, referred to as E100_W and E100_S, the vertical shear used in E100 was imposed onto the TC vortex at different intensities from the NOSH experiment namely, at 224 h in E100_W and at 24 h in E100_S as shown in Fig. 2b. The difference among experiments E100_W, E100, and E100_S is in that the initial intensity of the storm influenced by the vertical shear is different so that the dependence of the asymmetric vertical motion and relative flow on the storm intensity can be examined. The minimum sea level pressure of the storm is 974 hpa in E100_W, 940 hpa in E100, and 918 hpa in E100_S. Note that we have examined the shear in the coarser domains and found that the vertical shear has been maintained throughout the model simulations. As we can see from Fig. 2, the influence of weak shear (no more than 5 m s 21, as in E025 and E050) on the storm intensity is relatively small. The storm weakened in the first 6 24 h in the medium (about 10 m s 21, such as in E100, E10L E10U, E100_S, and E100_W) to strong (more than 15 m s 21, such as in E150, E175, and E200) shears. The duration of the weakening depends on both the magnitude and vertical profile of the shear. After the initial weakening, the storm turns to reintensify in almost all the sensitivity experiments except for that in the strongest shear experiment E200, in which the storm was totally destroyed by the shear and could not be tracked after 48 h of integration.

5 NOVEMBER 2013 X U A N D W A N G Development of asymmetric vertical motion In this section, we focus on the initial development of asymmetric vertical motion, which is defined as the difference between the total vertical motion and its axisymmetric component, in the simulated storms. For this purpose, we examine the asymmetric vertical motion averaged in the first 30 min after the shear was imposed based on every 6-min model outputs. To roughly show the location of the storm eyewall, the axisymmetric equivalent potential temperature in NOSH averaged in the first 30 min is shown in relevant figures as the proxy of the axisymmetric storm eyewall. As we can see from Fig. 3a, the asymmetric vertical motion for the storm in the quiescent environment is relatively weak and is mainly associated with the activity of vortex Rossby waves that propagates both radially and azimuthally (Montgomery and Kallenbach 1997; Wang 2001, 2002). The asymmetric vertical motion in the storm embedded in the environmental shear is much larger and is primarily confined in the inner-core region with upward (downward) motion downshear (upshear) (Figs. 3b f). The maximum downward motion occurs near the outer edge of the high equivalent potential temperature (354 K), almost collocated with the maximum eyewall updrafts in the NOSH experiment (Fig. 4a). Since the asymmetries in vertical motion are quite weak in the NOSH experiment, an alternative way to examine the asymmetries in vertical motion for storms embedded in vertical shear is to look at the differences between the vertical motion for the storms in vertical shear and that for the storm in the NOSH experiment as shown at 8.6-km height in Figs. 4c f and in the vertical cross sections along shear (east west) through the storm center in Fig. 5. As we can see from Figs. 4a and 5a, the eyewall updrafts in the NOSH experiment occur around 348- and 354-K surfaces of the equivalent potential temperature. This pattern changes after a vertical shear is imposed. The shear produces downdraft (updraft) upshear (downshear) near the eyewall no matter whether the magnitude of the shear is high or low, and whether the shear is imposed in the lower layer, upper layer, or deep layer (Figs. 4b f and 5b f). Current understanding of the initial development of asymmetric vertical motion for a TC embedded in vertical shear is mainly based on two mechanisms: one is the dynamical (thermal wind balance) adjustment to the vertical tilt of the cyclonic circulation induced by the vertical shear as proposed by Jones (1995) and the other is the balanced response to the differential horizontal advection of the high relative vorticity in the storm core by the sheared environmental flow as proposed by Wang and Holland (1996), Bender (1997), and Braun et al. (2006). In their numerical study for Hurricane Bonnie (1998), Braun et al. (2006) found that the vertical motion asymmetry was qualitatively consistent with an assumed balance between horizontal advection of relative vorticity by the relative flow and stretching of vorticity, with relative asymmetric inflow (convergence) at low levels and outflow (divergence) at upper levels on the downshear side of the eyewall. To examine contributions by diabatic and adiabatic processes to the initial development of the asymmetric vertical motion in our simulated storm embedded in vertical shear, we applied the quasi-balanced v equation and potential vorticity inversion developed by Zhang and Kieu (2005) to calculate the vertical motion forced by diabatic and adiabatic processes. The quasi-balanced v equation is written as z 2 v = 2 2 f 2 1 f h (z z a 2 z) 2m f h m z z a 2 z 1 f 2 h z 2 1 g u 0 = 2 _q 2 f z f y x 2 f x y z [(z a 2 z)2m v] v 5 f z (V h $h) 2 =2! 2 2 t z 2 f v 2 c z x x z 1 v 2 c 2 f v 2 x y y z z x y z 2 v 2 x y x z V h $ f c z x, c y 2 b 3 c t y z t z J f x x 1 f! y, (1) y where $ is a horizontal gradient operator, m 5 c y /R d, z a 5 C p u 0 /g, h is the absolute vertical vorticity, x is the velocity potential, c is the streamfunction, f is geopotential height, v is the vertical p velocity, _q is the latent heating rate, f x and f y are the frictional forcing in x and y directions, z is height, f is the Coriolis parameter, b is the meridional gradient of the Coriolis parameter, C y is the specific heat of constant volume, R d is the gas constant for dry air, g is the gravity, and u 0 is the basicstate potential temperature. The vertical motion can be inversed from Eq. (1), given the right-hand side (RHS) forcing terms that from left to right are the differential absolute vorticity advection (DAVA) and the Laplacian of thermal advection

6 3476 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 70 FIG. 3. Asymmetric vertical velocity (contour interval 1 m s 21 ) at 8.6 km averaged in the first 30 min after the shear was imposed based on every-6-min model outputs in (a) NOSH (with no shear), (b) E050 (with easterly shear of 5ms 21 ), (c) E100 (with easterly shear of 10 m s 21 ), (d) E150 (with easterly shear of 15 m s 21 ), (e) E10L (with easterly shear of 10 m s 21 in the lower level), and (f) E10U (with easterly shear of 10 m s 21 in the upper level). Symmetric equivalent potential temperature (.348 K) in NOSH is shown in shading to roughly mark the location of the storm eyewall.

7 NOVEMBER 2013 X U A N D W A N G 3477 FIG. 4. As in Fig. 3, but for (a) total vertical velocity in NOSH and vertical velocity difference between (b) E050, (c) E100, (d) E150, (e) E10L, (f) E10U, and the control experiment NOSH.

8 3478 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 70 FIG. 5. As in Fig. 4, but for the vertical cross section through the storm center along the shear (thick line shown in Fig. 4a).

9 NOVEMBER 2013 X U A N D W A N G 3479 FIG. 6. Vertical cross section through the storm center along the shear (thick line shown in Fig. 4a) for vertical velocity (interval: positive 2ms 21, negative 0.5 m s 21 ) directly from (a) E100, (b) E10L, (c) E10U, and (d) E150; vertical velocity forced by total RHS in (e) E100, (f) E10L, (g) E10U, and (h) E150; and vertical velocity forced by LHR in (i) E100, ( j) E10L, (k) E10U, and (l) E150 at 24 min after the shear was imposed. (LTA), the b effect, the Jacobian term, the Laplacian of the latent heating rate (LHR), and the surface fictional and boundary layer vertical mixing effects, respectively. The first four terms on the right-hand side in Eq. (1) are considered as the dry dynamical processes (DDP). The calculation method is the same as that used in Zhang and Kieu (2005). Compared with the vertical motion directly from the model output at 24 min after the vertical shear was imposed (Figs. 6a d), the quasi-balanced vertical motion forced by all terms on the RHS in Eq. (1) (Figs. 6e h) is small similar to the results of Zhang and Kieu (2005). The quasi-balanced downward motion on the upshear side in the eyewall is less than 30% of that directly from the model output (Figs. 6a h). The results also indicate that LHR (Figs. 6i l) is predominantly responsible for the balanced upward motion downshear, but the DDP contributes more to the typical wavenumber-1 asymmetry with downdraft upshear and updraft downshear (Figs. 7a d). DAVA and LTA are the main terms in DDP. The results suggest that the DAVA in the balanced response is not the major process in forcing the asymmetric downdraft (updraft) upshear (downshear) in the eyewall, while the thermal advection is dominant, which produces wavenumber-1 vertical motion with downdraft (updraft) upshear (downshear) (Figs. 7e l). Note that in agreement with Zhang and Kieu (2005), the vertical transverse circulation formed in the inner core acts to reduce the influence of the external vertical shear. Considering the fact that the inversion method of Zhang and Kieu (2005) is accurate enough in reproducing the balanced flow, the above results demonstrate that the

10 3480 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 70 FIG. 7. As in Fig. 6, but for vertical velocity (interval: 0.25 m s 21 ) and vertical circulation forced by DDP in (a) E100, (b) E10L, (c) E10U, and (d) E150; DAVA in (e) E100, (f) E10L, (g) E10U, and (h) E150; and LTA in (i) E100, (j) E10L, (k) E10U, and (l) E150. The vertical velocity is amplified by a factor of 5 in the vectors. balance dynamics only explain a small portion of the initially forced asymmetries in vertical motion for a TC embedded in the environmental vertical shear. This suggests that unbalanced processes should play important roles in the initial development of the asymmetric vertical motion in the simulations. Figure 8 shows the relationships among vertical motion, environmental vertical shear, and divergence. The vectors in Fig. 8 consist of environmental shear wind and vertical motion. The shear wind is calculated by averaging the horizontal winds in a radius of 120 km from the storm center. The shear winds shown in Fig. 8 are very close to their counterparts shown in Fig. 1b, indicating that the vertical wind shear is well retained in the early stage of simulations. In the quiescent experiment, quasiaxisymmetric vertical motion in the eyewall is accompanied by quasi-axisymmetric low-level convergence and upper-level divergence (Fig. 8a). Shortly after the vertical shear is imposed, significant convergence replaces the divergence upshear and the divergence increases downshear in the mid-upper troposphere (Figs. 8b d). Note that the convergence/divergence is confined in the narrow area in the eyewall in all shear experiments, while their vertical distribution is related not only to the

11 NOVEMBER 2013 X U A N D W A N G 3481 FIG. 8. As in Fig. 5, but for divergence (interval s 21 ) and the vectors composed of vertical velocity (amplified by a factor of 5) and environmental shear flow in (a) NOSH, (b) E100, (c) E10L, and (d) E10U. magnitude of the shear but also the vertical shear profiles (Fig. 8). Comparing results of E100, E10L, and E100U can further help explain the development of asymmetric vertical motion in the storm inner core. In E100 with the shear in a deep layer, the convergence in the eyewall upshear increases with height and reaches its maximum near the top of the shear (about 11 km in Fig. 8b). In E10L with the shear concentrated in the lower levels, the convergence in the eyewall upshear increases with height primarily in the lower levels where the wind shear is located. The increase in upshear convergence stops near the top of the shear (about 5 km in Fig. 8c) where the convergence has values similar to those in E100 at about 11 km in Fig. 8b. In E10U (Fig. 8d) with the shear in the upper levels, the convergence in the eyewall upshear and its increase with height just occur in the upper levels with little convergence in the lower levels. The relationship between convergence and wind shear profile suggests that the environmental wind directly contributes to convergence in the upshear eyewall. The descending motion is strongest in the upshear eyewall near the height where the convergence increases with height and appears at different heights among E10L, E10U, and E100, consistent with shear profiles (Figs. 6a d and 8). Figure 9 shows the results from E100_W and E100_S, in which the environmental wind shear is as in E100, but the storm has different intensities as the shear is imposed (Fig. 2b). The convergence (divergence) in the stronger storm in the upshear (downshear) and their vertical gradients are larger and lead to stronger asymmetric vertical motion than in E100. In E100_W, the downdraft (updraft) in the upshear (downshear) eyewall induced

12 3482 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 70 FIG. 9. (a),(b) As in Fig. 5, but in E100_W and E100_S, respectively, and (c),(d) as in Fig. 8, but in E100_W and E100_S, respectively. by the vertical shear is weaker than those in E100 and E100_S. As a result, the net vertical motion in the upshear eyewall remains upward in E100_W (Fig. 9b). The results from E100_S, E100_W, and E100 in Fig. 9 suggest that the asymmetric vertical motion forced by the vertical shear is not only determined by the shear magnitude and vertical shear profile but also the storm intensity. The above results support the idea that the eyewall of a mature TC acts as a vessel or obstacle (McWilliams 1984; Willoughby 1998; Braun et al. 2006). Based on this idea and the above results, a conceptual model of the initial development of the asymmetric vertical motion in a TC forced by the vertical wind shear can be drawn in Fig. 10. When a mature TC confronts environmental flow (large open arrows), the eyewall of the storm plays a role like a vessel or a material wall and the environmental flow induces horizontal convergence in the eyewall upshear and horizontal divergence in the eyewall downshear. The horizontal convergence/ divergence drives asymmetric vertical motion along the eyewall (thin solid arrows) following mass conservation. The stronger the storm is and the more intense the horizontal wind (of the shear flow) is (longer open arrows), the stronger the asymmetric vertical motion (longer thin solid arrows) will be forced. The magnitude of the convergence/divergence changes with height (Fig. 8), leading to downdraft and updraft (thin arrows in Fig. 10) along the eyewall. As a result, the sum of the nearby thin solid arrows causes the net vertical motion (thick solid arrow in Fig. 10). If there is no vertical shear in the environment, the storm would move with the environmental flow and thus no significant asymmetric divergence/convergence and thus no asymmetric vertical motion will be forced by the mechanism shown in Fig. 10.

13 NOVEMBER 2013 X U A N D W A N G 3483 FIG. 10. Schematic model for the development of downdraft (updraft) in upshear (downshear) eyewall for a mature tropical cyclone embedded in environmental vertical wind shear. Large black open arrows: environmental shear wind; thin black or blue solid arrows: vertical motion driven by horizontal convergence/ divergence; thick red solid arrows denote the net vertical motion; the sum of the thin black and blue solid arrows nearby as enclosed by the orange polygon. 4. Development of the horizontal relative flow Figures 11 and 12 show the first 30-min mean horizontal relative flows at upper level (8.6 km) and lower level (0.96 km), respectively, in E100, which is representative for all vertical shear experiments. Here, the relative flow is defined as the difference of the total horizontal wind between the shear experiment E100 and NOSH. Note that the sheared environmental flow initially imposed in E100 has been subtracted from the total wind before obtaining the differences shown in Figs. 11 and 12. Therefore, the relative flow defined above shows solely the horizontal flow induced by the interaction between the TC and the environmental shear. Figures 11b and 12b present the asymmetric winds obtained by subtracting both the axisymmetric wind and the initially imposed environmental shear flow from the total winds. The axisymmetric winds at different heights are calculated with the storm center at the surface. The asymmetric flow (Figs. 11b and 12b) is dominated by the wavenumber-1 structure (Figs. 11c and 12c). In the easterly shear environment, easterly winds appear inside the eyewall in the lower levels and westerly winds appear in the upper levels, which results in a vertical westerly shear of about 10 m s 21, similar to the strength of the imposed environmental shear. This opposing shear of the relative flow inside the eyewall has been suggested to reduce the vertical tilt of the storm in the inner-core region (Jones 1995; Zhang and Kieu 2005). The relative flows outside the eyewall show clear wavenumber-1 circulations in the upper level with cyclonic gyre downshear and anticyclonic gyre upshear. The gyres in the lower levels are not as clear as those in the upper levels. We further decomposed the horizontal asymmetric wind V h into the asymmetric divergent wind V x and asymmetric rotational wind V c, V h 5 V x 1 V c. Instead of obtaining the balanced horizontal relative flow using quasi-balanced equations as in Zhang and Kieu (2005), we obtain V x and V c by calculating x and c inversed directly from the asymmetric horizontal divergence D and the asymmetric vertical relative vorticity z using formulas: D 5 = 2 x and z 5 = 2 c. In this way, the asymmetric divergent and rotational winds are calculated quite accurately. The inversed asymmetric horizontal winds are similar to those directly from the model output (Figs. 11c f and 12c f), including their wavenumber- 1 components (Figs. 11e h and 12e h). The asymmetric divergent wind in the quiescent environment is transient and quite weak (Figs. 13a and 13b). Quasi-steady asymmetric divergent wind develops in the shear environment. In the environmental easterly shear, the asymmetric divergent wind is westerly at the upper levels and easterly at the lower levels inside the eyewall (Figs. 11g, 12g, and 13c f), forming a westerly vertical shear opposing the imposed environmental easterly shear, thus reducing the vertical tilt of the storm axis. The asymmetric divergent wind shown in Figs. 11g and 12g is 3 4 times larger than that obtained by the quasi-balanced equation (Fig. 7). This indicates that the unbalanced process is dominant in the early development of asymmetric divergent flow after the shear is imposed. The asymmetric divergent wind develops not only inside the eyewall but also outside the eyewall where the asymmetric divergent wind is almost in opposite direction to that inside the eyewall, consistent with the results of Braun and Wu (2007). The asymmetric divergent wind and the asymmetric vertical motion are closely related to each other. Similar to the asymmetric vertical motion, the asymmetric divergent wind is sensitive to the magnitude of the shear, the intensity of the storm, and the vertical shear profile. The interaction between stronger shear and the eyewall of a more intense storm induces stronger asymmetric downdraft (updraft) in the upshear (downshear) eyewall. To satisfy mass conservation, larger asymmetric divergence/convergence along the eyewall results in

14 3484 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 70 FIG. 11. (a) Horizontal relative flow difference between E100 and NOSH; (b) as in (a), but for the asymmetric flow; (c) as in (b), but for wavenumber 1; (d) difference between (b) and (c); (e) as in (c), but obtained from inverting divergence and vorticity; (f) difference between (c) and (e); (g) as in (e), but for divergence wind; and (f) as in (e), but for rotational wind at 8.6 km averaged at the first 30 min after the shear was imposed. Shading denotes the location of the storm eyewall as in Fig. 3.

15 NOVEMBER 2013 X U A N D W A N G 3485 FIG. 12. As in Fig. 11, but at 0.96 km.

16 3486 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 70 FIG. 13. As in Fig. 11, but for the calculated divergent wind in (a) NOSH at 8.6 km, (b) NOSH at 0.96 km, (c) E10L at 11.5 km, (d) E10U at 11.5 km, (e) E10L at 5.0 km, (f) E10U at 5.0 km, (g) E10L at 0.96 km, and (h) E10U at 0.96 km.

17 NOVEMBER 2013 X U A N D W A N G 3487 FIG. 14. As in Fig. 11, but for the calculated rotational wind at 8.6 km in (a) NOSH, (b) E10L, (c) E10U, and (d) E100_W. stronger asymmetric divergent winds of the opposite directions inside and outside of the eyewall (Fig. 12g). As a result, stronger asymmetric vertical shear within the eyewall associated with the relative flow would offset the imposed stronger environmental shear, reducing the vertical tilt of the storm. A more intense storm may develop stronger asymmetric divergent flow, which can help the storm to resist a stronger environmental shear, and thus supposedly to experience less vertical tilt. Figures 13c h show the asymmetric divergent winds in E10L and E10U two experiments with the same easterly shear of 10 m s 21 but different vertical profiles. The shear-induced downdraft/updraft and thus the asymmetric divergent winds along the eyewall are strongest at the lower levels in E10L and at higher levels in E10U (Figs. 6b and 6c). As a result, stronger asymmetric divergent wind occurs at the lower levels in E10L (Fig. 13f) while it occurs at higher levels in E10U (Fig. 13h). Such vertical distribution of the asymmetric divergent wind and the associated shear of the asymmetric relative flow inside the eyewall would again oppose the imposed environmental shear in the corresponding layer, as discussed earlier (Figs. 11g, 12g, and 13c h). The asymmetric rotational wind shows the development of a wavenumber-1 gyre structure across the eyewall in the sheared environment, with cyclonic (anticyclonic) gyre downshear (upshear) at the upper levels (Figs. 11h, 12h, and 14). The asymmetric rotational wind developed in the vertical shear is much stronger than that developed in a quiescent environment (Fig. 14a). The asymmetric rotational wind in the shear environment is generally stronger at the upper levels than at the lower levels (Figs. 11h and 12h). The development of the asymmetric rotational wind in vertical shear can be explained by vorticity advection or the vertical tilt of the vortex by the environmental shear flow (Jones 1995; Reasor et al. 2004; Braun et al. 2006). In an easterly shear such as in E100, the vorticity advection of the TC vortex by the shear flow is negative (positive) in the eastern (western) [upshear (downshear)] eyewall, resulting in the cyclonic gyre downshear and anticyclonic gyre upshear, as we can see from Figs. 11h and 14e. The asymmetric rotational wind in the core region developed in the vertical shear environment seems not sensitive to the vertical shear profile and the storm intensity, as we can see from Figs. 11h and 14. The asymmetric

18 3488 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 70 FIG. 15. As in Fig. 11, but for the wavenumber-1 (a) divergent wind at 8.6 km, (b) rotation wind at 8.6 km, (c) divergent wind at 0.96 km, and (d) rotational wind at 0.96 km averaged from 4- to 4.5-h integration after the shear was imposed. rotational wind developed in the shear experiments is very similar to the asymmetric flow in vertical shear in dry, adiabatic simulations of Jones (1995) and Reasor et al. (2004). This is in sharp contrast to the asymmetric divergent wind, which is shown to be closely related to the diabatic processes and is sensitive to the shear profile and storm intensity. This suggests that the initial development of the wavenumber-1 asymmetric rotational wind is mainly associated with dry dynamics namely, the vorticity advection by the vertically sheared environmental flow, and the moist diabatic processes are important for maintaining the vessel-like eyewall, which is responsible for strong asymmetric vertical motion and asymmetric divergent flow by interacting with the vertically sheared environmental flow. Both the asymmetric divergent and rotational flows develop immediately after the vertical shear is imposed and then rotate cyclonically around the eyewall slowly (Fig. 15). The influence of the asymmetric flows on the storm intensity has been investigated in previous studies based on both idealized simulations and real case analyses (Montgomery and Kallenbach 1997; Davis and Bosart 2001; Wu and Braun 2004; Yang et al. 2007). The asymmetric flows might increase (reduce) the storm intensity by strengthening (weakening) the axisymmetric flow. In their study on hurricane Diana (1984), Davis and Bosart (2001) calculated term 2u 0 h 0 in the axisymmetric tangential wind tendency equation (where the overbar denotes the azimuthal mean, u 0 is the asymmetric radial wind, and h 0 is the asymmetric vertical vorticity), which represents the primary role of the asymmetric eddy angular momentum transport. It was shown that the asymmetric flow contributed to the development of Hurricane Diana (1984) as the calculated 2u 0 h 0 was positive during the storm-deepening stage. Figure 16 shows the calculated results for NOSH and E100 the latter representing the general features of all shear experiments. The environmental shear induced asymmetric eddy angular momentum transport significantly reduces the axisymmetric vortex circulation and thus is responsible for the weakening of the storm in vertical shear, which is in agreement with the results of Wu and Braun (2004). Furthermore, the asymmetric eddy caused axisymmetric tangential wind decrease that

19 NOVEMBER 2013 X U A N D W A N G 3489 FIG. 16. Rate of change in the axisymmetric tangential wind due to asymmetric horizontal flow averaged in the first 30 min after the shear was imposed in (a) NOSH and (b) E100 (10 23 ms 22 ). Gray dashed lines roughly denote radius of maximum wind (RMW). is larger at the upper levels than at the lower levels. Frank and Ritchie (2001) noted that the storm in vertical shear weakened from top down owing to the asymmetric eddy flux of high equivalent potential temperature of the warm core. Here, we further show that in addition to the eddy radial heat flux (eddy ventilation effect), eddy angular momentum transport also weakens the storm in vertical shear from top down. 5. Conclusions A fully compressible, nonhydrostatic TC model has been used to conduct numerical experiments to understand the initial development of asymmetries of vertical motion and horizontal relative flow in a tropical cyclone embedded in environmental shear. These include a control experiment for a TC in a quiescent environment and sensitivity experiments for the same TC embedded in environments with different shear magnitudes, different vertical shear profiles, and different intensity storms. The results show that the asymmetric flows develop along the eyewall depending on not only the magnitude and vertical profile of the vertical shear imposed, but also the intensity of the storm itself. Strong asymmetric vertical motion with downdraft (updraft) develops in the upshear (downshear) eyewall of the storm in medium to strong vertical shear. We show that the balanced dry dynamics appears not to work properly in our simulations because not only the tilt is small, but also the phase relationship between the asymmetric vertical motion and the temperature anomaly is different from the pattern resulted from the dry dynamics described by Jones (1995). The quasi-balanced v equation and PV inversion algorithm of Zhang and Kieu (2005) was used to quantify the contributions of various forcing terms to the initial development of the asymmetric vertical motion in the eyewall of a storm embedded in vertical shear. The results show that the quasi-balanced vertical motion can only explain a small portion of the simulated asymmetric vertical motion, suggesting that the unbalanced processes must play important roles in the initial development of asymmetric vertical motion and horizontal relative flow for a TC in vertical shear. We show that the strong asymmetric vertical motion forced by vertical shear is confined in the eyewall. As the vertically sheared environmental wind is imposed onto a mature TC, the storm eyewall acts like a material wall or the outside of a vessel (Willoughby 1998), leading to the development of convergence (divergence) and downdraft (updraft) along the outer edge of the eyewall upshear (downshear). Results from the directly inversed asymmetric divergent and rotational winds from the model divergence and relative vorticity show that the asymmetric divergent winds developed in the storms embedded in vertical shear are much stronger than those obtained from the quasi-balanced dynamics, further demonstrating that the unbalanced dynamics are dominant in the development of the asymmetric flow in the storm influenced by vertical shear. The divergent wind produces a vertical shear in the inner-core region in the opposite direction, but of similar magnitude, to the imposed environmental vertical shear. This relative vertical shear thus plays an important role in reducing the vertical tilt of the storm axis. The divergent wind outside the eyewall, however, generally increases the environmental vertical shear. In addition, we also show that the asymmetric eddy angular momentum transport is responsible for the top-down weakening of the simulated storm in vertical shear.

20 3490 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 70 Our primary purpose is to examine the initial development of asymmetric vertical motion and horizontal relative flow in a mature tropical cyclone embedded in environmental vertical shear. It is worthwhile to briefly describe the vortex resilience (Reasor et al. 2004) another issue of tropical cyclone in environmental shear. Except for the one with the strongest vertical shear (20 m s 21 ) (E200 as shown in Figs. 1a and 2a), the results of all the sensitivity experiments show the tilt and the vortex resilience. After the imposition of the vertical shear, the tilt, though small, increases and rotates cyclonically owing to the development asymmetric vertical motion [downdraft (updraft) in upshear (downshear) eyewall], which gradually decreases (increases) vorticity in upshear (downshear) in the upper levels. After reaching its maximum in a few hours (e.g., about 6 h in the experiment with the shear of 10 m s 21 ), the tilt decreases and continuously rotates cyclonically accompanied by weakening of asymmetric vertical motion and horizontal flow. Wavenumber-1 asymmetric rotation flows show similar features as presented by Reasor et al. (2004). Acknowledgments. The authors thank Prof. Da-Lin Zhang for providing us the PV inversion program and the two anonymous reviewers for their helpful comments. This study has been partly supported by NSF Grant ATM to the University of Hawai i at Manoa and partly by the National Natural Science Foundation of China under Grants and , the National Basic Research Program of China (2009CB421504). Additional support has been provided by the JAMSTEC, NASA, and NOAA through their sponsorships of the International Pacific Research Center (IPRC) in the School of Ocean and Earth Science and Technology (SOEST) at the University of Hawai i at Manoa. 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