1. Introduction
While the dynamical mechanism for intensification of tropical cyclones (TCs) is relatively well understood (e.g., Charney and Eliassen 1964; Ooyama 1969; Emanuel 1986), that for the tropical cyclogenesis is much less understood. In order for the intensification to operate, a low-level cyclonic vortex of certain strength is required. Such a low-level cyclonic vortex may originate from external disturbances, such as disturbances associated with a monsoon in the northwestern Pacific (e.g., Ritchie and Holland 1999), African easterly waves in the Atlantic and the northeastern Pacific (e.g., Avila and Clark 1989), and the Madden–Julian oscillation (MJO; Madden and Julian 1994) in the Indian and the western Pacific Oceans (e.g., Frank and Roundy 2006; Camargo et al. 2009). However, the generation process of the initial low-level vortex and its route to the genesis of the TC is in general fairly complex.
Multiple mechanisms for the genesis of the initial low-level cyclonic vortex have been suggested and are categorized into “top down” and “bottom up.” In the top-down mechanism, some mesoscale convective vortices (MCVs) are initially present in the middle troposphere and they extend downward through mergers of several MCVs (Ritchie and Holland 1997; Simpson et al. 1997) or intensify sea surface flux due to boundary layer cooling caused by stratiform precipitation (Bister and Emanuel 1997), resulting in deep convection and associated low-level cyclonic vortex. On the other hand, in the bottom-up mechanism (Zhang and Bao 1996a,b; Hendricks et al. 2004; Montgomery et al. 2006; Houze et al. 2009), cumulus-scale vortices associated with strong convection, which are called vortical hot towers (VHTs), play an important role. VHTs are considered building blocks of mesoscale convective systems (e.g., Zhang et al. 2009). They are generated as the low-level horizontal vorticity associated with vertical wind shear below a midlevel MCV is tilted by convection, and cyclonic VHTs are selectively intensified through stretching of vertical vorticity since background vorticity in the MCV is cyclonic. The VHTs repeat mergers, resulting in upward cascade of the kinetic energy, and end up with a mesoscale cyclonic vortex. Recent studies tend to confirm the bottom-up mechanism (Zhang and Zhu 2012). However, it has not been clarified yet whether these mechanisms completely explain the genesis of the low-level cyclonic vortex. To understand the mechanism of the genesis of the initial low-level cyclonic vortex clearly, it is desirable to study a tropical cyclogenesis in a relatively simple configuration.
A breakdown of the intertropical convergence zone (ITCZ) seems to be the relatively simple mechanism to generate TCs in the absence of notable initial external disturbances. The ITCZ is a zonal band of convection in the tropics, which constitutes an upward branch of the Hadley circulation [e.g., Fig. 1 of Ferreira and Schubert (1997)]. This band sometimes undulates and breaks down into multiple tropical disturbances (e.g., Agee 1972; Thompson and Miller 1976; Hack et al. 1989). This process is referred to as “ITCZ breakdown” (Hack et al. 1989; Schubert et al. 1991; Guinn and Schubert 1993; Ferreira and Schubert 1997). After these tropical disturbances move northward, the ITCZ is regenerated.
ITCZ breakdown is an efficient mechanism to generate TCs especially in the central and eastern Pacific. Wang and Magnusdottir (2006) showed that 49 of 91 tropical cyclones generated during 1999–2003 (Unisys Weather 2015) were related to ITCZ breakdown and classified ITCZ breakdown into two categories: One is associated with westward-propagating disturbances (WPDs) such as easterly waves that interact with the ITCZ to generate initial vortices. The other is a vortex rollup (VR) mechanism in which low-level wind of the ITCZ becomes barotropically unstable and several vortices are generated spontaneously. Wang and Magnusdottir (2006) showed that the WPD mechanism occurs more frequently in the eastern Pacific where the easterly waves propagate, while VR mechanism occurs more frequently in the central Pacific where external disturbances scarcely propagate. In the WPD mechanism, vortices are formed from east to west while, in the VR mechanism, several vortices are formed almost simultaneously along a zonal line.
In the present study, we will focus on the VR mechanism, which operates in the following way: The ITCZ in the Pacific is characterized by a meridionally convergent flow at the low level. Since the ITCZ in the summer of the Northern Hemisphere is located to the north of the equator, southerly (northerly) wind in the southern (northern) part of the ITCZ is deflected to the east (west) by Coriolis force, resulting in a zonal cyclonic shear zone in the low level. This shear zone is subject to barotropic instability, and several vortices are formed. As these vortices are strengthened, the development through cooperation among the primary and secondary circulations of the vortex, latent heating due to cumulus convection and surface fluxes (herein referred to as “cooperative development”), such as conditional instability of the second kind (CISK; Charney and Eliassen 1964), cooperative intensification (Ooyama 1969), or wind-induced surface heat exchange (WISHE; Emanuel 1986), starts working. Hence, they eventually develop into TCs.
Using the Weather Research and Forecast (WRF) Model, which is a nonhydrostatic mesoscale model, Kieu and Zhang (2008, 2009, 2010) reproduced TC Eugene, which was generated as a result of ITCZ breakdown in the eastern Pacific in 2005, and showed that a merger of two MCVs resulted in the genesis and the development of Eugene. In such a realistic simulation, however, the environment is so complex that it is not easy to clarify detailed mechanisms of the tropical cyclogenesis.
To understand detailed processes of the tropical cyclogenesis due to VR, an idealized numerical experiment without significant initial disturbances may be useful. Using a five-layer hydrostatic model with cumulus parameterization, Yamasaki (1989) demonstrated that weak TCs can be generated from a meridionally sheared zonal flow that mimicked the ITCZ. Ferreira and Schubert (1997) used a shallow-water model with a zonal mass sink to demonstrate that several vortices are generated by barotropic instability. Wang and Magnusdottir (2005) made a similar study but by putting a zonal heat source in a primitive model and showed that ITCZ breakdown is promoted (suppressed) if the background meridional shear of the zonal flow is cyclonic (anticyclonic). Wang et al. (2010) performed a similar experiment to Wang and Magnusdottir (2005) but they used a model with cumulus parameterization. They showed that a “tail,” which is a precipitation area with large vorticity, is formed in the southwestern area of the major vortex and the vortex itself is strengthened as a result of condensational heat of water vapor. Nolan et al. (2010) used the WRF Model to study ITCZ breakdown by forcing the atmosphere by a zonal band of warm sea surface temperature (SST) and examined the effects of vortices on the structure of the meridional circulation of the ITCZ. Although these previous idealized numerical experiments illustrate a qualitative behavior of ITCZ breakdown due to the VR mechanism, there have been few quantitative studies on energy budget during the genesis stage of initial weak low-level cyclonic vortices and the transition stage from weak vortices to TCs.
Yokota et al. (2012, hereafter Y12) recently made an idealized numerical experiment on ITCZ breakdown with a nonhydrostatic mesoscale model and studied the change of the energy budget during a transition from weak vortices to TCs. In their model, however, the horizontal grid size was 20 km and cumulus convection was parameterized, so that dynamical interaction between cumulus-scale and TC-scale phenomena during the tropical cyclogenesis has not been studied. The purpose of the present study is to extend the numerical experiments by Y12 and to clarify the dynamics, the structure, and the developing mechanism of vortices generated as a result of ITCZ breakdown in more detail by use of a higher-resolution model without cumulus parameterization.
The structure of this paper is as follows. Section 2 describes our experimental design, and section 3 presents results of the experiment and discusses the influences of difference in the horizontal grid interval. The effects of the presence of the warm SST belt and the β effect on the occurrence of ITCZ breakdown are also discussed. Section 4 discusses tropical cyclogenesis from the viewpoint of horizontal shear stability. Section 5 examines the detailed dynamical processes of the tropical cyclogenesis including the impacts of the cumulus-scale dynamics through an energy budget analysis. Section 6 presents the results of a numerical simulation of ITCZ breakdown that occurred over the equatorial Pacific in July 1988 [cf. Fig. 1 of Ferreira and Schubert (1997)] and compares the energy budget for simulated vortices with that for the idealized numerical experiments. Section 7 presents the summary and discussion.
2. Model and experimental design
a. High-resolution experiment
The numerical model used in the present study is the Japan Meteorological Agency nonhydrostatic model (JMANHM; Saito et al. 2006), which is based on a fully compressible, nonhydrostatic equation system. The horizontal computational domain size is 3000 km × 3000 km. The horizontal grid size is 5 km and the vertical resolution ranges from 40 m at the surface to 1330 m at the top. The time step is 12 s. The calculations are made on an f plane at 10°N. Cumulus parameterization is not used.
The initial conditions for potential temperature and relative humidity are horizontally uniform. Potential temperature linearly increases from 300 K at the surface to 350 K at 15-km height and then at a rate of 20 K km−1 above. On the other hand, relative humidity linearly decreases from 90% at the surface to 0% at 15-km height and remains 0% above. The calculation was started by adding tiny white-noise perturbations of the potential temperature below 15-km height, where the perturbations have the random phase and a uniform amplitude of 
The horizontal boundary conditions are zonally cyclic and meridionally free slip and adiabatic. The lower boundary is the sea surface, and SST is fixed to 300 K everywhere except in a high-SST belt along the meridional center. The meridional width of this belt is 500 km. In this belt, the meridional distribution of SST is given by a sinusoidal function with a peak value of 305 K. Although this SST anomaly is unrealistically high, it is one of our purposes to compare results of the present experiment with those in Y12. Thus, the experimental design described above is the same as Y12 except the horizontal resolution, the time step, and cumulus parameterization. Hereafter, this experiment will be called “HRES” and the experiment of Y12 “CTL.” The detailed experimental design of HRES is outlined in Table 1.
The experimental design of HRES.
b. Additional experiments
In CTL and HRES, the artificial high-SST belt is imposed throughout the experiment. Moreover, the latitudinal variation of the Coriolis parameter, which may influence the horizontal shear stability and the movement of the vortices, is not considered. Hence, two additional experiments in which horizontal grid size is taken to be 20 km and cumulus parameterization (Kain and Fritsch 1990; Kain 2004) is used are performed to clarify the effects of the warm SST belt and the latitudinal variation of the Coriolis parameter on ITCZ breakdown. Because of the resolution and the experimental design, these two experiments cannot be used to discuss cumulus-scale dynamics.
In the first experiment, the high-SST belt is maintained for the first 24 h but is gradually diminished during the next 24 h. The rest of the experimental design is the same as those in CTL except that the integration time is 1200 h. Hereafter, this experiment will be called “NSST.”
Note that the larger meridional domain than CTL is used in BETA. This is because a preliminary calculation shows that, if the same meridional size of the domain as CTL is used, unrealistically strong vertical shear of the zonal flow is produced in association with the meridional circulation. Furthermore, vortices generated as a result of barotropic instability migrates northward to approach the northern boundary.
3. Overview of experimental results
Time series of maximum horizontal wind velocity at 20-m height 
Time series of (a) maximum wind velocity at 20-m height and (b) minimum sea level pressure, where 12-h moving averages are made. Red, green, blue, and black lines denote HRES, NSST, BETA, and CTL, respectively.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0328.1
For HRES, 
The horizontal distributions of relative vorticity and horizontal wind vectors at 10-m height in HRES are shown in Fig. 2. When the experiment is started, an updraft associated with low-level convergent and upper-level divergent flows is generated above the high-SST belt. Coriolis force acting on the convergent (divergent) flow causes cyclonic (anticyclonic) shear in the lower (upper) troposphere by 120 h. Figure 3 shows the meridional-height cross section of zonally averaged wind and mixing ratio of cloud water and ice at 120 h. The profile of cloud water and cloud ice and a cyclonic shear layer formed below 7-km height are similar to those of the “ITCZ” in CTL (Fig. 1 of Y12).1 This ITCZ gradually undulates and finally breaks down to generate three vortices simultaneously (Figs. 2a–d). After breakdown of the ITCZ, two of the three vortices merge while rotating counterclockwise (Figs. 2d and 2e) (cf. Fujiwhara 1921, 1923). The resulting two vortices then merge again to form a single TC above the high-SST belt (Figs. 2e and 2f). The TC is associated with a cloud-free eye and warm core near its center (not shown) and stronger than that in CTL (Figs. 1a and 1b). The difference of strength of the TC is consistent with the radius of maximum tangential wind (RMW): it is 40 km at 600 h in HRES and 120 km in CTL.
Relative vorticity (color shading; 
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0328.1
Meridional–height cross section of the zonally averaged quantities: mixing ratio of cloud water plus cloud ice (color shading; 
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0328.1
Both in NSST and BETA, multiple vortices are also simultaneously generated (Figs. 4a–c and Figs. 5a and 5b, respectively) and grow with time, although the development is slower than in CTL. At about 1032 h, 
As in Fig. 2, but for NSST.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0328.1
As in Fig. 2, but for BETA.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0328.1
Although vortices in NSST take much longer time to develop than those in CTL (see Figs. 1a and 1b), a single TC is eventually formed (Fig. 4d). The present results show that even though the SST forcing is stopped after the first 48 h, TCs develop from vortices that are presumably triggered by barotropic instability of the shear layer resulting from the meridionally converging flow at the “ITCZ.” In fact, the distribution of the zonally averaged cloud water and ice and the distribution of the zonally averaged wind at 120 h for NSST are similar to those in Fig. 3 (not shown), indicating that meridional circulation and horizontal shear associated with the ITCZ are maintained as a result of latent heating and resulting updraft even after the SST forcing is removed.
Initial vortices in BETA are advected northeastward because northeastward low-level flows on the southern side of vortices are stronger than southwestward flows on the northern side (Figs. 5b–f). Such an asymmetry of flows is also seen in idealized numerical experiments using a simpler model in which vortices are formed because of breakdown of the ITCZ-like structure (Yamasaki 1989; Ferreira and Schubert 1997). This is because the geostrophic wind in the south becomes stronger than that in the north owing to the asymmetry of Coriolis parameter f (see appendix A). Two vortices merge to eventually form a single TC (Figs. 5f and 5g). It is weaker than that in CTL (Figs. 1a and 1b) because it is not located above the high-SST belt. After the merger, the single TC moves to the west because of the β effect (Figs. 5g and 5h). The moving speed of the TC (about 3 m s−1) is consistent with the previous studies (e.g., DeMaria 1985).
4. Horizontal shear stability
Although general behavior of vortices in HRES is similar to that in CTL, the number of initial vortices formed presumably by barotropic instability is different: there are three in HRES (Figs. 2a–d) and two in CTL (Fig. 2 of Y12). Therefore, the period between the genesis of TCs and the formation of the single TC in HRES is longer.
The number of cyclonic vortices formed by barotropic instability is related to the width of the horizontal shear layer. Figures 6a and 6b show meridional distributions of the zonally averaged absolute vorticity and that of the zonally averaged zonal velocity, respectively, at 20-m height at 120 h. Since the absolute vorticity has a maximum near the meridional center, the necessary condition for barotropic instability (Kuo 1949) is satisfied in each experiment of HRES, NSST, BETA, and CTL.
Meridional distributions of (a) the zonally averaged absolute vorticity and (b) the zonally averaged zonal wind at 20-m height at 120 h. Red, green, blue, and black lines denote HRES, NSST, BETA, and CTL, respectively.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0328.1
Time series of the kinetic energy for zonal wavenumbers 1 (black), 2 (red), 3 (thick green), and 4 (blue) (
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0328.1
These results demonstrate that initial vortices are generated mainly as a result of barotropic instability of the zonal flow in the lower troposphere, and difference in the width of the horizontal shear layer 
In NSST, the cyclonic shear is also formed in the lower troposphere, and the zonally averaged absolute vorticity in the lower troposphere has a maximum at the meridional center (the green line in Fig. 6a). This feature is similar to CTL and HRES, and barotropic instability is important also for the genesis of vortices in NSST. However, more time is required for vortices to develop since the horizontal shear is weaker than that in CTL and HRES. If the zonally averaged zonal velocity at 20-m height in NSST (the green line in Fig. 6b) is fitted by Eq. (2), 
In BETA, the process of geneses of initial vortices (Figs. 5a–c) and time series of 
5. Energy budget analysis
In this section, the kinetic energy budget in HRES is analyzed in order to clarify how initial vortices are generated and intensified and especially to clarify the role of the cumulus-scale dynamics.
a. Energy production during tropical cyclogenesis
Figure 8 shows time series of CONV3, SPC3, and BP3 until 240 h when three TCs are present. SPUZ3, SPVZ3, SPWY3, and CWZ3 are not shown because they are much smaller than the other terms. Note that AD3, TT3, and PT3 become zero after integration over the whole area. The largest energy production term between 132 and 162 h is SPUY3, which is related to barotropic instability due to meridional shear of zonal wind. SPUY3 starts to decrease after 156 h, and BP3 rapidly increases after 156 h and become the dominant term after 162 h. Since BP3 is related to the cooperative development, a zonal wavenumber-3 component of vertically integrated water contents also increases while BP3 increases (dotted line in Fig. 8). CVY3 always remains smaller than SPUY3 or BP3. This shows that barotropic instability is responsible for the genesis of vortices between 132 and 162 h, but the cooperative development takes over to contribute to their intensification after 162 h. The energy conversion term from 
Time series of meridionally and vertically averaged energy production terms (
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0328.1
To clarify the cause of the regime shift from barotropic instability to the cooperative development at about 162 h, meridional-height distributions of SPUY3 and BP3 at 156 and 168 h are shown in Fig. 9. At 156 h, SPUY3 is positive in the lower and middle troposphere (Fig. 9a). By 168 h, however, it becomes negative in the lower troposphere (Fig. 9b), while BP3 rapidly increases in the middle and upper troposphere (Figs. 9c and 9d).
Meridional–height distributions of 
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0328.1
The decrease in SPUY3 during the 12 h may be consistent with axisymmetrization in the lower troposphere. Before 156 h, vortices are not axisymmetric and have a long axis in the northeast–southwest direction, resulting in 
Time series of the degree of axisymmetricity (red line with scale on left axis) and strength of the warm core (blue line with scale on right axis), where 12-h moving averages are made. The former is the horizontal and vertical average within a 100-km radius from the vortex center as defined by the minimum sea level pressure between 0- and 4-km heights. The latter is the vertical average between 6- and 10-km heights of the maximum potential temperature deviation (K) from the area-mean potential temperature over a 1000-km radius from the vortex center.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0328.1
On the other hand, BP3 (
These features of SPUY3 and BP3 are quite similar to CTL (Figs. 5–7 of Y12). This demonstrates that the qualitative features of the genesis and the intensification of TCs depend little on the horizontal resolution and cumulus parameterization of the model.
b. Energy conversion from the cumulus-scale kinetic energy
Figures 11 and 12 show SPCk,l, BPk,l, and CONVk,l on the zonal-meridional wavenumber space (
Vertically averaged (a) 
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0328.1
As in Fig. 11, but at 168 h.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0328.1
CONVk,l from 
The zonal computational domain of HRES (3000 km) is shorter than the length of the typical ITCZ and the horizontal grid size of HRES (5 km) is generally too coarse to resolve cumulus convection. However, additional experiments in which the zonal domain is 6000 km and the horizontal grid interval is 2.5 km (see appendix B) show that very similar results to those described above can be obtained. It seems that the zonal domain size of HRES is enough to study ITCZ breakdown and that important group of cumulus convection for the tropical cyclogenesis is resolved also in HRES.
c. Energy budget during mergers of vortices
The value of 
Figure 13a shows time series of the vertically averaged 
(a) Time series of the vertically averaged kinetic energy 
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0328.1
Figure 13b shows time series of the vertically averaged production terms for 
When 
If TCs would have become stronger mainly as a result of addition of the kinetic energy of multiple vortices, 
6. Case study of ITCZ breakdown in July 1988
In this section, the energy budget for ITCZ breakdown in the real atmosphere is compared with that in the idealized numerical experiments.
a. Overview of the case
In the summer of 1988, a representative ITCZ breakdown occurred in the central and eastern Pacific (Hack et al. 1989; Guinn and Schubert 1993; Ferreira and Schubert 1997). According to the best-track data of the U.S. National Hurricane Center, 15 TCs were generated in the northeastern Pacific in 1988. Among these TCs, Emilia, Fabio, Gilma, and Hector were generated as tropical depressions (TDs) between 27 and 30 July (for details, see Table 2). These four TCs are considered to be caused by ITCZ breakdown and properly expressed in the Japanese 25-year Reanalysis Project data (JRA-25; Onogi et al. 2007). Genesis potential index (GPI; Emanuel and Nolan 2004) and convective available potential energy (CAPE), which are averaged horizontally over 10°–15°N and 100°–130°W at 0000 UTC 26 July 1988 in the JRA-25 data, are 2.2 and 
The data of four TCs generated in the central and eastern Pacific between 27 and 30 Jul 1988 (Unisys Weather 2015).
b. Experimental design
The numerical experiment in this section is also performed by the JMANHM. The initial and boundary condition are given by the JRA-25 data: the initial time is at 0000 UTC 26 July 1988, when none of the four TCs reaches strength of TDs and 6-hourly data are linearly interpolated to give the boundary conditions. Cumulus parameterization, cloud microphysics, and a boundary layer scheme are the same as those in CTL. The computational domain is 7000 km (zonal) × 3000 km (meridional), which is large enough to cover the region where four TCs were generated. The horizontal grid interval is 20 km, which is larger than that of HRES but it is possible to reproduce ITCZ breakdown as shown by previous sections, and the integration time is 240 h. The detailed experimental design is summarized in Table 3.
The experimental design of the case study.
c. Results
Figure 14 shows the horizontal distributions of relative vorticity and horizontal wind vectors at 10-m height. A strong shear layer was formed over 10°–15°N by 1200 UTC 27 July. It started to undulate and finally broke down into several vortices, three of which were especially strong. Although the number of TCs and their paths are somewhat different from observed TCs [Fig. 1 of Ferreira and Schubert (1997)], simultaneous formation of several vortices between 27 and 30 July are qualitatively well reproduced.
As in Fig. 2, but for the case study in section 6.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0328.1
Figure 15 shows the zonally averaged mixing ratios of cloud water and ice and the zonally averaged wind over the computational domain at 1200 UTC 27 July before any tropical cyclones were generated. In this meridional–height cross section, the meridional flow converged in the lower troposphere, turned into an upward flow, and diverged in the upper troposphere at about 11.5°N. Coriolis force acting on the lower convergent and upper divergent flows produced cyclonic and anticyclonic horizontal shear, respectively. Absolute vorticity at 10-m height had a meridional maximum at about 11.5°N, and the necessary condition for barotropic instability (Kuo 1949) was satisfied (not shown). These features are qualitatively similar to those in HRES (Fig. 3). However, the low-level meridional convergence is stronger, the mixing ratio of cloud water and cloud ice is larger and the cloud base level is higher in this case study than in HRES. Since these differences from HRES are similar to those in CTL (Fig. 1 of Y12), they seem to be related to a coarse horizontal resolution and cumulus parameterization (Kain and Fritsch 1990; Kain 2004).
As in Fig. 3, but for the case study in section 6 at 1200 UTC 27 Jul.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0328.1
d. Energy budget analysis
In this subsection, an energy budget analysis is made to study the genesis mechanism of several vortices in Fig. 14d. An anelastic equation system [(3)–(6)] is also used in the present analysis. In what follows, the deviation of A from the zonal mean in the computational domain is written as 
Figure 16 shows the meridional-height distributions of SPUY and BP. Among vertically averaged production terms, SPUY was the largest at about 11.5°N at 1200 UTC 27 July (Figs. 16a and 16c). This shows that the shear production associated with meridional shear of the zonal wind mainly contributed to generate vortices at this time. By 0000 UTC 28 July, however, cumulus convection became active at about 11.5°N and vertically averaged BP became the largest term there (Figs. 16b and 16d). Although the region of large SPUY was located only below 2-km height and the region of large BP in the upper troposphere was wider than that in the idealized numerical experiments, the shift of the production terms from SPUY to BP is consistent with the results of the idealized numerical experiments. Therefore, initial vortices were generated as a result of barotropic instability of the zonal flow in the lower troposphere and then the cooperative development started to operate, which is similar to the findings in the idealized numerical experiments.
Meridional–height distributions of SPUY at (a) 1200 UTC 27 Jul and (b) 0000 UTC 28 Jul and of BP at (c) 1200 UTC 27 Jul and (d) 0000 UTC 28 Jul (
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0328.1
7. Summary and discussion
a. Summary
In the present study, the dynamics of the genesis and the intensification of TCs due to ITCZ breakdown is clarified by an idealized numerical experiment without cumulus parameterization on an f plane. An ITCZ-like structure is formed by placing a zonal belt of high SST in the region, which induces a zonally uniform cyclonic shear in the lower troposphere. This “ITCZ” starts to undulate gradually and finally breaks down into several vortices.
The number of vortices and the growth rate in this experiment are close to the theoretical prediction of barotropic instability. In fact, the eddy kinetic energy is initially increased mainly as a result of the shear production term associated with the meridional shear of the zonal flow. After vortices grow to a certain amplitude, however, the buoyancy production term increases rapidly. In other words, the cooperative development soon takes over to contribute to the intensification of TCs. On the other hand, the shear production decreases because of the axisymmetrization. These processes do not depend on cumulus-scale vortices but they do on the TC-scale shear and buoyancy productions. In addition, the energy budget among the kinetic energy in the wavenumber space suggests that the kinetic energy of the TC is not mainly supplied from the kinetic energy of larger wavenumbers. Hence, mergers of cumulus-scale vortices are not essential for the tropical cyclogenesis in this experiment, and the essential features of ITCZ breakdown can be reproduced even if the cumulus-scale dynamics is not simulated explicitly (e.g., Y12).
Several TCs resulting from barotropic instability repeat mergers. The intensification of each TC stops during a merger, and the rapid intensification starts again after the merger. During the merger, the conversion from the kinetic energy of other wavenumbers is larger than the buoyancy production, but the upward cascade of the kinetic energy does not contribute to the intensification of TCs. After the mergers end, the buoyancy production becomes larger, indicating that the cooperative development operates more effectively.
In the additional experiment in which SST forcing is switched off after 24 h, the ITCZ-like structure is also maintained because of latent heat release associated with cumulus convection, and vortices are generated as a result of barotropic instability. A single TC is finally formed from vortices, although more time is required than in the experiment in which SST forcing is maintained.
In the additional experiment with the β effect, TCs are also generated as a result of barotropic instability and are intensified by latent heating. TCs are advected northeastward because of meridional asymmetry of flows. After TCs merge, a single TC is formed and moves westward owing to the β effect.
Also performed is a numerical experiment on TCs generated as a result of ITCZ breakdown in the summer of 1988, where JRA-25 is used as the initial and boundary conditions. The simulated ITCZ was associated with a near-zonal cyclonic shear zone in the lower troposphere. It started to undulate and eventually broke down into several vortices. These characteristics are similar to those in the idealized numerical experiments. An energy budget analysis shows that vortices during their genesis stage develop through barotropic instability of the zonal flow in the lower troposphere and later through latent heating.
b. Discussion
ITCZ breakdown is one of the typical mechanisms to generate TCs in the absence of notable initial external disturbances. Several previous studies examined the dynamics of ITCZ breakdown using simple models (e.g., Ferreira and Schubert 1997) or models with cumulus parameterization (e.g., Y12). In the present study, however, the dynamics of ITCZ breakdown was clarified using the model without cumulus parameterization.
The process of the tropical cyclogenesis shown in the present study is not “top down” in the sense that the origin of these TCs is instability of the low-level horizontal shear. However, it is not like the “bottom up” hypothesis because mergers of cumulus-scale vortices (e.g., Hendricks et al. 2004; Montgomery et al. 2006; Houze et al. 2009) do not seem to play an essential role in the tropical cyclogenesis.
In the present paper, we have studied only one case of ITCZ breakdown in the central and eastern Pacific in the summer of 1988 besides the idealized experiments and have discussed a relative importance of low-level barotropic energy conversion and conversion from the cumulus-scale kinetic energy. Krishnamurti et al. (1981) and Cao et al. (2012) studied the geneses of initial vortices in the Arabian Sea and in the northwestern Pacific, respectively, and suggested that TC-scale low-level barotropic energy conversion played major roles in their geneses. To clarify what fraction of tropical cyclogeneses is due to TC-scale low-level barotropic energy conversion and what fraction is due to conversion from the cumulus-scale kinetic energy, it is necessary to make similar energy budget studies on more cases in the real atmosphere.
HRES in the present study utilized a horizontal resolution of 5 km. It may be argued that a horizontal resolution of 5 km is generally not sufficient for representing cumulus convection. An additional experiment with a horizontal resolution of 2.5 km shows, however, that the time evolution of the vortices and the energy conversion among wavenumbers are similar to those in HRES (appendix B and Figs. 17 and 18). This confirms that the results of HRES are reliable and that mergers of cumulus-scale vortices do not play an essential role in the tropical cyclogenesis due to ITCZ breakdown.
Relative vorticity (color shading; 
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0328.1
As in Fig. 11, but for HRES2.5.
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0328.1
Acknowledgments
We thank Prof. Keita Iga for many useful suggestions on fluid-mechanical aspects of the problem, Dr. Wataru Mashiko for instructions for the use of the JMANHM, and anonymous reviewers for thoughtful comments, which contributed to improve the manuscript significantly. This work was supported in part by a Grant-in-Aid for Scientific Research (A) 24244074 from the Japan Society for the Promotion of Science, the Cooperative Program (131, 2014) of Atmosphere and Ocean Research Institute, the University of Tokyo, and by High Performance Computing Infrastructure Strategic Program for Innovation Research Field 3 (ID: hp120282, hp130012, and hp140220). The computation was mainly carried out using the computer facilities at Atmosphere and Ocean Research Institute at the University of Tokyo. Supplemental idealized numerical experiments were carried out using K computer provided by the RIKEN Advanced Institute for Computational Science.
APPENDIX A
Meridional Asymmetry of the ITCZ Caused by the β Effect
At 120 h in BETA, the meridional circulation with the zonal-mean flow at the southern half of the calculation domain where the Coriolis parameter is smaller is stronger than that at the northern half. This is because geostrophic wind at lower latitude has to be stronger for a given pressure gradient.
APPENDIX B
Effects of the Horizontal Sizes of the Grid and Domain and of Cumulus Parameterization
To examine effects of the horizontal sizes of the grid and domain and of cumulus parameterization on the results, three additional idealized experiments in which the setting of HRES is slightly modified are performed: In the first experiment, “HRES2.5,” the horizontal grid size is reduced to 2.5 km. In the second one, “HRESW,” the zonal domain size is made twice as large (6000 km). In the third one, “HRESKF,” the same cumulus parameterization as CTL (Kain and Fritsch 1990; Kain 2004) is used. The number of low-level vortices at 168 h is three in HRES2.5 and in HRESKF and seven in HRESW (Figs. 17b,d,f). The number of those vortices and the RMW of the finally-formed TC (not shown) in each experiment are consistent with that in HRES.
Figure 18a–d shows the energy budget similar to the one in section 5 for HRES2.5. 
These show that results for HRES do not change largely when the horizontal grid size is decreased, the zonal size of the calculation domain is increased, or cumulus parameterization is used.
APPENDIX C
Shear Production Term Associated with an Axisymmetric Vortex
In HRES, the sign of 
Distributions of horizontal velocity vectors (arrows) and 
Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0328.1
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The cloud base level in HRES is lower than that in CTL because saturated grids in the lower level are more likely to appear in experiments with higher resolution. Although the precipitation from subgrid-scale clouds in the lower level is also treated by cumulus parameterization (Kain and Fritsch 1990; Kain 2004) in CTL, it is not reflected in Fig. 1 of Y12.
This calculation was made to examine the influence solely due to a difference in the horizontal resolution, so that cumulus parameterization (Kain and Fritsch 1990; Kain 2004) is as in CTL and is not tuned for 5-km horizontal resolution.
