1. Introduction
The development of an incipient tropical cyclone into a mature hurricane has been studied extensively for decades. The basic objective is to understand how the spinup mechanism and intensification rate depend on environmental conditions and vortex structure. Theoretical and observational studies suggest that a positive correlation exists between the maximum possible intensification rate and the environmentally determined potential intensity of a tropical cyclone (e.g., Xu et al. 2016; Emanuel 2012). The potential intensity parameter depends on several factors, but generally increases over warmer oceans (e.g., Xu et al. 2019). There is also evidence that the time scales of genesis and postgenesis intensification of a tropical cyclone tend to grow with the magnitude of a theoretically based ventilation index that increases with the ambient vertical wind shear and midlevel moisture deficit (Rappin et al. 2010, hereafter RNE10; Tang and Emanuel 2012).
On the other hand, sizable spreads of intensification rates may be found among tropical cyclones in similar environments (e.g., Hendricks et al. 2010). One might reasonably ask how well the variability can be predicted by differences in a limited number of basic vortex parameters. The highest intensification rates in a particular environment are often observed when the maximum wind speed of the tropical cyclone is a moderate fraction of its empirical or theoretical potential (Xu and Wang 2015; Tang and Emanuel 2012). Observationally based statistical studies have also suggested a negative correlation between the intensification rate and the radius of maximum wind speed (Xu and Wang 2015, 2018). On a related matter, observational and modeling studies suggest that the time scale required for an underdeveloped tropical cyclone to begin rapid intensification grows with the radius of maximum wind speed (Carrasco et al. 2014; Miyamoto and Takemi 2015).
Moreover, conventional wisdom maintains that a sufficiently large tilt of the tropical cyclone created by vertical wind shear or some other means will usually hinder the intensification process. The potential reasons are multifold. One proposed contributing factor is the attendant warming of the lower–middle troposphere above the inner core of the surface vortex, tied to maintenance of nonlinear balance (DeMaria 1996). Another proposed contributing factor is the enhancement of “downdraft ventilation,” whereby the tilt leads to an amplification of low-entropy downdrafts adulterating the boundary layer air that feeds inner-core convection (e.g., Riemer et al. 2010, 2013; Riemer and Laliberté 2015; Alland et al. 2021a, hereafter A21a). An appreciable tilt may also help reduce lower–middle-tropospheric relative humidity over a broad central-to-uptilt section of the inner core of the surface vortex by (i) facilitating the lateral advection of dry external air into the region or (ii) facilitating subsidence of the entering airstream (e.g., Zawislak et al. 2016, hereafter Z16; Alvey et al. 2020, hereafter AZZ20; Schecter and Menelaou 2020, hereafter SM20; Alland et al. 2021b). The potential effects of introducing tilt stated above could directly weaken the convective activity driving intensification, or keep convection far (downtilt) from the center of the surface circulation, where it is plausibly less efficient in accelerating the maximum cyclonic winds (e.g., Vigh and Schubert 2009; Pendergrass and Willoughby 2009; Schecter 2020, hereafter S20).
Of paramount importance is to understand the mechanism and time scale by which an incipient tropical cyclone might overcome the foregoing detrimental effects of tilt and strengthen into a hurricane. One strategy for addressing this issue has been through simplified modeling studies of weak tropical cyclones exposed to steady environmental vertical wind shear on the f-plane (e.g., Nolan and Rappin 2008; RNE10; Rappin and Nolan 2012, hereafter RN12; Tao and Zhang 2014, hereafter TZ14; Finocchio et al. 2016; Onderlinde and Nolan 2016; Rios-Berrios et al. 2018, hereafter RDT18; Gu et al. 2019). The aforementioned studies have underscored the potential importance of “precession” in regulating the time scale of hurricane formation.1 In the pertinent simulations, the tropical cyclone initially develops a downshear tilt in conjunction with downshear convection. The tilt vector (the vector difference between the midlevel and surface centers of rotation) then precesses in concert with the azimuthal propagation of convection toward the upshear semicircle. A transition to fast alignment and spinup tends to occur once the angle of the tilt vector measured cyclonically from the shear vector increases to or beyond the neighborhood of 90° (e.g., RN12; TZ14; RDT18). The relative importance of various kinematic and thermodynamic changes—coinciding with the reorientation of tilt—for the onset of fast alignment and spinup is a topic of ongoing research (ibid.; see also Chen and Gopalakrishnan 2015). One basic and seemingly important change is the nullification (or reversal) of the shear-induced misalignment forcing (e.g., Reasor et al. 2004).
Among the simplified modeling studies mentioned above, there have been a number of sensitivity tests involving variation of environmental parameters. TZ14 notably showed that raising the SST from 27° to 29°C without adjusting the initial environmental sounding toward one of radiative convective equilibrium (cf. Nolan and Rappin 2008; RNE10) expedites the transformation of a sheared (tilted) tropical cyclone into a hurricane. Such a result is intuitively reasonable based on the elevated level of moist entropy allowed near the surface, and the related expectation of enhanced diabatic forcing to support the lower-to-middle-tropospheric convergence of angular momentum that leads to intensification (further discussed by Črnivec et al. 2016). Adding to this, warming the ocean (in TZ14) appears to improve the efficiency of diabatic alignment processes in reducing tilt from an early stage of the tropical cyclone’s evolution. Such reduction of the tilt magnitude can limit the early detrimental impacts of misalignment, and accelerate the precession that brings forth a transition to fast spinup (TZ14; Schecter 2016; RDT18).
SM20 introduced a distinct line of idealized cloud-resolving modeling studies in which vertical wind shear is virtually eliminated from the environment of an initially tilted tropical cyclone. Such a setup was designed to address theoretical questions, but may have some direct relevance to situations in nature where tropical cyclones exposed to minimal shear have lingering tilts from prior forcing. SM20-type simulations are specifically intended to provide clear pictures of how tilt alone alters the organization of convection and the intensification rate. They are also intended to elucidate the efficiency of intrinsic alignment mechanisms in diminishing the detrimental impact of a tilt created in the past. The preceding issues are not adequately resolved by studies preceding SM20 in which tilt coexists with an everlasting environmental shear flow. The shear flow clouds the picture by potentially enhancing ventilation and altering surface fluxes. Moreover, a sufficiently strong dynamical coupling of tilt with the shear flow can fundamentally change the pathways of alignment and intensification. Whereas reorientation of the tilt vector through precession can be critical to enabling the onset of fast alignment and spinup when shear is present, reorientation of the tilt vector is irrelevant in a quiescent environment.
The numerical simulations of SM20 expectedly showed that initial tilt magnitudes exceeding the core radius of a tropical cyclone appreciably hinder its transformation into a hurricane. Of greater note, increasing the initial tilt magnitude to several times the core radius was found to extend the hurricane formation period (defined in section 3a) by an order of magnitude. A Sawyer–Eliassen-based analysis explicitly showed how the positive spinup tendency formally attributable to diabatic processes has trouble dominating the net negative tendency associated with other factors such as friction when a tropical cyclone is strongly misaligned. This condition of frustrated spinup generally ends upon sufficient decay of the tilt magnitude. SM20 analyzed various mechanisms working to reduce tilt, but did not thoroughly investigate the amount of alignment and other changes to the system required for a substantial boost of the intensification rate. Moreover, SM20 focused exclusively on systems with an SST of 28°C. A broader survey is necessary given the sensitivities of tilt dynamics and vortex intensification to variation of the SST that have been demonstrated by related studies incorporating vertical wind shear (e.g., TZ14).
The present study is essentially a continuation of SM20. Changes to the relationship between the initial tilt magnitude and the time scale of hurricane formation caused by warming or cooling the underlying ocean will be examined. The effects of changing the SST on the relationships between tilt, the core radius, and the spatial distribution of precipitation will also be investigated. Tilt-related thermodynamic impediments to intensification common among tropical cyclones over the full range of SSTs considered herein will be illustrated and explained; the main distinction from earlier illustrations will be in the removal of modulation by environmental vertical wind shear. Perhaps the most novel contribution of this paper will lie in an effort to quantify the reduction of tilt and attendant thermodynamic structural changes needed for an initially misaligned tropical cyclone to transition from a state of slow to fast spinup. This effort will notably reveal how changing the SST affects the requirements for such a transition to occur.
Before moving on, it is important to acknowledge the possibility of circumstances under which an initial misalignment could actually serve as a catalyst for spinup by stimulating strong downtilt convection (e.g., Jones 2000). Initially, convective activity far from the surface vortex center may not be optimal for spinup, but sufficiently strong convection concentrated downtilt could create a smaller vorticity core that quickly intensifies and soon dominates the parent cyclone. Analogous “core reformation” events involved in the rapid intensification of systems with moderate environmental vertical wind shear have been discussed at length in the literature (e.g., Nguyen and Molinari 2015; Chen et al. 2018). One might speculate that increasing the SST beyond some threshold in an SM20-type simulation could set the stage for downtilt convection that is sufficiently vigorous to reverse the otherwise negative influence of tilt on intensification. However, this fails to occur for the systems considered herein—which have SSTs ranging up to 30°C—and will therefore not be among the topics addressed below.
The remainder of this article is organized as follows. Section 2 explains the setup of the numerical simulations. Section 3 provides a basic overview of hurricane formation in the entire simulation set. Included in the overview is a discussion of how variation of the SST affects the growth of the time scale of hurricane formation with increasing values of the initial tilt magnitude. Section 4 takes a moment to show that the delay of hurricane formation caused by a large initial tilt far exceeds that which would be caused solely by the attendant early modification of the symmetric component of the tropical cyclone that is theoretically detrimental on its own. Section 5 examines details of the thermodynamic impediments to intensification that are common among the tilted tropical cyclones considered herein before the onset of fast spinup. Section 6 examines the structural changes that signal an imminent transition to fast spinup at various SSTs. Section 7 summarizes the findings of this study.
2. Methodology
a. Model configuration
The evolutions of weak tropical cyclones into hurricanes are simulated herein with release 19.5 of Cloud Model 1 (CM1; Bryan and Fritsch 2002). As in SM20, the model is configured with a variant of the two-moment Morrison microphysics parameterization (Morrison et al. 2005, 2009), having graupel as the large icy-hydrometeor category and a constant cloud-droplet concentration of 100 cm−3. The influence of subgrid turbulence above the surface is accounted for by an anisotropic Smagorinsky-type closure that is tailored for tropical cyclone simulations as explained in SM20. Surface fluxes are parameterized with bulk-aerodynamic formulas. The momentum exchange coefficient Cd increases with the surface wind speed from 10−3 to 0.0024 above 25 m s−1 [compare with Fairall et al. (2003) and Donelan et al. (2004)]. The enthalpy exchange coefficient is given by Ce = 0.0012 roughly based on the findings of Drennan et al. (2007). Heating associated with frictional dissipation is activated. Rayleigh damping is imposed above an altitude of z = 25 km. The model is computationally and physically simplified by eliminating radiative transfer. There is ample evidence in the literature that realistically distributed radiation tends to accelerate tropical cyclone development (e.g., Rios-Berrios 2020; Ruppert et al. 2020). Nevertheless, we provisionally assume that the simplified model captures the essential features of tilted tropical cyclone dynamics.
All simulations are conducted on a doubly periodic oceanic f-plane with a Coriolis parameter of 5 × 10−5 s−1. The SST is held constant in space and time. The simulations are separated into three groups distinguished by whether the SST is 26°, 28°, or 30°C. In the same order, these three groups will be called T26, T28, and T30. Ambient vertical wind shear is reduced to a negligible level after the tropical cyclones are misaligned (see section 2b).
The equations of motion are discretized on one of two stretched rectangular grids having relatively low resolution (LR) or high resolution (HR). All simulations from SM20 that are incorporated into the present study use the HR grid. The majority of new simulations use the LR grid for computational efficiency. Differences between LR and HR simulations seem limited to contextually unimportant details. In either case, the grid spans 2660 km in both horizontal dimensions, and extends upward to z = 29.2 km. The 800 × 800 km2 central region of the horizontal mesh has uniform increments of 2.5 (1.25) km in the LR (HR) simulations. At the four corners of the mesh, the LR (HR) increments are 27.5 (13.75) km. In the vertical, the LR (HR) grid has 40 (73) levels. For the LR (HR) grid, the spacing between levels increases from 0.1 to 0.7 to 1.4 (from 0.05 to 0.4 to 0.75) km as z increases from 0 to 8 to 29 km.
b. Initialization
Before describing the initialization and evolution of a tilted tropical cyclone, several notational conventions should be established. In this paper, r, φ, and z will always be used to represent (in order) the radius, azimuth, and height above sea level in a surface vortex centered cylindrical coordinate system. Time will be represented by t. The variables u, υ, and w will respectively represent the radial, azimuthal, and vertical velocity fields. Furthermore, an overline over an arbitrary fluid variable will denote an average of that variable over φ.
The tilted vortices in all simulations are derived from a vertically aligned incipient tropical cyclone that developed over a 99-h period from a weaker system in a shear-free environment with an SST of 28°C and an initial thermodynamic profile matching that of the Dunion (2011) moist tropical sounding in the far field. Interested readers may consult SM20 (Fig. 2 therein) for a detailed depiction of the kinematic and moist-thermodynamic structure of the basic state of this root vortex. Here we summarize only its most salient features. The basic state of the root vortex has an azimuthal velocity field
Before each simulation starts in earnest, the SST is adjusted (if necessary) to its group value without modifying any other aspect of the environment. Moreover, the root vortex is transformed into a tilted vortex using one of the three procedures that are thoroughly explained in SM20 (section 2a and appendix A therein). Implementation of several procedures over the simulation set is deemed beneficial in creating some variability of early convection and structural detail among systems with comparable initial misalignments, which may reduce potential bias in the presented results. The three tilting procedures are called the impulsive separation (IS), impulsive separation plus damping (ISPD), and dry separation plus damping (DSPD) methods. Each method creates a tilt by imposing a transient environmental shear flow that horizontally separates the upper and lower sections of the vortex that lie above and below a kilometer-scale transition layer centered at height zl, which is usually set to 5.25 km. The degree of horizontal separation (tilt) is determined by the strength and duration of the shear flow. For simulations that implement the IS or ISPD method, the forcing that turns the shear flow on and off is “impulsive” in lasting only 6 h. The ISPD method ends with a brief period of damping of the minimal domain-averaged winds that may unintentionally exist after the tilt is generated. Importantly, moist convection is allowed to stay active while the vortex is tilted when using either the IS or ISPD method. The DSPD method is similar to its ISPD counterpart in adding a brief period of corrective damping after the forcing ends, but the forcing can be longer and weaker. Moreover, moist convection is temporarily deactivated by removing hydrometeors and replacing water vapor with a passive tracer. When the procedure ends, moist convection is reactivated by changing the passive tracer back into water vapor, and t is reset to zero. Regardless of the method used, the initial tilting reduces relative humidity above the inner core of the surface vortex, and causes a convectively driven enlargement of rm during or shortly after implementation.2
c. Working definition of the tilt vector
The initial and subsequent misalignment of a tropical cyclone is quantified by the tilt vector. The tilt vector is defined by xcm − xcs, and its magnitude is denoted by tilt. As in SM20, xcs and xcm represent the centers of rotation of the cyclonic circulations in thin layers adjacent to the sea surface (subscript cs) and in the middle troposphere (subscript cm). The surface-adjacent layer extends up to z = 1.0 (1.2) km, and the middle-tropospheric layer spans the interval 7.3 ≤ z ≤ 8.1 (7.1 ≤ z ≤ 8.5) km for HR (LR) simulations. Each center of rotation precisely corresponds to the point at which one must place the origin of a polar coordinate system to maximize the peak value of
d. Tabulated synopsis of the constituent members of each SST group
For convenient reference, Table 1 summarizes the simulations considered for this study. As noted earlier, the simulations are separated into three groups according to their SST. Each SST group contains 9–11 LR simulations, but only T28 (which includes SM20 data) contains more than a few HR simulations. The initial tilt magnitude (tilt0) ranges from 0 to approximately 370 km in all SST groups.3 The rightmost columns of the table briefly describe and name the “featured” members of each SST group that will be selected for detailed analysis in various sections of the paper. The description contains the value of tilt0, and the time averages of tilt and rm (denoted by triangular brackets) over the hurricane formation period to be defined in section 3a. The suffix in the name of any particular group member indicates the resolution of the simulation (LR or HR), and is terminated by a letter (A or B) that differentiates one LR or HR simulation from another. While not of critical importance, all featured simulations are initialized using the DSPD tilting procedure with zl = 5.25 km. Time averages of tilt and rm are not given for T26-HRA, because in contrast to all other simulations, the tropical cyclone fails to complete hurricane formation within its 500-h duration. While T26-HRA will be incorporated into the discussions of section 5 and appendix C (Fig. C1a), it will be excluded from the analyses of all other sections.
(a) Length of the HFP (τhf) vs the initial tilt magnitude (tilt0). Filled (empty) symbols correspond to simulations having tilts initially generated by the DSPD (IS or ISPD) method. The color and shape of each symbol corresponds to the SST, and the relative size corresponds to model resolution as shown in the legend, which applies to all subfigures. The dashed lines are linear regressions for the color-matched data points (belonging to distinct SST groups) with tilt0 > 100 km. (b) Relationship between τhf and the HFP time-averaged radius of maximum surface wind speed 〈rm〉. Each dashed line is a linear regression as in (a), but covers all data points within the pertinent SST group. (c) Relationship between 〈rm〉 and tilt0 [the abscissas in (b) and (a)]. The linear regressions are as in (a), but are drawn only for groups T28 and T30.
Citation: Journal of the Atmospheric Sciences 79, 2; 10.1175/JAS-D-21-0051.1
Summary of the numerical simulations. NLR/HR denotes the number of low/high resolution simulations within a particular group. NIS/ISPD/DSPD denotes the number of simulations initialized with the IS/ISPD/DSPD tilting procedure. All other variables appearing in the table header are defined in the main text.
3. Overview of the simulations
a. Time scale of hurricane formation versus initial tilt, core size, and the SST
As in SM20, the hurricane formation period (HFP) is defined as the time interval during which the surface maximum of the φ-averaged tangential velocity (υm) intensifies from 12.5 to 32.5 m s−1. The length of the HFP will be denoted τhf, and the time average of an arbitrary variable h over the HFP will be represented by the expression 〈h〉. It is worth remarking that because υm differs from the conventionally defined maximum sustained surface wind speed of a tropical cyclone, the endpoint of the HFP does not precisely correspond to when an asymmetric hurricane would be officially declared.
Figure 1a demonstrates that τhf increases with tilt0, when the value of tilt0 exceeds the initial 100-km radial length scale of the core of the tropical cyclone. As noted in section 1, there is some theoretical basis for believing that the HFP should lengthen as the characteristic radius of convection increases. The positive correlation between τhf and tilt0 may therefore be a reflection of greater initial tilts leading to greater outward displacements of the dominant convective activity within a tropical cyclone. Because convection is statistically peaked near rm in the systems under consideration (SM20 and section 3b), moving convection outward generally coincides with creating a larger vortex core. Figure 1c verifies that the core size during hurricane formation tends to increase with the initial tilt magnitude when the latter exceeds roughly 100 km. Figure 1b shows how the growth of τhf with increasing tilt0 translates into the growth of τhf with increasing 〈rm〉 in each SST group.
Figure 1b further shows that τhf tends to grow with decreasing SST at a given value of 〈rm〉. Moreover, whereas (for moderate-to-high values of 〈rm〉) the length of the HFP increases on the order of 10 h from group T30 to T28, the length of the HFP increases on the order of 100 h from group T28 to T26.
(a) HFP time average of the precipitation rate integrated over a surface vortex centered disc of radius r for simulation groups T26 (blue), T28 (black), and T30 (red). Each thin dark line represents a group mean, and the thick light background curve extends vertically from one local standard deviation below the mean, to one above. (b) HFP time average of the precipitation rate integrated over a surface vortex centered disc of radius 1.2rm(t) vs the HFP time average of rm. The symbols are as in Fig. 1, and the dashed line is the linear regression for groups T28 and T30 combined.
Citation: Journal of the Atmospheric Sciences 79, 2; 10.1175/JAS-D-21-0051.1
Figure 2a shows the mean and spread of
Further analysis reveals that the highly nonlinear growth of τhf with decreasing SST for any sufficiently large value of 〈rm〉 (Fig. 1b) coincides with a highly nonlinear decay of the area-integrated precipitation rate in a disc bounded (approximately) by the maximum surface winds of the tropical cyclone. Figure 2b shows the 〈rm〉 dependence of
b. Basic structural similarities of tilted tropical cyclones at all SSTs
Despite differences in the precipitation rates found over relatively cool and warm oceans (Fig. 2), several basic structural features of the developing tropical cyclones do not vary much with the SST. Figure 3a shows a fairly insensitive positive linear relationship between the HFP time averages of the tilt magnitude and rm when both variables exceed 35 km. The minor displacement of all T30 tilt magnitudes above the plotted regression line in this parameter regime is notable, but of questionable importance given that two of the T26 data points have comparable upward shifts. Figure 3b shows that there is also an insensitive positive linear relationship between the HFP time averages of the precipitation radius rp and rm. As in SM20, rp is the radius from the surface vortex center at which the φ-averaged precipitation rate
(a) Relationship between the HFP time-averaged tilt magnitude 〈tilt〉 and 〈rm〉. The symbols are as in Fig. 1; the dashed line is a linear regression with a correlation coefficient of 0.87 for data with 〈rm〉 ≥ 35 km from all SST groups. (b) Relationship between the HFP time-averaged precipitation radius 〈rp〉 and 〈rm〉. The symbols are as in (a), but the dashed linear regression (with a correlation coefficient of 0.97) covers all values of 〈rm〉. The solid line corresponds to 〈rp〉 = 〈rm〉. (c) Radius–time Hovmöller plots of the logarithm of
Citation: Journal of the Atmospheric Sciences 79, 2; 10.1175/JAS-D-21-0051.1
Figure 3c shows a generic r–t Hovmöller plot of
Of additional note, changing the SST has no major consequence on the relationship between the tilt and the azimuthal distribution of P. For illustrative purposes, Fig. 4a shows a snapshot of the asymmetric precipitation rate existing within a moderately tilted tropical cyclone. Lower- and middle-tropospheric streamlines are superimposed on the plot to convey the horizontal separation of rotational centers defining the tilt vector. It is clear that P is mostly concentrated downtilt, similar to what is commonly seen in nature (e.g., Stevenson et al. 2014; Nguyen et al. 2017, hereafter NRR17).
(a) Snapshot of the logarithm of the precipitation rate P normalized to P0 = 0.5 cm h−1 within a typical tropical cyclone (from T28-HRA) during its HFP. Middle-tropospheric (z ≈ 7.7 km, white) and lower-tropospheric (z ≈ 1.2 km, black) streamlines are superimposed over the distribution. The long thick black arrow points in the direction of the tilt vector, which is parallel to the φ = 0 axis in the polar coordinate system used to construct the PPD. (b) The precipitation probability
Citation: Journal of the Atmospheric Sciences 79, 2; 10.1175/JAS-D-21-0051.1
In other words, the precipitation probability is the HFP time average of the integral of the precipitation rate over the area of quadrant-φ divided by the integral over the entire disc. The plotted probabilities are evaluated with a = 200 km to account for most of the precipitation within the relatively large cores of strongly tilted vortices. It is seen that there is minimal variation of the PPD with the SST for small and medium tilt magnitudes. In general, the downtilt (φ = 0) probability rapidly grows at the expense of its uptilt and lateral counterparts as the tilt magnitude increases from 20 to 60 km. Over this interval, the systems change from having statistically symmetric precipitation to having roughly 60% of the precipitation occurring downtilt. As the tilt magnitude increases beyond 60 km, the PPD for group T28 stays fairly constant. There is some hint that the T26 (T30) PPDs may become modestly more symmetric (asymmetric), but a definitive statement on the matter would require a greater number of large-tilt data points.6
4. Dynamical importance of the tilt-related structural asymmetry of a tropical cyclone
The preceding overview did not directly answer whether the structural asymmetry of the tropical cyclone associated with tilt is critical to impeding hurricane formation once the HFP officially begins. The answer is not entirely obvious, partly because systems with the largest tilt magnitudes tend to have the largest values of rm at the start of the HFP,7 and the developmental time scale tends to increase with the initial value of rm even in axisymmetric models (e.g., Rotunno and Emanuel 1987). The additional detriment of tilt to intensification can be verified for any particular case, if faster spinup can be shown to occur after restarting the simulation with only the symmetric component of the vortex. The following considers such restarts for simulations T26-LRA, T28-LRA, and T30-LRA at the beginning of the HFP (t = tb), when the tilt magnitudes are substantial and convective asymmetries are pronounced.8 The symmetric vortices in the restarts are obtained from the azimuthally averaged fields of the tilted tropical cyclones in a surface vortex centered coordinate system. Whereas the symmetric component of the water vapor mixing ratio is retained, hydrometeors are removed.
Figure 5 compares the evolutions of the surface azimuthal velocity fields in the tilted and symmetrized systems. The surface vortices of the tilted tropical cyclones retain their broad structures and slowly intensify. The intensification of outer winds actually outpaces that found in the symmetrized restarts. However, the inner core of each symmetrized tropical cyclone shortly enters a stage of faster spinup, coinciding with contraction of rm and rp. Faster spinup of the inner core obviously implies a shorter HFP.
(a) Evolution of
Citation: Journal of the Atmospheric Sciences 79, 2; 10.1175/JAS-D-21-0051.1
Figure 6a shows τhf plotted against 〈rm〉 for the tilted systems (filled symbols) and their symmetrized counterparts (empty symbols). The reductions of τhf resulting from symmetrization are seen to coincide with considerable reductions of 〈rm〉. Of note, the value of τhf for each symmetrized system falls roughly two root-mean-square deviations below the τhf versus 〈rm〉 regression line obtained for tilted vortices at the same SST. It stands to reason that the regressions are quantitatively unreliable when rm is not dynamically coupled to a misalignment. Note also that the data shown here (and in Figs. 6b–d) for the tilted systems do not appreciably change when hydrometeors are removed at t = tb, as in the symmetrized restarts, without modifying any other fields. Such insensitivity should allay concerns raised during peer review that removing hydrometeors at the restart time could be more important than symmetrization in altering the basic statistics of hurricane formation.
(a) Length of the HFP vs 〈rm〉 for the tilted tropical cyclones in simulations T26-LRA, T28-LRA, and T30-LRA (filled symbols), and for their counterparts in the initially symmetrized restarts (empty symbols). Each slanted dashed line is a linear regression obtained using data from all of the tilted tropical cyclone simulations in a particular SST group with 〈rm〉 ≥ 40 km; the thick color-matched background line extends vertically between plus and minus one root-mean-square deviation of these data from the regression line. The colors of all symbols and lines indicate the SST as shown in the legend. (b) Time averages of Pasym evaluated with a disc radius a equal to 1.2rm(t) (vertical axis) and 200 km (horizontal axis) for the tilted tropical cyclones and their initially symmetrized counterparts. Large (small) symbols correspond to HFP (shorter) time averages, as explained in the main text. The color scheme follows that in (a). The legend applies to (b)–(d). (c) As in (b), but for time averages of
Citation: Journal of the Atmospheric Sciences 79, 2; 10.1175/JAS-D-21-0051.1
Figure 6c is similar to Fig. 6b but for the area-integrated precipitation rate
In summary, without necessarily decreasing the average precipitation rate over the broader core of the surface vortex, or the inward mass flux in the 1-km-deep boundary layer, the existence of tilt at an early stage of development can effectively disable a relatively efficient intensification process that is found in our quasi-symmetric tropical cyclones.9 The tilt lingers as an integral part of an asymmetric tropical cyclone structure that evidently hinders the contraction of rm and rp. Hindering contraction of the inner core and inward migration of deep convection is believed to render the diabatic forcing less effective in supporting fast spinup of cyclonic winds in the lower troposphere during the HFP (see, for example, S20; Pendergrass and Willoughby 2009).
5. Detailed structure of a tilted tropical cyclone during slow intensification
A common feature of tilted tropical cyclone development in our simulations is a transition from slow to fast intensification prior to the emergence of a hurricane. As one might expect from the foregoing results, substantial reduction of the tilt magnitude is a common precursor of the transition (see section 6). To fully comprehend why a moderate-to-strong tilt tends to prevent fast spinup requires an understanding of the relationship between tilt and the internal moist-thermodynamic state of a tropical cyclone. This relationship is expounded below for simulations T30-HRA, T28-HRA, and T26-HRA. The tropical cyclone in T28-HRA is selected for detailed examination for continuity with a complementary analysis of the same system in SM20, where the simulation is named DSPD-X400Z5. The other systems are selected because of their similar resolutions and initial conditions, but distinct SSTs.
Figure 7 displays 6-h time averages of the velocity fields and moist-thermodynamic structures of the tilted tropical cyclones under present consideration when at moderate tropical storm intensity, before any potential transition to fast spinup. The start time of each averaging period will be denoted ts for future reference. In all cases, the misalignments of streamlines in the boundary layer and middle troposphere (left column of Fig. 7) are substantial, but appreciably reduced from their initial magnitudes. Consistent with the time-averaged precipitation statistics presented in section 3b, the strongest upper-tropospheric updrafts associated with deep convection (middle column) are concentrated downtilt near the radius of maximum surface wind speed. The moist-thermodynamic fields (middle and right columns) are not identical to each other, but have some common features that seem to resemble those found in earlier observational studies of tilted tropical cyclones (e.g., Dolling and Barnes 2012, hereafter DB12; Reasor et al. 2013; Z16; NRR17). The following examines the most notable features that are believed to help keep convection far downtilt from the surface vortex center, where it is theoretically inefficient in driving intensification.
(a)–(c) Depiction of the tilted tropical cyclone in T30-HRA, averaged over a 6-h interval starting in the midst of the HFP, well before fast spinup. (a) Horizontal streamlines in the middle troposphere (black lines) and boundary layer (gray lines), superimposed over the near-surface (z = 25 m) horizontal wind speed |us| in an Earth-stationary reference frame. (b) Vertical velocity (w) contours in the upper troposphere (z = 8.9 km) superimposed over the distribution of LCAPE [Eq. (5)]. (c) Lower–middle-tropospheric relative humidity
Citation: Journal of the Atmospheric Sciences 79, 2; 10.1175/JAS-D-21-0051.1
a. Lower–middle-tropospheric relative humidity
Compared to conditions downtilt, the values of lower–middle-tropospheric relative humidity uptilt and near the surface vortex center are fairly low (see Figs. 7c,f,i). There is longstanding evidence that low relative humidity above the boundary layer in combination with weak-to-moderate deep-layer CAPE (applicable to our systems) hinders deep convection by the dilution of updrafts if nothing else (e.g., Brown and Zhang 1997; James and Markowski 2010; Kilroy and Smith 2013; Tang et al. 2016). It stands to reason that the aforementioned relative humidity deficits help limit the invigoration of deep convection in the central and uptilt regions of the tropical cyclones under present consideration.
Figure 8 illustrates the moisture dynamics (in an Earth-stationary reference frame) maintaining the central and uptilt lower–middle-tropospheric relative humidity deficits for the representative case of simulation T28-HRA. All fields are averaged over the 6-h time period connected to Figs. 7d–f. Figures 8a and 8b are reference plots superimposing the lower–middle-tropospheric velocity field over (a) relative humidity and (b) the 2D hydrometeor mass density σc. The velocity and relative humidity fields are averaged between z = 2.3 and 7.7 km, and σc is obtained from an integral of the 3D hydrometeor mass density over the same interval. Figures 8c–h are various components of the z-averaged (between 2.3 and 7.7 km) relative humidity budget explained below.
Illustration of the lower–middle-tropospheric moisture dynamics occurring in the tropical cyclone of simulation T28-HRA while moderately tilted during a selected 6-h segment of the HFP (corresponding to that in Figs. 7d–f). All fields are time averaged over this segment and vertically averaged (except for σc, which is a vertical integral) as explained in the main text. The surface and middle-tropospheric vortex centers are respectively marked by + and × as in Fig. 7. (a) Reference plot of relative humidity
Citation: Journal of the Atmospheric Sciences 79, 2; 10.1175/JAS-D-21-0051.1
The
(a),(b) Contributions to the 3D advection term in Fig. 8g from (a) horizontal and (b) vertical advection. (c) Sum of contributions to the Dqυ/Dt and Dθ/Dt terms in Figs. 8d and 8e from evaporation (subscript e), sublimation (subscript s), and melting (subscript m).
Citation: Journal of the Atmospheric Sciences 79, 2; 10.1175/JAS-D-21-0051.1
The preceding analysis supports the notion that subsidence can be as effective as the direct intrusion of dry environmental air (which seems largely precluded by the streamlines in Fig. 8a) in maintaining the deficiency of lower–middle-tropospheric
Whereas the central and uptilt deficits of lower–middle-tropospheric relative humidity may be of primary interest, the maintenance of enhanced
b. LCAPE
The small values of inner-core LCAPE found away from downtilt convection are readily understood from the regional vertical profiles of the (pseudoadiabatic) entropy sp and saturation entropy
(a),(b) Vertical profiles of the entropy sp (dashed black) and saturation entropy
Citation: Journal of the Atmospheric Sciences 79, 2; 10.1175/JAS-D-21-0051.1
High saturation entropy in the lower–middle troposphere found away from downtilt convection in the inner core coincides with relatively warm air, or equivalently a regional lowering of θ surfaces (Fig. 11). By contrast, low saturation entropy in the vicinity of the downtilt convection zone coincides with cooler air and elevated θ surfaces. Such a configuration is at least qualitatively consistent with an atmosphere adjusted to nonlinear balance within a misaligned vortex (see DeMaria 1996). The deviations of the pressure and virtual potential temperature fields (from domain-averaged values) that are quantitatively consistent with nonlinear balance, given the vertical vorticity distribution (
(a) Height minus zm = 4.1 km (denoted δz) of the θ = 320.8-K isosurface of the tilted tropical cyclone in simulation T30-HRA, averaged over the 6-h time interval represented by Figs. 7a–c. (b) As in (a), but for the θ = 321.6-K isosurface of the tilted tropical cyclone in simulation T28-HRA over the 6-h interval in Figs. 7d–f. (c) As in (a), but for the θ = 321.6-K isosurface of the tilted tropical cyclone in simulation T26-HRA over the 6-h interval in Figs. 7g–i, and with zm = 4.4 km. The black w contours, diamonds, + and × are as in Figs. 7b, 7e, and 7h for (a), (b), and (c), respectively. Note the inversion of the usual blue-to-red colormap.
Citation: Journal of the Atmospheric Sciences 79, 2; 10.1175/JAS-D-21-0051.1
Near-surface moist-entropy deficits do not appear to have a role comparable to that of relatively warm air in the lower part of the troposphere above the boundary layer in causing relatively low values of LCAPE over much of the inner core. The right column of Fig. 7 shows the distributions of a conventional measure of the near-surface moist entropy—the boundary layer equivalent potential temperature θeb calculated as in Emanuel [1994, Eq. (4.5.11)]. The values of θeb in the T26 and T30 tropical cyclones are actually peaked near the centers of the surface vortices (Figs. 7c,i), where LCAPE is depressed. Such high entropy reservoirs, built up where deep convection is hindered by conditions aloft, are notably reminiscent of that described by DB12 in their study of Tropical Storm Humberto (2001). The T28 system differs in that much of its inner region has lower θeb than that which is found in the principal air mass entering the downtilt convection zone.12 However, the deficits of θeb are no more than 2 K below the core maximum, and do not seem to shape the distribution of LCAPE (compare Fig. 7e to Fig. 7f).
The swath of relatively low-entropy air in the boundary layer of the T28 tropical cyclone appears to result from the infusion of low-entropy downdrafts (not shown) in the vicinity of downtilt convection and the associated downwind stratiform precipitation. Though apparently not spreading as far toward the surface center of the tropical cyclone, similar swaths of relatively low-entropy air near and downwind of the convection zone exist in the T26 and T30 systems. While this low-entropy air may not have an obvious role in preventing deep convection at small radii, it could still infiltrate and weaken convective updrafts upon completing a recirculation cycle. The amount of low-entropy air that reaches the convective updrafts cannot be firmly ascertained without a trajectory analysis (cf. RDT18; A21a; Chen et al. 2021), but some insight on its potential impact is readily obtained by considering the time scale for its recovery under the action of the surface enthalpy fluxes13 depicted in the right column of Fig. 7. The time scale for surface enthalpy fluxes to raise θeb to the surface saturation level without impediments can be estimated by τs ∼ hb/Ceυ, in which hb is the characteristic depth (∼1 km) of the boundary layer. The velocity-independent ratio of τs to the circulation period τr ∼ 2πr/υ increases from 0.9 to 1.3 to 2.7 as r decreases from 150 to 100 to 50 km. Therefore, the negative impact of downdraft-adulterated air on the intensity of downtilt convection may not be too severe when recirculation occurs at a radius beyond approximately 100 km. Moreover, the streamlines suggest that much of the air mass entering the convection zone in the boundary layer derives not from regions of adulteration in the core, but from elsewhere in the outer vortex. Such would seem consistent with convection that is mechanically supported by the underlying frictional inflow (see appendix A).
6. Transition from slow to fast intensification
In our simulations, a major boost of the intensification rate generally entails significant changes to the previously described structure of a tropical cyclone (section 5). The following aims to identify the conditions required for a transition to fast spinup for a given SST. The transition point will be defined so as to occur when the intensification rate begins to sharply grow after maintaining a sufficiently small value over the preceding 20 h. Bear in mind that this does not necessarily correspond to the onset of rapid intensification (RI), which by its conventional definition occurs when the maximum sustained surface wind speed begins to grow at least 15.4 m s−1 (plus or minus a few meters per second) over 24 h (Kaplan and DeMaria 2003; Kaplan et al. 2010). Conventional RI may occur after the transition, but is not explicitly required.
a. The transition time
The transition time
Figure 12a is a scatterplot of
(a) Time interval between the beginning of the HFP and the transition to fast spinup (
Citation: Journal of the Atmospheric Sciences 79, 2; 10.1175/JAS-D-21-0051.1
b. Alignment and axisymmetrization at the time of transition
First and foremost, we should verify expectations based on section 4 and a number of complementary studies addressing the onset of RI in systems with moderate shear (e.g., Z16; Munsell et al. 2017; Miyamoto and Nolan 2018; RDT18; AZZ20) that the transition to fast spinup generally occurs after substantial reduction of tilt. Figure 13a depicts the evolving statistics of the tilt magnitude during a 2-day time interval centered at
Evolution of (a) the tilt magnitude, (b) the precipitation asymmetry, and (c) rm for systems undergoing transitions to fast spinup. Plots highlighted with yellow backgrounds correspond to the 12-h interval centered at the transition time
Citation: Journal of the Atmospheric Sciences 79, 2; 10.1175/JAS-D-21-0051.1
The preceding analysis supports the notion that a sufficient reduction of the tilt magnitude occurring simultaneously with a reduction of asymmetry in precipitating convection has an important role in enabling a transition to fast spinup. Overall, the coupled values of the tilt magnitude and Pasym that mark the transition for group T26 are appreciably smaller than their counterparts for groups T28 and T30 (see the middle panels of Figs. 13a,b). A fairly similar result is found for the transitional ratio of the tilt magnitude normalized to rm, which is 0.31 ± 0.12 for group T26, 0.54 ± 0.21 for group T28, and 0.74 ± 0.24 for group T30. AZZ20 notably reported that a comparable variable having a value below 0.75 was generally needed for RI in an ensemble of simulations of Tropical Cyclone Edouard (2014) over an SST of 28°–30°C. As an aside, it is worth remarking that the reductions of tilt and precipitation asymmetry seen here do not coincide with a transition to an approximate state of slantwise convective neutrality that is sometimes assumed in analytical intensification theories (see appendix B).
In contrast to the behavior of tilt and Pasym, the magnitude of rm tends not to appreciably decline during the day preceding the transition time
c. Moist-thermodynamic conditions at the time of transition
In the experiments under present consideration, the reduction of tilt coincides with modifications of the moist-thermodynamic conditions of the vortex core that in the aggregate are believed to facilitate the faster spinup that ensues. These modifications are best explained by way of an illustrative example. Consider the tropical cyclone in simulation T28-HRA. Figures 7d–f depict the state of the system 14–20 h prior to
(a)–(c) Depiction of simulation T28-HRA during a 6-h period centered at the transition time
Citation: Journal of the Atmospheric Sciences 79, 2; 10.1175/JAS-D-21-0051.1
Figure 14d compares the central vertical distributions of entropy and saturation entropy during the foregoing 6-h pretransitional and transitional time periods of the tropical cyclone evolution. The distributions are averaged within a 35-km radius of the surface vortex center. In contrast to the pretransitional state, the transitional state exhibits monotonic decay of
The forthcoming analysis will confirm that the key inner-core enhancements of relative humidity and LCAPE seen above to precede fast spinup are common across the broader spectrum of shear-free systems under present consideration. The analysis will also determine how the moist-thermodynamic aspects of the transition from slow to fast spinup vary quantitatively with the SST.
(a) Table showing the pretransitional (−) and transitional (*) values of various core moist-thermodynamic parameters and the tilt magnitude. Mean values plus or minus the standard deviations are shown in separate columns for each SST-segregated simulation group. (b) The fractional change of each parameter (specified near the top of each panel) in going from the pretransitional to transitional state. Each color-filled box in a given panel extends vertically from the first to third quartiles of the dataset for the SST printed underneath. The median is represented by the dashed horizontal line. Small symbols (triangles, circles, and diamonds) show individual data points, excluding no more than a few outliers from group T28.
Citation: Journal of the Atmospheric Sciences 79, 2; 10.1175/JAS-D-21-0051.1
The distribution of
Referring to Fig. 15b, all SST groups show appreciable median fractional boosts of
Whereas some of the moist-thermodynamic changes coinciding with alignment over the day before
d. Comparison to moist-thermodynamic preconditioning for fast spinup in symmetrized systems
Section 4 showed that removing a large tilt while leaving the symmetric part of the vortex unchanged can hasten the formation of a hurricane. The following demonstrates that the shorter HFP is generally linked to faster achievement of the moist-thermodynamic conditions seen above to signal (alongside reduced tilt) an imminent transition to fast spinup. When such conditions initially exist, symmetrization will be found to prevent their early breakdown.
Figure 16 shows time series of various tropical cyclone parameters for the three LR simulations considered in section 4 from (left to right) groups T30, T28, and T26. These parameters include (top to bottom) υm, LCAPEc,
(a)–(d) Time series of (a) υm, (b) LCAPEc, (c)
Citation: Journal of the Atmospheric Sciences 79, 2; 10.1175/JAS-D-21-0051.1
(a) The accumulated rainfall (color) and time-averaged w contours over the interval −6 ≤ t − ts ≤ 0 h in simulation T28-HRA. The w contour levels are as in Fig. 7e. Both the rainfall and w fields are horizontally smoothed over an approximate 6.25-km radius. As usual, the + and × respectively mark the time-averaged rotational centers of the surface and middle-tropospheric circulations. (b) As in (a), but for the interval 0 ≤ t − ts ≤ 6 h. (c) Evolution of the radial distribution of the effective radial mass flux (
Citation: Journal of the Atmospheric Sciences 79, 2; 10.1175/JAS-D-21-0051.1
(a) Saturation entropy that assumes liquid-only condensate (dashed black-and-white contours; J kg−1 K−1) and absolute angular momentum (
Citation: Journal of the Atmospheric Sciences 79, 2; 10.1175/JAS-D-21-0051.1
(a) Time series of the tilt magnitudes for tropical cyclones initialized with 318 ≤ tilt0 ≤ 367 km and zl = 5.25 km. The thin-dark and thick-semitransparent curves represent the mean and spread of the time series in each SST group, as explained in the main text. The time coordinate used for the graph is defined by t′ ≡ t − t0, in which t0 = 0 (6 h) for tropical cyclones initially tilted with the DSPD (IS or ISPD) method described in section 2b. The three stages of alignment are indicated in the general vicinities of where they occur for group T28. (b) The tilt angle φtilt vs
Citation: Journal of the Atmospheric Sciences 79, 2; 10.1175/JAS-D-21-0051.1
The principal T30 simulation and T30R1 begin the HFP with LCAPEc and
The principal T28 simulation begins the HFP having LCAPEc within and
It has been shown that our symmetrized tropical cyclones expeditiously begin accelerated intensification in conjunction with LCAPEc and
7. Summary and conclusions
A cloud-resolving numerical model has been used to examine how depression-strength tilted tropical cyclones evolve into hurricanes over oceans having a range of SSTs. The simulations analyzed herein were distinguished from those of earlier studies (barring SM20) in focusing on the evolution that occurs when environmental vertical wind shear—which may have created the initial tilt—is reduced to a negligible level. The length τhf of the hurricane formation period (HFP) at any SST was shown to exhibit approximate linear growth with either the initial tilt magnitude (above a threshold) or the positively correlated time average of the radius of maximum wind speed rm. Moreover, decreasing the SST led to superlinear growth of τhf. For a given time average of rm exceeding approximately 40 km, the growth of τhf upon cooling the ocean surface from 30° to 28°C was an order of magnitude smaller than the growth upon further cooling to 26°C. The disproportionately smaller growth of τhf over the first two-degree drop coincided with a disproportionately smaller (negligible by the measure in Fig. 2b) reduction of the precipitation rate integrated over the core of the surface vortex.
The evolution of a strongly tilted tropical cyclone was often found to have a prolonged phase of slow (or neutral) intensification followed by fast spinup. The slow phase of intensification persists while the tropical cyclone maintains a state of substantial vertical misalignment with deep convection concentrated far downtilt from the center of the surface vortex. There was some concern that an early expansion of the inner core that occurs in response to the initial misalignment (SM20) could have set the tropical cyclone on course for slow intensification regardless of whether the structural asymmetry is retained. The preceding concern was allayed upon finding considerably faster development in a number of restarts beginning with the tilt-related asymmetry removed after the inner core expands.
The off-center asymmetric organization of convection associated with sustained tilt and slow spinup was analyzed for selected tropical storms at several SSTs. While details may differ to some extent, results were qualitatively similar at all SSTs, and in many respects resembled those reported in earlier studies of real and realistically simulated tropical cyclones that are tilted by moderate environmental vertical wind shear (as explained in section 5). The analyses suggested that a combination of reduced lower–middle-tropospheric relative humidity
The transition to fast spinup occurs after the tilt magnitude becomes sufficiently small through an alignment process discussed in SM20 and appendix C. This geometrical change was shown to coincide with enhancements of lower–middle-tropospheric
Two notable elements of a natural system—radiative forcing and environmental vertical wind shear—were left out of the simulations considered for this study. Including a realistic parameterization of radiative transfer in the model is expected to accelerate hurricane formation, but the detailed consequences on the foregoing results are presently unknown. There presumably exists a parameter regime of sufficiently weak shear in which there is no radical change to the relationship between the tilt magnitude and the moist-thermodynamic structure of the tropical cyclone seen here under quiescent environmental conditions. In the same parameter regime, there would be no obvious reason to expect a major change to the coupled kinematic and moist-thermodynamic conditions that enable a transition from slow to fast spinup, or to the alignment process that goes hand in hand with creating those conditions (SM20). Determination of the precise level of shear at which major deviations begin to emerge has been left for future study.
While sometimes given a more restrictive definition, the term “precession” herein refers to rotation of the tilt vector over time by any adiabatic, diabatic, or hybrid mechanism. Likewise, the term “alignment” refers to contraction of the tilt vector by any means.
A few details omitted from the preceding discussion should be noted. In contrast to all other simulations, eight of the HR simulations in group T28 split the vortex at zl = 3.5 or 1.75 (as opposed to 5.25) km. All but one of the HR simulations in group T28 are taken directly from SM20; these include the control run and the 21 tilted tropical cyclone simulations described in Table 1 therein. A variant of the minimal-tilt control run of SM20 is repeated here, starting with an axisymmetrized version of the root vortex (the a-root vortex) that includes the water vapor distribution but excludes the secondary circulation and all hydrometeors. The same initial condition is used for the T26, T28-LR, and T30 simulations with zero initial tilt. Moreover, the ISPD procedure of SM20 has been slightly modified for the new LR simulations by replacing the unfiltered root vortex with the a-root vortex prior to tilting.
To be precise, tilt0 is the maximum tilt magnitude measured during the interval 0 ≤ t ≤ 6 h, in which t = 0 corresponds to the start of the 6-h impulsive IS or ISPD tilting procedure, or the end of the generally nonimpulsive DSPD procedure.
Lin et al. (2015) reports a similar observational dependence of tropical cyclone precipitation on relative SST.
Sensitivity tests with wc raised to 10 m s−1 or with w+ evaluated at z = 4 km (and wc varied between 2.5 and 5 m s−1) consistently produced values of 〈rw〉 fairly close to 〈rp〉. Regarding technical procedures, the search for rw is restricted to r < 3rm, and the time average of rw is computed excluding occasional brief intervals in which w (at the evaluation height) is less than wc everywhere in the search region. Moreover, HR simulation data are locally averaged onto the LR grid before computing w+.
It should be noted that the PPD varies to some extent with the disc radius a. Repeating the preceding analysis with a = 1.2rm increases the HFP time-averaged precipitation probability in the φ = π/2 (downwind of downtilt) quadrant mostly at the expense of that in the φ = 3π/2 (upwind of downtilt) quadrant, but does not introduce any notable differences between the SST groups. The φ = 0 (downtilt) precipitation probability gains dominance over its φ = π/2 counterpart (and all others) as 〈tilt〉 increases beyond approximately 40 km.
Considering systems with tilt0 > 100 km, the correlation coefficients between tilt0 and rm averaged over the first 6 h of the HFP are 0.81 for group T26, 0.79 for group T28, and 0.88 for group T30.
The values of tb are 18.2, 25.1, and 31.0 h for simulations T30-LRA, T28-LRA, and T26-LRA, respectively. For all simulations in Table 1, tb ranges from 6.6 to 66 h.
This process is presumably akin to that of other vertically aligned systems reviewed elsewhere (e.g., Montgomery and Smith 2014).
The sum of the vapor and potential temperature terms would exactly cancel the pressure term for a saturated cloudy air parcel governed by reversible thermodynamics, in which water substance is conserved and changes phase instantaneously. Otherwise,
The parcel buoyancy is calculated as in the getcape subroutine included in the CM1 software package.
The absence of a (relatively) high entropy reservoir near the surface center is believed to be a result of chance, as opposed to being a general characteristic of tilted tropical storms over SSTs of 28°C; such reservoirs under depressions of LCAPE are seen in other tropical storms belonging to group T28.
The surface enthalpy flux Fk is calculated here with the conventional approximation in Zhang et al. (2008). The kinematic surface flux of equivalent potential temperature is approximately given by Fk/ρcpd, in which ρ denotes density (e.g., De Ridder 1997).
Here and elsewhere, a ± b denotes the mean (a) plus or minus one standard deviation (b) of a dataset.
The author has verified the existence of a similar pattern in the vertical profile of the central temperature difference between balanced vortices having the same ζ distributions as the actual transitional and pretransitional vortices.
The deep-layer CAPE is defined here as the positive contribution to the vertical buoyancy integral of a 500-m mixed-layer parcel ascending pseudoadiabatically to the highest tropospheric equilibrium level. The highest equilibrium level is usually near the tropopause and may exceed the lowest equilibrium level. Thus, the deep-layer CAPE ignores potential termination of ascent in the lower troposphere.
Lower–middle-tropospheric relative humidity is measured in the following analysis as in section 5 by taking a vertical average between z = 2.3 and 7.7 (7.8) km for HR (LR) simulations.
With
Acknowledgments.
The author gratefully acknowledges the thorough and constructive feedback of several anonymous reviewers. The author also thanks Dr. George Bryan of the National Center for Atmospheric Research (NCAR) for providing the cloud-resolving model (CM1) that was used to simulate the development of the tilted tropical cyclones considered herein. Finally, the author thanks Peter Rosenthal for running and conducting preliminary analyses on numerous simulations used for this study during a summer internship at NorthWest Research Associates. All work for this paper including that related to the aforementioned internship was supported by the National Science Foundation under Grant AGS-1743854. The computational resources required to conduct the HR simulations were provided by NCAR’s Computational and Information Systems Laboratory (doi:10.5065/D6RX99HX). Archived simulation output and configuration files are presently maintained by the author and can be made available upon request to any researcher with a legitimate need.
APPENDIX A
The Role of Surface Friction in Maintaining Deep Convection Downtilt
Figure A1 provides some verification of the reasonable presumption that forcing of updrafts by frictional convergence in the boundary layer has an important role in maintaining the vigor of deep convection that occurs downtilt during the HFP. Figures A1a and A1b show two sequential plots of the 6-h accumulated precipitation and the 6-h time-averaged upper-tropospheric vertical velocity field in simulation T28-HRA. The sequence begins at t = ts − δt, in which ts is the start time of the averaging window in Figs. 7d–f, and δt = 6 h. Figures A1d and A1e show similar plots for a restart of the simulation at time ts − δt, with the surface drag coefficient Cd homogenized and reduced by two orders of magnitude so as to equal 2.5 × 10−5. Evidently, the reduction of Cd causes convection to rapidly dissipate and virtually vanish within 12 h. Such dissipation coincides with pronounced decay of the inward boundary layer mass flux seen in a complementary Hovmöller plot of
The preceding result should not be overgeneralized, but raises questions on the importance of certain hypothetical boosters for deep convection downtilt. One possible booster is adiabatic upgliding to the right of the tilt vector, which could lift initially unsaturated air to its level of free convection downtilt. It is unclear why convection supported by such a mechanism would so rapidly break down upon the reduction of surface drag. Another booster could be a robust cold pool downstream of convection, but there is no evidence of this scenario appreciably compensating for the removal of frictional convergence in the tropical storm considered above. The extent to which asymmetries in Ekman-like pumping may help give rise to a downtilt bias for deep convection near rm has not been investigated for the systems at hand. However, a concentration of deep convection downtilt would seem to be the most likely outcome of the broader frictional inflow, given the less conducive moist-thermodynamic conditions existing elsewhere.
APPENDIX B
Distinction between the Transition to Fast Spinup and the Transition to SCN
There has been a longstanding interest in tropical cyclone intensification theories that assume an azimuthally averaged state in which angular momentum contours arising from the vicinity of maximum wind speed are congruent with saturation entropy contours above the boundary layer (e.g., Emanuel 1997, 2012; Peng et al. 2018). Such a condition of slantwise convective neutrality (SCN) and any dependent theory are generally inapplicable to cloud-resolving simulations of early development. However, there is some computational evidence that SCN may be a reasonable approximation after an axisymmetric tropical cyclone intensifies beyond a transition point along its path toward equilibrium, where SCN in the eyewall is ideally exact (e.g., Peng et al. 2018).
To be clear, the transition to fast spinup in the present simulations entails a reduction of asymmetry, but generally does not coincide with a transition to SCN in an emergent eyewall. Figure B1 depicts the azimuthal-mean states of selected T26, T28, and T30 tropical cyclones, time averaged over 6-h intervals centered at (top row)
APPENDIX C
Alignment and Precession
Given that sufficiently large tilt magnitudes are correlated to unfavorable moist-thermodynamic conditions for intensification in our simulations, the time scale for the onset of fast spinup is linked to the time scale of vertical alignment. The time scale of alignment depends on the specific mechanism, which can be diabatic, adiabatic or more generally some hybrid of the two. Efforts to understand the mechanisms operating in prehurricane vortices, which partly involves elucidating the roles played by different facets of moist-convection, are ongoing (e.g., Nguyen and Molinari 2015; Chen et al. 2018; RDT18; SM20; AZZ20; Rogers et al. 2020). SM20 began to examine the alignment process for the HR T28 simulations of the present study and identified 3 distinct stages. The first stage is characterized by a rapid decay of the tilt magnitude that involves the swift diabatically driven migration of the surface center toward deep convection downtilt, and in some cases the reformation of the middle-tropospheric vorticity core closer to the surface center. The second stage is characterized by transient growth of the tilt magnitude, and is most pronounced in tropical cyclones initialized with the largest misalignments. In one system selected for detailed analysis (T28-HRA of this paper), the transient growth seemed partly caused by the emergence of a peripheral patch of anticyclonic vorticity (in the middle troposphere) that nudges the principal part of the midlevel cyclonic vorticity distribution away from the surface center; diabatic processes appeared to modulate the drift. The third stage of alignment identified in SM20 operates during much of the HFP, and typically involves gradual decay of the tilt magnitude. In the aforementioned case study, the gradual decay was driven by a complex interplay between diabatic forcing and adiabatic vortex dynamics, and failed to occur when moisture was removed from the simulation. Bear in mind that the third stage of alignment is not always purely gradual or monotonic, in that it sometimes contains notable secondary episodes of rapid decay or transient growth of the tilt magnitude.
While providing valuable insights, SM20 did not consider how the alignment process depends on the SST. Figure C1a addresses the foregoing deficiency by showing how the time series of the tilt magnitude varies with the SST for the illustrative subset of simulations with 318 ≤ tilt0 ≤ 367 km and a splitting altitude (see section 2b) of zl = 5.25 km. The narrow range of tilt0 and common value of zl is to ensure that all included simulations have comparable initial conditions. The thin dark curves in the plot correspond to the group mean values of tilt, and the thick semitransparent background curves extend vertically from the minimum to maximum group values of tilt. Note that the number of simulations in any particular group can decrease with time, since each time series is terminated at the end of the HFP.
Figure C1a demonstrates (for strongly misaligned systems) that increasing the SST from 26° to 30°C intensifies the initial decay of the tilt magnitude and diminishes the subsequent transient growth. Consequently, increasing the SST decreases the tilt magnitude at the end of stage 2 of the alignment process. Moreover, the mechanisms working to align the tropical cyclones during stage 3 appear to be least efficient in the long term over the coolest ocean.
As mentioned in section 1, reducing the environmental vertical wind shear to a negligible level eliminates the potential importance of tilt reorientation to the alignment process. However, precession of the tilt vector can still factor into the time scale for alignment. Before discussing how, let us first examine the nature of precession for the systems considered herein. Figure C1b illustrates the evolution of the tilt angle (φtilt, measured counterclockwise from the positive x direction in Fig. 7) for all simulations having well-defined transitions to fast spinup before the end of the HFP. The tropical cyclones in all SST groups exhibit a precession frequency (dφtilt/dt) of order 10−5 s−1 in the days leading up to
S20 theorized that the azimuthal propagation of downtilt convection coinciding with precession can either hinder or help the diabatically induced migration of the surface center toward the midlevel center of the tropical cyclone. In theory, the potentially positive influence becomes most evident when the azimuthal velocity of the propagation exceeds a certain threshold that allows lower-tropospheric vorticity to very efficiently amplify in the convection zone, thereby causing core reformation. The aforementioned threshold depends on several factors, and most notably decreases with increasing strength of the diabatic forcing that enhances convergence in the downtilt convection zone. For the simulations considered above, the precession leading up to fast spinup has a much smaller angular velocity than the characteristic rotation frequency of the cyclonic circulation (
As a final remark on the subject, a number of theoretical studies preceding S20 suggested that a wave-flow resonance associated with precession might be able to efficiently damp the tilt of a tropical cyclone (e.g., Reasor and Montgomery 2001; Schecter and Montgomery 2003, 2007). SM20 considered the potential relevance of resonant damping during the HFP, and provisionally concluded that it should not have substantial impact when precession tends to be as slow as that seen here before the onset of fast spinup.
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