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John Persing and Michael T. Montgomery

Abstract

High spatial and temporal resolution simulations using the Rotunno and Emanuel axisymmetric, cloud-resolving, hurricane model are found to greatly exceed Emanuel’s energetically based upper bound for maximum potential intensity (E-MPI).

Using a control simulation similar to that of Rotunno and Emanuel with a sea surface temperature (SST) of 26.13°C, the E-MPI is exceeded after 15 simulation days, after the warming of the eye is able to extend down to the ocean surface. At still higher resolution, the modeled storm greatly exceeds E-MPI more quickly, during initial spinup, and the resulting intensity for the standard numerical and microphysical parameters is found to converge with, respectively, radial and vertical grid spacing of 3.75 km and 312.5 m with maximum tangential winds (V max) of ≈90 m s–1. This is notably greater than the energetically based upper bound of V max = 55 m s–1. This “superintensity” occurs only in the presence of an enhancement of low-level eye entropy. The high-entropy air is entrained into the eyewall primarily by a breakdown of an azimuthal vortex sheet at the inner edge of the eyewall. Among the many underlying assumptions of E-MPI, only the violation of the related assumptions that the eyewall is neutral to moist ascent and that no entropy is fluxed from the eye to the eyewall can explain the degree of superintensity observed; other assumptions may be individually violated but their impacts on the intensity estimates are much smaller. The impact of the entrainment of heat from the eye to the eyewall on E-MPI theory is estimated through an ad hoc increase in the effective SST as a way of accounting for a second source of heat. This procedure produces a close estimate of the modeled intensity, but the problem is not closed since the degree of eyewall heating is not known a priori.

Published observations and recent three-dimensional, cloud-resolving modeling studies are reviewed that appear to present various aspects of the observed entropy structure and the eye–eyewall interaction of the superintensity mechanism.

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Michael T. Montgomery and Chungu Lu

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To understand the nature of coupling between a hurricane vortex and asymmetries in its near-core region, it is first necessary to have an understanding of the spectrum of free waves on barotropic vortices. As foundation for upcoming work examining the nonaxisymmetric initial-value problem in inviscid and swirling boundary layer vortex flows, the complete spectrum of free waves on barotropic vortices is examined here.

For a variety of circular vortices in gradient balance the linearized momentum and continuity equations are solved as a matrix eigenvalue problem for perturbation height and wind fields. Vortex eigensolutions are found to fall into two continuum classes. Eigenmodes with frequencies greater than the advective frequency for azimuthal wavenumber n are modified gravity–inertia waves possessing nonzero potential vorticity in the near-core region. Eigenmodes whose frequencies scale with the advective frequency comprise both gravity–inertia waves and Rossby–shear waves. Linearly superposing the Rossby–shear waves approximates the sheared disturbance solutions. For wavenumbers greater than a minimum number, Rossby–shear waves exhibit gravity wave characteristics in the near-vortex region. Although such eigenstructure changes are not anticipated by traditional scaling analyses using solely external flow parameters, a criterion extending Rossby’s characterization of “balanced” and “unbalanced” flow to that of azimuthal waves on a circular vortex is developed that correctly predicts the observed behavior from incipient vortices to hurricane-like vortices. The criterion is consistent with asymmetric balance theory. Possible applications of these results to the wave-mean-flow dynamics of geophysical vortex flows are briefly discussed.

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Janice Enagonio and Michael T. Montgomery

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This work examines further the problem of tropical cyclogenesis by convective generation of vertical vorticity within a preexisting cyclonic circulation whose initial maximum tangential wind is approximately 5 m s−1. This paper validates and extends recent work examining the suggested upscale cascade mechanism in a three-dimensional quasigeostrophic framework using a simple shallow water primitive equation (SWPE) numerical model and helps clarify certain aspects of the Rossby adjustment problem on a nonresting basic state for finite-amplitude nonaxisymmetric disturbances. The SWPE approach serves as a meaningful intermediate step between the quasigeostrophic and full-physics frameworks and allows a simple investigation of the effects of unbalanced dynamics (contributions of gravity waves) and Rossby numbers of order unity.

The authors compare quantitative results of the two models on the storm spinup time and magnitude. For asymmetric initial conditions whose mass and wind field are out of balance, robust spinup is still obtained provided the initial asymmetries possess a significant vortical component. Episodic convective forcing parameterized via unbalanced vorticity anomalies is shown to lead to spinup of a tropical storm strength vortex on a timescale of approximately 40 h.

When the convective vorticity anomaly has a large amplitude compared to the initial 5 m s−1 basic-state vortex, the convective anomaly becomes the dominant or “master vortex,” remaining essentially intact and shearing the basic-state vortex. This behavior is understood heuristically in terms of a “vortex beta Rossby number,” which provides a local measure of the strength of the nonlinear terms in the vorticity equation compared to the corresponding linear vortex Rossby wave restoring term.

Additional experiments show that, if the convection in a single pulse mode occurs in multiple patches (or“subclusters”) rather than in a single cluster with equal cyclonic circulation, a reduced spinup is obtained. This effect is captured in simulations with a nonlinear nondivergent semispectral model, establishing that gravity wave dynamics are not responsible for the reduction of spinup in the multiple-cluster case. A wave-mean-flow approximation with the nondivergent model also reproduces the effect of a reduced spinup with multiple-cluster convection. The applicability of the wave-mean-flow approximation at these finite amplitudes is explained by the fact that the vortex beta Rossby number of these configurations is not large.

A case study using satellite observations shows that, although the observations are for a tropical storm rather than for genesis, an intensification mechanism similar to that discussed here is suggested. Further tests of the theory are proposed.

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Michael T. Montgomery and Janice Enagonio

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This work investigates the problem of tropical cyclogenesis in three dimensions. In particular, the authors examine the interaction of small-scale convective disturbances with a larger-scale vortex circulation in a nonlinear quasigeostrophic balance model. Convective forcing is parameterized by its estimated net effect on the potential vorticity (PV) field. Idealized numerical experiments show that vortex intensification proceeds by ingestion of like-sign potential vorticity anomalies into the parent vortex and expulsion of opposite-sign potential vorticity anomalies during the axisymmetrization process. For the finite-amplitude forcing considered here, the weakly nonlinear vortex Rossby wave mean-flow predictions for the magnitude and location of the spinup are in good agreement with the model results. Vortex development is analyzed using Lagrangian trajectories, Eliassen–Palm flux vectors, and the Lorenz energy cycle.

Using numerical estimates of the magnitude of PV injection based on previous observational and theoretical work, the authors obtain spinup to a 15 m s−1 cyclone on realistic timescales. Simulation of a midlevel vortex with peripheral convection shows that axisymmetrization results in the spinup of a surface cyclone. The axisymmetrization mechanism demonstrates the development of a warm-core vortex. The relative contribution from eddy-heat and eddy-momentum fluxes to the warm core structure of the cyclone is investigated.

The vortex spinup obtained shows greater than linear dependence on the forcing amplitude, indicating the existence of a nonlinear feedback mechanism associated with the vortex Rossby waves.

Building on recent work by several authors, this work further clarifies the significance of the axisymmetrization process for the problem of tropical cyclogenesis. The theory is shown to be consistent with published observations of tropical cyclogenesis. Further observational and modeling tests of the theory, specific to the dynamics examined here, are proposed.

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John Persing and Michael T. Montgomery

Abstract

In numerical simulations using an axisymmetric, cloud-resolving hurricane model, hurricane intensity shows quasi-steady-state behavior. This quasi-steady intensity is interpreted as the maximum possible intensity (MPI) of the model.

Within the literature, numerical demonstrations have confirmed theoretically anticipated influences on hurricane intensity such as sea surface temperature, outflow temperature, and surface exchange coefficients of momentum and enthalpy. Here these investigations are extended by considering the role of environmental convective available potential energy (CAPE) on hurricane intensity. It is found that environmental CAPE (independent of changes to the outflow level) has no significant influence on numerically simulated maximum hurricane intensity. Within this framework, MPI theories that are sensitive to environmental CAPE should be discarded.

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Michael T. Montgomery and John Persing

Abstract

This study investigates a claim made by Heng et al. in an article published in 2017 and intimated soon after in their article published in 2018 that axisymmetric “balanced dynamics can well capture the secondary circulation in the full-physics model” during hurricane spinup. Using output from a new, convection-permitting, three-dimensional numerical simulation of an intensifying hurricane, azimuthally averaged forcings of tangential momentum and heat are diagnosed to force an axisymmetric Eliassen balance model under strict balance conditions. The balance solutions are found, inter alia, to poorly represent the peak inflow velocity in the boundary layer and present a layer of relatively deep inflow extending well above the boundary layer in the high-wind-speed region of the vortex. Such a deep inflow layer, a hallmark of the classical spinup mechanism for tropical cyclones comprising the radial convergence of absolute angular momentum above the boundary layer, is not found in the numerical simulation during the period of peak intensification. These deficiencies are traced to the inability of the balance model to represent the nonlinear boundary layer spinup mechanism. These results are contrasted with a pseudobalance Eliassen formulation that improves the solution in some respects while sacrificing strict thermal wind balance. Overall, the quantitative results refute the Heng et al. claim and implicate the general necessity of the nonlinear boundary layer spinup mechanism to explain the spinup of a hurricane in realistic model configurations and in reality.

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Michael M. Bell and Michael T. Montgomery

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Unprecedented observations of Hurricane Isabel (2003) at category 5 intensity were collected from 12 to 14 September. This study presents a detailed analysis of the inner-core structure, atmospheric boundary layer, sea surface temperature, and outflow layer of a superintense tropical cyclone using high-resolution in situ flight-level, NCAR GPS dropwindsonde, Doppler radar, and satellite measurements. The analysis of the dropwindsonde and in situ data includes a comprehensive discussion of the uncertainties associated with this observational dataset and provides an estimate of the storm-relative axisymmetric inner-core structure using Barnes objective analysis. An assessment of gradient and thermal wind balance in the inner core is also presented. The axisymmetric data composites presented in this study suggest that Isabel built a reservoir of high moist entropy air by sea-to-air latent heat flux inside the low-level eye that was utilized as an additional energy source to nearly maintain its extreme intensity even after crossing the cool wake of Hurricane Fabian. It is argued here that the combined mean and asymmetric eddy flux of high moist entropy air from the low-level eye into the eyewall represents an additional power source or “turbo boost” to the hurricane heat engine. Recent estimates of the ratio of sea-to-air enthalpy and momentum exchange at high wind speeds are used to suggest that Isabel utilized this extra power to exceed the previously assumed intensity upper bound for the given environmental conditions on all three days. This discrepancy between a priori potential intensity theory and observations may be as high as 35 m s−1 on 13 September.

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Michael M. Bell and Michael T. Montgomery

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Observations from the Pre-Depression Investigation of Cloud Systems in the Tropics (PREDICT), Genesis and Rapid Intensification Processes (GRIP), and Intensity Forecast Experiment (IFEX) field campaigns are analyzed to investigate the mesoscale processes leading to the tropical cyclogenesis of Hurricane Karl (2010). Research aircraft missions provided Doppler radar, in situ flight level, and dropsonde data documenting the structural changes of the predepression disturbance. Following the pre-Karl wave pouch, variational analyses at the meso-β and meso-α scales suggest that the convective cycle in Karl alternately built the low- and midlevel circulations leading to genesis episodically rather than through a sustained lowering of the convective mass flux from increased stabilization. Convective bursts that erupt in the vorticity-rich environment of the recirculating pouch region enhance the low-level meso-β- and meso-α-scale circulation through vortex stretching. As the convection wanes, the resulting stratiform precipitation strengthens the midlevel circulation through convergence associated with ice microphysical processes, protecting the disturbance from the intrusion of dry environmental air. Once the column saturation fraction returns to a critical value, a subsequent convective burst below the midlevel circulation further enhances the low-level circulation, and the convective cycle repeats. The analyses suggest that the onset of deep convection and associated low-level spinup were closely related to the coupling of the vorticity and moisture fields at low and midlevels. Our interpretation of the observational analysis presented in this study reaffirms a primary role of deep convection in the genesis process and provides a hypothesis for the supporting role of stratiform precipitation and the midlevel vortex.

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Eric A. Hendricks and Michael T. Montgomery

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On 9–10 September 2002, multiple mesovortices were captured in great detail by rapid scan visible satellite imagery in subtropical, then later, Tropical Storm Gustav. These mesovortices were observed as low-level cloud swirls while the low-level structure of the storm was exposed due to vertical shearing. They are shown to form most plausibly via vortex tube stretching associated with deep convection; they become decoupled from the convective towers by vertical shear; they are advected with the low-level circulation; finally they initiate new hot towers on their boundaries. Partial evidence of an axisymmetrizing mesovortex and its hypothesized role in the parent vortex spinup is presented. Observations from the mesoscale and synoptic scale are synthesized to provide a multiscale perspective of the intensification of Gustav that occurred on 10 September. The most important large-scale factors were the concurrent relaxation of the 850–200-hPa-deep layer vertical wind shear from 10–15 to 5–10 m s−1 and movement over pockets of very warm sea surface temperatures (approximately 29.5°–30.5°C). The mesoscale observations are not sufficient alone to determine the precise role of the deep convection and mesovortices in the intensification. However, qualitative comparisons are made between the mesoscale processes observed in Gustav and recent full-physics and idealized numerical simulations to obtain additional insight.

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Michael T. Montgomery and Brian F. Farrell

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We previously examined surface frontogenesis as an initial value problem in a dry inviscid semigeostrophic Eady model focusing on the frontal dynamics associated with interior potential vorticity anomalies. This work explores frontogenesis associated with potential vorticity anomalies in the presence of latent heat release using a generalization of the two-dimensional) semigeostrophic Eady model that insures that the heating term gives correct asymptotic behavior at high and low temperatures. A variety of initial conditions are considered in which upper-level potential vorticity disturbances induce strong positive potential vorticity anomalies near the lower surface. With uniform interior potential vorticity, baroclinic coupling between the upper and surface induced disturbance is weak despite a near neutral moist stability. On the other hand, examples of initial disturbances with interior potential vorticity show greatly enhanced baroclinic coupling between upper and lower disturbances. Comparison with a recent observational study suggests these represent a simple phenomenological description of squall line development.

We also find that latent heat release destabilized surface concentrated disturbances which do not intensify in the dry problem. These frontal developments are not primarily baroclinic. Rather, the source of energy is latent heat released in ascent regions and the attendant generation of surface potential vorticity. Development is slow in comparison to baroclinic frontogenesis but is not dependent on the presence of large amplitude perturbations. This diabatic surface development also appears in examples involving upper-level potential vorticity disturbances as a slow intensification of meridional surface winds following the more rapid baroclinic interaction between upper- and lower-level disturbances. Examples suggestive of observed polar low development comprise an initial baroclinic growth phase followed by a slow intensification due to diabatic effects.

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