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James P. Kossin and Wayne H. Schubert
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James P. Kossin and Matthew D. Eastin

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Using aircraft flight-level data, the present work demonstrates that the kinematic and thermodynamic distributions within the eye and eyewall of strong hurricanes are observed to evolve between two distinct regimes. In the first regime, angular velocity is greatest within the eyewall and relatively depressed within the eye. In the second regime, radial profiles of angular velocity are nearly monotonic, with maxima found at the eye center. Considering sequential profiles within individual hurricanes, the authors find that the evolution of the kinematic distribution is often marked by a transition from the first regime to the second. The transition can occur in less than 1 h.

Also noted during the transition are dramatic changes in the thermodynamic structure of the hurricane. Prior to the transition (regime 1), the eye is typically very warm and dry, and the equivalent potential temperature is often elevated within the eyewall and relatively depressed within the eye. After the transition (regime 2), eye temperatures may be lower, higher, or unchanged; dewpoints are higher; and equivalent potential temperature profiles are often nearly monotonic with maxima at the hurricane center.

A mechanism is suggested, based on horizontal vorticity mixing, whereby the observed transitions within the hurricane eye and eyewall might be well explained within an idealized 2D barotropic framework.

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James P. Kossin and Wayne H. Schubert

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The present work considers the two-dimensional barotropic evolution of thin annular rings of enhanced vorticity embedded in nearly irrotational flow. Such initial conditions imitate the observed flows in intensifying hurricanes. Using a pseudospectral numerical model, it is found that these highly unstable annuli rapidly break down into a number of mesovortices. The mesovortices undergo merger processes with their neighbors and, depending on initial conditions, they can relax to a monopole or an asymmetric quasi-steady state. In the latter case, the mesovortices form a lattice rotating approximately as a solid body. The flows associated with such vorticity configurations consist of straight line segments that form a variety of persistent polygonal shapes.

Associated with each mesovortex is a local pressure perturbation, or mesolow. The magnitudes of the pressure perturbations can be large when the magnitude of the vorticity in the initial annulus is large. In cases where the mesovortices merge to form a monopole, dramatic central pressure falls are possible.

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Jason C. Knievel, David S. Nolan, and James P. Kossin

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The authors examine the degree of hydrostatic and gradient balances in a mesoscale convective vortex (MCV) in the stratiform region of a mesoscale convective system (MCS) that crossed Oklahoma on 1 August 1996. Results indicate that the MCV was partially unbalanced because the cool layer at the base of its core was too cool and too shallow to balance the tangential winds about the MCV's axis. The apparent imbalance may have been due to strong, unsteady forcing on the vortex; insufficient or unrepresentative data; approximations used in the analysis; or reasons that are unknown.

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James P. Kossin, Wayne H. Schubert, and Michael T. Montgomery

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Intense tropical cyclones often exhibit concentric eyewall patterns in their radar reflectivity. Deep convection within the inner, or primary, eyewall is surrounded by a nearly echo-free moat, which in turn is surrounded by an outer, or secondary ring of deep convection. Both convective regions typically contain well-defined tangential wind maxima. The primary wind maximum is associated with large vorticity just inside the radius of maximum wind, while the secondary wind maximum is usually associated with relatively enhanced vorticity embedded in the outer ring. In contrast, the moat is a region of low vorticity. If the vorticity profile across the eye and inner eyewall is approximated as monotonic, the resulting radial profile of vorticity still satisfies the Rayleigh necessary condition for instability as the radial gradient twice changes sign.

Here the authors investigate the stability of such structures and, in the case of instability, simulate the nonlinear evolution into a more stable structure using a nondivergent barotropic model. Because the radial gradient of vorticity changes sign twice, two types of instability and vorticity rearrangement are identified: 1) instability across the outer ring of enhanced vorticity, and 2) instability across the moat. Type 1 instability occurs when the outer ring of enhanced vorticity is sufficiently narrow and when the circulation of the central vortex is sufficiently weak (compared to the outer ring) that it does not induce enough differential rotation across the outer ring to stabilize it. The nonlinear mixing associated with type 1 instability results in a broader and weaker vorticity ring but still maintains a significant secondary wind maximum. The central vortex induces strong differential rotation (and associated enstrophy cascade) in the moat region, which then acts as a barrier to inward mixing of small (but finite) amplitude asymmetric vorticity disturbances. Type 2 instability occurs when the radial extent of the moat is sufficiently narrow so that unstable interactions may occur between the central vortex and the inner edge of the ring. Because the vortex-induced differential rotation across the ring is large when the ring is close to the vortex, type 2 instability typically precludes type 1 instability except in the case of very thin rings. The nonlinear mixing from type 2 instability perturbs the vortex into a variety of shapes. In the case of contracting rings of enhanced vorticity, the vortex and moat typically evolve into a nearly steady tripole structure, thereby offering a mechanism for the formation and persistence of elliptical eyewalls.

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Christopher M. Rozoff, Wayne H. Schubert, Brian D. McNoldy, and James P. Kossin

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Intense tropical cyclones often possess relatively little convection around their cores. In radar composites, this surrounding region is usually echo-free or contains light stratiform precipitation. While subsidence is typically quite pronounced in this region, it is not the only mechanism suppressing convection. Another possible mechanism leading to weak-echo moats is presented in this paper. The basic idea is that the strain-dominated flow surrounding an intense vortex core creates an unfavorable environment for sustained deep, moist convection. Strain-dominated regions of a tropical cyclone can be distinguished from rotation-dominated regions by the sign of S 2 1 + S 2 2ζ 2, where S 1 = uxυy and S 2 = υx + uy are the rates of strain and ζ = υxuy is the relative vorticity. Within the radius of maximum tangential wind, the flow tends to be rotation-dominated (ζ 2 > S 2 1 + S 2 2), so that coherent structures, such as mesovortices, can survive for long periods of time. Outside the radius of maximum tangential wind, the flow tends to be strain-dominated (S 2 1 + S 2 2 > ζ 2), resulting in filaments of anomalous vorticity. In the regions of strain-dominated flow the filamentation time is defined as τ fil = 2(S 2 1 + S 2 2ζ 2)−1/2. In a tropical cyclone, an approximately 30-km-wide annular region can exist just outside the radius of maximum tangential wind, where τ fil is less than 30 min and even as small as 5 min. This region is defined as the rapid filamentation zone. Since the time scale for deep moist convective overturning is approximately 30 min, deep convection can be significantly distorted and even suppressed in the rapid filamentation zone. A nondivergent barotropic model illustrates the effects of rapid filamentation zones in category 1–5 hurricanes and demonstrates the evolution of such zones during binary vortex interaction and mesovortex formation from a thin annular ring of enhanced vorticity.

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Eric A. Hendricks, Wayne H. Schubert, Richard K. Taft, Huiqun Wang, and James P. Kossin

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The asymmetric dynamics of potential vorticity mixing in the hurricane inner core are further advanced by examining the end states that result from the unforced evolution of hurricane-like vorticity rings in a nondivergent barotropic model. The results from a sequence of 170 numerical simulations are summarized. The sequence covers a two-dimensional parameter space, with the first parameter defining the hollowness of the vortex (i.e., the ratio of eye to inner-core relative vorticity) and the second parameter defining the thickness of the ring (i.e., the ratio of the inner and outer radii of the ring). In approximately one-half of the cases, the ring becomes barotropically unstable, and there ensues a vigorous vorticity mixing episode between the eye and eyewall. The output of the barotropic model is used to (i) verify that the nonlinear model approximately replicates the linear theory of the fastest-growing azimuthal mode in the early phase of the evolution, and (ii) characterize the end states (defined at t = 48 h) that result from the nonlinear chaotic vorticity advection and mixing. It is found that the linear stability theory is a good guide to the fastest-growing exponential mode in the numerical model. Two additional features are observed in the numerical model results. The first is an azimuthal wavenumber-2 deformation of the vorticity ring that occurs for moderately thick, nearly filled rings. The second is an algebraically growing wavenumber-1 instability (not present in the linear theory because of the assumed solution) that is observed as a wobbling eye (or the trochoidal oscillation for a moving vortex) for thick rings that are stable to all exponentially growing instabilities. Most end states are found to be monopoles. For very hollow and thin rings, persistent mesovortices may exist for more than 15 h before merging to a monopole. For thicker rings, the relaxation to a monopole takes longer (between 48 and 72 h). For moderately thick rings with nearly filled cores, the most likely end state is an elliptical eyewall. In this nondivergent barotropic context, both the minimum central pressure and maximum tangential velocity simultaneously decrease over 48 h during all vorticity mixing events.

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Christopher M. Rozoff, David S. Nolan, James P. Kossin, Fuqing Zhang, and Juan Fang

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The Weather and Research and Forecasting Model (WRF) is used to simulate secondary eyewall formation (SEF) in a tropical cyclone (TC) on the β plane. The simulated SEF process is accompanied by an outward expansion of kinetic energy and the TC warm core. An absolute angular momentum budget demonstrates that this outward expansion is predominantly a symmetric response to the azimuthal-mean and wavenumber-1 components of the transverse circulation. As the kinetic energy expands outward, the kinetic energy efficiency in which latent heating can be retained as local kinetic energy increases near the developing outer eyewall.

The kinetic energy efficiency associated with SEF is examined further using a symmetric linearized, nonhydrostatic vortex model that is configured as a balanced vortex model. Given the symmetric tangential wind and temperature structure from WRF, which is close to a state of thermal wind balance above the boundary layer, the idealized model provides the transverse circulation associated with the symmetric latent heating and friction prescribed from WRF. In a number of ways, this vortex response matches the azimuthal-mean secondary circulation in WRF. These calculations suggest that sustained azimuthal-mean latent heating outside of the primary eyewall will eventually lead to SEF. Sensitivity experiments with the balanced vortex model show that, for a fixed amount of heating, SEF is facilitated by a broadening TC wind field.

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Christopher M. Rozoff, James P. Kossin, Wayne H. Schubert, and Pedro J. Mulero

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In hurricane eyewalls, the vertical stretching effect tends to produce an annular ring of high vorticity. Idealized, unforced nondivergent barotropic model results have suggested such rings of vorticity are often barotropically unstable, leading to strong asymmetric mixing events where vorticity is mixed inward into a more stable configuration. Such mixing events most often result in weakened maximum winds. The manner in which forcing modifies these unforced simulations remains an open question.

In the current study, a forced, two-dimensional barotropic model is used to systematically study the sensitivity of vorticity rings to ring geometry and spatially and temporally varying forcing. The simulations reveal an internal mechanism that interrupts the intensification process resulting from vorticity generation in the hurricane eyewall. This internal control mechanism is due to vorticity mixing in the region of the eye and eyewall and can manifest itself in two antithetical forms—as a transient “intensification brake” during symmetric intensification or as an enhancer of intensification through efficient transport of vorticity from the eyewall, where it is generated, to the eye.

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Wayne H. Schubert, Michael T. Montgomery, Richard K. Taft, Thomas A. Guinn, Scott R. Fulton, James P. Kossin, and James P. Edwards

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Hurricane eyewalls are often observed to be nearly circular structures, but they are occasionally observed to take on distinctly polygonal shapes. The shapes range from triangles to hexagons and, while they are often incomplete, straight line segments can be identified. Other observations implicate the existence of intense mesovortices within or near the eye region. Is there a relation between polygonal eyewalls and hurricane mesovortices? Are these phenomena just curiosities of the hurricane’s inner-core circulation, or are they snapshots of an intrinsic mixing process within or near the eye that serves to determine the circulation and thermal structure of the eye?

As a first step toward understanding the asymmetric vorticity dynamics of the hurricane’s eye and eyewall region, these issues are examined within the framework of an unforced barotropic nondivergent model. Polygonal eyewalls are shown to form as a result of barotropic instability near the radius of maximum winds. After reviewing linear theory, simulations with a high-resolution pseudospectral numerical model are presented to follow the instabilities into their nonlinear regime. When the instabilities grow to finite amplitude, the vorticity of the eyewall region pools into discrete areas, creating the appearance of polygonal eyewalls. The circulations associated with these pools of vorticity suggest a connection to hurricane mesovortices. At later times the vorticity is ultimately rearranged into a nearly monopolar circular vortex. While the evolution of the finescale vorticity field is sensitive to the initial condition, the macroscopic end-states are found to be similar. In fact, the gross characteristics of the numerically simulated end-states are predicted analytically using a generalization of the minimum enstrophy hypothesis. In an effort to remove some of the weaknesses of the minimum enstrophy approach, a maximum entropy argument developed previously for rectilinear shear flows is extended to the vortex problem, and end-state solutions in the limiting case of tertiary mixing are obtained.

Implications of these ideas for real hurricanes are discussed.

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