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Konstantinos Menelaou and M. K. Yau

Abstract

Although intense tropical cyclones (TCs) are considered to be axisymmetric vortices, observations reveal that they are often highly asymmetric. Better understanding of the underlying asymmetric dynamics is a critical step toward advancing TC intensity forecasting. In this paper, we revisit the mechanisms behind one of the most frequent asymmetric patterns: the deformation of the core into an elliptical shape. Previously, elliptical eyewalls were primarily thought to be an outcome of barotropic instability, a mechanism that involves the coupling and mutual growth of counterpropagating vortex Rossby (VR) waves. These results were largely based on simplified numerical models that filter out inertia–gravity (IG) waves. Consideration of IG waves introduces the possibility of an additional instability mechanism, one that involves a VR wave that spontaneously emits a spiral IG wave into the environment. We provide evidence that elliptical eyewalls, which may form within a three-dimensional primitive-equation nonlinear model that supports both instability types, can solely originate by the mechanism of spontaneous radiative imbalance. These evidences are supported by a number of nonlinear simulations, supplemental linear eigenmode analysis, and a linear simulation. The potential role of a multimechanistic instability is also briefly addressed.

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David A. Schecter and Konstantinos Menelaou

Abstract

A method is outlined for quantitatively assessing the impact of inertia–gravity wave radiation on the multimechanistic instability modes of a columnar stratified vortex that resembles an intense tropical cyclone. The method begins by decomposing the velocity field into one part that is formally associated with sources inside the vortex and another part that is attributed to radiation. The relative importance of radiation is assessed by comparing the rates at which the two partial velocity fields act to amplify the perturbation of an arbitrary tracer field—such as potential vorticity—inside the vortex. Further insight is gained by decomposing the formal vortex contribution to the amplification rate into subparts that are primarily associated with distinct vortex Rossby waves and critical-layer perturbations.

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David A. Schecter and Konstantinos Menelaou

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A cloud-resolving model is used to examine the virtually shear-free evolution of incipient tropical cyclones initialized with different degrees of misalignment between the lower- and middle-tropospheric centers of rotation. Increasing the initial displacement of rotational centers (the tilt) from a negligible value to several hundred kilometers extends the time scale of hurricane formation from 1 to 10 days. Hindered amplification of the maximum tangential velocity υ m at the surface of a strongly perturbed system is related to an extended duration of misalignment resulting from incomplete early decay and subsequent transient growth of the tilt magnitude. The prolonged misalignment coincides with a prolonged period of asymmetric convection peaked far from the surface center of the vortex. A Sawyer–Eliassen model is used to analyze the disparity between azimuthal velocity tendencies of selected pre–tropical storm vortices with low and high degrees of misalignment. Although no single factor completely explains the difference of intensification rates, greater misalignment is linked to weaker positive azimuthal velocity forcing near υ m by the component of the mean secondary circulation attributed to heating by microphysical cloud processes. Of note regarding the dynamics, enhanced tilt only modestly affects the growth rate of kinetic energy outside the core of the surface vortex while severely hindering intensification of υ m within the core for at least several days. The processes controlling the evolution of the misalignment associated with inefficient development are examined in detail for a selected simulation. It is found that adiabatic mechanisms are capable of driving the transient amplification of tilt, whereas diabatic processes are essential to ultimate alignment of the tropical cyclone.

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Konstantinos Menelaou and M. K. Yau

Abstract

The role of asymmetric convection to the intensity change of a weak vortex is investigated with the aid of a “dry” thermally forced model. Numerical experiments are conducted, starting with a weak vortex forced by a localized thermal anomaly. The concept of wave activity, the Eliassen–Palm flux, and eddy kinetic energy are then applied to identify the nature of the dominant generated waves and to diagnose their kinematics, structure, and impact on the primary vortex. The physical reasons for which disagreements with previous studies exist are also investigated utilizing the governing equation for potential vorticity (PV) perturbations and a number of sensitivity experiments.

From the control experiment, it is found that the response of the vortex is dominated by the radiation of a damped sheared vortex Rossby wave (VRW) that acts to accelerate the symmetric flow through the transport of angular momentum. An increase of the kinetic energy of the symmetric flow by the VRW is shown also from the eddy kinetic energy budget. Additional tests performed on the structure and the magnitude of the initial thermal forcing confirm the robustness of the results and emphasize the significance of the wave–mean flow interaction to the intensification process.

From the sensitivity experiments, it is found that for a localized thermal anomaly, regardless of the baroclinicity of the vortex and the radial and vertical gradients of the thermal forcing, the resultant PV perturbation follows a damping behavior, thus suggesting that deceleration of the vortex should not be expected.

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Georgina Paull, Konstantinos Menelaou, and M. K. Yau

Abstract

This study examines the influences of an axisymmetric heat source on the tangential wind structure of a tropical cyclone (TC). Specifically, the response of a TC due to the effect of convection located in varying inertial stability profiles was calculated. Using an idealized heat source, the thermodynamic efficiency hypothesis and the dynamic hypothesis for lower-level tangential wind acceleration are studied with the use of a balanced 2D model. These two frameworks for calculating the lower-level tangential wind acceleration are then compared to an idealized but thermally forced version of a nonlinear 3D model (WRF). It is found that using either of the 2D balanced model approaches to calculate the tangential wind acceleration results in an underestimation when compared to the full nonlinear simulation. In addition, the thermodynamic efficiency approach also shows a radial shift in the location of the maximum lower-level tangential wind acceleration. Sensitivity experiments in the context of the WRF Model in varying background inertial instabilities were investigated. It is shown that as the eyewall-like heating is shifted to larger values of inertial stability, there is a decrease in the induced secondary circulation in tandem with a spinup of the lower-level tangential winds. This intensification appears to be modulated by the low-level radial advection of absolute vorticity.

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Konstantinos Menelaou, M. K. Yau, and Yosvany Martinez

Abstract

In this study, a simple two-dimensional (2D) unforced barotropic model is used to study the asymmetric dynamics of the hurricane inner-core region and to assess their impact on the structure and intensity change. Two sets of experiments are conducted, starting with stable and unstable annular vortices, to mimic intense mature hurricane-like vortices. The theory of empirical normal modes (ENM) and the Eliassen–Palm flux theorem are then applied to extract the dominant wave modes from the dataset and diagnose their kinematics, structure, and impact on the primary vortex.

From the first experiment, it is found that the evolution and the lifetime of an elliptical eyewall, described by a stable annular vortex perturbed by an external wavenumber-2 impulse, may be controlled by the inviscid damping of sheared vortex Rossby waves (VRWs) or the decay of an excited quasimode. The critical radius and structure of the quasimode obtained by the ENM analysis are shown to be consistent with the predictions of a linear eigenmode analysis of small perturbations. From the second experiment, it is found that the outward-propagating VRWs that arise due to barotropic instability and the inward mixing of high vorticity in the unstable annular vortex affect the primary circulation and create a secondary ring of enhanced vorticity that contains a secondary wind maximum. Sensitivity tests performed on the spatial extent of the initial external impulse verifies the robustness of the results. That the secondary eyewall occurs close to the critical radius of some of the dominant modes emphasizes the important role played by the VRWs.

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Konstantinos Menelaou, M. K. Yau, and Yosvany Martinez

Abstract

An analysis of a high-resolution dataset from a realistic simulation of Hurricane Wilma (2005) was performed to understand the mechanism for the formation of a prominent polygonal eyewall and mesovortices during the rapid intensifying stage of the hurricane. The impact of these asymmetries on the intensity change of the hurricane vortex was assessed using the empirical normal mode (ENM) method and Eliassen–Palm (EP) flux calculations.

The results indicated that the eyewall of Wilma exhibited an early azimuthal wavenumber-4 (m = 4) asymmetry followed by a transition to lower-wavenumber asymmetries. The simulated reflectivity and the spatial structure of potential vorticity (PV) anomalies strongly suggest that barotropic instability is the most likely driving mechanism for these asymmetries. From the ENM analysis, it was found that the dominant modes for m = 4 and m = 3 asymmetries are vortex Rossby waves (VRWs) that possess characteristics of unstable modes, supporting the importance of barotropic instability. The EP flux calculations associated with these modes indicate that the VRWs act to decelerate the flow at the initial radius of maximum wind while they act to accelerate the flow radially inside and outside of this location, suggesting that VRWs may provide a positive impact to the intensification of the vortex.

The present results complement previous findings of theoretical and highly idealized numerical studies that a polygonal eyewall and mesovortices are the result of barotropic instability, thereby furnishing a bridge between idealized studies and observations. The work also provides new insight on the role of asymmetries and VRWs in the intensification of hurricanes.

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Georgina Paull, Konstantinos Menelaou, and M. K. Yau

Abstract

Latent heat release from condensational heating has been recognized as one of the dominating energy sources of a tropical cyclone. Here we argue that other microphysical processes may also play an important role. From an analysis of a real-case simulation of Hurricane Katrina (2005), it was found that cooling from evaporation and melting of some frozen hydrometeors radially outside the eyewall region can have similar magnitudes as condensational heating. Based on this finding, idealized thermally forced experiments were performed. The specified heating and cooling functions mimic those found in the Hurricane Katrina run. The results indicated that the addition of cooling enhances the lower-level inward radial winds, which in turn increases the acceleration of the lower-level tangential winds through an enhanced transport of absolute vorticity. Sensitivity experiments on varying the structure of the cooling functions and the background state of the vortex demonstrate that the lower-level tangential wind acceleration is more sensitive to changes in the vertical structure and location of the cooling than the radial characteristics. In addition, the lower-level acceleration is sensitive to variations in the inertial and static stabilities rather than the vertical tangential wind shear of the initial vortex and its environment.

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Konstantinos Menelaou, David A. Schecter, and M. K. Yau
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Konstantinos Menelaou, M. K. Yau, and Tsz-Kin Lai

Abstract

It is known that concentric eyewalls can influence tropical cyclone (TC) intensity. However, they can also influence TC track. Observations indicate that TCs with concentric eyewalls are often accompanied by wobbling of the inner eyewall, a motion that gives rise to cycloidal tracks. Currently, there is no general consensus of what might constitute the dominant triggering mechanism of these wobbles. In this paper we revisit the fundamentals. The control case constitutes a TC with symmetric concentric eyewalls embedded in a quiescent environment. Two sets of experiments are conducted: one using a two-dimensional nondivergent nonlinear model and the other using a three-dimensional nonlinear model. It is found that when the system is two-dimensional, no wobbling of the inner eyewall is triggered. On the other hand, when the third dimension is introduced, an amplifying wobble is evident. This result contradicts the previous suggestion that wobbles occur only in asymmetric concentric eyewalls. It also contradicts the suggestion that environmental wind shear can be the main trigger. Examination of the dynamics along with complementary linear eigenmode analysis revealed the triggering mechanism to be the excitation of a three-dimensional exponentially growing azimuthal wavenumber-1 instability. This instability is induced by the coupling of two baroclinic vortex Rossby waves across the moat region. Additional sensitivity analyses involving reasonable modifications to vortex shape parameters, perturbation vertical length scale, and Rossby number reveal that this instability can be systematically the most excited. The growth rates are shown to peak for perturbations characterized by realistic vertical length scales, suggesting that this mechanism can be potentially relevant to actual TCs.

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