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Sarah C. Jones

Abstract

The ability of dry tropical-cyclone-like vortices to resist vertical shear is discussed. An idealized model calculation is presented in which a dry vortex remains nearly upright during 4 days under the influence of environmental vertical shear. It is shown that the outer portion of the vortex tilts more strongly than the inner core and that the pattern of vertical velocity is related to the vertical tilt of the outer portion of the vortex. This result is discussed with relation to observations of the location of convection in tropical cyclones. An alternative definition of the vortex center is proposed for cases in which the vertical tilt of the vortex is of importance. The average vertical shear across the center of the vortex is shown to depend on both the vortex tilt and the presence of large-scale potential vorticity asymmetries in the outer regions of the vortex. The average vertical shear is a function of time and of the area of the circle over which the averaging is carried out. Thus, the initial environmental shear may not be a reliable measure of the vertical shear felt by the vortex at later times.

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J. Dominique Möller
and
Sarah C. Jones

Abstract

A three-dimensional model is developed, based upon the recently derived asymmetric balance (AB) formulation of Shapiro and Montgomery, to study the evolution of rapidly rotating vortices, including hurricanes. A particular advantage of the AB theory, unlike other balanced models, is its ability to incorporate divergence of the same order as the vorticity. The main assumption of the AB theory is that the squared local Rossby number ≪1, where the squared local Rossby number is defined by the ratio of the orbital frequency squared to the inertial stability. The AB theory leads to a set of prognostic equations that are manipulated so that the first- and second-order local time tendencies can be evaluated diagnostically at a given time. Using the diagnostic version of the AB equations the potential vorticity (PV) distribution from a primitive equation (PE) model is inverted to obtain the corresponding balanced height and wind fields. As far as the authors are aware, this is the first time that the AB equations have been solved in three dimensions.

A calculation is described in which the PE model is initialized with an axisymmetric barotropic vortex in a vertical shear flow. Vertical shear leads to a wavenumber 1 asymmetry in the PV distribution. Associated with this asymmetry is a component of flow across the vortex center, which has an influence on the vortex motion. In this calculation the PE model provides not only the PV distribution but also the data to test the accuracy of the newly derived AB theory. The wavenumber 1 distributions of the radial, tangential, and vertical velocity fields diagnosed using the AB theory are compared with the results of the PE model. The agreement in amplitude and orientation is found to be good. The relative error between the amplitude maxima of the velocities in the PE calculations and the diagnostically derived AB fields is comparable with the maximum size of the squared local Rossby number. Although the main assumption of the AB theory is not strictly satisfied in these calculations, meaningful comparisons can be made between the PE results and the AB solutions. Presenting the results of the velocity fields in the moving coordinate system and use of the piecewise inversion makes it possible to isolate the influence of the upper-level PV anomaly on the lower-level part of the vortex and the influence of the lower-level PV anomaly on the upper-level part of the vortex.

In a further calculation a vortex is initialized in a horizontal shear flow and diabatic heating and friction are included. The prescribed heating is related to the boundary layer convergence. The heating produces strong vertical gradients in the tangential wind so that the PV of the symmetric vortex becomes negative after 24 h. As in the nonlinear balance equations, the AB formulation requires the PV to be positive in order to be able to find a solution.

A comparison between the velocity fields of the PE model and the diagnostically derived AB solutions after 12 h shows a good agreement in amplitude and orientation at lower levels but significant differences in amplitude at upper levels. At upper levels a vortex has not developed after 12 h and the standard Rossby number is the appropriate measure of the validity and accuracy as in the quasigeostrophic approximation. As in the case with no heating the agreement between the velocity components of the AB and PE model depends on the magnitude of the squared local Rossby number or standard Rossby number.

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Leonhard Scheck
,
Sarah C. Jones
, and
Vincent Heuveline

Abstract

In this study the structure and evolution of singular vectors (SVs) for stable and unstable hurricane-like vortices in background flows with horizontal shear are investigated on f and β planes using a nondivergent barotropic model. With increasing shear strength, the singular values for stable vortices increase and the sensitive regions extend farther away from the vortex. The formation of β gyres leads to significant changes in the SV structure but has only weak influence on the singular values. For sufficiently strong anticyclonic shear, the initial SVs are aligned with streamlines connected to stagnation points. The evolved SVs are dominated by dipole structures, indicating a displacement of the vortex. The displacement is caused by the circulation associated with the initial SV perturbation outside of the vortex core, which grows by untilting and unshielding. This process is strongly enhanced by anticyclonic background shear. For both cyclonic and anticyclonic shear, the displacement by the perturbation circulation causes an additional displacement that is proportional to the shear strength. The shear-enhanced barotropic growth mechanism in stable vortices results in singular values that are comparable to those for unstable vortices without background shear. Perturbation growth involving the normal mode in barotropically unstable vortices suffers from background shear. The shear-induced modifications of the outer vortex regions cause a strong decrease of the singular value with increasing shear. For sufficiently strong shear, the SVs for unstable vortices grow by the same mechanism as for stable vortices.

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Leonhard Scheck
,
Sarah C. Jones
, and
Martin Juckes

Abstract

The interaction of a tropical cyclone and a zonally aligned tropopause front is investigated in an idealized framework. A nondivergent barotropic model is used in which the front is represented by a vorticity step, giving a jetlike velocity profile. The excitation of frontal waves by a cyclone located south of the front and the impact of the wave flow on the cyclone motion is studied for different representations of the cyclone and the jet. The evolution from the initial wave excitation until after the cyclone has crossed the front is discussed. The interaction becomes stronger with increasing jet speed. For cyclone representations containing negative relative vorticity, anticyclones develop and can influence the excitation of frontal waves significantly. Resonant frontal waves propagating with a phase speed matching the zonal translation speed of the cyclone are decisive for the interaction. The frontal wave spectrum excited by a cyclone on the front is dominated by waves that are in resonance in the initial phase. These waves have the largest impact on the cyclone motion.

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Leonhard Scheck
,
Sarah C. Jones
, and
Martin Juckes

Abstract

The influence of frontal waves on the interaction of a tropical cyclone and a tropopause front is investigated in an idealized framework. In a nondivergent barotropic model the front is represented by a vorticity step with a superimposed sinusoidal perturbation. This gives rise to a jet that meanders to the north and south and can be viewed as a sequence of upper-level troughs and ridges. The model evolution depends sensitively on the position of the cyclone relative to the troughs and ridges. Here a bifurcation point is identified that is located on the trough axis at a distance where the zonal speed of the background flow equals the phase speed of the wave. Arbitrarily small displacements from this position determine whether a cyclone is advected toward the front or repelled. Only a limited range of wavelengths can lead to track bifurcations. The largest effects are obtained for resonant frontal waves propagating with a phase speed matching the initial zonal translation speed of the cyclone. Weak and large-scale vortices can be disrupted when approaching the bifurcation point, where they are exposed to continuously strong shear deformation.

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Christopher A. Davis
,
Sarah C. Jones
, and
Michael Riemer

Abstract

Simulations of six Atlantic hurricanes are diagnosed to understand the behavior of realistic vortices in varying environments during the process of extratropical transition (ET). The simulations were performed in real time using the Advanced Research Weather Research and Forecasting (WRF) model (ARW), using a moving, storm-centered nest of either 4- or 1.33-km grid spacing. The six simulations, ranging from 45 to 96 h in length, provide realistic evolution of asymmetric precipitation structures, implying control by the synoptic scale, primarily through the vertical wind shear.

The authors find that, as expected, the magnitude of the vortex tilt increases with increasing shear, but it is not until the shear approaches 20 m s−1 that the total vortex circulation decreases. Furthermore, the total vertical mass flux is proportional to the shear for shears less than about 20–25 m s−1, and therefore maximizes, not in the tropical phase, but rather during ET. This has important implications for predicting hurricane-induced perturbations of the midlatitude jet and its consequences on downstream predictability.

Hurricane vortices in the sample resist shear by either adjusting their vertical structure through precession (Helene 2006), forming an entirely new center (Irene 2005), or rapidly developing into a baroclinic cyclone in the presence of a favorable upper-tropospheric disturbance (Maria 2005). Vortex resiliency is found to have a substantial diabatic contribution whereby vertical tilt is reduced through reduction of the primary vortex asymmetry induced by the shear. If the shear and tilt are so large that upshear subsidence overwhelms the symmetric vertical circulation of the hurricane, latent heating and precipitation will occur to the left of the tilt vector and slow precession. Such was apparent during Wilma (2005).

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Simon T. K. Lang
,
Sarah C. Jones
,
Martin Leutbecher
,
Melinda S. Peng
, and
Carolyn A. Reynolds

Abstract

The sensitivity of singular vectors (SVs) associated with Hurricane Helene (2006) to resolution and diabatic processes is investigated. Furthermore, the dynamics of their growth are analyzed. The SVs are calculated using the tangent linear and adjoint model of the integrated forecasting system (IFS) of the European Centre for Medium-Range Weather Forecasts with a spatial resolution up to TL255 (~80 km) and 48-h optimization time. The TL255 moist (diabatic) SVs possess a three-dimensional spiral structure with significant horizontal and vertical upshear tilt within the tropical cyclone (TC). Also, their amplitude is larger than that of dry and lower-resolution SVs closer to the center of Helene. Both higher resolution and diabatic processes result in stronger growth being associated with the TC compared to other flow features. The growth of the SVs in the vicinity of Helene is associated with baroclinic and barotropic mechanisms. The combined effect of higher resolution and diabatic processes leads to significant differences of the SV structure and growth dynamics within the core and in the vicinity of the TC. If used to initialize ensemble forecasts with the IFS, the higher-resolution moist SVs cause larger spread of the wind speed, track, and intensity of Helene than their lower-resolution or dry counterparts. They affect the outflow of the TC more strongly, resulting in a larger downstream impact during recurvature. Increasing the resolution or including diabatic effects degrades the linearity of the SVs. While the impact of diabatic effects on the linearity is small at low resolution, it becomes large at high resolution.

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