[1] Convectively coupled equatorial waves (CCEWs) control a substantial fraction of tropical rainfall variability. Their horizontal structures and dispersion characteristics correspond to Matsuno's (1966) solutions of the shallow water equations on an equatorial beta plane, namely, Kelvin, equatorial Rossby, mixed Rossby-gravity, and inertio-gravity waves. Because of moist processes, the tilted vertical structures of CCEWs are complex, and their scales do not correspond to that expected from the linear theory of dry waves. The dynamical structures and cloud morphology of CCEWs display a large degree of self-similarity over a surprisingly wide range of scales, with shallow convection at their leading edge, followed by deep convection and then stratiform precipitation, mirroring that of individual mesoscale convective complexes. CCEWs have broad impacts within the tropics, and their simulation in general circulation models is still problematic, although progress has been made using simpler models. A complete understanding of CCEWs remains a challenge in tropical meteorology.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2008RG000266

Convectively-coupled equatorial waves

A series of numerical simulations of tropical cyclones in idealized large-scale environments is performed to examine the effects of vertical wind shear on the structure and intensity of hurricanes. The simulations are performed using the nonhydrostatic Pennsylvania State University‐National Center for Atmospheric Research fifth-generation Mesoscale Model using a 5-km fine mesh and fully explicit representation of moist processes. When large-scale vertical shears are applied to mature tropical cyclones, the storms quickly develop wavenumber one asymmetries with upward motion and rainfall concentrated on the left side of the shear vector looking downshear, in agreement with earlier studies. The asymmetries develop due to the storm’s response to imbalances caused by the shear. The storms in shear weaken with time and eventually reach an approximate steady-state intensity that is well below their theoretical maximum potential intensity. As expected, the magnitude of the weakening increases with increasing shear. All of the storms experience time lags between the imposition of the large-scale shear and the resulting rise in the minimum central pressure. While the lag is at most a few hours when the storm is placed in very strong (15 m s21) shear, storms in weaker shears experience much longer lag times, with th e5ms 21 shear case showing no signs of weakening until more than 36 h after the shear is applied. These lags suggest that the storm intensity is to some degree predictable from observations of largescale shear changes. In all cases both the development of the asymmetries in core structure and the subsequent weakening of the storm occur before any resolvable tilt of the storm’s vertical axis occurs. It is hypothesized that the weakening of the storm occurs via the following sequence of events: First, the shear causes the structure of the eyewall region to become highly asymmetric throughout the depth of the storm. Second, the asymmetries in the upper troposphere, where the storm circulation is weaker, become sufficiently strong that air with high values of potential vorticity and equivalent potential temperature are mixed outward rather than into the eye. This allows the shear to ventilate the eye resulting in a loss of the warm core at upper levels, which causes the central pressure to rise, weakening the entire storm. The maximum potential vorticity becomes concentrated in saturated portions of the eyewall cloud aloft rather than in the eye. Third, the asymmetric features at upper levels are advected by the shear, causing the upper portions of the vortex to tilt approximately downshear. The storm weakens from the top down, reaching an approximate steady-state intensity when the ventilated layer can descend no farther due to the increasing strength and stability of the vortex at lower levels.

Effects of Vertical Wind Shear on the Intensity and Structure of Numerically Simulated Hurricanes

In this paper we examine further the physics of vortex axisymmetrization, with the goal of elucidating the dynamics of outward-propagating spiral bands in hurricanes. the basic shysics is illustrated most simply for stable vorticity monopoles on an f-plane. Unlike the dynamics of sheared disturbances in rectilinear shear flow, axisymmetrizing disturbances on a vortex are accompanied by outward-propagating vortex Rossby-waves whose restoring mechanism is associated with the radial gradient of storm vorticity. Expressions for both phase and group velocities are derived and verified; they confirm earlier speculations on the existence of vortex Rossbywaves in hurricanes. Effects of radially propagating vortex Rossby-waves on the mean vortex are also analysed. In conjunction with sustained injection of vorticity near the radius of maximum winds, these results reveal a new mechanism of vortex intensification. the basic theory is then applied to a hurricane-like vortex in a shallow-water asymmetric-balance model. the wave mechanics developed here shows promise in elucidating basic mechanisms of hurricane evolution and structure changes, such as the formation of secondary eye-walls. Radar observations possessing adequate temporal resolution are consistent with the predictions of this work, though more refined observations are needed to quantify further the impact of mesoscale banded disturbances on the evolution of the hurricane vortex.

A theory for vortex rossby-waves and its application to spiral bands and intensity changes in hurricanes

Real-time forecasts of five landfalling Atlantic hurricanes during 2005 using the Advanced Research Weather Research and Forecasting (WRF) (ARW) Model at grid spacings of 12 and 4 km revealed performance generally competitive with, and occasionally superior to, other operational forecasts for storm position and intensity. Recurring errors include 1) excessive intensification prior to landfall, 2) insufficient momentum exchange with the surface, and 3) inability to capture rapid intensification when observed. To address these errors several augmentations of the basic community model have been designed and tested as part of what is termed the Advanced Hurricane WRF (AHW) model. Based on sensitivity simulations of Katrina, the inner-core structure, particularly the size of the eye, was found to be sensitive to model resolution and surface momentum exchange. The forecast of rapid intensification and the structure of convective bands in Katrina were not significantly improved until the grid spacing ap...

/pdf/prediction-of-landfalling-hurricanes-with-the-advanced-zhep826sm6.pdf

Prediction of Landfalling Hurricanes with the Advanced Hurricane WRF Model

The behaviour of initially-barotropic vortices in vertically-sheared environmental flows is investigated. the strength and structure of the vortices used are representative of tropical cyclones. the calculations are performed using a primitive-equation numerical model on an f-plane. It is found that the initial response of the vortex to the vertical shear is to tilt in the plane of the shear. As soon as a tilt is established, the upper- and lower-level centres begin to rotate cyclonically about the mid-level centre. This rotation can be understood in terms of upper- and lower-level potential-vorticity anomalies which are displaced in the horizontal relative to one another. the flow associated with the vertical projection of each anomaly advects the other anomaly, leading to the observed cyclonic rotation. the rotation rate decreases with time, so that the direction of tilt becomes constant, but the magnitude of the tilt continues to increase. We argue that the observed rotation acts to oppose the destructive action of the vertical shear on the vortex, even in the absence of diabatic processes.

The role of the vertical circulation is considered in detail. It is shown that the vertical circulation develops in a manner which is consistent with the model flow remaining balanced. It is found that the mesoscale nature of the vertical circulation leads to a distortion of the axisymmetric vortex. This results in the inner core having a smaller vertical tilt than the outer region. the vertical circulation does not act on a large enough scale to explain why the vortex is not destroyed by the vertical shear.

The behaviour of the vortex is found to depend on various parameters. Results are presented where the vertical shear, the strength and size of the vortex, the Coriolis parameter, and the static stability are varied. With the exception of the vertical shear, altering any of these parameters alters the vertical penetration of a potential-vorticity anomaly. the results show that increasing the penetration depth leads to an increase in the rotation rate of the upper- and lower-level vortex centres about the mid-level centre, and to a reduction in the magnitude of the vertical tilt.

The evolution of vortices in vertical shear. I: Initially barotropic vortices

The β-effect on tropical cyclone motion is studied using an analytical as well as a numerical model in a nondivergent barotropic framework. The analytical model and the linear version of the numerical model give essentially the same result: the linear β-effect causes a westward stretching of the model vortex but no significant movement of the vortex center. An east-west asymmetry in the meridional wind field is also created. It is the inclusion of the nonlinear term that produces the northwestward movement of the vortex previously found by other investigators (e.g., Kitade, 1981). This northwestward movement increases with both the maximum wind speed and the radius of maximum wind in a constant-shape vortex. A wind maximum is also found to the northeast of the vortex, which appears to be consistent with the observational findings of Shea and Gray. This asymmetry plays an important role in the vortex motion.

Analytical and Numerical Studies of the Beta-Effect in Tropical Cyclone Motion. Part I: Zero Mean Flow

An important issue in the formation of concentric eyewalls in a tropical cyclone is the development of a symmetric structure from asymmetric convection. It is proposed herein, with the aid of a nondivergent barotropic model, that concentric vorticity structures result from the interaction between a small and strong inner vortex (the tropical cyclone core) and neighboring weak vortices (the vorticity induced by the moist convection outside the central vortex of a tropical cyclone). The results highlight the pivotal role of the vorticity strength of the inner core vortex in maintaining itself, and in stretching, organizing, and stabilizing the outer vorticity field. Specifically, the core vortex induces a differential rotation across the large and weak vortex to strain out the latter into a vorticity band surrounding the former. The straining out of a large, weak vortex into a concentric vorticity band can also result in the contraction of the outer tangential wind maximum. The stability of the out...

/pdf/the-formation-of-concentric-vorticity-structures-in-typhoons-2ssl6y7o5j.pdf

The formation of concentric vorticity structures in typhoons

An elliptical eye that rotated cyclonically with a period of approximately 144 minutes in Typhoon Herb 1996 was documented. The elliptical region had a semimajor axis of 30 km and a semiminor axis of 20 km. Two complete periods of approximately 144 min were observed in the Doppler radar data. The rotation of the elliptical eye in the context of barotropic dynamics at three levels were explored: linear waves on a Rankin vortex, a nonlinear Kirchhoff vortex, and with a nonlinear spectral model. The linear wave theory involves the existence of both the high (potential) vorticity gradient near the eye edge and the cyclonic mean tangential flow in the typhoon. The propagation of (potential) vorticity waves in the cyclonic mean flow makes the elliptical eye rotate cyclonically. The rotation period is longer than the period of a parcel trajectory moving in the cyclonic mean flow around the circumference, because the vorticity wave propagates upwind. The nonlinear theory stems from the rotation of Kirchhoff’s vortex. Estimates of the eye rotation period from both linear and nonlinear theories agree with observations of the eye rotation period when the observed maximum wind from Herb is used. Nonlinear numerical computations suggest the importance of the interaction of neutral vorticity waves, which determine the shape and the rotation period of the eye. The calculations also support the rotation of the eye in approximately 144 min in the presence of axisymmetrization, vorticity redistribution, wave breaking, and vortex merging processes.

/pdf/a-possible-mechanism-for-the-eye-rotation-of-typhoon-herb-2kj40wcgrd.pdf

A Possible Mechanism for the Eye Rotation of Typhoon Herb

The interactions between monsoon circulations and tropical disturbances in the Northwest Pacific, where the low-level mean flow is westerly in the west and easterly in the east, are studied with a barotropic model. The authors’ model results suggest that the scale contraction by the confluent background flow, the nonlinear dynamics, the β effect, and the large-scale convergence are important for the energy and enstrophy accumulation near the region where the zonal flow reverses. The energy/enstrophy accumulation can be maintained with a continuous Rossby wave emanation upstream. The largest accumulation occurs when the emanating zonal wavelength is around 2000 km. Longer Rossby waves experience less scale contraction and nonlinear effects while shorter Rossby waves cannot hold a coherent structure against dispersive effects. The nonlinear energy/enstrophy accumulation mechanism is significantly different from previous linear energy accumulation theories. In the linear theories this is primarily a...

/pdf/rossby-waves-in-zonally-opposing-mean-flow-behavior-in-j4i3cvw4mx.pdf

Rossby Waves in Zonally Opposing Mean Flow: Behavior in Northwest Pacific Summer Monsoon

Tropical cyclones and dynamically similar model vortices robustly maintain a near-axisymmetric horizontal structure where the vortex flow is strongly nonlinear in spite of persistent asymmetric forcing represented by horizontal variations in the environmental winds and the Coriolis parameter. Since tropical cyclone motion relative to environmental “steering” has been associated with vortex asymmetries in even the simplest numerical models, identification of a barotropic mechanism that stabilizes vortices to dispersive influences is important. A nondivergent, barotropic analytical model is used to identify the asymmetry-damping influence of symmetric angular windshear as the mechanism by which a barotropic vortex resists asymmetric forcing. Solutions are obtained for the evolution of linear asymmetric perturbations imposed as initial conditions on a steady, Rankine vortical flow. Perturbations combining various radial and azimuthal structures that might be expected from environmental and convectiv...

R. T. Williams

Papers

Analytical and Numerical Studies of the Beta-Effect in Tropical Cyclone Motion. Part I: Zero Mean Flow

The formation of concentric vorticity structures in typhoons

A Possible Mechanism for the Eye Rotation of Typhoon Herb

Rossby Waves in Zonally Opposing Mean Flow: Behavior in Northwest Pacific Summer Monsoon

Barotropic Vortex Stability to Perturbations from Axisymmetry