Radial-vertical Circulation Research Articles

On the forced tangentially-averaged radial-vertical circulation within vortices. Part II: The transformation of Tropical Storm Haima (2004)

A real case study for the transformation of Tropical Storm (TS) Haima (2004) into an extratropical cyclone (EC) is carried out numerically since, after landfall, Haima (2004) (as an EC) brought severe weather to a large area (from the south to the north) in China during 13–16 September 2004. With the linear diagnostic model (derived in a previous study) for the tangentially-averaged radial-vertical circulation within vortices moving on the spherical Earth, Haima’s (2004) life cycle is reconstructed noticeably well. Therefore, the major contributor could be identified confidently for Haima’s (2004) extratropical transition based on the diagnostic model outputs. The quantitative comparison shows that up to a 90% contribution to the innerregion updraft and a 55% contribution to the upper-layer outflow come from latent heating during Haima’s (2004) TS stage. Up to a 90% contribution to the inner-region updraft and nearly a 100% contribution to the upper-layer outflow come from the upper-layer eddy angular momentum advection (EAMA) during Haima’s (2004) EC stage. Representing the asymmetric structure of the storm, the predominantly positive contribution of the upper-layer EAMA to Haima’s (2004) transformation is closely associated with the Sshaped westerlies in the upper layer with two jets. One jet in the cyclonic-curvature area carries cyclonic angular momentum into the storm, and the other jet in the anticyclonic-curvature area carries anticyclonic angular momentum out of the storm. Consequently, the newly-increased cyclonic tangential wind is deflected by the Coriolis force to the right to form the upper-layer outflow accompanied by the central-area rising motion, leading to Haima’s (2004) extratropical transition after its landfall.

Mesoscale Aspects of the Downshear Reformation of a Tropical Cyclone

Abstract The downshear reformation of Tropical Storm Gabrielle (2001) was investigated using radar reflectivity and lightning data that were nearly continuous in time, as well as frequent aircraft reconnaissance flights. Initially the storm was a marginal tropical storm in an environment with strong 850–200-hPa vertical wind shear of 12–13 m s−1 and an approaching upper tropospheric trough. Both the observed outflow and an adiabatic balance model calculation showed that the radial-vertical circulation increased with time as the trough approached. Convection was highly asymmetric, with almost all radar return located in one quadrant left of downshear in the storm. Reconnaissance data show that an intense mesovortex formed downshear of the original center. This vortex was located just south of, rather than within, a strong downshear-left lightning outbreak, consistent with tilting of the horizontal vorticity associated with the vertical wind shear. The downshear mesovortex contained a 972-hPa minimum central pressure, 20 hPa lower than minimum pressure in the original vortex just 3 h earlier. The mesovortex became the new center of the storm, but weakened somewhat prior to landfall. It is argued that dry air carried around the storm from the region of upshear subsidence, as well as the direct effects of the shear, prevented the reformed vortex from continuing to intensify. Despite the subsequent weakening of the reformed center, it reached land with greater intensity than the original center. It is argued that this intensification process was set into motion by the vertical wind shear in the presence of an environment with upward motion forced by the upper tropospheric trough. In addition, the new center formed much closer to the coast and made landfall much earlier than predicted. Such vertical-shear-induced intensity and track fluctuations are important to understand, especially in storms approaching the coast.

On the forced tangentially-averaged radial-vertical circulation within vortices part I: Concepts and equations

A linear partial differential equation is derived in cylindrical-isobaric coordinates on the earth for the diagnostic study of the tangentially-averaged radial-vertical circulation within translating vortices. In the hydrodynamic stable atmosphere, the circulation will be forced through many dynamic and thermodynamic processes. These processes are associated with frictional torque, inertial torque, the horizontal and vertical divergence of eddy angular momentum, diabatic heating, adiabatic heating, and eddy temperature advection. For a given forcing, the intensity of circulation will increase with the decrease of static, inertial, and baroclinic stabilities. This paper also presents an explanation on the data interpolation from the latitude-longitude grid to the vortex volume gird and a brief discussion on the forcing processes.

The role of diabatic heating, torques and stabilities in forcing the radial-vertical circulation within cyclones part ii: case study of extratropical and tropical cyclones

Utilizing Eliassen's concepts, the forcing of the isentropic azimuthally-averaged mass-weighted radial-vertical circulation by diabatic heating and torques within an extratropical cyclone and a typhoon was studied through numerical simulations based on the linear diagnostic equation derived previously. The structure of the forcing associated with diabatic heating and torques was determined from quasi-Lagrangian diagnostic analyses of actual case studies. The two cyclones studied were the Ohio extratropical cyclone of 25-27 January 1978 and typhoon Nancy of 18-23 September 1979. The Ohio cyclone, which formed over the Gulf Coast and moved through Ohio and eastern Michigan, was one of the most intense storms with blizzard conditions to ever occur in this region. Typhoon Nancy which occurred over the South China Sea during the FGGE year was selected since relatively high quality assimilated data were available. Within the Ohio cyclone, the dominant internal processes forcing the mean circulation with embedded relatively strong hydrodynamic stability were the pressure torque associated with baroclinic (asymmetric) structure and the horizontal eddy angular momentum transport associated with the typical S-shaped thermal and wind structures of self-development. Within typhoon Nancy, the dominant internal process forcing the mean circulation with embedded weak hydrodynamic stability was the latent heat release. This analysis shows that the simulated azimuthally-averaged mass-weighted radial motions within these two cyclones agree quite well with the “ observed≓ azimuthally-averaged mass-weighted radial motions. This isentropic numerical study also provides insight into the relatively important internal forcing processes and the trade off between forcing and stability within both extratropical and tropical cyclones.

On the forcing of the radial-vertical circulation within cyclones—part 1: concepts and equations

Following the theoretical result of Eliassen, the Sawyer-Eliassen equation for frontal circulations and the equation for forcing the meridional circulation within a circumpolar vortex are extended in isentropic coordinates to des-cribe the forcing of the azimuthally averaged mass-weighted radial-vertical circulation within translating extratropical and tropical cyclones. Several physical processes which are not evident in studies employing isobaric coordinates are isolated in this isentropic study. These processes include the effects of pressure torque, inertial torque and storm translation that are associated with the asymmetric structure in isentropic coordinates. This isentropic study also includes the effects of eddy angular momentum transport, diabatic heating and frictional torque that are common in both isentropic and isobaric studies. All of the processes are modulated by static, inertial and baroclinic stabilities.

The Formation of Hurricane Frederic of 1979

A high-resolution global model forecast of the formation of Hurricane Frederic of 1979 is analyzed by means of several diagnostic computations on the model's output history. The formation is addressed from an analysis of limited-area energetics where the growth of eddy kinetic energy is examined. The question on internal versus external forcing during the formative stage of the hurricane is explored by means of the Kuo-Eliassen framework for the radial-vertical circulation of the hurricane. The intensity of the predicted hurricane is diagnosed from a detailed angular momentum budget following the three-dimensional motion of parcels arriving at the maximum wind belt. Overall, the successful simulation of the hurricane has enabled us to make such a detailed diagnosis of the predicted hurricane at a high resolution. The principal findings of this study are that a north-south-oriented beating function maintained a zonal easterly flow that supplied energy barotropically during the growth of an African wave. The growth of eddy kinetic energy is somewhat monotonic and slow throughout the history of the computations. The initial development of the easterly wave appears to be related to the widespread weak convective heating that contributes to a covariance of heating and temperature and of temperature and vertical velocity. The hurricane development period is seen as one where both the barotropic and convective processes contribute to the growth of eddy kinetic energy. During this developing stage, the growth of radial-vertical circulation is largely attributed to convective, radiative, and frictional forcings. The role of eddy convergence of momentum flux appears to be insignificant. The intensity issue of the storm (maximum wind of the order of 37 m s−1) was addressed by means of a detailed angular momentum budget following parcel motion. The pressure torque in the model simulation had a primary role in explaining the intensity of the predicted storm. It is only in the storm's inner rain area where the frictional stress becomes quite large. But at these small radii the frictional torque is still smaller compared to the contribution from the (small but significant) azimuthal asymmetries of the pressure field and the resulting pressure torques.

Numerical simulation of tropical-cyclone circulation using Arakawa-Schubert cumulus parameterization

Tropical cyclone is simulated from a weak balanred vortex in a numerical model using Arakawa-Schubert cumulus parameterization scheme. A six-level axisymmetric primitive equation model incorporating the cumulus effects is designed for this study. The model consists of four layers in the free atmosphere and one layer for a mixed layer. Three cloud types with tops at 12 km, 8 km and 4 km are possible to form in this model. The results of this numerical experiment clearly indicate the development of a tropical cyclone and the model-derived circulation and structure of the cyclone agree with the observed features. The intensification of the cyclone, the development of radial-vertical circulation and the formation of the eye are well simulated in this experiment. It may be inferred that this parameterization scheme realistically produces tropical-cyclone circulation and will be useful in studies of tropical systems.

Budget Analysis of a Tropical Cyclone Simulated in an Axisymmetric Numerical Model

A tropical cyclone simulated in an axisymmetric numerical model is analyzed in detail from various aspects in order to deepen the understanding of the basic mechanisms of its evolution. Namely, the budget equations of temperature, moisture, relative angular momentum, vorticity, radial-vertical circulation, and kinetic energy are investigated for the different stages of the development of a tropical cyclone. The spatial distributions of each term in the budget equations are shown and their role in the following processes are discussed. In the pre-deepening stage of a large weak vortex in a conditionally unstable atmosphere, a solenoidal field is formed as a result of a delicate heat budget which depends on the static stability and the moisture content. The baroclinicity field thus established drives the system into a deepening stage. A positive feedback process builds up a warm moist core, accelerates the radial-vertical circulation, and intensifies the moist convection. A net outflow of mass from the central region and a resultant drop of central surface pressure take place during this period. The relative angular momentum of the inner column as a whole increases through convergence of relative angular momentum. In terms of relative vorticity, intensification and shrinking of the vortex is due to the combined effects of advection, horizontal convergence and twisting. At the end of the deepening stage, conditional instability in the central region is neutralized. The moment due to Coriolis force acting on the intensified azimuthal flow counterbalances the baroclinicity vector, so that the acceleration of radial-vertical flow ceases. Concentration of relative angular momentum and vorticity in the central region also levels off. In the budget of these quantities, the role of both vertical and lateral steam becomes important. In the troposphere, except the upper part and the boundary layer, the gradient wind relationship is established between the pressure field and the azimuthal flow. In the mature stage, the status in the inner region is quasi-stationary while that of the outer area keeps changing slowly. The importance of evaporation at the central area for the maintenance of an intense tropical cyclone is demonstrated in an additional experiment.

Structure of a Tropical Cyclone Developed in a Three-Dimensional Numerical Simulation Model

Abstract A three-dimensional, 11-level, primitive equation model has been constructed for a simulation study of tropical cyclones. The model has four levels in the boundary layer and its 70×70 variable grid mesh encloses a 4000-km square domain with a 20-km resolution near the center. Details of the model, including the parameterization scheme for the subgrid-scale diffusion and convection processes, are described. A weak vortex in the conditionally unstable tropical atmosphere is given as the initial state for a numerical integration from which a tropical cyclone develops in the model. During the integration period of one week, the sea surface temperature is fixed at 302K. The central surface pressure drops to about 940 mb, while a warm moist core is established. The azimuthal component of mean horizontal wind is maximum at about 60 km from the center at all levels. A strong in-flow is observed in the boundary layer. At upper levels, a secondary radial-vertical circulation develops in and around the regi...