Absolute Angular Momentum Research Articles

Analysis of the Wind Field Evolution Associated with the Extratropical Transition of Bonnie (1998)

Abstract Extratropical transition brings about a number of environmentally induced structural changes within a transitioning tropical cyclone. Of particular interest among these changes is the acceleration of the wind field away from the cyclone’s center of circulation along with the outward movement of the radial wind maximum, together termed wind field expansion. Previous informal hypotheses aimed at understanding this evolution do not entirely capture the observed expansion, while a review of the literature shows no formal work done upon the topic beyond analyzing its occurrence. This study seeks to analyze the physical and dynamical mechanisms behind the wind field expansion using model simulations of a representative transition case, North Atlantic Tropical Cyclone Bonnie of 1998. The acceleration of the wind field along the outer periphery of the cyclone is found to be a function of the net import of absolute angular momentum within the cyclone’s environment along inflowing trajectories. This evolution is shown to be a natural outgrowth of the development of isentropic conveyor belts and asymmetries associated with extratropical cyclones. Asymmetries in the outer-core wind field manifest themselves via the tightening and development of height and temperature gradients within the cyclone’s environment. Outward movement of the radial wind maximum occurs coincident with integrated net cooling found inside the radius of maximum winds. Tests using a secondary circulation balance model show the radial wind maximum evolution to be similar yet opposite to the response noted for intensifying tropical cyclones with contracting eyewalls.

A Barotropic Model of the Angular Momentum–Conserving Potential Vorticity Staircase in Spherical Geometry

Abstract An idealized analytical model of the barotropic potential vorticity (PV) staircase is constructed, constrained by global conservation of absolute angular momentum, perfect homogenization of PV in mixing zones between (prograde) westerly jets, and the requirement of barotropic stability. An imposed functional relationship is also assumed between jet speed and latitudinal separation using a multiple of the “dynamical Rossby wave” Rhines scale inferred from the strength of westerly jets. The relative simplicity of the barotropic system provides a simple relation between absolute angular momentum and PV (or absolute vorticity). A family of solutions comprising an arbitrary number of jets is constructed and is used to illustrate the restriction of jet spacing and strength imposed by the constraints of global conservation of angular momentum and barotropic stability. Asymptotic analysis of the theoretical solution indicates a limiting ratio of jet spacing to the dynamical Rhines scale equal to the square root of 6, meaning that westerly jets are spaced farther apart than predicted by the dynamical Rhines scale. It is inferred that an alternative “geometrical” Rhines scale for jet spacing can be obtained from conservation of absolute angular momentum on the sphere if the strength of zonal jets is known from other considerations. Numerical simulations of the full (nonaxisymmetric) equations reveal a pattern of zonal jet evolution that is consistent with our construction of ideal PV staircases in spherical geometry (which can be considered as limiting cases), as well as with the asymptotic analysis of a geometrical Rhines scale. The evolution of the PV staircase originating from an upscale cascade of energy in the barotropic model is therefore seen to depend on conservation of energy (for the strength of jets) and conservation of absolute angular momentum (for the spacing and number of jets). Further analysis of the numerical results confirms a “Taylor identity” relating the flux of eddy potential vorticity to mean-flow acceleration. Eddy fluxes are responsible for the occasional transitions between mode number as well as for maintaining the sharp westerly jets against small-scale dissipation. Suggestions are made for extending the theoretical model to PV staircases that are asymmetric between hemispheres or with latitudinal variation of amplitude, as modeled in the shallow-water system.

A Climatology of the Tropospheric Thermal Stratification Using Saturation Potential Vorticity

AbstractThe condition of convective neutrality is assessed in the troposphere by calculating the saturation potential vorticity P* from reanalysis data. Regions of the atmosphere in which saturation entropy is constant along isosurfaces of absolute angular momentum, a state indicative of slantwise-convective neutrality, have values of P* equal to zero. In a global reanalysis dataset spanning the years 1970–2004, tropospheric regions are identified in which P* is near zero, implying that vertical convection or slantwise convection may be important in determining the local thermal stratification. Convectively neutral air masses are common not only in the Tropics but also in higher latitudes, for example, over midlatitude continents in summer and in storm tracks over oceans in winter. Large-scale eddies appear to stabilize parts of the lower troposphere, particularly in winter.

Modeling the Effects of Land–Sea Roughness Contrast on Tropical Cyclone Winds

Abstract The fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) is used to simulate tropical cyclone (TC) wind distribution near landfall. On an f plane at 15°N, the effects of the different surface roughness between the land and sea on the wind asymmetry is examined under a strong constraint of a dry atmosphere and time-invariant axisymmetric mass fields. The winds are found to adjust toward a steady state for prelandfall (50, 100, and 150 km offshore), landfall, and postlandfall (50, 100, and 150 km inland) TC positions. The TC core is asymmetric even when it lies completely offshore or inland. The surface (10 m) wind asymmetry at the core for pre- (post) landfall position is apparently related to the acceleration (deceleration) of the flow that has just moved over the sea (land) as a response to the sudden change of surface friction. For prelandfall TC positions, the resulted strong surface inflow to the left and front left (relative to the direction pointing from sea to land) also induces a tangential (or total) wind maxima at a smaller radius, about 90° downstream of the maximum inflow, consistent with the absolute angular momentum advection (or work done by pressure). The surface maximum wind is of similar magnitude as the gradient wind. There is also a small region of weak outflow just inside the wind maxima. For postlandfall TC positions, inflow is weakened to the right and rear right associated with the onshore flow. Both onshore and offshore flows affect the surface wind asymmetry of the core in the landfall case. Above the surface and near the top of the planetary boundary layer (PBL), the wind is also asymmetric and a strongly supergradient tangential wind is primarily maintained by vertical advection of the radial wind. Much of the steady-state vertical structure of the asymmetric wind is similar to that forced by the motion-induced frictional asymmetry, as found in previous studies. The associated asymmetry of surface and PBL convergences has radial dependence. For example, the landfall case has stronger PBL convergence to the left for the 0–50-km core region, due to the radial inflow, but to the right for the 100–500-km outer region, due to the tangential wind convergence along the coastline. The strong constraint is then removed by considering an experiment that includes moisture, cumulus heating, and the free adjustments of mass fields. The TC is weakening and the sea level pressure has a slightly wavenumber-1 feature with larger gradient wind to the right than to the left, consistent with the drift toward the land. The asymmetric features of the wind are found to be very similar to those in the conceptual experiments.

Inertial instability in rotating and stratified fluids: barotropic vortices

The unfolding of inertial instability in intially barotropic vortices in a uniformly rotating and stratified fluid is studied through numerical simulations. The vortex dynamics during the instability is examined in detail. We demonstrate that the instability is stabilized via redistribution of angular momentum in a way that produces a new equilibrated barotropic vortex with a stable velocity profile. Based on extrapolations from the results of a series of simulations in which the Reynolds number and strength of stratification are varied, we arrive at a construction based on angular momentum mixing that predicts the infinite-Reynolds-number form of the equilibrated vortex toward which inertial instability drives an unstable vortex. The essential constraint is conservation of total absolute angular momentum. The construction can be used to predict the total energy loss during the equilibration process. It also shows that the equilibration process can result in anticyclones that are more susceptible to horizontal shear instabilities than they were initially, a phenomenon previously observed in laboratory and numerical studies.

Impacts of Ice Phase Processes on Tropical Cyclone Development

Idealized cloud-resolving simulations with the horizontal resolution of 2 km are carried out to investigate effects of ice-phase processes on the development and structures of tropical cyclones (TCs). A comparison between cold-rain and warm-rain simulations shows that ice-phase processes delay the TC organization, and decrease the area-averaged kinetic energy. The ice-phase processes also shrink the TC size; for example, the radius of the storm-force wind area (over 25 m s−1) in the cold-rain simulation is two-thirds of that in the warm-rain one.The TC evolution depends greatly on strong cooling due to melting and sublimation of snow and graupel around the melting layer outside of the TC eyewall. The cooling reduces the pressure gradient below the melting level, and weakens the inflow toward the TC center. It suppresses the inward transport of high absolute angular momentum (AAM), and decreases the energy conversion rate from the available potential energy to kinetic energy of axisymmetric flows. As a result, the reduction of AAM around the eyewall shrinks the TC eyewall size, and the reduction of energy conversion rate delays the TC organization.The influence of the terminal fall velocities ofsnow and graupel is also examined by performing sensitivity experiments, with the horizontal resolution of 5 km. The results show that the increased terminal fall velocity lowers the actual melting altitude, and enhances the TC development through the change in the vertical profile of diabatic heating.

A GCM Study on the Roles of the Seasonal Marches of the SST and Land-Sea Thermal Contrast in the Onset of the Asian Summer Monsoon

The influences of the SST and land surface temperature on the onset of the Asian summer monsoon are studied by using an atmospheric GCM, Global Spectral Model (GSM) of Japan Meteorological Agency (JMA). After confirming from five-year control run with the climatological SST that the model performs the Asian summer monsoon well, we make the impacts of two kinds of main experiments, i.e., SST fixed run and solar fixed run, focusing on the Asian summer monsoon onset.In the SST fixed run, the model is run from Apri1 lst until June 30th under the SST, which is fixed at the value of April 1st. To see impacts systematically, an ensemble average over five cases is compared with that of the control run. The fixed SST considerably reduces the Somali jet, the cross equatorial water vapor transport, the northern-hemispheric evaporation, and then suppresses the ITCZ jump from the southern hemisphere to the northern hemisphere. It also reduces the low-level westerlies from Southeast Asia, which brings the monsoon onset. In the solar fixed run, the model is run from April 1st until June 30th under the solar condition, which is fixed at that of April 1st. The fixed solar condition reduces the land-sea thermal contrast, suppresses the heat low over the continent, and reduces low level westerlies in a geostrophic sense.The above experiments indicate that both land-sea thermal contrast and SST considerably contribute to the onset of the Asian summer monsoon. The land-sea thermal contrast induces low-level wind surrounding the Eurasian continent, and makes a primary contribution to the formation of the Asian monsoon westerlies. The seasonal march of the SST destabilizes the stratification, induces the ITCZ jump from the southern to the northern hemisphere, strengthens the Hadley circulation, and then enhances the monsoon westerlies through effective transport of the absolute angular momentum.

Absolute angular momentum generation & its vertical transport in the field of mid-tropospheric cyclones

A quasi-stationary synoptic system is usually seen on the weather charts during southwest monsoon period over the north-east Arabian Sea and adjoining area of Gujarat and north Konkan. The transport of absolute angular momentum, for the atmospheric weather systems, plays a significant role during the southwest monsoon period.
 In this paper, the mean absolute angular momentum and its vertical transport associated with MTC have been discussed. The expected accumulation of momentum throughout the troposphere upto 800 km around the centre of MTC has been calculated and displayed. The transport of angular momentum to the underlying surface and momentum loss or gain has also been discussed. Estimates have been made of surface stress by means of angular momentum transferred.
 The study reveals that the flux of angular momentum found to be dominated mostly between surface and 500 hPa and the values of shearing stress are positive from the centre of MTC to 500 km.

Derivation of the Equations of Atmospheric Motion in Oblate Spheroidal Coordinates

Since Earth is more nearly an oblate spheroid than a sphere, it is of at least theoretical interest to develop the atmospheric equations of motion in spheroidal coordinates. In this system the horizontal unit vectors are oriented eastward and northward along the surfaces of ellipsoids, while the orthogonal unit vector is oriented vertically along the surfaces of intersecting confocal hyperboloids. Using the theory of orthogonal curvilinear coordinates, the spheroidal equations of relative atmospheric motion are derived from the vector equation of absolute motion. With the exception of two terms in the meridional and vertical equations of motion that are unique to the spheroidal system, all of the metric and rotational terms in the spheroidal system correspond to those found in the familiar spherical formulation, but now have coefficients that are functions of both the spheroidal latitude and elevation. The unique spheroidal terms arise from the resolution of the difference between the directions of apparent gravity and Newtonian gravitation, which is neglected in the spherical formulation. The complete spheroidal equations conserve both absolute angular momentum and total kinetic energy, and in the limit as Earth’s focal distance or eccentricity approaches zero, reduce to the familiar spherical equations in both the general and hydrostatic cases. The differences between solutions of the spheroidal and spherical equations are not expected to be significant in most applications, although there is the possibility of the accumulation of systematic differences in long-term integrations.

Angular momentum of forced 2D turbulence in a square no-slip domain

Self-organization of forced two-dimensional (2D) turbulence in a square no-slip domain may drive the global angular momentum to sudden peak values. This ‘spin-up’ process was observed in several direct numerical simulations (DNS) for intermediate integral-scale Reynolds numbers. The development of viscous boundary layers at the no-slip walls destabilizes the spin-up state, causing it to break-down in semi-regular intervals. After each break-down a new event of self-organization takes place, possibly with a different of rotation. If certain a priori bounds are satisfied, the evolution of the kinetic energy and the absolute angular momentum may be nearly similar in the spin-up state. Such a similarity defines a large-scale energy saturation time, which is shown to exhibit a lower bound scaling behaviour with respect to the usual turbulent time τ , based upon the averaged enstrophy dissipation η .

Orbital polarization from DC slice imaging: S(1D2) alignment in the photodissociation of ethylene sulfide

Abstract DC slice imaging [Rev. Sci. Instrum. 74 (2003) 2530], a recently developed high-resolution `slicing' approach that directly provides the full 3D product distribution in imaging experiments, has been adapted to yield the absolute speed-dependent angular momentum alignment anisotropy parameters in a photodissociation experiment. We present the theoretical machinery for interpretation of a small basis set of sliced experimental images recorded under different laser polarization geometries and then demonstrate its application in the study of electronic orbital angular momentum alignment of excited state S( 1 D 2 ) atoms following 193.3 nm photodissociation of ethylene sulfide. We find the slicing approach to be a highly sensitive and widely applicable technique for the study of orbital polarization, even in instances where the magnitude of such effects is small. The approach outlined here represents a direct route to the determination of recoil-angle dependent orbital alignment for a continuous range of photofragment kinetic energy release.

Seasonal Variations of Tropospheric Wind over Indonesia: Comparison between Collected Operational Rawinsonde Data and NCEP Reanalysis for 1992-99

Seasonal variations of wind in the troposphere are analyzed based on operational rawinsondes at 11 stations over Indonesia for 1992-1999 and the results are compared with NCEP reanalysis. For meridional wind, an annual oscillation caused by north-south shift of a meridional (Hadley-type) circulation is clearly found. Winter-poleward flow of the upper-tropospheric meridional circulation is stronger than summer-poleward flow. The winter (southern) hemispheric cell in northern summer has a larger invasion across the equator (as suggested in the zonal-mean Hadley cell), and weaker meridional flows than the winter (northern) hemispheric cell in northern winter. Along the boundary of twin meridional circulation cells, a zonal (Walker-type) circulation seems to exist, and has easterly (westerly) wind in the upper (lower) troposphere in the Indonesian region. The zonal circulation is also shifted from the equator associated with the meridional circulation cell boundary. However, a semiannual oscillation, which has easterly maxima in January-February and July-August is more clearly observed in the upper-tropospheric zonal wind, which is consistent with a consideration on conservation of absolute angular momentum for the upper-tropospheric winter-poleward (equatorward) air mass transport associated with the winter-hemispheric meridional circulation cell, invading the summer hemisphere across the equator. In comparison with the seasonal-vertical variations based on the operational rawinsonde data, the NCEP reanalysis seems to overestimate the upper-tropospheric northerly and easterly maxima during northern summer. In other words, the NCEP reanalysis produces a winter hemispheric side meridional circulation cell with similar intensities between both solsticial seasons, in spite that in the operational rawinsonde data the winter hemispheric side meridional circulation cell in northern summer is weaker than that in northern winter. The overestimation of easterly may also be related with an insufficient reproduction of the winter-hemispheric meridional circulation cell-such as too large northward invasion.

Comparison of an axisymmetric hurricane model with the corresponding slab‐symmetric ITCZ model

AbstractWe examine the difference between the evolution of a hurricane‐like vortex in an axisymmetric model and that of an intertropical convergence‐zone‐ like disturbance in a slab‐symmetric model, starting from an initial disturbance with the same lateral structure. The main calculations are carried out using a hurricane model similar to that formulated by DeMaria and Pickle (1988), supplemented by a few calculations using a recently developed model by Nguyen et al. (2002). We show that, although the two flow configurations have many similarities, the slab‐symmetric model does not provide a dynamical surrogate for the hurricane. The main difference can be attributed to a geometrical factor in the formula for the conservation of absolute angular momentum in the axisymmetric model, which for an inward‐moving air parcel permits much larger tangential wind speeds to be attained than in the slab‐symmetric model. As a result, the sea‐surface latent‐heat flux, which is wind‐speed dependent, is much larger in the axisymmetric model, providing a larger energy supply to the growing disturbance per unit area than in the slab‐symmetric case. A further geometrical effect is that for the same inflow velocity profile in the boundary layer, there is larger convergence in the axisymmetric model. Because this convergence determines the deep cumulus mass flux in the DeMaria and Pickle model, the cumulus heating is larger in the axisymmetric configuration. The non‐development of the slab‐symmetric perturbation is a feature also of calculations using the Nguyen et al. (2002) model, even though two of the closures on the deep‐cumulus mass flux used do not depend on the mass convergence in the boundary layer. A few numerical details of the main model are described, including the method of solution, which differs from that used by DeMaria and Pickle (1988). Copyright © 2002 Royal Meteorological Society

A Multiscale Numerical Study of Hurricane Andrew (1992). Part IV: Unbalanced Flows

Despite considerable progress in understanding the hurricane vortex using balanced models, the validity of gradient wind balance in the eyewall remains controversial in observational studies. In this paper, the structure and development of unbalanced forces and flows in hurricanes are examined, through the analyses of the radial momentum and absolute angular momentum (AAM) budgets, using a high-resolution (i.e., Δx = 6 km), fully explicit simulation of Hurricane Andrew (1992). It is found from the radial momentum budgets that supergradient flows and accelerations, even after temporal and azimuthal averaging, are well organized from the bottom of the eye center to the upper outflow layer in the eyewall. The agradient accelerations are on average twice greater than the local Coriolis force, and caused mainly by the excess of the centrifugal force over the pressure gradient force. It is shown by the AAM budgets that supergradient flows could occur not only in the inflow region as a result of the inward AAM transport, but also in the outflow region through the upward transport of AAM. The eyewall is dominated by radial outflow in which the upward transport of AAM overcompensates the spindown effect of the outflow during the deepening stage. The intense upper outflow layer is generated as a consequence of the continuous outward acceleration of airflows in the eyewall updrafts. In spite of the pronounced agradient tendencies, results presented here suggest that the azimuthally averaged tangential winds above the boundary layer satisfy the gradient wind balance within an error of 10%. The analyses of instantaneous fields show pronounced asymmetries and well-organized wavenumber-2 structures of the agradient flows and forces in the form of azimuthally propagating vortex–Rossby waves in the eyewall. These waves propagate cyclonically downstream with a speed half the tangential winds near the top of the boundary layer and vertically upward. Agradient flows/forces and AAM transport in the eye are also discussed.

The role of cumulus convection in hurricanes and its representation in hurricane models

This paper reviews our understanding of the role of cumulus convection in hurricanes as well as the various convective parameterization schemes that have been used in hurricane models. Elementary principles show that the primary (tangential) circulation of a vortex intensifies as rings of rotating air converge inward while conserving their (absolute) angular momentum. Thus intensification requires a mechanism to produce enough flow convergence above the surface boundary layer to counter the divergence induced there by the boundary layer itself. Typically, such convergence is associated with the inward branch of the secondary circulation and is produced by an unbalanced negative radial gradient of buoyancy above the boundary layer resulting from condensational heating in the inner region of the vortex. The fact that such buoyancy gradients are produced by all the parameterization schemes, as well as by explicit schemes for latent heat release, explains why all the models are able to simulate hurricane intensification with some degree of realism. In a weak vortex the secondary circulation is dominated by buoyant forcing, but as the vortex intensifies the contribution from surface friction increases until in the mature stage, the buoyantly induced convergence must closely balance the frictionally induced divergence just above the boundary layer. Only a handful of the more recent hurricane models and only two of those in which convection is parameterized represent the effects of convective downdrafts. These downdrafts cool and dry the subcloud layer, tending to suppress further convection, so that acting alone they would serve as a brake on hurricane intensification. The strength of downdrafts decreases when the middle‐tropospheric relative humidity increases as a result of sustained cumulus convection over an area. If surface wind speeds are high enough, surface fluxes of sensible and latent heat can more than counteract the cooling and drying effects of convective downdrafts, allowing continued warming of the troposphere in the inner region of the vortex so that vortex intensification can proceed. Accordingly, the surface fluxes provide the energy source for the hurricane, while convection transfers this energy vertically through the troposphere, creating a suitable radial gradient of buoyancy to drive the secondary circulation of the vortex.

Is angular impulse always equal to the change of angular momentum in collisions between rigid bodies?

The relationships between angular impulse and angular momentum have been derived in the particular case of collisions between rigid bodies. It is shown that the change in absolute angular momentum about an arbitrary reference point is always equal to the angular impulse. However, the change in relative angular momentum is equal to the angular impulse only when it is calculated about particular points. We illustrate with two examples the differences between both equations. Laburpena: Bultzada angeluarraren eta momentu angeluarraren arteko erlazioak partikularizatuta solido zurrunaren talken kasurako aztertu dira. Momentu angeluar absolutoaren aldaketa edozein puntutan kalkulatuta beti dela bultzada angeluarra frogatzen da. Baina momentu angeluar erlatiboaren aldaketa da bultzada angeluarra puntu berezietan kalkulatzen bada. Ekuazioen arteko ezberdintasunak bi adibideren laguntzarekin erakusten ditugu.

Mechanisms of Zonal Index Variability in an Aquaplanet GCM

Abstract Data from a 2025-day Geophysical Fluid Dynamics Laboratory aquaplanet GCM integration are used to examine the temporal evolution of the zonal index, defined as the principal component of the first EOF of the zonally and vertically integrated absolute angular momentum. This EOF represents meridional displacements of the subtropical jet. Positive (negative) values of the zonal index correspond to poleward (equatorward) displacements of the subtropical jet and are referred to as the high (low) zonal index. Composites of various quantities are used to examine the temporal evolution of both the zonal-mean zonal winds and the eddy fields associated with either index. The high index is initiated by an enhancement in the equatorward wave activity propagation, which causes the subtropical jet to move in a poleward direction. The low index is led by a weakening in the equatorward propagation, which results in an equatorward displacement of the subtropical jet. More importantly, for the high index, the corr...

The Role of Terrain and Pressure Stresses in Rocky Mountain Lee Cyclones

The earth–atmosphere exchange of storm absolute dynamic circulation by mountain-induced surface pressure stress and the response of the circulation in a Rocky Mountain Ice cyclone is examined. Surface pressure stresses that transfer horizontal momentum across the earth-atmosphere interface stem from the hydrostatic weight of the atmosphere resting against the inclined surfaces of orography. In a Ice cyclone. mass asymmetries must be combined with terrain variability for net transfer across the interface. Within the storm structure, the acceleration of the dynamic circulation by the pressure gradient force is determined by the line integral of the azimuthally directed components of pressure stress, in effect an angular momentum pressure torque. The pressure torque is compared to the tendencies of specific relative circulation and absolute dynamic circulation in a lee cyclone simulated by the eta model. The mountain-induced pressure torque is found to be negative in the lower layers of the cyclone vortex throughout the simulation. Negative pressure torque, which indicates the transfer of absolute dynamic circulation from the cyclone to the mountain, acts, in conjunction with other processes, to force convergence of the mass transport in the lower layers of the cyclone. The import of absolute angular momentum from the storm's environment by the converging mass circulation exceeds the loss of angular momentum to the earth by pressure and viscous stresses, and thus leads to the spinup of the storm-relative circulation. The negative pressure torque diagnosed in the simulated cyclone results from an asymmetric distribution of surface pressure stress about the cyclone's circulation center in conjunction with a stronger pressure gradient to the north and northwest of the cyclone than to the south. This asymmetry is shown to be a characteristic of Rocky Mountain Ice cyclones and the results illuminate its relation to the storm's life cycle.

Numerical simulation of tropical cyclones by an axisymmetric nonhydrostatic model

As an approach to study the mesoscale processes within a typhoon, an axisymmetric nonhydrostatic numerical model is developed without the use of convective parameterization. Many simulated characteristics are consistent with radar and aircraft observations, such as the maximum of vertical and tangential wind, the inflow concentrated near the surface, the outward slope of the eyewall updraft, etc. The model duplicates not only the outward propagation of mesoscale convective systems, but also the inward movement of convective rings, the rate of which coincides with the observation. Besides, the model gives good simulations of the life cycle of convective rings, and indicates that the convective rings far from the eyewall play important roles in the fluctuation of typhoon intensity. Numerical results also exhibit the existence of coupling between outer and inner core structure. Analyses of the simulations show that convective momentum transport generates local maximum absolute angular momentum in the middle and upper troposphere. The momentum anomaly results in symmetric instability, which provides the environment to form convective rings. While the momentum anomaly moves outward with the outflow in the middle and upper troposphere, it initiates a series of convective rings with aid of other direct factors, which explains the outward propagation of convective systems. The simulations exhibit the life cycle of a typical convective ring in terms of three stages, or the developing, mature and dissipating stage. Analysis shows that the symmetric instability and the convective instability promote each other, and their cooperation makes the life of convective rings longer.

順圧不安定による擾乱の発達の上限を求める数値的手法

Two numerical methods are presented for calculating rigorous upper bounds on the finite-amplitude growth of barotropic instabilities to zonal jets on a rotating sphere. One of the methods is based on Shepherd (1988)'s analytic method, which uses the conservation law of domain-averaged pseudomomentum density. A variational minimization problem is solved numerically with a quasi-Newton method after discretization. The other is the authors' original method to solve a minimization problem under the constraints of the conservation laws of all Casimir invariants and total absolute angular momentum. The convex simplex method, which has been used in operations research, is applied to solve a quadratic programming problem. The two methods are applied to estimate the upper bounds for several profiles of the initial unstable jet and the bounds are compared with the results of non-linear time integrations from the unstable jet with a high-resolution model (Ishioka and Yoden, 1994). The two bounds are found to be almost completely identical to each other. Evidence from high-resolution numerical experiments is that the bounds overestimate the actual wave-enstrophy achieved in numerical experiments by a factor of 1.2 to 2.3.