Mesoscale Barotropic Instability of Vortex Rossby Waves in Tropical Cyclones

In this study, the barotropic stability of vortex Rossby waves （VRWs） in 2D inviscid tropical cyclone （TC）-like vortices is explored in the context of rotational dynamics on an f-plane. Two necessary instable conditions are discovered： （a） there must be at least one zero point of basic vorticity gradient in the radial scope; and （b） the relative propagation velocity of perturbations must be negative to the basic vorticity gradient, which reflects the restriction relationship of instable energy. The maximum growth rate of instable waves depends on the peak radial gradient of the mean vorticity and the tangential wavenumber （WN）. The vortex-semicircle theorem is also derived to provide bounds on the growth rates and phase speeds of VRWs. The typical basic states and different WN perturbations in a tropical cyclone （TC） are obtained from a high resolution simulation. It is shown that the first necessary condition for vortex barotropic instability can be easily met at the radius of maximum vorticity （RMV）. The wave energy tends to decay （grow） inside （outside） the RMV due mainly to the negative （positive） sign of the radial gradient of the mean absolute vorticity. This finding appears to help explain the developemnt of strong vortices in the eyewall of TCs.

The Roles of Barotropic Instability and the Beta Effect in the Eyewall Evolution of Tropical Cyclones

Diabatic heating by convection in the eyewall often produces an annular region of high potential vorticity(PV)around the relatively low PV eye in a strong tropical cyclone(TC).Such a PV ring is barotropically unstable and can encourage the exponential growth of PV waves.In this study,such instability and the subsequent nonlinear evolution of three TC-like vortices having PV rings with different degrees of hollowness on an f-plane are first examined using an unforced,inviscid shallow-water-equation model.Results show that the simulated eyewalls evolve similarly to those in the nondivergent barotropic model.It is also found that the polygonal eyewall structure can be decomposed into vortex Rossby waves(VRWs)of different wavenumbers with different amplitudes,allowing for wave-wave interactions to produce complicated behaviors of mesovortices in the TC eyewall.The same set of PV rings has been examined on a beta-plane.Although the beta effect has been rendered unimportant to the eyewall evolution due to the relatively small scale of the inner-core circulation,this study shows that the beta effect may erode the coherent structure of mesovortices in the eyewall of an initially hollow PV-ring vortex.Mesovortices modeled on the beta-plane with a greater beta parameter tend to experience an earlier breakdown and enhanced radial gradients of the basic-state(azimuthally mean)angular velocity,followed by wave-wave,wave-flow interactions,leading to earlier merger and axisymmetrization processes.This result implies that the beta effect could be one of the forcings that shorten the lifetime of quasi-steady mesovortices in the eyewall of real TCs.

ON THE BAROTROPIC INSTABILITY OF LARGE SCALE VORTICES

By using the linearized barotropic vorticity equation in polar coordinates the stability of pertur- bations on a large scale circular basic flow is transformed into a generalized eigenvalue problem, yielding the relationship between the growth rate of the amplitude of perturbations and the az- imuthal wave number. Then, numerical experiments whose integration time is 60 model hours are performed in terms of a quasi-geostrophic barotropic model in Cartesian coordinates using the per- turbation stream function field of unstable mode superimposed on a strong and weak circular basic flows as the initial fields. The experimental results reveal that the amplitudes of the initial pertur- bations in the model atmosphere grow with time. The amplitude of the perturbations superimposed on the strong circular basic flow grows quicker and forms a spiral-band-like structure.

NONLINEAR BAROTROPIC INSTABILITY INCLUDING FRICTION DISSIPATION, THERMAL DRIVING AND LARGE TOPOGRAPHY

From a nonlinear quasi-geostrophic barotropic vorticity equation including frictional dissipation, thermal driving and large topography used by Charney in investigation of the multiple flow equilibria and blocking, using the Serrin-Joseph energy method and the variational principle, we found the nonlinear barotropic stability criteria of the zonal basic flow with the total energy, total enstrophy and their linear combination respectively, and compared the criteria with Charney's results.

LINEAR AND NONLINEAR BAROTROPIC INSTABILITY

Based on a non-frictional and non-divergent nonlinear barotropic vorticity equation and its solutions of travelling waves,the criteria for linear and nonlinear barotropic instability are gained respectively at an equilibrium point of the equation on a phase plane.The linear and nonlinear analytical solutions to instability waves are also found.The computational results show that if their amplitudes are equal at the initial time,the amplitude increments of nonlinear instable barotropic wave are always less than those of linear instable barotropic wave. The nonlinear effects can slow down the exponential growth of linear instability.The time needed for making the amplitude double that of initial time by instabilities,is about 6h for linear instability and about 18h for nonlinear instability,the latter is in agreement with the observations in the real atmosphere.

A Further Investigation of the Decadal Variation of ENSO Characteristics with Instability Analysis

Based on instability theory and some former studies, the Simple Ocean Data Assimilation （SODA） data are analyzed to further study the difference between the propagation of the ENSO-related oceanic anomaly in the off-equatorial North Pacific Ocean before and after 1976. The investigation shows that after 1976 in the off-equatorial North Pacific Ocean, there is a larger area where the necessary conditions for baroclinic and/or barotropic instability are satisfied, which may help oceanic anomaly signals propagating in the form of Rossby waves to absorb energy from the mean currents so that they can grow and intensify. The baroclinic energy conversion rate in the North Pacific after 1976 is much higher than before 1976, which indicates that the baroclinic instability has intensified since 1976. Prom another perspective, the instability analysis gives an explanation of the phenomena that the ENSO-related oceanic anomaly signal in the North Pacific has intensified since 1976.

Barotropic Process Contributing to the Formation and Growth of Tropical Cyclone Nargis

This study reveals the barotropic dynamics associated with the formation and growth of tropical cyclone Nargis in 2008,during its formation stage.Strong equatorial westerlies occurred over the southern Bay of Bengal in association with the arrival of an intraseasonal westerly event during the period 22-24 April 2008. The westerlies,together with strong tropical-subtropical easterlies,constituted a large-scale horizontal shear flow,creating cyclonic vorticity and thereby promoting the incipient disturbance that eventually evolved into Nargis.This basic zonal flow in the lower troposphere was barotropically unstable,with the amplified disturbance gaining more kinetic energy from the easterly jet than from the westerly jet during 25-26 April. This finding suggests that more attention should be paid to the unstable easterly jet when monitoring and predicting the development of tropical cyclones.Energetics analyses reveal that barotropic energy conversion by the meridional gradient of the basic zonal flow was indeed an important energy source for the growth of Nargis.

Snowstorm over the Southwestern Coast of the Korean Peninsula Associated with the Development of Mesocyclone over the Yellow Sea

This study investigates the characteristics of a heavy snowfall event over the southwestern part of the Korean Peninsula on 4 December 2005. The snowstorm was a type of mesoscale maritime cyclone which resulted from barotropic instability, and diabatic heating from the warm ocean in continental polar air masses. Based on surface observations, radiosonde soundings, MTSAT-1R satellite data and the 10-km grid RDAPS （Regional Assimilation and Prediction System based on the PSU/NCAR MM5） data, the evolution of the mesocyclone is explained by the following dynamics; （1） In the initial stage, the primary role in the cyclogenesis process of the mesocyclone is a barotropic instability in the horizontal shear zone. （2） In the developing stage, the mesocyclone moves and deepens into a baroclinic zone corresponding to the surface heating and moistening. （3） In the mature stage, it is found that the mesocyclone is intensified by the destabilization caused by enhanced low-level heating and condensation, the moisture flux convergence, and the interaction between upper and lower-level potential vorticity anomalies. We suggest that a checklist with stepwise indicators responsible for development be prepared for the forecasting of heavy snowfall over the southwestern part of the Korean Peninsula.

The decadally modulating eddy field in the upstream Kuroshio Extension and its related mechanisms

Both the level of the high-frequency eddy kinetic energy（HF-EKE） and the energy-containing scale in the upstream Kuroshio Extension（KE） undergo a well-defined decadal modulation, which correlates well with the decadal KE path variability. The HF-EKE level and the energy-containing scales will increase with unstable KE path and decrease with stable KE path. Also the mesoscale eddies are a little meridionally elongated in the stable state, while they are much zonally elongated in the unstable state. The local baroclinic instability and the barotropic instability associated with the decadal modulation of HF-EKE have been investigated. The results show that the baroclinic instability is stronger in the stable state than that in the unstable state, with a shorter characteristic temporal scale and a larger characteristic spatial scale. Meanwhile, the regional-averaged barotropic conversion rate is larger in the unstable state than that in the stable state. The results also demonstrate that the baroclinic instability is not the dominant mechanism influencing the decadal modulation of the mesoscale eddy field, while the barotropic instability makes a positive contribution to the decadal modulation.

INSTABILITY PROPERTIES OF ATMOSPHERIC DISTURBANCES

There are some basic problems in previous theoretical studies of baroclinic instability.The derived critical baroclinity was considerably lower than the time averaged mean meridional temperature gradient,especially in the lower troposphere.Also,the linear mechanism of baroclinic disturbance development which is noted restricted by the critical baroclinity was not studied sufficiently.The realistic critical baroclinity and disturbance development are discussed in this study.It will be shown that the critical condition of instability and typical time and space scales of disturbances de- pend on three-dimensional structures of atmosphere and sphericity of the earth,other than the horizontal temperature gradient alone.The variant behaviour of atmospheric disturbances depends highly on their specific scales that may be described by the same theoretical model.Thus,there would be no substantial differences in the basic instability mecha- nism of many disturbances including the polar lows and explosive cyclones.

Characteristics and mechanism of vertical coupling in the genesis of tropical cyclone Durian(2001)

The vertical coupling(VC)process and mechanism during the genesis of a tropical cyclone(TC)implied by the weak vertical shear of horizontal wind,one of the key factors impacting TC genesis,constitute important but unanswered fundamental scientific problems.This paper carried out a targeted investigation of this problem through numerical simulation and theoretical analyses.The main conclusions are as follows.Even if TC genesis occurs in a barotropic environment,a VC process still occurs between the trough(vortex)at the middle level and that at the lower level in the TC embryo area.VC mainly occurs at the tropical disturbance(TDS)stage.Only after the VC is accomplished can the tropical depression(TD)organize further by itself and develop into the tropical storm(TS)stage or the stronger tropical typhoon(TY)stage through the WISHE(wind-induced surface heat exchange)mechanism.In the VC process,vortical hot towers(VHTs)play vertical connecting roles and are the actual practitioners of the VC.Through the VHTs’vertical connections,the middle-and lower-troposphere trough axes move towards each other and realize the VC.VHTs can produce intensive cyclonic vorticity in the lower troposphere,which is mainly contributed by the stretching term.The tilting term can produce a single dipole or double dipole of vorticity,but the positive and negative vorticity pairs offset each other roughly.While the stretching term ensures that the cyclonic rotations of the wind field in the middle and lower levels tend to be consistent,the tilting term acts to uniformly distribute the horizontal wind in the vertical direction,and both terms facilitate the VC of the wind field.With the latent heat of condensation,VHTs heat the upper and middle troposphere so that the 352 K equivalent potential temperature contour penetrates vertically into the 925–300 hPa layer,realizing the VC of the temperature field.While forming cloud towers,VHTs make the ambient air become moist and nearly saturated so that the 95%relative humidity contour penetrates vertically into the 925–400 hPa layer,realizing the VC of the humidity field.Due to the collective contributions of the VHTs,the embryo area develops into a warm,nearly saturated core with strong cyclonic vorticity.The barotropic instability mechanism may also occur during TC genesis over the Northwest Pacific and provide rich large-scale environmental vorticity for TC genesis.The axisymmetric distribution of VHTs is an important sign of TC genesis.When a TC is about to form,there may be accompanying phenomena between the axisymmetric process of VHTs and vortex Rossby waves.

Drastic change in dynamics as Typhoon Lekima experiences an eyewall replacement cycle

Why does the 1909 typhoon,Lekima,become so destructive after making landfall in China?Using a newly developed mathematical apparatus,the multiscale window transform(MWT),and the MWT-based localized mutliscale energetics analysis and theory of canonical transfer,this study is intended to give a partial answer from a dynamical point of view.The ECMWF reanalysis fields are first reconstructed onto the background window,the TC-scale window,and the convection-scale window.A localized energetics analysis is then performed,which reveals to us distinctly different scenarios before and after August 8–9,2019,when an eyewall replacement cycle takes place.Before that,the energy supply in the upper layer is mainly via a strong upper layer-limited baroclinic instability;the available potential energy thus-gained is then converted into the TC-scale kinetic energy,with a portion to fuel Lekima’s upper part,another portion carried downward via pressure work flux to maintain the cyclone’s lower part.After the eyewall replacement cycle,a drastic change in dynamics occurs.First,the pressure work is greatly increased in magnitude.A positive baroclinic transfer almost spreads throughout the troposphere,and so does barotropic transfer;in other words,the whole air column is now both barotropically and baroclinically unstable.These newly occurred instabilities help compensate the increasing consumption of the TC-scale kinetic energy,and hence help counteract the dissipation of Lekima after making landfalls.