Conversion Characteristics between Barotropic and Baroclinic Circulations of the SAH in Its Seasonal Evolution

In the context of 1958–1997 NCEP/ NCAR re-analyses, the South Asia high (SAH) was divided into two components, barotropic and baroclinic, the former based on mass weighed vertical integration and the latter on the difference between the measured circulation and the barotropic component counterpart, whereupon the barotropic and baroclinic circulation conversion features were addressed of the research SAH during its seasonal variation. Evidence suggests that i) in summer (winter), the SAH is a thermal (dynamical) system, with dominant baroclinicity (barotropicity), either of the components accounting for approximately 70% of the total contribution; ii) as time progresses from winter to summer, accompanied by the barotropic SAH evolving into its baroclinic analog, the SAH is moving under the “ thermal guidance” of its baroclinic component circulation, suggesting that the component circulation precedes the system itself in variation; iii) the reversal happens when it goes from summer to winter, with the SAH displacement under the “ dynamic steering” of its barotropic component circulation. Key words SAH (South Asia high) - Barotropic circulation - Baroclinic circulation - Seasonal variation (1)This work is supported by the National Natural Sciences Foundation of China under Grant No.49735170.

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.

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.

Asymptotic solution of a weak nonlinear model for the mid-latitude stationary wind field of a two-layer barotropic ocean

A weak nonlinear model of a two-layer barotropic ocean with Rayleigh dissipation is built.The analytic asymptotic solution is derived in the mid-latitude stationary wind field,and the physical meaning of the corresponding problem is discussed.

Variations in Wave Energy and Amplitudes along the Energy Dispersion Paths of Nonstationary Barotropic Rossby Waves

The variations in the wave energy and the amplitude along the energy dispersion paths of the barotropic Rossby waves in zonally symmetric basic flow are studied by solving the wave energy equation,which expresses that the wave energy variability is determined by the divergence of the group velocity and the energy budget from the basic flow.The results suggest that both the wave energy and the amplitude of a leading wave increase significantly in the propagating region that is located south of the jet axis and enclosed by a southern critical line and a northern turning latitude.The leading wave gains the barotropic energy from the basic flow by eddy activities.The amplitude continuously climbs up a peak at the turning latitude due to increasing wave energy and enlarging horizontal scale(shrinking total wavenumber).Both the wave energy and the amplitude eventually decrease when the trailing wave continuously approaches southward to the critical line.The trailing wave decays and its energy is continuously absorbed by the basic flow.Furthermore,both the wave energy and the amplitude oscillate with a limited range in the propagating region that is located near the jet axis and enclosed by two turning latitudes.Both the leading and trailing waves neither develop nor decay significantly.The jet works as a waveguide to allow the waves to propagate a long distance.

Charney’s Model—the Renowned Prototype of Baroclinic Instability—Is Barotropically Unstable As Well

The Charney model is reexamined using a new mathematical tool, the multiscale window transform(MWT), and the MWT-based localized multiscale energetics analysis developed by Liang and Robinson to deal with realistic geophysical fluid flow processes. Traditionally, though this model has been taken as a prototype of baroclinic instability, it actually undergoes a mixed one. While baroclinic instability explains the bottom-trapped feature of the perturbation, the second extreme center in the perturbation field can only be explained by a new barotropic instability when the Charney–Green number γ 1, which takes place throughout the fluid column, and is maximized at a height where its baroclinic counterpart stops functioning.The giving way of the baroclinic instability to a barotropic one at this height corresponds well to the rectification of the tilting found on the maps of perturbation velocity and pressure. Also established in this study is the relative importance of barotropic instability to baroclinic instability in terms of γ. When γ 1, barotropic instability is negligible and hence the system can be viewed as purely baroclinic;when γ 1, however, barotropic and baroclinic instabilities are of the same order;in fact, barotropic instability can be even stronger. The implication of these results has been discussed in linking them to real atmospheric processes.

A BAROTROPIC QUASI-GEOSTROPHIC MODEL WITH LARGE-SCALE TOPOGRAPHY, FRICTION AND HEATING

Based on the barotropic equations including large-scale topography, friction and heat factor, a barotropic quasi-geostrophic model with large-scale topography, friction and heating is obtained by means of scale analysis and small parameter method. It is shown that this equation is a basic one, which is used to study the influence of the Tibetan Plateau on the large-scale flow in the atmosphere. If the friction and heating effect of large-scale topography are neglected, this model will degenerate to the general barotropic quasi-geostrophic one.

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.

The Structure and Propagation of Stationary Planetary Wave Packet in the Barotropic Atmosphere

Monthly or seasonally mean anomalies of large-scale atmospheric circulation are better represented by wave packets or their combination. Both qualitative and quantitative analyses of equations of wave packet dynamics, which are obtained by the use of WKB approximation, are very helpful for the understanding of structure, formation and propagation of stationary and quasi-stationary planetary wave packet patterns in the atmosphere. Indeed, these equations of wave packet dynamics can be directly solved by the method of characteristic lines, and the results can be simply and clearly interpreted by physical laws. In this paper, a quasi-geostrophic barotropic model is taken for simplicity, and the wave packets superimposed on several ideal profiles of the basic current and excited by some ideal forcings are investigated in order to make comparison of the accuracy of calculation with the analytical solution. It is revealed that (a) the rays of stationary planetary wave packet do not coincide with but go away from the great circle with significant difference if the shear of the basic zonal flow is not too small; (b) being superimposed on a westerly jet flow with positive shear (Uλ/y>0), the stationary wave packets excited by low-latitudinal forcing are first intensified during their northeastward propagation in the Northern Hemisphere, then reach their maximum of amplitude at some critical latitude, and after that weaken again; (c) the connected line of extremes (the positive and negative centres) of wave packet does not coincide with but crosses the ray by an angle, the larger the scale of external forcing, the larger the angle; and (d) the whole pattern of a trapped stationary wave packet is complicated by the interference between the incident and reflected waves.

Quasi-40-Day Oscillation and Its Teleconnection Structure together with the Possible Dependence on Conversion of Barotropic Unstable Energy of Temporal Mean Flow

A study is made of the distribution of the diagnostic quantity vector E and the teleconnection structure of 30-50 (quasi-40) day oscillation, together with the dependence on the conversion of barotropic unstable energy of mean flow in terms of ECWMF daily 500 hPa grid data in winter, indicating that the energy transportation is closely associated with the westerly jet position, with zonal (meridional) propagation in the strong (weak) wind region, that considerable conversion of barotropic energy occurs at the jet exit region where low-frequency oscillation gains energy from the mean flow, leading to maximum kinetic energy for the oscillation observed there, which is marked by evident barotropy in striking contrast to the baroclinicity at low latitudes and that the teleconnection core is related to the center of action in the atmosphere and bound up with the pattern of the west wind.

A THREE-DIMENSIONAL COASTAL BAROTROPIC MODEL IN GENERALIZED CURVILINEAR GRIDS

The method of automatically generating generalized curvilinear meshes has many advantages and is beginning to be used in ocean simulations. This three dimensional (3 D) coastal barotropic model in generalized curvilinear grids was developed to simulate the M 2, S 2, K 1 and O 1 tidal waves in the Bohai Sea, China. The numerical results agreeing with observations showed that the method is an effective tool for improving accuracy of simulations in shallow shelf seas, especially in the near coast region, if the pseudo effect there usually caused by rectangular grids can be removed.

Numerical Physical Mechanism and Model of Turbulent Cascades in a Barotropic Atmosphere

In a barotropic atmosphere, new Reynolds mean momentum equations including turbulent viscosity, dispersion, and instability are used not only to derive the KdV-Burgers-Kuramoto equation but also to analyze the physical mechanism of the cascades of energy and enstrophy. It shows that it is the effects of dispersion and instability that result in the inverse cascade. Then based on the conservation laws of the energy and enstrophy, a cascade model is put forward and the processes of the cascades are described.

Variations in Amplitudes and Wave Energy along the Energy Dispersion Paths for Rossby Waves in the Quasigeostrophic Barotropic Model

Variations in wave energy and amplitude for Rossby waves are investigated by solving the wave energy equation for the quasigeostrophic barotropic potential vorticity model.The results suggest that compared with rays in the nondivergent barotropic model,rays in the divergent model can have enhanced meridional and zonal propagation,accompanied by a more dramatic variability in both wave energy and amplitude,which is caused by introducing the divergence effect of the free surface in the quasigeostrophic model.For rays propagating in a region enclosed by a turning latitude and a critical latitude,the wave energy approaches the maximum value inside the region,while the amplitude approaches the maximum at the turning latitude.Waves can develop when both the wave energy and amplitude increase.For rays propagating in a region enclosed by two turning latitudes,the wave energy approaches the minimum value at one turning latitude and the maximum value at the other latitude,while the total wavenumber approaches the maximum value inside the region.The resulting amplitude increases if the total wavenumber decreases or the wave energy increases more significantly and decreases if the total wavenumber increases or the wave energy decreases more significantly.The matched roles of the energy from the basic flow and the divergence of the group velocity contribute to the slightly oscillating wave energy,which causes a slightly oscillating amplitude as well as the slightly oscillating total wavenumber.

THE DIABATIC WAVES IN BAROTROPIC MODEL

The equations of barotropic model are used to discuss the effects of diabatic factors such as heat-ing of convective condensation, evaporation-wind feedback and CISK on the Rossby wave and the Kelvin wave. In low latitudes we have obtained the angular frequency and analyzed the period and stability of waves. The result shows the existence of the diabatic factors not only enlarges the period of adiabatic waves but also changes the stability of waves. Thus we think that the so-called intraseasonal oscillation and some other low-frequency oscillations are a kind of diabatic waves which are important factors producing the long-term weather changes and short-term climatic evolution.

The Generalized Energy Equation and Instability in the Two-layer Barotropic Vortex

The linear two-layer barotropic primitive equations in cylindrical coordinates are used to derive a gen- eralized energy equation, which is subsequently applied to explain the instability of the spiral wave in the model. In the two-layer model, there are not only the generalized barotropic instability and the super high- speed instability, but also some other new instabilities, which fall into the range of the Kelvin-Helmholtz instability and the generalized baroclinic instability, when the upper and lower basic flows are different. They are perhaps the mechanisms of the generation of spiral cloud bands in tropical cyclones as well.

DEVELOPMENT OF A TROPICAL CYCLONE IN BAROTROPIC ENVIRONMENTAL FLOWS

ＤＥＶＥＬＯＰＭＥＮＴＯＦＡＴＲＯＰＩＣＡＬＣＹＣＬＯＮＥＩＮＢＡＲＯＴＲＯＰＩＣＥＮＶＩＲＯＮＭＥＮＴＡＬＦＬＯＷＳＬｉＸｉａｏｆａｎ（李小凡）（ＤｅｐａｒｔｍｅｎｔｏｆＭｅｔｅｏｒｏｌｏｇｙ，ＵｎｉｖｅｒｓｉｔｙｏｆＨａｗａｉｉａｔＭａｎｏａ，Ｈ...

Nondispersive Periodic Solution of a Barotropic Semi-Geostrophic Model

The existence and solution of the non-dispersive periodic solution are achieved concerning nonlinear barotropic Rossby waves of a barotropic semi-geostrophic model, demonstrating the likelihood of the Taylor evolution, together with the related dimensionless a-criterion. Finally, the wave velocity expression is proposed with some diagnostic relations among the wave parameters.

Analysis-Prediction Experiments over Indian Region Using Primitive Equation Barotropic Model

The impact of initial guess and grid resolutions on the analysis and prediction has been investigated over the Indian region. For this purpose, an univariate objective analysis scheme and a primitive equation barotropic model have been used. The impact of initial guess and the resolutions on analysis and prediction is discussed.

A numerical study for some efficient time-integration schemes using barotropic equations

Three kinds of methods, i. e., explicit, semi-implicit, and semi-implicit and semi-Lagrangian method, are tested in the time-integration of shallow-water equations on rotating sphere. Helpful results are available from experiments, especially about the accuracy and efficiency of different semi-implicit and semi-Lagrangian schemes.

The Dynamics of Barotropic Vortex Merging

The merging of multiple vortices is a fundamental process of the dynamics of Earth＇s atmosphere and oceans. In this study, the interaction of like-signed vortices is analytically and numerically examined in a framework of two-dimensional inviscid barotropic flows. It is shown that barotropic vortex interaction turns out to be more intricate than simple merging scenarios often assumed in previous studies. Some particular configurations exist in which the vortex merging process is never complete despite strong interaction of like-signed vortices, regardless of the strengths or distances between the vortices.While the conditions for a complete vortex merging process introduced in this study appear to be too strict for most practical applications, this study suggests that careful criteria for vortex mergers should be properly defined when simulating the interaction of vortices, because the merging may not always result in a final enhanced circulation at the end of the interaction,as usually assumed in the literature.