Impacts Of Basic-state Vortex Distribution On The Change Of Structure And Intensity In Tropical Cyclone

From the perspective of characteristics of the basic state structure,we research on the dynamic of the structure and intensity in the tropic cyclone.Firstly,the effect of the shape of basic-state potential vorticity(PV)profile on the stability of the tropical cyclone(TC)-like vortices possessing hollow PV structure is discussed in a two-dimensional(2D)shallow water barotropic model.Under the premise of the same basic-state maximum wind and the radius of maximum wind(RMW),a sequence of 170 numerical simulations are conducted by setting two structural parameters of basic-state PV,with the first parameter defining the thickness of the ring(i.e.,the ratio between the inner and outer radii of the ring)and the second parameter defining the hollowness of the ring(i.e.,the ratio of eye to inner-core relative vorticity).The eigenfrequency and growth rate of the most unstable mode in systems(MUMSs)as well as the most unstable wavenumber(MUWN)with the different basic-state PV profiles are examined.The results show that(1)the MUWN for thicker rings are more prone to lower wavenumber(WNs),and the corresponding MUMSs possess lower intrinsic frequencies and small growth rates;(2)thinner rings are more prone to higher wavenumber growth,and the more filled the rings become,the higher wavenumber(WN)the MUWN;and(3)for thin and hollow rings,MUMSs possess high frequencies and large growth rates.However,in real cases,the structure and intensity of the basic state vortex are changing at any time during the development of TCs.Thus,in order to make the study more completely,sensitivity of intensity of the basic state vortex to the stability of system is further conducted by setting three different hollow PV structures in a two-dimensional(2D)shallow water barotropic model.The results show that the intensity of the basic state vortex mainly affects the strength of the instability,and the disturbance growth rates become larger with an increase of the strength of vortices in the same PV structure,while the shape of the PV profile is the key factor to determine the stability of a vortex.Considering that the instability is selective for the azimuthal wavenumbers(WNs),the instability properties and disturbances development of different WNs are analyzed.For thick and filled PV rings,the weak instability is more likely to occur at lower WNs,and the wavenumber one disturbance appears to be algebraically growing.For moderate thick and hollow PV rings,the perturbation kinetic energy at the MUWN increases exponentially and the disturbance growth of the MUWN is much faster than that of other WNs.For thin and hollow PV rings,the disturbance development depends mainly on the instability of higher WNs.And the growth rates of the fastest growing mode(largest dimensionless growth rate)for two or more different WNs are very close,which causes the disturbance growth of multiple WNs are approaching.The dynamics of the asymmetric structure in the inner core of TC-like vortices are further advanced.It is found that for weakly unstable rings,the wave structure of MUMSs have typical characteristics of Vortex Rossby Waves(VRWs),while for the strongly unstable rings,the wave structure of MUMSs possess typical properties of the mix waves.To confirm the above results,a high resolution dataset from a realistic simulation is used to examine the impacts of the evolution of PV ring on intensity and structure change of TCs.It is shown that the polygonal features appearing in the TC eyewall are highly consistent with the MUWN determined by the radial distribution of the basic state PV at the current time.This indicates that the basic state PV profile is selective to the most unstable growth of WN,which is beneficial to the disturbance growth at the MUWN.Moreover,the dataset also demonstrates the dynamic instability with the evolution of PV ring is closely related with the development stage of TC.Moreover,the WRF model is employed to simulate the life cycle of tropical cyclones possessing different basic state vortex structures in the dry atmosphere.The simulation results well reflected the breakdown of the hollow PV tower,as well the asymmetric structure in the horizontal distribution associated with the dry dynamic instability are clearly presented.A PV bridge,similar to that previously found in full-physics hurricane simulations,develops as a result of mixing at the lower levels where unstable PV waves grow most rapidly.Using the method of asymmetric wave decomposition,the development of asymmetric disturbances for various azimuthal wavenumbers and the evolution of symmetric vortex are investigated.The growth and damping of asymmetric perturbations respectively correspond to the formation of the polygonal eyewall and the breakdown of the hollow structure.It is found that the growth of asymmetric perturbations occur during the formation of the polygonal eyewall,and the disturbance growth rate at a certain wavenumber which is closely related to the polygonal structure is the largest.Both the vorticity tendency equaton for the asymmetric motion and the azimuthal mean PV are applied to deeply explore the asymmetric dynamics of the structure and intensity change in TCs.The results show that for the basic state vortex with a hollow structure,dynamic instability causes the rapid growth of the disturbance at lower levels in TCs.With the growth of the disturbances,the polygonal structure corresponding to the optimal perturbation appears gradually in the horizontal direction of the TCs.Then,the high PV is continuously mixed into the eye which causes the dynamic conditions of the basic state vortex be changed and lead to hollow tower breakdown,with the vortex becoming stable.The response of symmetric vortices to the asymmetries development in two typical basic state vortices are compared.The results indicate that the hollow structure of basic state vortex is closely related to the response period and structural and intensity change in symmetric vortex.For enough thick and filled hollow vorticity(or PV)rings,small perturbations grow slowly,and lead to the longer response period.Although the change rates of both the central pressure and the maximum wind speed are varying,it still can not change the trend that the central pressure increases and the maximum wind speed decreases.In contrast,for thinner and hollow vorticity(or PV)rings,the asymmetric disturbance grows fast,and result in the rapid response of the symmetric vortex to the disturbance development.Moreover,the response is that the minimum central pressure and maximum azimuthal mean velocity simultaneously decrease,consistent with previous barotropic results.