doi:10.1007/s00376-016-6006-1

Brown M. R., 1997: Experimental evidence of rapid relaxation to large-scale structures in turbulent fluids: Selective decay and maximal entropy. Journal of Plasma Physics, 57, 203- 229.10.1017/S0022377896005211

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http%3A%2F%2Fjournals.cambridge.org%2Fabstract_S0022377896005211

refpaperuri:(1a0b78c914dbf25e21c7d7f8ca319ff8)

http://journals.cambridge.org/abstract_S0022377896005211There is abundant experimental, theoretical and computational evidence that certain constrained turbulent fluid systems self-organize into large-scale structures. Examples include two-dimensional (geostrophic) fluids, guiding-centre plasmas and pure-electron plasmas, as well as two- and three-dimensional magnetofluids such as reversed-field pinches and spheromaks. The theoretical understanding of relaxation phenomena is divided into two quite different constructs: selective decay and maximal entropy. Theoretical foundations of both of these principles are largely due to Montgomery and his collaborators. In this paper, selective decay and maximal entropy theories of turbulent relaxation of fluids are reviewed and experimental evidence is presented. Experimental evidence from both 2D fluids and from 3D magnetofluids is consistent with the selective decay hypothesis. However, high-resolution computational evidence strongly suggests that formation of large-scale structures is dictated by maximal-entropy principles rather than selective decay.

Canzani Y., 2013: Notes for analysis on manifolds via the Laplacian. Harvard University. [Available online at http://www.math.harvard.edu/\simcanzani/docs/Laplacian.pdf.]

Cerretelli C., C. H. K. Williamson, 2003: The physical mechanism for vortex merging. J. Fluid Mech., 475, 41- 77.10.1017/S0022112002002847

1d23548a0980665e88d9488b3709791f

http%3A%2F%2Fjournals.cambridge.org%2Farticle_S0022112002002847

http://journals.cambridge.org/article_S0022112002002847We study the physical mechanism for merging of two co-rotating trailing vortices. We directly measure the structure of the antisymmetric vorticity field that causes the vortices to merge, and we find that the form of the antisymmetric vorticity comprises two counter-rotating vortex pairs, whose induced velocity field readily pushes the two centroids together. If one observes the streamlines in a rotating reference frame, then one finds an inner and outer recirculating region of the flow bounded by a separatrix streamline. Initially, when the vortices grow large enough, diffusion across the separatrix places vorticity into the outer recirculating region of the flow, and this leads to the generation of the antisymmetric quadrupole, causing merger. There are four distinct phases in these interactions. The first stage is diffusive, while the second (convective) stage corresponds with the motion of the vortex centroids towards each other. A diffusive third stage (a symmetrisation process) causes the final merging into one vorticity structure, which is ultimately followed by the diffusion of the merged single vortex structure. Further details are found in Cerretelli & Williamson (JFM, 2002).

Dritschel D. G., D. W. Waugh, 1992: Quantification of the inelastic interaction of un-equal vortices in two-dimensional vortex dynamics. Physics of Fluids A: Fluid Dynamics, 4, 1737- 1744.10.1063/1.858394

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http%3A%2F%2Fscitation.aip.org%2Fcontent%2Faip%2Fjournal%2Fpofa%2F4%2F8%2F10.1063%2F1.858394

refpaperuri:(eb85cab19c05d9ca2c1bbab983e0a0bd)

http://scitation.aip.org/content/aip/journal/pofa/4/8/10.1063/1.858394The interaction of two isolated vortices having uniform vorticity is examined in detailed contour dynamics calculations, and quantified using a diagnostic that measures the coherence of the final state. The two vortices have identical vorticity, leaving two basic parameters that determine the evolution: the radius ratio and separation distance. It is found that the term ‘‘vortex merger’’ inadequately describes the general interaction that takes place. Five regimes are found: (1) elastic interaction, (2) partial straining‐out, (3) complete straining‐out, (4) partial merger, and (5) complete merger. Regime 5 is what used to be called ‘‘merger,’’ but occurs in less than one‐quarter of the parameter space. Contrary to popular belief, inelastic vortex interactions (IVI’s) do not always lead to vortex growth. In fact, in over half of the parameter space, smaller vortices are produced. These results bring into question commonly accepted ideas about nearly inviscid two‐dimensional turbulence.

Ferreira R. N., W. H. Schubert, 1997: Barotropic aspects of ITCZ breakdown. J. Atmos. Sci., 54, 261- 285.bd77399ff1540417e84a6a2e895346a5

http%3A%2F%2Fadsabs.harvard.edu%2Fcgi-bin%2Fnph-data_query%3Fbibcode%3D1997JAtS...54..261N%26db_key%3DPHY%26link_type%3DEJOURNAL

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Hendricks E. A., M. T. Montgomery, and C. A. Davis, 2004: The role of "Vortical" hot towers in the formation of tropical cyclone Diana (1984). J. Atmos. Sci., 61, 1209- 1232.10.1175/1520-0469(2004)061<1209:TROVHT>2.0.CO;2

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http://www.researchgate.net/publication/253063511_The_Role_of_Vortical''_Hot_Towers_in_the_Formation_of_Tropical_Cyclone_Diana_(1984)

http://www.researchgate.net/publication/253063511_The_Role_of_Vortical''_Hot_Towers_in_the_Formation_of_Tropical_Cyclone_Diana_(1984)Abstract A high-resolution (3-km horizontal grid spacing) near-cloud-resolving numerical simulation of the formation of Hurricane Diana (1984) is used to examine the contribution of deep convective processes to tropical cyclone formation. This study is focused on the 3-km horizontal grid spacing simulation because this simulation was previously found to furnish an accurate forecast of the later stages of the observed storm life cycle. The numerical simulation reveals the presence of vortical hot towers, or cores of deep cumulonimbus convection possessing strong vertical vorticity, that arise from buoyancy-induced stretching of local absolute vertical vorticity in a vorticity-rich prehurricane environment. At near-cloud-resolving scales, these vortical hot towers are the preferred mode of convection. They are demonstrated to be the most important influence to the formation of the tropical storm via a two-stage evolutionary process: (i) preconditioning of the local environment via diabatic production of multiple small-scale lower-tropospheric cyclonic potential vorticity (PV) anomalies, and (ii) multiple mergers and axisymmetrization of these low-level PV anomalies. The local warm-core formation and tangential momentum spinup are shown to be dominated by the organizational process of the diabatically generated PV anomalies; the former process being accomplished by the strong vertical vorticity in the hot tower cores, which effectively traps the latent heat from moist convection. In addition to the organizational process of the PV anomalies, the cyclogenesis is enhanced by the aggregate diabatic heating associated with the vortical hot towers, which produces a net influx of low-level mean angular momentum throughout the genesis. Simpler models are examined to elucidate the underlying dynamics of tropical cyclogenesis in this case study. Using the Sawyer-揈liassen balanced vortex model to diagnose the macroscale evolution, the cyclogenesis of Diana is demonstrated to proceed in approximate gradient and hydrostatic balance at many instances, where local radial and vertical accelerations are small. Using a shallow water primitive equation model, a characteristic -渕oist- (diabatic) vortex merger in the cloud-resolving numerical simulation is captured in a large part by the barotropic model. Since a moist merger results in a stronger vortex and occurs twice as fast as a dry merger, it is inferred (consistent with related work) that a net low-level convergence can accelerate and intensify the merger process in the real atmosphere. Although the findings reported herein are based on a sole case study and thus cannot yet be generalized, it is believed the results are sufficiently interesting to warrant further idealized simulations of this nature.

Holton J. R.2004: An Introduction to Dynamic Meteorology. 4th ed., Academic Press, 535 pp.6bf55d6fdd75e2bd869f655ee8c358ac

http%3A%2F%2Fwww.elsevier.com%2Fbooks%2Fan-introduction-to-dynamic-meteorology-48%2Fholton%2F978-0-12-354355-4

http://www.elsevier.com/books/an-introduction-to-dynamic-meteorology-48/holton/978-0-12-354355-4This revised text presents a cogent explanation of the fundamentals of meteorology, and explains storm dynamics for weather-oriented meteorologists. It discusses climate dynamics and the implications posed for global change. The Fourth Edition features a CD-ROM with MATLAB0003 exercises and updated treatments of several key topics. Much of the material is based on a two-term course for seniors majoring in atmospheric sciences.

Huang H. M., X.-L. Xu, 2010: Simulation on motion of particles in vortex merging process. Applied Mathematics and Mechanics, 31, 461- 470.10.1007/s10483-010-0406-x

bb34a9e408917afade2a481e5267601d

http%3A%2F%2Fwww.cnki.com.cn%2FArticle%2FCJFDTotal-YYSL201004006.htm

http://d.wanfangdata.com.cn/Periodical_yysxhlx-e201004006.aspxIn a two-phase flow,the vortex merging influences both the flow evolution and the particle motion.With the blobs-splitting-and-merging scheme,the vortex merging is calculated by a corrected core spreading vortex method (CCSVM).The particle motion in the vortex merging process is calculated according to the particle kinetic model.The results indicate that the particle traces are spiral lines with the same rotation direction as the spinning vortex.The center of the particle group is in agreement with that of the merged vortex.The merging time is determined by the circulation and the initial ratio of the vortex radius and the vortex center distance.Under a certain initial condition,a stretched particle trail is generated,which is determined by the viscosity,the relative position between the particles and the vortex,and the asymmetrical circulation of the two merging vortices.

Jang W., H. Y. Chun, 2015: Characteristics of binary tropical cyclones observed in the Western North Pacific for 62 years (1951-2012). Mon. Wea. Rev., 143, 1749- 1761.

Josser C., M. Rossi, 2007: The merging of two co-rotating vortices: A numerical study. European Journal of Mechanics-B/Fluids, 26, 779- 794.10.1016/j.euromechflu.2007.02.005

92f63e9cdae9085936a04122b59fea28

http%3A%2F%2Fwww.sciencedirect.com%2Fscience%2Farticle%2Fpii%2FS0997754607000295

http://www.sciencedirect.com/science/article/pii/S0997754607000295Not Available

Kieu C. Q., D. L. Zhang, 2009: Genesis of tropical storm Eugene (2005) from merging vortices associated with ITCZ breakdowns. Part II: Roles of vortex merger and ambient potential vorticity. J. Atmos. Sci., 67, 1980- 1996.10.1175/2008JAS2905.1

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http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2009JAtS...66.1980K

refpaperuri:(ba340e445233dfc0d39781f73090b1ff)

http://adsabs.harvard.edu/abs/2009JAtS...66.1980KNot Available

Kuo H. C., W. H. Schubert, C. L. Tsai, and Y. F. Kuo, 2008: Vortex interactions and Barotropic aspects of concentric eyewall formation. Mon. Wea. Rev., 136, 5183- 5198.10.1175/2008MWR2378.1

e8913d7dd52dec0a594585c16432bd00

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2008MWRv..136.5183K

http://adsabs.harvard.edu/abs/2008MWRv..136.5183KConcentric eyewall formation can be idealized as the interaction of a tropical cyclone core with nearby weaker vorticity of various spatial scales. This paper considers barotropic aspects of concentric eyewall formation from modified Rankine vortices. In this framework, the following parameters are found to be important in concentric eyewall formation: vorticity strength ratio, separation distance, companion vortex size, and core vortex skirt parameter. A vorticity skirt on the core vortex affects the filamentation dynamics in two important ways. First, the vorticity skirt lengthens the filamentation time, and therefore slows moat formation in the region just outside the radius of maximum wind. Second, at large radii, a skirted core vortex induces higher strain rates than a corresponding Rankine vortex and is thus more capable of straining out the vorticity field far from the core. Calculations suggest that concentric structures result from binary interactions when the small vortex is at least 409恪6 times as strong as the larger companion vortex. An additional requirement is that the separation distance between the edges of the two vortices be less than 609恪7 times the smaller vortex radius. Broad moats form when the initial companion vortex is small, the vorticity skirt outside the radius of maximum wind is small, and the strength ratio is large. In concentric cases, an outer vorticity ring develops when the initial companion vortex is large, the vorticity skirt outside the radius of maximum wind is small, and the strength ratio is not too large. In general, when the companion vortex is 3 times as strong as the core vortex and the separation distance is 409恪6 times the radius of the smaller vortex, a core vortex with a vorticity skirt produces concentric structures. In contrast, a Rankine vortex produces elastic interaction in this region of parameter space. Thus, a Rankine vortex of sufficient strength favors the formation of a concentric structure closer to the core vortex, while a skirted vortex of sufficient strength favors the formation of concentric structures farther from the core vortex. This may explain satellite microwave observations that suggest a wide range of radii for concentric eyewalls.

Land er, M., G. J. Holland, 1993: On the interaction of tropical-cyclone-scale vortices. I: Observations. Quart. J. Roy. Meteor. Soc., 119, 1347- 1361.10.1002/qj.49711951406

702d82b9d057c113794da41cc0329d1b

http%3A%2F%2Fonlinelibrary.wiley.com%2Fdoi%2F10.1002%2Fqj.49711951406%2Fabstract

http://onlinelibrary.wiley.com/doi/10.1002/qj.49711951406/abstractAbstract A detailed analysis is made of the observed behaviour in interaction, tropical-cyclone-scale vortices in the western North Pacific region. It is found that all multiple-vortex interactions can be broken down into a common model of binary interaction. The classical Fujiwhara model of converging cyclonic rotation about a centroid followed by merger is rarely followed. Capture tends to occur rapidly, within several hours, and is followed by a period of relatively stable cyclonic orbit. Cyclone merger occurs by one vortex experiencing a loss of convective organization, followed by horizontal shearing and incorporation into the outer circulation of the other vortex. However, a substantial proportion of interacting cyclones escape from the interaction, and the changeover from a stable orbiting configuration occurs rapidly. A model of binary interaction is presented. Cases where swarms of mesoscale vortices are formed in convectively active regions without tropical cyclones are also documented. These vortices have a much narrower range of influence (a few hundred kilometres) then that observed for tropical cyclones. When groups of vortices come within this range they are observed to conform to the same interaction model as observed for tropical cyclones.

Lansky I. M., T. M. O'Neil, and D. A. Schecter, 1997: A theory of vortex merger. Physical Review Letters, 79, 1479- 1482.01c7f760d2c3422282cbf0f7799a90a4

http%3A%2F%2Fscitation.aip.org%2Fgetabs%2Fservlet%2FGetabsServlet%3Fprog%3Dnormal%26id%3DPRLTAO000079000008001479000001%26idtype%3Dcvips%26gifs%3DYes

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Luo D. H., J. Cha, L. H. Zhong, and A. G. Dai, 2014: A nonlinear multiscale interaction model for atmospheric blocking: The eddy-blocking matching mechanism. Quart. J. Roy. Meteor. Soc., 140, 1785- 1808.10.1002/qj.2337

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http%3A%2F%2Fonlinelibrary.wiley.com%2Fresolve%2Fdoi%3FDOI%3D10.1002%252Fqj.2337

refpaperuri:(ef5d30768a06fa5020316496877d1504)

http://onlinelibrary.wiley.com/resolve/doi?DOI=10.1002%2Fqj.2337In this article, a nonlinear multiscale interaction (NMI) model is used to propose an eddy‐blocking matching (EBM) mechanism to account for how synoptic eddies reinforce or suppress a blocking flow. It is shown that the spatial structure of the eddy vorticity forcing (EVF) arising from upstream synoptic eddies determines whether an incipient block can grow into a meandering blocking flow through its interaction with the transient synoptic eddies from the west. Under certain conditions, the EVF exhibits a low‐frequency oscillation on time‐scales of 2–3 weeks. During the EVF phase with a negative‐over‐ positive dipole structure, a blocking event can be resonantly excited through the transport of eddy energy into the incipient block by the EVF. As the EVF changes into an opposite phase, the blocking decays. The NMI model produces life cycles of blocking events that resemble observations. Moreover, it is shown that the eddy north–south straining is a response of the eddies to a dipole‐ or Ω‐type block. In our model, as in observations, two synoptic anticyclones (cyclones) can attract and merge with one another as the blocking intensifies, but only when the feedback of the blocking on the eddies is included. Thus, we attribute the eddy straining and associated vortex interaction to the feedback of the intensified blocking on synoptic eddies. The results illustrate the concomitant nature of the eddy deformation, the role of which, as a potential vorticity source for the blocking flow, becomes important only during the mature stage of a block. Our EBM mechanism suggests that an incipient block flow is amplified (or suppressed) under certain conditions by the EVF coming from the upstream of the blocking region. This also suggests that weather and climate models need to be run with a grid size below 100 km in order to simulate the matching EVF and thus atmospheric blocking.

Montgomery M. T., J. Enagonio, 1998: Tropical cyclogenesis via convectively forced vortex Rossby waves in a three-dimensional quasigeostrophic model. J. Atmos. Sci., 55, 3176- 3207.10.1175/1520-0469(1998)055<3176:TCVCFV>2.0.CO;2

fd45a550a24949f394b26b9e47fb1f9d

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1998JAtS...55.3176M

http://adsabs.harvard.edu/abs/1998JAtS...55.3176MAbstract This work investigates the problem of tropical cyclogenesis in three dimensions. In particular, the authors examine the interaction of small-scale convective disturbances with a larger-scale vortex circulation in a nonlinear quasigeostrophic balance model. Convective forcing is parameterized by its estimated net effect on the potential vorticity (PV) field. Idealized numerical experiments show that vortex intensification proceeds by ingestion of like-sign potential vorticity anomalies into the parent vortex and expulsion of opposite-sign potential vorticity anomalies during the axisymmetrization process. For the finite-amplitude forcing considered here, the weakly nonlinear vortex Rossby wave mean-flow predictions for the magnitude and location of the spinup are in good agreement with the model results. Vortex development is analyzed using Lagrangian trajectories, Eliassen-alm flux vectors, and the Lorenz energy cycle. Using numerical estimates of the magnitude of PV injection based on previous observational and theoretical work, the authors obtain spinup to a 15 m s 1 cyclone on realistic timescales. Simulation of a midlevel vortex with peripheral convection shows that axisymmetrization results in the spinup of a surface cyclone. The axisymmetrization mechanism demonstrates the development of a warm-core vortex. The relative contribution from eddy-heat and eddy-momentum fluxes to the warm core structure of the cyclone is investigated. The vortex spinup obtained shows greater than linear dependence on the forcing amplitude, indicating the existence of a nonlinear feedback mechanism associated with the vortex Rossby waves. Building on recent work by several authors, this work further clarifies the significance of the axisymmetrization process for the problem of tropical cyclogenesis. The theory is shown to be consistent with published observations of tropical cyclogenesis. Further observational and modeling tests of the theory, specific to the dynamics examined here, are proposed.

Nica M., 2011: Eigenvalues and Eigenfunctions of the Laplacian, The Waterloo Mathematics Review, 1, 23- 34.

Prieto R., B. D. McNoldy, S. R. Fulton, and W. H. Schubert, 2003: A classification of binary tropical cyclone-like vortex interactions. Mon. Wea. Rev., 131, 2656- 2666.10.1175/1520-0493(2003)131<2656:ACOBTC>2.0.CO;2

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http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2003MWRv..131.2656P

refpaperuri:(166a20a958d21915afbe508ba483d078)

http://adsabs.harvard.edu/abs/2003MWRv..131.2656PNot Available

Rodrguez-Marroyo, R., À. Viùdez, S. Ruiz, 2011: Vortex merger in oceanic tripoles. J. Phys. Oceanogr., 41, 1239- 1251.10.1175/2011JPO4582.1

c739f2c1468473fd3c3da47c634f4964

http%3A%2F%2Fconnection.ebscohost.com%2Fc%2Farticles%2F62522986%2Fvortex-merger-oceanic-tripoles

http://connection.ebscohost.com/c/articles/62522986/vortex-merger-oceanic-tripolesAbstract A new type of vortex merger is experimentally reported and numerically investigated. The merging process of two anticyclones under the influence of a cyclone (a three-vortex interaction) was observed in sea surface height (SSH) altimetry maps south of the Canary Islands. This three-vortex interaction is investigated using a process-oriented three-dimensional (3D), Boussinesq, and f -plane numerical model that explicitly conserves potential vorticity (PV) on isopycnals. The initial conditions consist of three static and inertially stable baroclinic vortices: two anticyclones and one cyclone. The vortex cores form a triangle in a configuration similar to that found south of the Canary Islands. The numerical results show, in agreement with SSH observations, that two corotating vortices, sufficiently close to each other and in presence of a third counterrotating vortex, merge, leading to a new elongated vortex, which couples with the counterrotating vortex, forming a dipole. Thus, the merging process occurred south of the Canary Islands is consistent with simplified vortex dynamics (basically PV conservation). The merging process depends on the initial PV density extrema, vertical extent, and the angle spanned by the corotating vortices. It is found that the presence of the third counterrotating vortex importantly affects the critical angle of merger and the processes of axisymmetrization and filamentation associated with the two corotating merging vortices. The torque exerted by the counterrotating vortex on the two corotating vortices delays, but does not prevent, their merger.

Simpson J., E. Ritchie, G. J. Holland , J. Halverson, and S. Stewart, 1997: Mesoscale interactions in tropical cyclone genesis. Mon. Wea. Rev., 125, 2643- 2661.4a0bbb8305845d225ad7c60c9f4255cc

http%3A%2F%2Fadsabs.harvard.edu%2Fcgi-bin%2Fnph-data_query%3Fbibcode%3D1997MWRv..125.2643S%26db_key%3DPHY%26link_type%3DABSTRACT%26high%3D545ab6db6a23402

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Tallapragada V., C. Kieu, 2014: Real-Time Forecasts of Typhoon Rapid Intensification in the North Western Pacific Basin with the NCEP Operational HWRF Model. Tropical Cyclone Research and Review, 3, 63- 77.c42a59c6df6a4dde59cb2379d9a129a1

http%3A%2F%2Fwww.researchgate.net%2Fpublication%2F268035291_Real-Time_Forecasts_of_Typhoon_Rapid_Intensification_in_the_North_Western_Pacific_Basin_with_the_NCEP_Operational_HWRF_Model

http://www.researchgate.net/publication/268035291_Real-Time_Forecasts_of_Typhoon_Rapid_Intensification_in_the_North_Western_Pacific_Basin_with_the_NCEP_Operational_HWRF_Model

Wang C.-C., G. Magnusdottir, 2006: The ITCZ in the central and eastern Pacific on synoptic time scales. Mon. Wea. Rev., 134, 1405- 1421.3a71a909d523c94534f6573fd7767ebe

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2006mwrv..134.1405w

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Yamazaki A., H. Itoh, 2013: Vortex-vortex interactions for the maintenance of blocking. Part I: The selective absorption mechanism and a case study. J. Atmos. Sci., 70, 725- 742.10.1175/JAS-D-11-0295.1

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refpaperuri:(f93e9fc9016ed6d230b04b217797b272)

http://onlinelibrary.wiley.com/resolve/reference/XREF?id=10.1175/JAS-D-11-0295.1Not Available

Yasuda I., 1995: Geostrophic vortex merger and streamer development in the ocean with special reference to the merger of Kuroshio warm core rings. J. Phys. Oceanogr., 25, 979- 996.10.1175/1520-0485(1995)025<0979:GVMASD>2.0.CO;2

1a29dc9813736ef35248b36e0abf27f1

http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F1995JPO....25..979Y

http://adsabs.harvard.edu/abs/1995JPO....25..979YNot Available

Yu Z. F., X. D. Liang, H. Yu, and J. C. L. Chan, 2010: Mesoscale vortex generation and merging process: A case study associated with a post-landfall tropical depression. Adv. Atmos. Sci.,27, 356-370, doi: 10.1007/s00376-009-8091-x.10.1007/s00376-009-8091-x

4a11c1fe48fb608522002fd605b0e3a6

http%3A%2F%2Fd.wanfangdata.com.cn%2FPeriodical_dqkxjz-e201002014.aspx

http://d.wanfangdata.com.cn/Periodical_dqkxjz-e201002014.aspxAn observational analysis of satellite blackbody temperature (TBB) data and radar images suggests that the mesoscale vortex generation and merging process appeared to be essential for a tropical-depression-related heavy rain event in Shanghai, China. A numerical simulation reproduced the observed mesoscale vortex generation and merging process and the corresponding rain pattern, and then the model outputs were used to study the related dynamics through diagnosing the potential vorticity (PV) equation. The tropical depression (TD) was found to weaken first at lower levels and then at upper levels due to negative horizontal PV advection and diabatic heating effects. The meso-vortices developed gradually, also from the lower to the upper levels, as a result of positive horizontal PV advection and diabatic heating effects in the downshear left quadrant of the TD. One of these newly-generated vortices, V1, replaced the TD ultimately, while the other two, V2 and V3, merged due to the horizontal PV advection process. Together with the redevelopment of V1, the merging of V2 and V3 triggered the very heavy rain in Shanghai.