Natural Hazards

, Volume 94, Issue 3, pp 1293–1304 | Cite as

Tropical cyclone: expressions for velocity components and stability parameter

  • Indrajit GhoshEmail author
  • Nabajit Chakravarty
Original Paper


Tropical cyclones are the most devastating natural calamity forming in the ocean bed and die out in land. The life cycle of a tropical cyclone is mainly classified into four stages: (a) formation or genesis stage, (b) intensification stage, (c) mature stage and (d) decay stage. The intensification and mature stages are also known as tropical storm and cyclone (hurricane) stage, respectively. To develop the model of tropical cyclone we have taken the momentum conservation equation, equation of continuity and equation of hydrostatic balance in cylindrical coordinate system. Also the equation of state and the equation relating the velocity component and stream function are taken into account. We have assumed a suitable analytic form of the radial component of velocity as a function of radial distance (r) from the axis of the cyclone and vertical distance (z) from the sea bed. So in our model we have taken a cyclone as a rotating cylinder. With the use of the expression of the radial component velocity we have solved the governing nonlinear equation in the cylindrical coordinate system of a cyclone using ‘Wentzel–Kramers–Brillouin approximation’ and estimated the transverse velocity on the sea bed and in the vicinity of the eye wall of the cyclone. From the results we also get a path to generalize the tropical cyclone model as a vortex which is a generating curve of a cyclone. We also determine the vertical component of velocity of the cyclone. In this work we define a new parameter called the cyclone stability parameter (CSP). The CSP helps to determine the stability of a tropical cyclone from its genesis.


Tropical cyclone Analytic model Radial velocity Nonlinear Transverse velocity 



The author I.G. is highly grateful to the Director of College of Engineering and Management, Kolaghat, for providing the necessary opportunity to continue this research and make it a success. The author N.C. is highly grateful to the Director General, India Meteorological Department (Dr. K. J. Ramesh), for his continuous support and encouragement to do this work. Authors are also grateful to anonymous references for their valuable suggestions to improve this work.


  1. Arora K, Dash P (2016) Towards dependence of tropical cyclone intensity on sea surface temperature and its response in a warming world. MDPI Article Climate 4:30. CrossRefGoogle Scholar
  2. Bretherton CS, Peters EM, Back LE (2004) Relationship between water vapour path and precipitation over tropical oceans. J Clim 17:1517–1528.<1517:RBWVPA>2.0.CO;2 CrossRefGoogle Scholar
  3. Crinivec N, Smith RK, Kilroy G (2015) Dependence of tropical cyclone intensification rate on sea surface temperature. Q J R Meteorol Soc 141:1618–1627. CrossRefGoogle Scholar
  4. De Maria M, Kaplan J (1994a) A statistical hurricane intensity prediction scheme (SHIPS) for the Atlantic basin. Weather Forecast 9:209–220CrossRefGoogle Scholar
  5. De Maria M, Kaplan J (1994b) Sea-surface temperature and the maximum intensity of Atlantic tropical cyclones. J Clim 7:1324–1334CrossRefGoogle Scholar
  6. De Maria M, Kaplan J (1999) An updated statistical hurricane intensity prediction scheme (SHIPS) for the Atlantic and East North Pacific basins. Weather Forecast 14:326–337CrossRefGoogle Scholar
  7. Dean L, Emanuel KA, Chavas DR (2009) On the size distribution of Atlantic tropical cyclones. Geophys Res Lett 36:L14803. CrossRefGoogle Scholar
  8. Emanuel K (2005) Increasing destructiveness of tropical cyclones over the past 30 years. Nature 436:686–688. CrossRefGoogle Scholar
  9. Emanuel K (2007) Environmental factors affecting tropical cyclone power dissipation. J Clim 20:5497–5509. CrossRefGoogle Scholar
  10. Emanuel K (2011) Time-dependant axisymmetric model phrased in R-space. Accessed Spring (2011)
  11. Ghosh I, Chakravarty N (2017) Extreme weather situations: tropical cyclones, some analytic perspectives. National seminar on Thunderstorms: socio-economic impacts, early warning and risk management by IMD and IMSGoogle Scholar
  12. Giaiotti DB, Stel F (2006) The Rankine vortex model. Accessed 4 Oct 2006
  13. Griffiths DJ (2005) Introduction to quantum mechanics, 2nd edn. Pearson Education, ChennaiGoogle Scholar
  14. Holton JR (1972) An introduction to dynamic meteorology, 4th edn. Academic Press, London, p 535Google Scholar
  15. Kieu CQ (2004a) An analytical theory for the early stage of the development of hurricanes: part-1. arXiv:physics/0407073. Accessed (2004)Google Scholar
  16. Kieu CQ (2004b) An analytical theory for the early stage of the development of hurricanes: part-2. arXiv:physics/0408044. Accessed (2004)Google Scholar
  17. Kilroy G, Montgomery MT, Smith RK (2014) Why do model tropical cyclones intensify more rapidly at low latitudes? J Atmos Sci 72:1783–1804. CrossRefGoogle Scholar
  18. Kotal SD, Kundu PK, Roy Bhowmik SK (2009) An analysis of sea surface temperature and maximum potential intensity of tropical cyclones over the Bay of Bengal between 1981 and 2000. Meteorol Appl 16:169–177. CrossRefGoogle Scholar
  19. Lala S et al (2014) Mathematical explanation of earlier dissipation of the energy of tilted cyclone. J Climatol Weather Forecast 2:113. CrossRefGoogle Scholar
  20. Mandal JC (1986) A model of tropical storm from temperature anomaly distributions. Mausam 39:367–374Google Scholar
  21. Powell DM, Reinhold AT (2007) Tropical cyclone destructive potential by integrated kinetic energy. Bull Am Meteorol Soc 88:513–526. CrossRefGoogle Scholar
  22. Raga GB, Raymond DJ (2003) Convective forcing in the inter tropical convergence zone of the Eastern Pacific. J Atmos Sci 60:2064–2082.<2064:CFITIC>2.0.CO;2 CrossRefGoogle Scholar
  23. Sampson RC, Knaff AJ (2015) A consensus forecast for tropical cyclone gale wind radii. Weather Forecast 30:1397–1403. CrossRefGoogle Scholar
  24. Sessions SL, Fuchs Z, Raymond DJ (2007) A theory for the spinup of tropical depressions. Q J R Meteorol Soc 133:1743–1754. CrossRefGoogle Scholar
  25. Smith RK (2006) Lectures on tropical cyclones. Accessed 2 June 2006
  26. Sobel HA, Sessions SL, Raymond DJ et al (2009) The mechanics of gross moist stability. J Adv Model Earth Syst 1:9. CrossRefGoogle Scholar
  27. Wang LX (2016) Inter-comparison of extra tropical cyclone activity in nine reanalysis data sets. J Atmos Res 181:133–153. CrossRefGoogle Scholar
  28. Wang Y, Wu CC (2004) Current understanding of tropical cyclone structure and intensity changes—a review. Meteorol Atmos Phys 87:257–278. CrossRefGoogle Scholar
  29. Wang Y, Xu J (2010) Energy production, frictional dissipation and maximum intensity of a numerically simulated tropical cyclone. J Atmos Sci 67:97–116. CrossRefGoogle Scholar
  30. Whitney LD, Hobgood JS (1997) The relationship between sea surface temperatures and maximum intensities of tropical cyclones in the Eastern North Pacific Ocean. J Clim 10:2921–2930.<2921:TRBSST>2.0.CO;2 CrossRefGoogle Scholar
  31. Williams GJ, Taft RK (2013) Shock like structures in the tropical cyclone boundary layer. J Adv Model Earth Syst 5:338–353. CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Basic SciencesCollege of Engineering and Management KolaghatEast MedinipurIndia
  2. 2.Meteorological Office, Imphal, New ATS Building, Imphal International AirportImphal WestIndia

Personalised recommendations