Computational Mathematics and Mathematical Physics

, Volume 59, Issue 9, pp 1493–1507

# Mathematical Modeling of Tropical Cyclones on the Basis of Wind Trajectories

• M. Aouaouda
• H. Fujita Yashima
Article

### Abstract

A mathematical model of the development of a tropical cyclone is considered. It consists of a family of equations obtained by transforming the equation of inviscid non-heat conductive gas (air) motion to the form of equations on wind trajectories in an axially symmetric cylindrical domain. The numerical solution of these equations shows the increase of the wind velocity in accordance with the steam condensation and air warming; later, the velocity becomes stable as the liquid or small pieces of ice accumulate in the air and the friction of water against air decelerates the air updraft.

## Keywords:

tropical cyclone wind trajectories air equations of motion steam condensation finite difference method

## Notes

### ACKNOWLEDGMENTS

We are grateful to Prof. O. Díaz Rodríguez from the Institute of Meteorology, Habana (Cuba) for elucidating the physical aspects of tropical cyclones and to Dr. D. Remaoun Bourega from the Science and Technology University, Oran (Algerie) for help in numerical computations. We are also grateful to S.L. Skorokhodov from the Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow for his help in preparing the text of the paper.

## REFERENCES

1. 1.
A. P. Khain, Mathematical Modeling of Tropical Cyclones(Gidrometeoizdat, Leningrad, 1984) [in Russian].Google Scholar
2. 2.
W. Cotton, G. Bryan, and S. van den Heever, Storm and Cloud Dynamics, 2nd ed. (Academic Press, 2011).Google Scholar
3. 3.
V. Ooyama Katsuyuki, “Conceptual evolution of the tropical cyclone,” J. Meteor. Soc. Japan. 60, 369–379 (1981).
4. 4.
K. A. Emanuel, “An air-sea interaction theory for tropical cyclones. Part I: Steady-state maintenance,” J. Atmos. Sci. 43, 585–604 (1986).
5. 5.
R. Rotunno and K. A. Emanuel, “An air-sea interaction theory for tropical cyclones. Part II: Evolutionary study using a non-hydrostatic axisymmetric numerical model,” J. Atmos. Sci. 44, 542–561 (1987).
6. 6.
G. J. Holland, “The maximum potential intensity of tropical cyclones,” J. Atmos. Sci. 54, 2519–2541 (1997).
7. 7.
J. P. Camp and M. T. Montgomery, “Hurricane maximum intensity: Past and present,” Monthly Weather Rev. 129, 1704–1717 (2001).
8. 8.
V. I. Vlasov, S. L. Skorokhodov, and H. Fujita Yashima, “Simulation of air flow in a typhoon lower layer,” Russ. J. Num. Anal. Math. Mod. 26, 85–111 (2011).
9. 9.
M. T. Montgomery and R. K. Smith, “Recent developments in the fluid dynamics of tropical cyclones,” Trop. Cycl. Res. Rep. 1, 1–24 (2016).Google Scholar
10. 10.
L. D. Landau and E. M. Lifshitz, Fluid Mechanics, 2nd ed. (Nauka, Moscow, 1986; Pergamon Press, Oxford, 1987).Google Scholar
11. 11.
H. Fujita Yashima, “Simulation of the internal structure of tropical cyclones: The flow equation on wind trajectories,” Itogi Nauki Tekh., Ser.: Sovr. Mat. Pril. 137, 118–130 (2017).Google Scholar
12. 12.
S. Ghomrani, J. Marín Antuña J., and H. Fujita Yashima, “Un modelo de la subida del aire ocasionada por la condensación del vapor y su cálculo numeric,” Rev. Cuba Fís. 32, 3–8 (2015).Google Scholar
13. 13.
D. Remaoun Bourega, M. Aouaouda, and H. Fujita Yashima, “Oscillation de la pluie dans un modèle mathématique de l’orage,” Ann. Math. Afr. 7, 19–35 (2018).Google Scholar
14. 14.
A. K. Kikoin and I. K. Kikoin, Molecular Physics (Nauka, Moscow, 1976) [in Russian].Google Scholar
15. 15.
L. T. Matveev, Foundations of General Meteorology: Physics of the Atmosphere (Gidrometeoizdat, St. Petersburg, 2000) [in Russian].Google Scholar