# American Institute of Mathematical Sciences

• Previous Article
Repulsion effects on boundedness in a quasilinear attraction-repulsion chemotaxis model in higher dimensions
• DCDS-B Home
• This Issue
• Next Article
Eventual smoothness and asymptotic behaviour of solutions to a chemotaxis system perturbed by a logistic growth
October  2018, 23(8): 3047-3070. doi: 10.3934/dcdsb.2017196

## On the scale dynamics of the tropical cyclone intensity

 1 Department of Earth and Atmospheric Sciences, Indiana University, Bloomington, IN 47405, USA 2 Department of Mathematics, Sichuan University, Sichuan Sheng, China

* Corresponding author: ckieu@indiana.edu

Received  March 2017 Published  July 2017

Fund Project: This research was supported by the NOAA HFIP funding (Award NA16NWS4680026), the ONR funding (Grant N000141410143), and the Vice Provost for Research through the Indiana University Faculty Research Support Program

This study examines the dynamics of tropical cyclone (TC) development in a TC scale framework. It is shown that this TC-scale dynamics contains the maximum potential intensity (MPI) limit as an asymptotically stable point for which the Coriolis force and the tropospheric stratification are two key parameters responsible for the bifurcation of TC development. In particular, it is found that the Coriolis force breaks the symmetry of the TC development and results in a larger basin of attraction toward the cyclonic (anticyclonic) stable point in the Northern (Southern) Hemisphere. Despite the sensitive dependence of intensity bifurcation on these two parameters, the structurally stable property of the MPI critical point is maintained for a wide range of parameters.

Citation: Chanh Kieu, Quan Wang. On the scale dynamics of the tropical cyclone intensity. Discrete & Continuous Dynamical Systems - B, 2018, 23 (8) : 3047-3070. doi: 10.3934/dcdsb.2017196
##### References:

show all references

##### References:
A bifurcation diagram in terms of the $v$ component of the critical points as a function of the stratification parameter $s$ with fixed values $f =0.01$ and $r = 0.01$
A bifurcation diagram in terms of the $v$ component of the critical points as a function of the Coriolis parameter $f$ with fixed values $s = 0.1, r = 0.01$
a) Flow trajectories for four different initial points in the phase space of $(u, v, b)$ that represent an incipient weak anticyclonic vortex (-0.1, -0.1, 0.1) (red); a mature TC near the MPI equilibrium with a weak warm core (-1, 1, 0.5) (cyan); a mature TC with intensity significant above the MPI equilibrium limit (-1, 1.4, 1) (green); and a mature TC near the MPI equilibrium limit with too weak low level convergence (-0.1, 1, 1) (blue) for the case of $f = 0.05$; (b) Time series of $v$ during the entire simulation; and (c)-(d) Similar to (a)-(b) but for the case of $f=0$
 [1] Franco Maceri, Michele Marino, Giuseppe Vairo. Equilibrium and stability of tensegrity structures: A convex analysis approach. Discrete & Continuous Dynamical Systems - S, 2013, 6 (2) : 461-478. doi: 10.3934/dcdss.2013.6.461 [2] Simion Filip. Tropical dynamics of area-preserving maps. Journal of Modern Dynamics, 2019, 14: 179-226. doi: 10.3934/jmd.2019007 [3] Tian Ma, Shouhong Wang. Tropical atmospheric circulations: Dynamic stability and transitions. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1399-1417. doi: 10.3934/dcds.2010.26.1399 [4] Emine Kaya, Eugenio Aulisa, Akif Ibragimov, Padmanabhan Seshaiyer. Stability analysis of inhomogeneous equilibrium for axially and transversely excited nonlinear beam. Communications on Pure & Applied Analysis, 2011, 10 (5) : 1447-1462. doi: 10.3934/cpaa.2011.10.1447 [5] Tsuyoshi Kajiwara, Toru Sasaki. A note on the stability analysis of pathogen-immune interaction dynamics. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 615-622. doi: 10.3934/dcdsb.2004.4.615 [6] Xiong Li. The stability of the equilibrium for a perturbed asymmetric oscillator. Communications on Pure & Applied Analysis, 2006, 5 (3) : 515-528. doi: 10.3934/cpaa.2006.5.515 [7] Xiong Li. The stability of the equilibrium for a perturbed asymmetric oscillator. Communications on Pure & Applied Analysis, 2007, 6 (1) : 69-82. doi: 10.3934/cpaa.2007.6.69 [8] Jürgen Saal. Wellposedness of the tornado-hurricane equations. Discrete & Continuous Dynamical Systems - A, 2010, 26 (2) : 649-664. doi: 10.3934/dcds.2010.26.649 [9] Salvatore Rionero. A nonlinear $L^2$-stability analysis for two-species population dynamics with dispersal. Mathematical Biosciences & Engineering, 2006, 3 (1) : 189-204. doi: 10.3934/mbe.2006.3.189 [10] Thomas Blanc, Mihaï Bostan. Multi-scale analysis for highly anisotropic parabolic problems. Discrete & Continuous Dynamical Systems - B, 2020, 25 (1) : 335-399. doi: 10.3934/dcdsb.2019186 [11] MirosŁaw Lachowicz, Tatiana Ryabukha. Equilibrium solutions for microscopic stochastic systems in population dynamics. Mathematical Biosciences & Engineering, 2013, 10 (3) : 777-786. doi: 10.3934/mbe.2013.10.777 [12] Robert Stephen Cantrell, Chris Cosner, William F. Fagan. Edge-linked dynamics and the scale-dependence of competitive. Mathematical Biosciences & Engineering, 2005, 2 (4) : 833-868. doi: 10.3934/mbe.2005.2.833 [13] Jan Prüss, Laurent Pujo-Menjouet, G.F. Webb, Rico Zacher. Analysis of a model for the dynamics of prions. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 225-235. doi: 10.3934/dcdsb.2006.6.225 [14] Andrey V. Kremnev, Alexander S. Kuleshov. Nonlinear dynamics and stability of the skateboard. Discrete & Continuous Dynamical Systems - S, 2010, 3 (1) : 85-103. doi: 10.3934/dcdss.2010.3.85 [15] Shunfu Jin, Wuyi Yue, Shiying Ge. Equilibrium analysis of an opportunistic spectrum access mechanism with imperfect sensing results. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1255-1271. doi: 10.3934/jimo.2016071 [16] Oksana Koltsova, Lev Lerman. Hamiltonian dynamics near nontransverse homoclinic orbit to saddle-focus equilibrium. Discrete & Continuous Dynamical Systems - A, 2009, 25 (3) : 883-913. doi: 10.3934/dcds.2009.25.883 [17] Xiao-Bing Li, Xian-Jun Long, Zhi Lin. Stability of solution mapping for parametric symmetric vector equilibrium problems. Journal of Industrial & Management Optimization, 2015, 11 (2) : 661-671. doi: 10.3934/jimo.2015.11.661 [18] Guangying Lv, Hongjun Gao, Jinlong Wei, Jiang-Lun Wu. The effect of noise intensity on parabolic equations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 0-0. doi: 10.3934/dcdsb.2019248 [19] Shengji Li, Chunmei Liao, Minghua Li. Stability analysis of parametric variational systems. Numerical Algebra, Control & Optimization, 2011, 1 (2) : 317-331. doi: 10.3934/naco.2011.1.317 [20] Ismail Abdulrashid, Abdallah A. M. Alsammani, Xiaoying Han. Stability analysis of a chemotherapy model with delays. Discrete & Continuous Dynamical Systems - B, 2019, 24 (3) : 989-1005. doi: 10.3934/dcdsb.2019002

2018 Impact Factor: 1.008