# American Institute of Mathematical Sciences

July  2012, 17(5): 1575-1584. doi: 10.3934/dcdsb.2012.17.1575

## Impact of $\alpha$-stable Lévy noise on the Stommel model for the thermohaline circulation

 1 School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China, China 2 State Key Laboratory of Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100029, China 3 Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616

Received  November 2011 Revised  January 2012 Published  March 2012

The Thermohaline Circulation, which plays a crucial role in the global climate, is a cycle of deep ocean due to the change in salinity and temperature (i.e., density). The effects of non-Gaussian noise on the Stommel box model for the Thermohaline Circulation are considered. The noise is represented by a non-Gaussian $\alpha$-stable Lévy motion with $0<\alpha < 2$. The $\alpha$ value may be regarded as the index of non-Gaussianity. When $\alpha=2$, the $\alpha$-stable Lévy motion becomes the usual (Gaussian) Brownian motion.
Dynamical features of this stochastic model is examined by computing the mean exit time for various $\alpha$ values. The mean exit time is simulated by numerically solving a deterministic differential equation with nonlocal interactions. It has been observed that some salinity difference levels remain in certain ranges for longer times than other salinity difference levels, for different $\alpha$ values. This indicates a lower variability for these salinity difference levels. Realizing that it is the salinity differences that drive the thermohaline circulation, this lower variability could mean a stable circulation, which may have further implications for the global climate dynamics.
Citation: Xiangjun Wang, Jianghui Wen, Jianping Li, Jinqiao Duan. Impact of $\alpha$-stable Lévy noise on the Stommel model for the thermohaline circulation. Discrete & Continuous Dynamical Systems - B, 2012, 17 (5) : 1575-1584. doi: 10.3934/dcdsb.2012.17.1575
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