September  2012, 17(6): 1795-1807. doi: 10.3934/dcdsb.2012.17.1795

Interactions of point vortices in the Zabusky-McWilliams model with a background flow

1. 

Warwick Mathematics Institute and Warwick Centre for Complexity Science, University of Warwick, Coventry, CV4 7AL, United Kingdom

2. 

Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, 24–29 St Giles’, Oxford OX1 3LB, United Kingdom

Received  May 2011 Revised  December 2011 Published  May 2012

We combine a simple quasi-geostrophic flow model with the Zabusky-McWilliams theory of atmospheric vortex dynamics to address a hurricane-tracking problem of interest to the insurance industry. This enables us to make predictions about the "follow-my-leader" phenomenon.
Citation: Colm Connaughton, John R. Ockendon. Interactions of point vortices in the Zabusky-McWilliams model with a background flow. Discrete and Continuous Dynamical Systems - B, 2012, 17 (6) : 1795-1807. doi: 10.3934/dcdsb.2012.17.1795
References:
[1]

I. J. Benczik, T. Tél and Z. Köllö, Modulated point-vortex couples on a beta-plane: Dynamics and chaotic advection, J. Fluid Mech., 582 (2007), 1-22. doi: 10.1017/S002211200700571X.

[2]

W. Bin, R. L. Elsberry, W. Yuqing and W. Liguang, Dynamics in tropical cyclone motion: A review, Chinese J. Atm. Sci., 22 (1998), 416-434.

[3]

J. G. Charney, On a physical basis for numerical prediction of large-scale motions in the atmosphere, J. Meteor, 6 (1949), 371-385.

[4]

M. Lander and G. J. Holland, On the interaction of tropical-cyclone-scale vortices. I: Observations, Quart. J. Roy. Met. Soc., 119 (1993), 1347-1361. doi: 10.1002/qj.49711951406.

[5]

L. MacManus, et al, Modelling hurricane track memory, Report of 73rd European Study Group with Industry, 2010. Available from: http://www.maths-in-industry.org/miis/view/studygroups/esgi73/.

[6]

NOAA, "Hurricane Basics," 1999. Available from: http://hurricanes.noaa.gov/pdf/hurricanebook.pdf.

[7]

J. Pedlosky, "Geophysical Fluid Dynamics," 2nd ed., Springer, New York, 1987.

[8]

O. U. Velasco Fuentes and F. A. Velázquez Muñoz, Interaction of two equal vortices on a $\beta$-plane, Phys. Fluids, 15 (2003), 1021-1032. doi: 10.1063/1.1556293.

[9]

N. J. Zabusky and J. C. McWilliams, A modulated point-vortex model for geostrophic $\beta$-plane dynamics, Phys. Fluids, 25 (1982), 2175-2182. doi: 10.1063/1.863709.

show all references

References:
[1]

I. J. Benczik, T. Tél and Z. Köllö, Modulated point-vortex couples on a beta-plane: Dynamics and chaotic advection, J. Fluid Mech., 582 (2007), 1-22. doi: 10.1017/S002211200700571X.

[2]

W. Bin, R. L. Elsberry, W. Yuqing and W. Liguang, Dynamics in tropical cyclone motion: A review, Chinese J. Atm. Sci., 22 (1998), 416-434.

[3]

J. G. Charney, On a physical basis for numerical prediction of large-scale motions in the atmosphere, J. Meteor, 6 (1949), 371-385.

[4]

M. Lander and G. J. Holland, On the interaction of tropical-cyclone-scale vortices. I: Observations, Quart. J. Roy. Met. Soc., 119 (1993), 1347-1361. doi: 10.1002/qj.49711951406.

[5]

L. MacManus, et al, Modelling hurricane track memory, Report of 73rd European Study Group with Industry, 2010. Available from: http://www.maths-in-industry.org/miis/view/studygroups/esgi73/.

[6]

NOAA, "Hurricane Basics," 1999. Available from: http://hurricanes.noaa.gov/pdf/hurricanebook.pdf.

[7]

J. Pedlosky, "Geophysical Fluid Dynamics," 2nd ed., Springer, New York, 1987.

[8]

O. U. Velasco Fuentes and F. A. Velázquez Muñoz, Interaction of two equal vortices on a $\beta$-plane, Phys. Fluids, 15 (2003), 1021-1032. doi: 10.1063/1.1556293.

[9]

N. J. Zabusky and J. C. McWilliams, A modulated point-vortex model for geostrophic $\beta$-plane dynamics, Phys. Fluids, 25 (1982), 2175-2182. doi: 10.1063/1.863709.

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