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 & 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.  doi: 10.1017/S002211200700571X.  Google Scholar

[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.   Google Scholar

[3]

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

[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.  doi: 10.1002/qj.49711951406.  Google Scholar

[5]

L. MacManus, et al, Modelling hurricane track memory,, Report of 73rd European Study Group with Industry, (2010).   Google Scholar

[6]

NOAA, "Hurricane Basics," 1999., Available from: \url{http://hurricanes.noaa.gov/pdf/hurricanebook.pdf}., ().   Google Scholar

[7]

J. Pedlosky, "Geophysical Fluid Dynamics," 2nd ed.,, Springer, (1987).   Google Scholar

[8]

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

[9]

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

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.  doi: 10.1017/S002211200700571X.  Google Scholar

[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.   Google Scholar

[3]

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

[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.  doi: 10.1002/qj.49711951406.  Google Scholar

[5]

L. MacManus, et al, Modelling hurricane track memory,, Report of 73rd European Study Group with Industry, (2010).   Google Scholar

[6]

NOAA, "Hurricane Basics," 1999., Available from: \url{http://hurricanes.noaa.gov/pdf/hurricanebook.pdf}., ().   Google Scholar

[7]

J. Pedlosky, "Geophysical Fluid Dynamics," 2nd ed.,, Springer, (1987).   Google Scholar

[8]

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

[9]

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

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