A skewed eddy of Batchelor-modon type
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A Batchelor-modon eddy is a highly specialized nonlinear vortex pair, whose potential vorticity depends linearly on the stream function viewed from the coordinates moving with the translation velocity of the eddy. To generalize it, a skewed model is developed by introducing a cubic nonlinearity in addition to the linear term.
A perturbation analysis shows that the eddy region is no longer a circle but is elongated longitudinally or transversely according as the sign of the cubic term. Moreover, the eddy is slightly flattened or steepened. The cubic term increases or decreases the translation velocity, if the average radius and the amplitude are fixed.
A numerical experiment on anf-plane is carried out to show that these skewed eddies retain their initial forms even after they turn a corner of the basin; they are as stable as (first-mode) standard Batchelor-modon eddies. The present skewed model gives a reasonable qualitative interpretation of deformed eddies which result from merging of two eddies or from initially Gaussian eddies near the boundary.
KeywordsVortex Vorticity Numerical Experiment Stream Function Linear Term
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