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Using the barotropic model, an analytical expression for the motion of a cyclone embedded in a uniform flow is obtained. The solution contains as parameters the radius of the vortex, the maximum velocity in the vortex, the velocity of the uniform flow and the variation of the Coriolis parameter. It is shown that, if the variation of the Coriolis parameter is neglected, a cyclone initially embedded in a uniform flow moves with the velocity of the flow. However, superimposed with that motion there always exists a north-westward translation due to the variation of the Coriolis parameter that in some cases represents a non-negligible percentage of the total displacement of a hurricane.DOI: 10.1111/j.2153-3490.1960.tb01308.x
Comparison of the values of columns 4 and 5 of Table I shows that a cyclone of radius r0 = 1000 Km is translated to the west due to the variation of the Coriolis parameter, approximately at the rate of 1.5 m/sec; for ro = 500 Km a t the rate of 0.4 m/sec; for Y, = 350 Km at 0.2 m/sec; and for yo = 200 Km a t 0.1 m/sec. If we consider that the effective radius of our vortex model is practically 0.7 Y, we conclude that in a hurricane of effective radius of 700 Km embedded in an easterly flow of 5 m/sec, the 8-term contributes 23 % of the easterly translation of the hurricane, while for effective radius of 350 Km and 140Km, its contribution is of 7 % and 4 %, respectively.
The northward translation of the cyclone, due to the variation of the Coriolis parameter that is given in column 6 of Table I, contains t a as factor and therefore cannot easily be compared with the translationdue to the meridional flow which contains only t as factor.
From the values of column 6 and its comparison with column 4 it is clear that the importance of this term increases when we deal with cyclones with a large radius and strongwind velocities.
When the meridional component of the flow is zero (B = 0)the j3t2-term is the only one responsible for the northward displacement of tropical cyclones (in the Northern Hemisphere).
Besides the 8t2-term, the computation of J2y/2t2yields additional terms in solution (5) of the form