Tellus, 49A, 474-485

Scaling Laws for Barotropic Vortex Beta-Drift

Ronald B. SMITH
Department of Geology and Geophysics, Yale University, New Haven, Connecticut

Xiaofan LI and Bin WANG
Department pf Meteorology, University of Hawaii at Manoa, Honolulu, Hawaii

(Manuscript received 10 July 1996, in final form 11 March 1997)

A steady-state formulation of dimensional analysis is used to consolidate vortex beta drift data from over 100 single-layer numerical simulations. The physical problem of beta drift considered here includes 5 parameter: vortex radius, vortex maximum wind, beta, a dimentionless vortex profile exponent and the strength of the meridional shear of the zonal environmental wind. The use of dimentional analysis reduces these 5 parameters to 3, and the further use of the square root scaling proposed by Smith reduces the problem to 2 parameters, the vortex exponent b and a shear parameter S. The non-dimensional speed and directions of beta drift are given by V=(b,S)B-1/2 and d=D(b,S), where the functions C(b,S) and D(b,S) are determined empirically. The quantity B is a non-dimensional beta parameter. The proportionality between drift velocity and the square root of beta arises because the magnitude of the beta gyre vorticity is proportional to the square root of beta. An application of an empirical barotropic drift law to ensemble hurricane track forecasting is proposed.

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