Scaling laws for barotropic vortex beta-drift

Abstract

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 parameters: vortex radius, vortex maximum wind, beta, a dimensionless vortex profile exponent and the strength of the meridional shear of the zonal environmental wind. The use of dimensional 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 nondimensional speed and direction of beta drift are given by V = C(b, S)B-^1/2 and θd = D(b, S), where the functions C(b, S) and D(b, S) are determined empirically. The quantity B is a nondimensional 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.