Normal-Mode Initialization of Barotropic Vortex Motion Models

Abstract

An important limitation of numerical hurricane track forecasts is the difficulty in coaxing the vortex to assume the correct initial motion. Results from a semispectral, barotropic, linear model suggest a remedy. When the model is initialized from axisymmetry and rest in a quiescent environment on a Northern Hemisphere ? plane, the vortex moves toward the northwest. The asymmetric streamfunction field is a dipole such that flow between the cyclonic and anticyclonic gyres advects the vortex. This asymmetry appears to reflect a free oscillation because the asymmetric structure, and the induced motion, persists for a long time in the absence of forcing. When the ? effect is turned off, the motion continues on an f plane, and the dipole can be rotated and scaled to product any desired initial motion. In the normal-mode interpretation a vortex with cyclonic circulation throughout accelerates poleward rapidly because the ? effect forces a neutral mode at zero frequency. A vortex with angular momentum reduced to zero by encirclement of the cyclonic core with an annulus of anticyclonic flow experiences weaker forcing of a mode at the most anticyclonic orbital frequency of the axisymmetric circulation. Although the latter mode has a weak barotropic instability, acceleration along the curving track is slow, so that this vortex is promising for track forecasting. By careful choice of vortex position and the normal-mode asymmetry's amplitude and orientation at some time before the beginning of the forecast calculation, it is possible to ?preinitialize? the vortex to pass through a target initial position at the initial time with an arbitrarily chosen initial velocity. In completely cyclonic vortices that have asymptotic decay of the swirling flow with radius, radial wave energy propagation damps the mode at zero frequency. Experimentation with a variety of axisymmetric vortex structures suggests that, with this single qualification, existence of the previously described modes is a general property of barotropic vortices scaled to resemble hurricanes.