Abstract
A linear nondivergent barotropic model is developed to obtain the asymmetric circulation associated with a vortex moving on the β-plane. The total system is transformed to a coordinate system moving with the vortex. The direction and speed of movement is specified from full nonlinear model results. Two wavenumber one gyres are obtained from the asymmetric vorticity equation. The inner gyres move in the azimuthal direction whose maximum amplitude is located at the radius of maximum wind. These inner gyres are associated either with the unstable mode or the neutral mode depending on the resolution of the model. The outer gyres, whose orientations are always along the track direction specified by the movement, correspond to the β-gyres obtained in the nonlinear numerical model. The strength of the inner gyres is much larger than the strength of the outer gyres. For the steady state solution with high finite difference resolution, only the inner gyres are present. In a steady state solution, the outer β-gyres can be isolated by modifying the inner part of the basic wind profile or by reducing the resolution of the mode. In a time dependent solution, the inner gyres will not form if there is no discrete mode existing in the free model system. The outer β-gyres thus obtained have the correct orientation and magnitude when compared to the solutions of the full nonlinear model. These solutions can be used as a tool for bogusing the vortex into a numerical hurricane forecast model.
