An energetics analysis is presented to reveal the mechanisms by which the environmental flows affect hurricane beta-gyre intensity and beta drift speed. The two-dimensional environmental flow examined in this study varies in both zonal and meridional directions with a constant shear.
It is found that positive (negative) shear strain rate of the environmental flow accelerates (decelerates) beta-drift. The horizontal shear of the environmental flow contains an axially symmetric component that is associated with vertical vorticity and an azimuthal wavenumber two component that is associated with shear strain rate. It is the latter that interacts with the beta gyres, determining the energy conversion between the environmental flow and beta gyres. A positive shear strain rate is required for transfering kinetic energy from the environmental flow to the beta gyres. As a result, the positive shear strain rate enhances the beta gyres and associated steering flow that, in turn, accelerates the beta drift.
In this paper we have analyzed the causes for the development of the beta gyres and the effects of the development on beta-drift (propagation) speed for a barotropic cyclone embedded in a horizontally-varying environmental flow with constant shear. Such environmental flow can represent a variety of patterns which resemble some typical environmental flow fields surrounding tropical cyclones. For instance, when the meridional shear of the zonal wind component (Uy) and zonal shear of the meridional wind component (Vx) have opposite signs (thus the shear strain rate vanishes), the flow patterns describe either a subtropical anticyclone or a monsoon depression, depending on the sign of the relative vorticity. When both Uy and Vx have positive signs and the relative vorticity vanishes, the flow pattern represents a saddle field with anticyclonic circulation to the east and west and cyclonic circulation to the south and north, resembling a flow west of a subtropical ridge. In general, the pattern of a linear flow is determined by the ratio of the relative vorticity to shear strain rate of the flow, and the horizontal aspect ratio of the flow pattern depends on the ratio of |Uy| to |Vx|.
Recent studies (Ulrich and Smith 1991; Williams and Chan 1994) showed that in a linear zonal flow an anticyclonic(cyclonic) environmental vorticity can accelerate (decelerate) beta drift. We have shown here that in a linear meridional flow an anticyclonic (cyclonic) environmental vorticity decelerates (accelerates) the beta drift. This opposing result indicates that the relative vorticity of an environmental flow does not control beta-drift speed.
We have further demonstrated that the beta drift speeds depend on the environmental shear strain rates. The horizontal shear of an environmental flow contains an axially symmetric component that is associated with the relative vorticity and an azimuthal wavenumber two component that is associated with the shear strain rate (Eq.(3.4)). The energetics analysis reveals that the azimuthal wavenumber-two component of the horizontal shear, interacts with the gyres, determining the energy conversion between the environmental flow and the gyres. The energy conversion from the linear environmental flow to the gyres requires a positive shear strain rate of the environmental flow.
The present study focuses only on the factors that determine beta-drift speed. The factors that control the rotation of the beta gyres and the direction of the beta drift will be reported in an accompanying paper.
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