An energetics analysis is carried out to investigate the development of the asymmetric gyres and associated propagation of a barotropic cyclone which is embedded in a meridionally varying zonal flow on a beta-plane. Two types of zonal flows are considered: one with a constant relative vorticity resembling those in the vicinity of a subtropical ridge or monsoon trough, and the other with a constant relative vorticity gradient as in the vicinity of an easterly jet. The environmental flow interacts with the gyres and the symmetric circulation of the cyclone, affecting the development of the gyres and thereby the cyclone propagation (beta-drift).
The zonal flow with a constant relative vorticity changes the generation rate of the gyre kinetic energy (GKE) through exchanging energy directly with the gyres. A zonal flow with anticyclonic (cyclonic) vorticity feeds (extracts) kinetic energy to (from) the gyres. The magnitude of this energy conversion is proportional to the magnitude of the zonal flow vorticity and the gyre intensity. As a result, the gyres are stronger and the beta-drift is faster near the subtropical ridge than within a monsoon trough.
The zonal flow with a constant relative vorticity gradient affects gyre intensity via two processes that have opposing effects. A southward vorticity gradient, on the one hand, weakens the gyres by decelerating the energy conversion from the symmetric circulation to the gyres; on the other hand, it enhances the gyres by indirectly feeding energy to the symmetric circulation whose strengthening in turn accelerates the energy conversion to the gyres. The effect of the second process tends to eventually become dominant.
Tropical cyclone motion normally differs from an environmental steering (George and Gray 1976; Chan and Gray 1982; Carr and Elsberry 1990). The difference is attributed to a propagation component that arises from the interaction of the tropical cyclone circulation with embedded environment. Current understanding of such propagation is mainly based on theoretical or numerical models.
Theoretically, the translation of an initially axially symmetric cyclonic vortex embedded in a spatially-varying environmental flow on a beta-plane may be advantageously partitioned into two components: a steering caused by the advection of axially symmetric vorticity by the environmental flow, and a propagation induced by the advection of symmetric vorticity by axially asymmetric flows near the vortex center. The asymmetric flows result from the interaction between the vortex circulation and the planetary vorticity gradient (the beta-effect), and relative vorticity gradient of the environmental flows.
An example of pure steering was given by Adem and Lezama (1960) who showed that a barotropic symmetric vortex embedded in a uniform environmental flow on an f-plane moves exactly with the uniform flow, i.e., the vortex has no propagation. An example of pure propagation was first studied by Rossby (1948) who showed that the meridional variation of planetary vorticity can drive a rigid-body-rotation vortex northward in the absence of the environmental flow. More recent numerical investigations have found that in a quiescent environment on a beta-plane, the propagation of a barotropic symmetric vortex (the beta-drift) is determined by the advection of symmetric vorticity by the asymmetric flow between a pair of counter-rotating gyres (the beta-gyres), which are generated by the advection of planetary vorticity by the symmetric vortex circulation (Chan and Williams 1987; Willoughby 1988; Fiorino and Elsberry 1989; Peng and Williams 1990; Shapiro and Ooyama 1990; Smith et al. 1990; Li and Wang 1993; and others).
In the presence of both beta-effect and environmental flow, vortex translation is a combination of steering and propagation. In the simplest case, in which the environmental flow is uniform and time-independent, the movement of a barotropic vortex can be viewed as a simple addition of a pure steering by the environmental flow with a pure beta-drift due to the beta-effect. When a barotropic environmental flow is latitude-dependent (as will be studied in this paper) or varies with time and space in general, the environmental flow not only provides a steering effect but also interacts with the vortex circulation, modifying the beta-gyres and affecting propagation.
Sasaki (1955) and Kasahara (1957) discussed the effect of an environmental relative vorticity gradient which causes a cyclonic vortex move in a direction 90o to the left of the relative vorticity gradient. DeMaria (1985) showed that an environmental absolute vorticity gradient causes a cyclonic vortex drift relative to the environmental flow with a component in the direction of the gradient and a component 90o to the left of the gradient. To isolate the effect of environmental relative vorticity gradient on vortex motion, Ulrich and Smith (1991) designed an experiment on an f-plane in which environmental flow has a constant meridional relative vorticity gradient that equals . They found that the northward displacement of a cyclonic vortex in the Northern Hemisphere is much smaller than that in the case with a quiescent environment on a beta-plane. But how the vortex propagation is affected remains an open question.
The meridionally-varying environmental flow may affect propagation even in the absence of the relative vorticity gradient. Ulrich and Smith (1991), and Smith (1991) examined the effect of zonal environmental flows with constant shear on vortex motion on a beta-plane. They found that although the environmental flows have no relative vorticity gradient, the northward component of the cyclonic vortex motion in a constant anticyclonic-shear case is significantly larger than that in a constant cyclonic-shear case. Williams and Chan (1993) repeated this. After subtracting out the advection by the environmental flow, they found that the tracks in the cases with constant cyclonic- and anticyclonic-shear flows have the same orientation as the track in the case without environmental flow; however, the cyclonic-shear track is slightly shorter than that without environmental flow, whereas the anticyclonic-shear track is significantly longer. Again, what accounts for these differences are unclear.
The purpose of this paper is to elucidate the mechanisms via which meridionally-varying zonal flows affect vortex propagation on a beta-plane. A typical environmental mid-lower troposphere pressure field in the northwestern Pacific, for example, consists of a subtropical ridge and a monsoon trough to its south. The corresponding zonal wind varies with latitude as illustrated in Fig. 1. Near a subtropical ridge and a monsoon trough, the zonal flow can be idealized as a linear function of latitude, whereas in the region of an easterly jet between the subtropical ridge and monsoon trough, the zonal flow may be approximately described as a summation of a parabolic function of latitude and a uniform easterly flow. It follows that two elementary meridionally-varying zonal flows are interesting, one is a zonal flow with a constant relative vorticity, and the other is a zonal flow with a constant relative vorticity gradient (the easterly jet case). Since the propagation is in accord with the evolution of the asymmetric gyres for both constant vorticity and constant vorticity gradient cases (Williams and Chan 1993), a central question is how these meridionally-varying environmental flows affect the intensities of the asymmetric gyres and modify the propagation component of the vortex motion. Sections 3 and 4 will address these questions through energetics analyses. The kinetic energy equations of the gyres will be first derived in the next section. The last section gives a summary.
The mechanism via which meridionally-varying steady zonal flows affect cyclonic vortex propagation in the presence of planetary vorticity gradient is studied using kinetic energy analysis in a shallow water model.
In a uniform zonal flow the vortex propagation is the same as the beta-drift of the vortex in a quiescent environment; the beta-gyres grow by extracting kinetic energy from the symmetric circulation and their intensity determines the vortex propagation speed. In a meridionally-varying zonal flow, there are three major kinetic energy transfer processes: the conversion between the symmetric circulation and the gyres, the conversion between the environmental flow and the gyres, and the conversion between the environmental flow and the symmetric circulations.
In a zonal flow with a constant relative vorticity, the exchange of kinetic energy between the environmental flow and the beta-gyres is a key process. In the negative constant-vorticity case, the beta-gyres intensify more rapidly by extracting extra energy from the environmental flow. As a result, the vortex propagates significantly faster than without environmental flow. The opposite is true for the positive constant-vorticity case. Therefore, the presence of environmental relative vorticity can effectively modify the asymmetric beta-gyres and change vortex propagation speed.
In a zonal flow with a constant relative vorticity gradient, the presence of the environmental relative vorticity gradient affects the strength of the beta-gyres by directly changing the energy conversion from the symmetric vortex to the gyres, (Ks, Kg), and through indirectly changing the energy conversion between the environmental flow and the symmetric vortex. In the beginning, the gyres grow primarily by extracting energy from the symmetric vortex. It has been shown that a portion of (Ks, Kg) is associated with the advection of symmetric circulation by the environmental flow. The presence of a northward (southward) relative vorticity gradient in the environmental flow enhances (reduces) (Ks, Kg). Thus, the gyres are stronger and the vortex propagates faster in the case of a positive relative vorticity gradient (case D2) than in the case of a negative vorticity gradient (case D1). At the same time, the kinetic energy conversion from the environmental flow to the symmetric vortex, changes the intensity of the symmetric vortex. The presence of a positive (negative) relative vorticity gradient in the environmental flow weakens (strengthens) the symmetric vortex by transferring (extracting) energy to (from) the environmental flow. This process leads to an enhanced symmetric vortex in case D1 and a dramatically weakened one in case D2 in the later stages (after 48 hours). Because the beta-conversion (a major portion of the (Ks, Kgs, Kg) in case D1 becomes much larger than that in case D2. As a result the gyres are stronger and the vortex propagates faster in case D1 than in case D2.
The results here imply that in the vicinity of a steady monsoon trough (subtropic ridge) where a constant positive (negative) relative vorticity exists, the beta-drift will be weaker (stronger). In the vicinity of an easterly jet between the subtropical ridge and monsoon trough, where a southward relative vorticity gradient exists, the beta-drift may be accelerated due to the strengthening of the symmetric vortex. The above conclusions are confined to a situation in which the longitudinal and temporal variation of the environmental flows are not significant.
When the zonal and meridional length scales of the environmental flow are comparable, zonal variations of the meridional component of the environmental flow may have significant effects on the beta-gyres and vortex propagation. The propagation of a vortex embedded in a zonally-varying meridional flow and an environmental flow which has both zonal and meridional components requires further investigation.
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