Место издания:Publishing House of the Shirshov Institute of Oceanology Moscow
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Аннотация:Looking at Jupiter’s Great Red Spot (JGRS) as the core of the vortex, the authors propose a quasigeostrophic model of this vortex formation, consisting of two vortices nested in each other. The vortex structure with an “attachment” is called a composite vortex. According to measurements obtained in interplanetary missions and on the Hubble Space Telescope (HST), the main outer part of the vortex is anticyclonic, while the inner region is in cyclonic rotation. It is natural to expect that the JGRS is a practically stationary baroclinic vortex, which is under the influence of a barotropic shear flow. The authors propose two variants of the model of such a vortex within the framework of the quasi-geostrophic approach in the approximation of the f-plane motion of the stratified atmosphere. There are two possible cases for mutual combinations of the components of the composite vortex formation proposed by us as a model of the JGRS. A stationary composite vortex composed of two ellipsoidal focal vortices in a horizontal zonal barotropic flow with constant shear. An exact solution of this nonlinear problem has been obtained within the framework of a rotating stratified atmosphere in the quasi-geostrophic f-plane approximation. The solution is based on the results of the study of the ellipsoidal vortex problem, described earlier in [1]. An important condition here is the stationary shape of both vortices. In such a campaign, with a given geometry of vortices and a shift in the background flow, the potential vortices of both vortices are uniquely determined. The main vortex has the same sign of potential vorticity as the background current. The nested vortex has the opposite vorticity. At the same time, the energy of a composite vortex exceeds the energy of a homogeneous stationary vortex without attachment. A combination of a stationary external vortex and a non-stationary embedded vortex, provided that it has little effect on the behavior of the boundary of the main vortex. Both vortices here have an ellipsoidal core shape and are under the influence of the same external flow, a barotropic zonal flow with a shift, as in the first case. The potential vorticity of the main vortex is calculated precisely, and the vorticity of the nested vortex can be arbitrary. The inner vortex moves as a whole in elliptical orbits inside the main vortex. At the same time, the deformations of its core change periodically with a limited oscillation of the horizontal semi-axes. When the centers of the vortices coincide, the inner vortex, remaining in place, can rotate with limited deformation of its boundary. If the embedded vortex has a vorticity opposite to the main vortex, then the energy of the composite vortex turns out to be less than the energy of a homogeneous vortex without attachment. The latter property indicates the energy preference of the existence of composite vortices with a non-stationary embedding that weakly affects the boundary of the main vortex. The proposed theory is compared with the results of observations of the JGRS [2] in the Voyager, Casino, Galileo and HST space missions. Both possible variants of the composite BCL model give qualitatively similar flow patterns, however, the model with an unsteady cyclonic investment requires less energy to maintain it, which speaks in favor of its more realistic applicability to the description of the properties of BCL, which includes, in particular, the unsteadiness of internal movements. The described mathematical method is also applicable to the description of stationary mesoscale ocean vortices in barotropic horizontal shear flows. Keywords: Jupiter’s Great Red Spot, baroclinic vortex, quasi-geostrophic approach, mesoscale ocean vortices References [1] Zhmur, V. V., Pankratov, K. K. Dynamics of an ellipsoidal near-surface vortex in an inhomogeneous flow // Oceanology, 1989, 29 (2), 205–211 (in Russian). [2] David S. Choi, Don Banfield, Peter Jerash, Adam, P. Showman Measuring the velocity and vorticity of Jupiter’s Great Red Spot using automated cloud feature tracking // Icarus, 2007, 188, 35–46, https://doi.org/10.1016/j.icarus.2006.10.037.
