Mikhail V. Nezlin

Cyclonic-anticyclonic asymmetry and a new soliton concept for Rossby vortices in the laboratory, oceans and the atmospheres of giant planets

Abstract It is demonstrated in laboratory experiments with rotating shallow water that large scale Rossby vortices, greater than the Rossby-Obukhov radius in size, have dispersive and non-linear properties that are fundamentally different for the two possible polarities. We call this “cyclonic-anticyclonic asymmetry”. This asymmetry manifests itself in the following way: first, anticylones, unlike cyclones, do not undergo the dispersive spreading inherent in a linear wave packet. and therefore, having a considerably longer natural lifetime, are obvious candidates for Rossby solitons; second, dipolar vortices are, because of the comparatively rapid decay of a cyclone, transformed into anticyclonic solitons; third, anticyclones are much more readily generated by zonal flows of the type existing in planetary atmospheres. The evident dominance of anticyclones amongst the long-lived vortices in the atmospheres of giant planets strongly suggests that the cyclonic-anticyclonic symmetry plays a decisive role in t...

Centrifugal instability in rotating shallow water and the problem of the spiral structure in galaxies

Abstract A new instability predicte by theory to occur in rotating shallow water in which the rotation velocity has a discontinuity, in a regime where the flow velocity exceeds the characteristics velocity of the waves, has been found experimentally. The instability develops when the radial gradient of the angular velocity across the discontinuity is negative; such an instability is likely to be responsible for the formation of the spiral structure in galaxies which have a similar rotational velocity profile.

Rotating shallow water modeling of planetary,astrophysical and plasma vortical structures (plasma transport across a magnetic field,model of the jupiter's GRS, prediction of existence of giant vortices in spiral galaxies)

Three kinds of results have been described in this paper. Firstly, an experimental study of the Rossby vortex meridional drift on the rotating shallow water has been carried out. Owing to the stringent physical analogy between the Rossby vortices and drift vortices in the magnetized plasma, the results obtained have allowed one to make a conclusion that the transport rate of the plasma, trapped by the drift vortices, across the magnetic field is equivalent to the “gyro-Bohm” diffusion coefficient. Secondly, a model of big vortices of the type of the Great Red Spot of Jupiter, dominating in the atmospheres of the outer planets, has been produced. Thirdly, the rotating shallow water modeling has been carried out of the hydrodynamical generation mechanism of spiral structures in galaxies. Trailing spiral waves of various azimuthal modes, generated by a shear flow between fast rotating “nucleus” and slow rotating periphery, were produced. The spirals are similar to those existing in the real galaxies. The hydrodynamical concept of the spiral structure formation in galaxies has been substantiated. Strong anticyclonic vortices between the spiral arms of the structures under study have been discovered for the first time. The existence of analogous vortices in real galaxies has been predicted. (This prediction has been reliably confirmed recently in special astronomical observations, carried out on the basis of the mentioned laboratory modeling and the prediction made – see the paper by A. Fridman et al. (Astrophysics and Space Science, 1997, 252, 115.)

Milestones in rotating shallow water modeling of Rossby vortices, plasma drift vortices, and spiral structures in galaxies

A review and the current status is given of laboratory experiments on the modeling, using rotating shallow water, of the largest and longest-lived vortical structures in planetary atmospheres, oceans, magnetized plasmas and spiral galaxies. Basic theoretical ideas, partly preceding the experiments mentioned and partly essentially inspired by the latter, are also presented.

Solitonic Model of Natural Vortices

This chapter describes a model of long-lived, large-scale Rossby vortices in planetary atmospheres and in the oceans. In spite of all the distinctions between such vortices with respect to the ambient media and to their dimensions (thousands of kilometers in atmospheres and dozens of kilometers in the oceans), they have the following major features in common: (1) they possess a clearly manifested cyclone-anticyclone asymmetry — all of them, with little exception, are anticyclones; and (2) their sizes are somewhat greater than the Rossby radius r i. These and other properties of such vortices make it possible to describe them with a model which is based on the theory of vortical Rossby solitons and discussed in the next sections.

Rossby Vortices and Solitons in Free Motion

The theory of anticyclonic vortical Rossby solitons has been discussed in Chap. 5. The solitonic concept of anticyclonic Rossby vortices has been used as a foundation for the theoretical solitonic models of the JGRS and similar long-lived vortices in the atmospheres of giant planets and in the oceans. The first consistent solitonic theory of the JGRS was proposed in 1976 (see below). In the light of these theoretical results, it appeared quite important to obtain a Rossby soliton in laboratory experiment. The present chapter describes how this problem was solved.

Physical Prerequisites of the Laboratory Simulation of Large-Scale Rossby Vortices and Galactic Spiral Structures

The simulation of astrophysical phenomena, described in this book, is not based on their outward resemblance to the structures observed in the experiments but rather on the generality of the physical laws governing the dynamics of both laboratory and real-life phenomena, despite the immense difference in their spatial and temporal scales. To illustrate this generality, we start with a very instructive example.

Laboratory Simulation of Galactic Spiral Structures

The present series of experiments is, from the hydrodynamic viewpoint, a logical sequel to the experiments described in the previous chapter where differentially rotating shallow water was considered a model of an ocean or atmosphere. In this chapter, it will serve as a model for the gaseous disk of a galaxy.

Shallow-Water Simulation of Drift Vortices and Solitons in Magnetized Plasma

The physical analogy outlined in Chap. 5 makes it possible to simulate drift (or gradient) vortices and solitons in magnetized plasma, using simple experiments with rotating shallow water. The results of such simulations are presented in this chapter.

Laboratory Simulation of Rossby Vortices and Solitons in Planetary Atmospheres and Oceans

The experiments described in this chapter and in Chaps. 9–11 have been performed in the following succession. First, Rossby vortices and solitons were studied in a liquid rotating as a single body. In these experiments, the vortex under investigation was generated with a local pulsed (single-action) source and then propagated along the parallel in the free-travel regime through the rotating parabolic layer of shallow water. The lifetime of the vortex was limited by viscosity, apart from any other factors [7.1–3]. Next, experiments were carried out on generating Rossby vortices with stationary, axially symmetrical geostrophic counterflows. These experiments produced steadily drifting chains of vortices, from ten vortices in a chain when the flow velocity was low to one when it was high. This second series of experiments is of particular interest since it fits much better with the actual process of Rossby vortex generation by zonal flows in planetary atmospheres, therefore this series will be the first to be described. On the other hand, to elucidate the physical nature of the vortices in question one has to investigate them in their free-travel regime. Without such a study, it is impossible to tell whether there are any Rossby solitons among the observed vortices and whether they simulate plasma drift vortices and solitons. This series of experiments is described in Chaps. 9–11.