Evgenii N. Snezhkin

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.

Physical Basis for the Experimental Investigation of Rossby Solitons and Laboratory Simulation of Drift Vortices and Solitons in Magnetized Plasma

Structures similar to Rossby vortices in rapidly rotating hydrodynamic media can also exist in strongly magnetized plasma. This follows from the analogy between the motion of a neutral particle in a noninertial (rotating) frame under the influence of the Coriolis force and the motion of a charged particle under the influence of the Lorentz force. In order to understand the physics underlying this analogy, we begin with a few simple examples.

The Natural Phenomena Simulated in Rotating Shallow Water Experiments

In this book we deal with the simulation of large-scale and long-lived structures generated in planetary atmospheres, oceans, and galaxies. In order to outline the scope of the relevant phenomena, we must first define the physical scales of length, proper rotation velocity, and lifetime. Having done this, we shall concentrate our attention on the phenomena of planetary scale (those occurring in planetary atmospheres and oceans). The conditions existing in galaxies will be considered at a later point.

Dipolar Rossby Vortices

Experiments with monopolar Rossby vortices have been described in Chaps. 7, 9. This chapter describes experiments with vortices of different structure — dipoles, consisting of a cyclone-anticyclone pair. Such structures can also be solitons, as mentioned in Sect. 5.5. (They are called solitary waves in the original theoretical study [11.1]. See Sect. 5.4 on our attitude to such terminology.) We conducted an experimental search for such structures using first our small paraboloid (in the preliminary experiments) and then the large one (Table 6.1). Technique “a” is used in both series of experiments: a perturbation extended along the parallel is generated with the pumping disk and later shapes itself into a vortex pair. We shall now describe the experiments in the above order.

Common Features of the Simulated Natural Phenomena

According to astronomical observations, natural structures which at first sight are very different, such as the spiral arms of gaseous galactic disks and the large Rossby vortices in the atmospheres of giant planets, exhibit many common features. Their similarity is the theme of this chapter.