The understanding of the complex dynamics in plasmas, in meteorological and astrophysical systems etc. is of great relevance not only to academic research but also to our daily lives. Computer simulations are still a long way from yielding satisfactory results and it is thus all the more striking that the simple (hydrodynamic) laboratory simulations devised by the authors provide so much insight into the nature of these phenomena and even facilitate predictions.

Table of Contents:
1. Introduction.- 2. The Natural Phenomena Simulated in Rotating Shallow Water Experiments.- 2.1 Length, Rotation Velocity, and Lifetime of the Structures.- 2.2 Large-Scale, Long-Lived Rossby Vortices in the Atmospheres of Giant Planets. The Cyclone-Anticyclone Asymmetry.- 2.3 Rossby Vortices in the Oceans.- 2.3.1 Open Sea Vortices.- 2.3.2 Rings of the Gulf Stream and the Kuroshio Current.- 2.3.3 Internal Thermoclinic Vortices (Lenses).- 2.4 Spiral Structures in Galaxies.- 3. Common Features of the Simulated Natural Phenomena.- 3.1 Quasi-Two-Dimensionality.- 3.2 Structure Generation by Flows with Horizontal Velocity Shear.- 3.3 Horizontal Dimensions Exceeding the Characteristic Rossby Radius.- 4. Physical Prerequisites of the Laboratory Simulation of Large-Scale Rossby Vortices and Galactic Spiral Structures.- 4.1 The Analogy Between Two-Dimensional Gas Dynamics and the Dynamics of Shallow Water.- 4.1.1 Theory.- 4.1.2 Experiment.- 4.2 Principal Similarity Parameters in Nature and Experiment.- 5. Physical Basis for the Experimental Investigation of Rossby Solitons and Laboratory Simulation of Drift Vortices and Solitons in Magnetized Plasma.- 5.1 Two-Dimensional Motion of Charged Particles in Magnetized Plasma and Particles in Rotating Shallow Water.- 5.2 General Nonlinear Equation for Drift Motion.- 5.3 Linear Rossby Waves and Plasma Drift Waves.- 5.4 Linear Packet of Rossby Waves and the Time of its Dispersion Decay. Definition of a Soliton.- 5.5 Nonlinear Rossby Waves: Vortices and Solitons.- 5.6 Viscous Damping of Rossby Vortices.- 6. Experimental Configurations.- 6.1 Geometry and Rotation Regime of the Vessels for the Observation of Rossby Solitons.- 6.2 Techniques for Local Generation of Rossby Vortices.- 6.3 Devices for Generating Rossby Vortices by Counterflows.- 6.4 Devices for the Simulation of Galactic Spiral Structures.- 6.5 Diagnostic Techniques.- 7. Laboratory Simulation of Rossby Vortices and Solitons in Planetary Atmospheres and Oceans.- 7.1 Generation of Rossby Vortex Chains by Zonal Counterflows in Rotating Shallow Water. The Cyclone-Anticyclone Asymmetry.- 7.2 Self-Organizing Solitary Anticyclonic Rossby Vortex in Zonal Flows as a Model of Jovian Great Red Spot.- 7.3 Regularity in the Generation of Chains with Different Numbers of Vortices and the Problems of Uniqueness and Stationarity of the JGRS.- 7.4 Two- and Three-Dimensional Models of the JGRS.- 7.5 Alternative JGRS Laboratory Models.- 7.6 Stationary Rossby Vortices in Flows and the Blocking Phenomenon.- 8. Laboratory Simulation of Galactic Spiral Structures.- 8.1 Generation of Spiral Structures in Differentially Rotating Shallow Water.- 8.2 Spiral-Vortex Structures.- 8.3 The Common Mechanism Generating Solitary Rossby Vortices in Planetary Atmospheres and Spirals in Galaxies.- 8.4 Asymmetrical and Outbranching Spirals.- 8.5 The Influence of Viscosity and Friction.- 8.6 Laboratory Simulation and Astronomical Observations. Predictions for Astronomers.- 9. Rossby Vortices and Solitons in Free Motion.- 9.1 A Short History of the Experiments.- 9.2 Rossby Solitons in the Laboratory and Their Properties.- 9.3 Collisions of Rossby Vortices.- 9.4 Cyclone-Anticyclone Asymmetry.- 9.5 Quasi-Two-Dimensionality of Rossby Vortices. The Non-Principal Role of Viscosity.- 9.6 Vortex-Wave Dualism.- 9.7 Comparison between Experiment and Theory.- 10. Solitonic Model of Natural Vortices.- 10.1 Solitonic Model of the JGRS and Other Large-Scale, Long-Lived Vortices in Planetary Atmospheres.- 10.2 An Alternative Model of the JGRS: Numerical Calculation.- 10.3 Solitonic Vortices in the Oceans.- 11. Dipolar Rossby Vortices.- 11.1 Preliminary Experiments.- 11.2 Dipolar Vortex Decay for Moderate Liquid Depths.- 11.3 Solitonic Properties of Dipolar Vortices for Large Liquid Depths.- 12. Shallow-Water Simulation of Drift Vortices and Solitons in Magnetized Plasma.- 12.1 Prediction of Drift Soliton Properties Based on Shallow-Water Simulation. Drawbacks of the "Purely Wave" Concept.- 12.2 Vortical Mechanism for the Enhanced Diffusion of Plasma Across a Strong Magnetic Field.- 13. Conclusion.- S. Supplements.- References.