Nonlinear Surface Waves in Two Dimensions
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Two-dimensional flow is a very useful model for practising applications of differential geometry in fluid dynamics. This flow still contains all the special features of the compact three-dimensional flow but is simpler in calculations. In addition, it is not just an idealization, because there are systems that can be modeled with two-dimensional drop systems. Examples of such systems are highly flattened droplets in gravity moving frictionless on rigid surfaces, cell motility and division, electron drops in high magnetics field, long wavelength jets emitted from orifices, evolution of oil spots surrounded by water in oil extraction or ecologic accidents, or closed polymer chains surrounding water bodies. In the following, we discuss some general geometrical properties of two-dimensional flow, and then we study a model of a two-dimensional drop in oscillation, both theoretical and experimental (see Fig. 12.1).