Escaping flatland: Three-dimensional kinematics and hydrodynamics of median fins in fishes

In the classic book Flatland, E. A. Abbott describes a world of two dimensions, a world in which the inhabitants live in ignorance of the third dimension, a world in which it is impossible to distinguish circles from squares, and squares from pentagons – everything looks like a line in the two-dimensional world of Flatland (Abbott, 1899). Then, a disruptive Sphere enters to make inhabitants aware of a third dimension, causing consternation and ultimately sending the narrator to jail. The Flatland of Abbott’s book is an appropriate metaphor for much of the current literature on undulatory locomotion in fishes, which is largely devoted to analyses of fish swimming in the horizontal (two-dimensional, 2D) plane. This 2D world has, so far, been an appropriate place to conduct our studies of fish locomotion: fewer cameras are needed to acquire data, analyses are simpler, and theoretical models can be generated more easily (e.g. Schultz and Webb, 2002). But fish are three-dimensional (3D), with prominent median and paired fins that project into the water, and with clearly defined edges that demark the dorsal, ventral and caudal body surface. Although thinking in three dimensions may complicate our lives, it is nonetheless a critical next step that experimental and computational analyses of fish undulatory locomotion are only now starting to grapple with. Like the residents of Flatland, we must learn to deal with the 3D world. The 3D nature of fish functional design is clearly seen in the enormous diversity of body shapes and swimming modes in fishes, but the precise advantage of one shape or mode over another is less clear. Generalizations from hydrodynamic theories combined with observations of typical swimming behavior have led to much speculation on the adaptations of certain morphologies to different situations (Lighthill, 1975; Marshall, 1971). Tunas, for example, are highly specialized in many ways, many of which are probably adaptations to their active, pelagic lifestyle (Block and Stevens, 2001). However, eels, which have a different body shape and swimming mode from tunas, also migrate thousands of kilometers The Journal of Experimental Biology 211, 187-195 Published by The Company of Biologists 2008 doi:10.1242/jeb.008128