Complex modal analysis of the movements of swimming fish propelled by body and/or caudal fin

Most fish generate thrusts by undulating their body and/or caudal fin (BCF). The movement of a fish body can typically be described as a propulsive wave with an increasing amplitude. In this study, we decompose the midline motions of swimming fish into travelling and standing components based on the complex orthogonal decomposition (COD) analysis. The travelling index, i.e., the relative ratio between the magnitudes of the travelling and standing components, is employed to analyze the typical locomotion of BCF fish. Using existing biological data, we find that anguilliform swimmers prefer wave motions with high travelling index (0.74∼0.90), while the motions of thunniform fish are dominated by a standing wave with the travelling index around 0.36∼0.64. For subcarangiform and carangiform fish, their motions are mixed by the travelling and standing waves with a medium travelling index (0.52∼0.78). The locomotion of BCF fish can be broadly classified into three categories by the travelling index: the standing-wave form, the mixture wave form, and the travelling-wave form. The new criterion is firstly applied to classify the locomotion of BCF fish, different from the traditional classification based on the fraction of fish body with lateral displacement. Moreover, the travelling index can also be used to evaluate the swimming performance, and to analyze the fish swimming dynamics.