Abstract

Most of biologically interesting flows consist of four dimensional (4D), i.e. of three spatial and one temporary dimensions, motion. This is always true regardless it is the internal or the external biological flow field. In the blood flow, one of representative internal flows, the blood vessel has extremely complex 3D configuration and the flow is highly unsteady due to an oscillatory driving pressure generated by the heart. Respiratory flow, which is another important internal flow in the living animals, is a purely oscillatory flow with null mean in time. The airway is also as complex as the vascular system in its configuration and constitution. External flow phenomena are not exceptions to this. Flows passing over wings of flying animals and fins of swimming animals are also strongly unsteady due to oscillatory motion of these propelling structures. The shape of wings and fins is far from simple and their motion is complex in the spatial three dimensions.

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