E3 Swimming Modes and Reynolds Number

Topic

Fish swimming modes are classified according to two criteria: which part of the body actively participates in propulsion, and the flow regime in which the fish swims—characterized by the Reynolds number. The Reynolds number compares the fluid's inertial forces with its viscous forces and depends on swimming speed, fish size, and water viscosity: when the Reynolds number is less than one, fluid viscosity dominates, as seen in fish larvae or in swimming via a flagellated tail; when the Reynolds number is between one and one thousand, the flow is in a transitional regime; and when the Reynolds number exceeds one thousand, inertial forces dominate, giving rise to the conventional vortex-generating hydrodynamics described in an earlier model in this collection.

In addition to this flow regime, the kinematic classification of swimming modes distinguishes between modes utilizing the body and caudal fin—where undulation propagates from the head or mid-body toward the tail—and modes utilizing median and paired fins, where the pectoral, dorsal, or pelvic fins generate thrust while the rest of the body remains rigid.

Within the modes utilizing the body and caudal fin, there is a spectrum based on how much of the body participates in the undulation: the anguilliform mode, typical of the eel, propagates a large-amplitude wave along the entire body; the subcarangiform mode, typical of the trout, concentrates that undulation in the posterior third of the body; the carangiform mode, typical of the mackerel, uses only the caudal peduncle and the caudal fin itself; ...and the thunniform mode, characteristic of tuna, keeps the body completely rigid, limiting all undulatory movement to the beating of the caudal fin at a high Strouhal number.

In any of these swimming modes, the speed at which the kinematic wave travels along the fish's body must exceed the fish's own swimming speed to generate net forward thrust; the ratio between the swimming speed and the speed of that kinematic wave defines, precisely, the kinematic efficiency of the swimming mode. In the limiting case where the swimming speed equals the kinematic wave speed, no thrust remains available, and the fish's undulating body simply moves without generating net propulsion—much like an eel undulating its body in a mode of pure displacement without advancing.

The expected behavior across this spectrum of swimming modes is that modes concentrated on the caudal fin—such as the thunniform mode—are more efficient at high speeds, whereas modes involving undulation of the entire body—such as the anguilliform mode—offer greater maneuverability at low speeds and within a moderate Reynolds number regime (the same Reynolds number introduced earlier in this model as one of the two criteria used to classify fish swimming modes).

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