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Fig. 7. Mean vortex circulation changes along the body. All plots have the same
x axis: body position in L. (A) Example of raw data used for
the vortex circulation. Peak positive and negative circulation for the dorsal
fin vortex are shown. Color indicates circulation magnitude (mag.); squares
and diamonds are from positive and negative circulation vortices,
respectively. Broken and dotted lines indicate flow speed and wave speed,
respectively, and are spaced 50% of the tail beat cycle apart. (B,C) Results
of the regression of circulation on phase and body position, detailed in Eqn
4, showing the amplitude of the oscillation in circulation (B) and the phase
of the positive circulation peak (C). Line color indicates specific vortices,
shown schematically at the bottom of B. Phase trajectories in C that wrap
around from 100% back to 0% are indicated with arrowheads and -tails. Although
the regression from Eqn 4 is linear in the amplitude of the sine and cosine
terms separately, the joint amplitudes and phases can have nonlinearities due
to the differing weights of the coefficients. See text for more details.
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