Table 1.
Test fish parameters.
Fig 1.
Points on the body axis.
Fig 2.
Model used in the CFD analysis.
Fig 3.
Analytical area for CFD analysis of solitary swimming: (a) Top view and (b) side view.
Fig 4.
Mesh partitioning in CFD analysis of solitary swimming.
Fig 5.
Analytical area for CFD analysis of parallel swimming: (a) Plan view and (b) side view.
Fig 6.
Mesh partitioning in CFD analysis of parallel swimming.
Fig 7.
Decomposition of force Fi on elements of the fish body surface.
U is the inlet flow speed, V0 is the velocity of the element, ui is the velocity of the element in the direction of travel, vi is the velocity of the element in the lateral direction, is the thrust acting on the element, and
is the lateral force acting on the element.
Fig 8.
Time-series of the data for each point on the body axis of the fish.
A comparison is shown between the measured data (solid line) and the results obtained from the swimming motion function (dashed line) at a swimming speed of 1.52 BL s−1.
Table 2.
Constants a, b, c, and d in Eq 2 and wavelength (λ) and frequency of caudal fin (f) in Eq 3.
Fig 9.
Thrust and drag acting on the fish model surface.
These forces acted during three strokes of tail beating at a swimming speed of 1.52 BL s−1.
Fig 10.
Model surface pressure distributions.
These show the right (1) and left (2) sides of the caudal fin tail tip at maximum speed (a) at a swimming speed of 1.52 BL s−1.
Table 3.
Time-averaged values of thrust and drag (defined as FT and FD, respectively) compared at each swimming speed.
Fig 11.
Velocity distribution around the model: (a) individual distance of 0.4L and inphase; (b) individual distance of 0.4L and antiphase; (c) individual distances of 0.8L and inphase; (d) individual distance of 0.8L and antiphase; (e) individual distance of 1.2L and inphase; and (f) individual distance of 1.2L and antiphase.
Fig 12.
Velocity value at each point of the velocity distribution.
The horizontal axis represents the distance from the origin on a dotted line parallel to the x-axis with the midpoint of the snout of the two individuals as the origin at an individual distance of 0.8L and under antiphase condition. The vertical axis represents the velocity values on the dotted line. The long-dashed line indicates the inlet flow speed (1.52 BL s−1).
Fig 13.
Swimming efficiency of two individuals swimming in parallel under inphase (solid line) and antiphase (dashed line) conditions.
Fig 14.
Surface pressure contour plot at the maximum velocity of caudal fin amplitude motion: (a) Inter-individual distance of 0.4L, (b) individual distance of 2.0L.