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First published online March 14, 2005
Journal of Experimental Biology 208, 1125-1146 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01507

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Jet flow in steadily swimming adult squid

Erik J. Anderson and Mark A. Grosenbaugh^*

Department of Applied Ocean Physics and Engineering, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543, USA

View larger version (22K): [in a new window]   Fig. 1. Sketch of the structures and propulsive mechanisms of the long-finned squid, L. pealei. The approximate change in jet orifice shape during jetting is shown.

View larger version (8K): [in a new window]   Fig. 2. Vorticity contour plots for jets emitted from a pipe with a sharp trailing edge into still water. (A) L/D=4.3, t=6.7 s, t/tj=3.4, and (B) L/D=16, t=6.7 s, t/tj=0.8, where L is the piston stroke length and D is the pipe inside diameter (2.39 cm). Piston velocity, up=5.0 cm s-1. Red contours represent counterclockwise, or positive, vorticity and blue contours represent clockwise vorticity. Contour magnitudes are 0.5, 1.0, 1.5 and 2.0 rad s-1. Magnitude increases monotonically from the outermost (0.5 rad s-1) contour to the interior of any jet structure. Note that in B the closing of contours near the jet nozzle is an artifact of DPIV. In reality, these contours originate on the inner and outer surfaces of the pipe from which the jet is emitted.

View larger version (66K): [in a new window]   Fig. 3. Velocity magnitude (A,C,E) and vorticity contour plots (B,D,F) during three separate, consecutive jets of an adult L. pealei holding position at 25 cm s-1. Flume flow is from left to right. The aft section of the squid is shown in white in the velocity magnitude plots and in black in the corresponding vorticity contour plots. The elongated region of fast moving fluid is the jet. The magnitudes of vorticity contours are (B) 4, 6, 10, 15 and 20 rad s-1, (D) 2, 4, 6, 10, 15 and 20 rad s-1, and (F) 3, 4, 6, 10, 15 and 20 rad s-1. See explanation of contour identification in Fig. 2. These are not consecutive image pair visualizations; rather each set of plots represents the flow at some instant during the jet period of three consecutive jets. (A,B) t=0.3 s, t/tj=1.0, (C,D) t=0.7 s, t/tj=1.2, and (E,F) t=0.5 s, t/tj=0.9.

View larger version (53K): [in a new window]   Fig. 4. Velocity magnitude (A,C,E) and vorticity contour plots (B,D,F) during three jets from three different adult L. pealei holding position at approximately the same swimming speed. (A,B) 25 cm s-1, (C,D) 26 cm s-1, (E,F) 27 cm s-1. The magnitudes of vorticity contours are (B) 4, 6, 10, 15 and 20 rad s-1, and (D,F) 3, 4, 6, 10, 15 and 20 rad s-1. See explanation of contour identification in Fig. 2. (A,B) t=0.3 s, t/tj=0.5, (C,D) t=0.3 s, t/tj=0.5, and (E,F) t=0.7 s, t/tj=1.2.

View larger version (56K): [in a new window]   Fig. 5. Velocity magnitude (A,C,E) and vorticity contour plots (B,D,F) during three jets from three different adult L. pealei holding position at three different swimming speeds. (A,B) 13 cm s-1, (C,D) 25 cm s-1, (E,F) 56 cm s-1. Note the decrease in jet angle subtended from the horizontal with increasing swimming speed. The magnitudes of vorticity contours are (B,F) 3, 4, 6, 10, 15 and 20 rad s-1, and (D) 4, 6, 10, 15 and 20 rad s-1. See explanation of contour identification in Fig. 2. (A,B) t=0.5 s, t/tj=1.3, (C,D) t=0.3 s, t/tj=0.5, and (E,F) t=0.2 s, t/tj=1.0.

View larger version (63K): [in a new window]   Fig. 6 .Velocity magnitude (A,C,E) and vorticity contour plots (B,D,F) showing the later development of three jets from the same adult L. pealei holding position at 25 cm s-1. (A,B) An apparent chain of vortex-rings; (C,D) the typical jet breakdown into more or less coherent packets of vorticity; (E,F) the transition of unstable jet flow to turbulence. The magnitudes of vorticity contours are 2, 4, 6, 10, 15 and 20 rad s-1. See explanation of contour identification in Fig. 2. (A,B) t=0.6 s, t/tj=2.0, (C,D) t=0.53 s, t/tj=1.6, and (E,F) t/tj>1.0.

View larger version (86K): [in a new window]   Fig. 7. (A) Representative velocity field including vectors near the aft region of a steadily swimming squid during jet emission, U=25 cm s-1, t=0.3 s, t/tj=0.5. In (A) the aft section of the squid is shown in white. Every other vector has been removed from the original data for clarity. (B) The sub-region of the velocity field in A surrounding the jet. The region was rotated so that the jet axis (x') is horizontal and a regular grid of vectors was interpolated at the approximate resolution of the original data. The white regions in the lower left- and right-hand corners are regions of no data.

View larger version (47K): [in a new window]   Fig. 8. (A) Velocity field, (B) tangential profile and (C) normal profile of the jet from Fig. 7 with freestream flow velocity subtracted. The velocity magnitude contour in A reveals the jet structure as defined in this work as the locus of points for which velocity drops to within 5% of the freestream flow. Blank grid points represent locations of zero relative velocity. Broken lines in profile plots (B,C) are profile axes. Profiles are solid curves. Profile values to the right of axis of a given profile in B and C represent flow in the positive x'- and y'-directions, respectively, in the rotated reference frame.

View larger version (19K): [in a new window]   Fig. 9. Histogram of the ratio of jet structure length to jet diameter, Lj/D, based on the maximum length of each jet in the field of view visualized for all squid jets in which the squid was holding position (116 jets). The black section of each bar represents measurements that appeared to be good estimates of the total length of the jet structure. The white section of each bar represents measurements considered to be underestimates because the jet structure extended out of the field of view or the squid swam at a slight angle to the laser plane. Bin centers start at 2 and bin width is 2.

View larger version (20K): [in a new window]   Fig. 10. Histograms of estimated upper (A) and lower-bound (B) distributions of the ratio of jet plug length to jet diameter, L/D, based on jet velocity and jet period for squid jets in which the squid was holding position and the jet nozzle was visible (89 out of 116 jets). Bin centers start at 2 and bin width is 2.

View larger version (29K): [in a new window]   Fig. 11. (A,B) Average jet velocity j, (C) L/D from average jet velocity, j, jet period and jet diameter, (D) jet period, (E) jet frequency and average jet frequency, and (F) jet angle as functions of swimming speed. Swimming speed is in Lm s-1, except in A. Each data point represents a jet. Jet period (D) looks discretized because of the precise timing of image exposures. In E, the open squares represent average jet frequencies, favg, for all sets of 3 or more jet events of individual squid at the same swimming speed. The curve in E is a parabolic fit to the average jet frequencies, favg. Jet angle (F) is measured in degrees subtended from the horizontal.

View larger version (28K): [in a new window]   Fig. 12. (A) Slip, (B,C) propulsive efficiency and (D) jet thrust as functions of swimming speed. Equations of curve fits, when shown, are for solid curves. (A) Slip calculated as uj/(Ucosß)-1 (data points and solid curve) and uj/U-1 (broken curve). (B) Jet propulsive efficiency as calculated from Eq. 3. (C) Jet propulsive efficiency as calculated from a three-dimensional approximation of jet kinetic energy (data points and solid curve) with the fit curve from (B) for comparison (broken line). (D) A comparison of average jet thrust determined from jet velocity, the change in momentum in successive jet visualizations, and the unsteady jet analysis of Anderson and DeMont (2000). Error bars represent 95% confidence limits.

View larger version (32K): [in a new window]   Fig. 13. Vorticity contour plots of pipe jet events with increasing levels of background flow (U/up) for the cases of L/D=4.3 (A,C,E) and L/D=16 (B,D,F). (A,B) Background flow velocity less than piston velocity, U/up=0.5 (U=5 cm s-1; up=10 cm s-1; D=2.39 cm). (C,D) Background flow velocity equal to piston velocity, U/up=1.0 (U=5 cm s-1; up=5 cm s-1; D=2.39 cm). (E,F) Background flow velocity greater than piston velocity, U/up=2.0 (U=5 cm s-1; up=2.5 cm s-1; D=2.39 cm). The magnitudes of vorticity contours are 0.4, 0.5, 1.0, 1.5 and 2.0 rad s-1. See explanation of contour identification in Fig. 2. (A) t=3 s, t/tj=3, (B) t=3 s, t/tj=0.8, (C) t=4 s, t/tj=2, (D) t=4.7 s, t/tj=0.6, (E) t=8 s, t/tj=2, and (F) t=6 s, t/tj=0.4.