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First published online May 1, 2009
Journal of Experimental Biology 212, 1506-1518 (2009)
Published by The Company of Biologists 2009
doi: 10.1242/jeb.026948
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Pulsed jet dynamics of squid hatchlings at intermediate Reynolds numbers

Ian K. Bartol1,*, Paul S. Krueger2, William J. Stewart1 and Joseph T. Thompson3

1 Department of Biological Sciences, Old Dominion University, Norfolk, VA 23529, USA
2 Department of Mechanical Engineering, Southern Methodist University, Dallas, TX 75275, USA
3 Department of Biology, Franklin and Marshall College, Lancaster, PA 17604, USA


Figure 1
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  		Fig. 1. Illustration of squid and relevant structures during mantle cavity refilling (left) and mantle contraction (right). The black arrows indicate movement of the mantle.

 

Figure 2
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  		Fig. 2. Convolved (A,C) and deconvolved (B,D) velocity and vorticity fields for a paralarval Doryteuthis pealeii swimming at 1.3 cm s–1 (7.0 DML s–1). {eta}p is the propulsive efficiency, r is the radial coordinate relative to the jet centerline, z is the longitudinal coordinate along the jet axis, Formula 3r is the unit vector in the radial direction relative to the jet centerline, Formula 3z is the unit vector in the longitudinal direction relative to the jet centerline and DML is the dorsal mantle length.

 

Figure 3
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  		Fig. 3. Convolved (A,C) and deconvolved (B,D) velocity and vorticity fields for a paralarval Doryteuthis pealeii swimming at 1.8 cm s–1 (10.0 DML s–1). {eta}p is the propulsive efficiency and DML is the dorsal mantle length.

 

Figure 4
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  		Fig. 4. Convolved vorticity fields for paralarvae Doryteuthis pealeii swimming at 1.4 cm s–1 (7.8 DML s–1) (A,B), 1.9 cm s–1 (10.6 DML s–1) (C), 1.2 cm s–1 (6.5 DML s–1) (D), 2.2 cm s–1 (11.9 DML s–1) (E) and 2.1 cm s–1 (11.3 DML s–1) (F). The insets represent deconvolved vorticity fields that have been adjusted for laser sheet thickness. L{omega} is the length of jet based on vorticity extent, D{omega} is the distance between vorticity peaks; {eta}cp is the convolved propulsive efficiency, {eta}dp=deconvolved propulsive efficiency and DML is the dorsal mantle length.

 

Figure 5
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  		Fig. 5. Ratios of the length of jet based on the vorticity extent (L{omega}) to the distance between vorticity peaks (D{omega}) plotted as a function of mean swimming speed during mantle contraction (U) (A), length of the jet based on the velocity extent (LV) to the maximum funnel diameter (DF) plotted as a function of U (B), mean jet velocity along the jet centerline (Uj) to the mean swimming speed during mantle contraction (U) plotted as a function of U (C) and maximum jet velocity along the jet centerline (Ujmax) to the maximum swimming speed during mantle contraction (Umax) plotted as a function of Umax (D).

 

Figure 6
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  		Fig. 6. Mean jet velocity along the jet centerline (Uj) plotted as a function of mean swimming speed during mantle contraction (U) (A), maximum jet velocity along the jet centerline (Ujmax) plotted as a function of maximum swimming speed during mantle contraction (Umax) (B) and pulse duration plotted as a function U.

 

Figure 7
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  		Fig. 7. Mean impulse and mean thrust plotted as a function of the ratio of jet length based on the vorticity extent to the distance between vorticity peaks (L{omega}/D{omega}) (A, C, respectively) and mean impulse and mean thrust plotted as a function of mean swimming speed during mantle contraction (U) (B, D, respectively).

 

Figure 8
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  		Fig. 8. Propulsive efficiency ({eta}p) plotted as a function of mean swimming speed during mantle contraction (U) for convolved (A) and deconvolved (B) data and propulsive efficiency ({eta}p) plotted as a function of the ratio of jet length based on the vorticity extent to the distance between vorticity peaks (L{omega}/D{omega}) for convolved (C) and deconvolved (D) data. The gray rectangles in C and D highlight values for spherical vortex rings.

 

Figure 9
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  		Fig. 9. Linear regression of jet vortex circulation ({Gamma}) on time for Doryteuthis pealeii paralarvae.

 

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