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Hydrodynamic stability of swimming in ostraciid fishes: role of the carapace in the smooth trunkfish Lactophrys triqueter (Teleostei: Ostraciidae)

Ian K. Bartol^1,*, Morteza Gharib², Daniel Weihs³, Paul W. Webb⁴, Jay R. Hove² and Malcolm S. Gordon¹

¹ Department of Organismic Biology, Ecology, and Evolution, University of California, Los Angeles, CA 91606, USA
² Options of Bioengineering and Aeronautics, California Institute of Technology, Pasadena, CA 91125, USA
³ Department of Aerospace Engineering, Technion, Haifa, 3200, Israel
⁴ School of Natural Resources and Department of Biology, University of Michigan, Ann Arbor, MI 48109, USA

View larger version (20K): [in a new window]   Fig. 1. Anterior, posterior and lateral views of a smooth trunkfish Lactophrys triqueter. Scale bars, 1 cm.

View larger version (33K): [in a new window]   Fig. 2. Characteristics of the carapace of a CT-scanned smooth turnkfish (17.0 cm total length, 12.3 cm carapace length) plotted as a function of percentage of carapace length. Dimensions (carapace width, carapace height, and eye ridge width) are depicted on the left y-axis, while mean ventro-lateral keel angle and dorsal keel angle are depicted on the right y-axis.

View larger version (38K): [in a new window]   Fig. 3. Concavity and convexity measurements of the carapace of a CT-scanned smooth trunkfish (17.0 cm total length, 12.3 cm carapace length) plotted as a function of percentage of carapace length. Maximum convexity (A) and concavity (C) are the maximum distances that the body extends and indents, respectively, relative to a segment connecting either the tips of the dorsal and ventro-lateral keels (SL) (lateral measurements) or the tips of the two ventro-lateral keels (SV) (ventral measurements). The location of maximum lateral convexity (B) is the distance from the dorsal keel to the point of maximum extension along the segment, SL. The location of maximum lateral/ventral concavity (D) is the distance from the ventro-lateral keel to the point of maximum indentation along segments SL (lateral) or SV (ventral). Data on lateral maximum convexity and concavity are mean measurements of the two sides of the carapace. Data on ventral concavity are mean measurements of the two regions of ventral concavity found along SV. In B the location of ventral maximum convexity occurs equidistant between ventro-lateral keels.

View larger version (50K): [in a new window]   Fig. 4. Velocity vector (B) and vorticity contour (C) fields around and in the wake of the smooth trunkfish model positioned at a pitching angle of attack of +10°. The data are viewed in transverse planes at various locations along the body and in the wake. Each plot is the mean result of 30 velocity fields (1 representative trial). From left to right, the locations (A) are: eye ridge, maximum girth, midpoint between maximum girth and posterior edge of the carapace, posterior edge of the carapace, caudal peduncle and wake. The shadows beneath the models represent areas that were shielded from laser light. Mean circulation magnitude and mean peak vorticity magnitude values for a dorsal vortex (D and PD, respectively) and a ventral vortex (V and PV, respectively) are included beneath the vorticity contour plots for measurements along the body. In the wake, dorsal and ventral distinctions are not necessary since ventral and dorsal vortices merge.

View larger version (46K): [in a new window]   Fig. 5. Velocity vector (B) and vorticity contour (C) fields around and in the wake of the smooth trunkfish model positioned at a pitching angle of attack of -10°. The data are viewed in transverse planes at various locations along the body and in the wake. Each plot is the mean result of 30 velocity fields (1 representative trial). From left to right, the locations (A) are: eye ridge, maximum girth, midpoint between maximum girth and posterior edge of the carapace, posterior edge of the carapace, caudal peduncle and wake. The shadows on the sides of or above models represent areas that were shielded from laser light. Mean circulation magnitude and mean peak vorticity magnitude values for a dorsal vortex (D and PD, respectively) and a ventral vortex (V and PV, respectively) are included beneath the vorticity contour plots for measurements along the body. In the wake, dorsal and ventral distinctions are not necessary since ventral and dorsal vortices merge.

View larger version (48K): [in a new window]   Fig. 6. Velocity vector (B) and vorticity contour (C) fields around the posterior edge of the carapace of the smooth trunkfish model positioned at pitching angles of attack of (left to right): +20°, +10°, 0°, -10° and -20°. The data are viewed in transverse planes, and sampling locations are indicated (A). Each plot is the mean result of 30 velocity fields (1 representative trial). The shadows underneath or to the side of models represent areas that were shielded from laser light. Mean circulation magnitude and mean peak vorticity magnitude values for a dorsal vortex (D and PD, respectively) and a ventral vortex (V and PV, respectively) are included beneath the vorticity contour plots.

View larger version (48K): [in a new window]   Fig. 7. Velocity vector (B) and vorticity contour (C) fields around and in the wake of the smooth trunkfish model positioned at an angle of attack of 0°. The data are viewed in transverse planes at various locations along the body and in the wake. Each plot is the mean result of 30 velocity fields (1 representative trial). From left to right, the locations (A) are: eye ridge, maximum girth, midpoint between maximum girth and posterior edge of the carapace, posterior edge of the carapace, caudal peduncle and wake. The shadows underneath the model represent areas that were shielded from laser light. Mean circulation magnitude and mean peak vorticity magnitude values for a dorsal vortex (D and PD, respectively) and a ventral vortex (V and PV, respectively) are included beneath the vorticity contour plots for measurements along the body. In the wake, dorsal and ventral distinctions are not necessary since ventral and dorsal vortices merge.

View larger version (49K): [in a new window]   Fig. 8. Velocity vector (B) and vorticity contour (C) fields around the posterior edge of the carapace of the smooth trunkfish model positioned at yawing angles of attack of (left to right): 0°, 10°, 20° and 30°. The data are viewed in transverse planes, and sampling locations are indicated using illustrations of models viewed from above (A). Each plot is the mean result of 30 velocity fields (1 representative trial). The shadows underneath models represent areas that were shielded from laser light. Circulation magnitude and peak vorticity magnitude values for a dorsal vortex (D and PD, respectively) and a ventral vortex (V and PV, respectively) are included beneath the vorticity contour plots.

View larger version (37K): [in a new window]   Fig. 9. Pressure coefficients (CP) plotted as a function of location (pressure port) along various dorso-ventral transects on the smooth trunkfish model positioned at positive pitching angles of attack. The locations of the pressure ports included in each graph are highlighted in images of the model. Note pressure ports A2, A4 and A6 are located in the middle of the ventral region of the carapace, which is not visible in the images. The dorso-ventral transects considered are: (A) eye ridge, (B) maximum girth, (C) midpoint between maximum girth and the posterior edge of the carapace and (D) posterior edge of the carapace. Values are means ± 1 S.D.

View larger version (39K): [in a new window]   Fig. 10. Pressure coefficients (CP) plotted as a function of location (pressure port) along various dorso-ventral transects on the smooth trunkfish model positioned at negative pitching angles of attack. The locations of the pressure ports included in each graph are highlighted in images of the model. Note pressure ports A2, A4, and A6 are located in the middle of the ventral region of the carapace, which is not visible in the images. The dorso-ventral transects considered are: (A) eye ridge, (B) maximum girth, (C) midpoint between maximum girth and the posterior edge of the carapace and (D) posterior edge of the carapace. Values are means ± 1 S.D.

View larger version (32K): [in a new window]   Fig. 11. Pressure coefficients (CP) plotted as a function of location (pressure port) along dorsal antero-posterior transects (A,C) and ventral antero-posterior transects (B,D) on the smooth trunkfish model positioned at different pitching angles of attack. Positive pitching angles of attack are depicted in A and B, while negative pitching angles of attack are depicted in C and D. The locations of the pressure ports included in each graph are highlighted in images of the model in A and B. Values are means ± 1 S.D.

View larger version (18K): [in a new window]   Fig. 12. Pressure coefficients (CP) plotted as a function of location (pressure port) along a dorso-ventral transect at the maximum girth point of a smooth trunkfish model positioned at different yawing angles of attack. The graph on the left depicts conditions when the transect is in the far field, i.e. shielded from flow, whereas the graph on the right depicts conditions when the transect is in the near field, i.e. exposed to flow. The locations of the pressure ports included in each graph are highlighted in the image of the model. A4 is located in the middle of the ventral region of the carapace.

View larger version (29K): [in a new window]   Fig. 13. Lift coefficients (CL; A), drag coefficients (CD; B), lift to drag ratios (L/D; C), and pitching moment coefficients about the center of mass (CM; D) for the smooth trunkfish model positioned at various pitching angles of attack. In the lift coefficient plot (A), smooth trunkfish coefficients are depicted as open circles, while delta wing coefficients are depicted as filled circles. The delta wing has a similar aspect ratio (0.83) to that of the smooth trunkfish. Delta wing data are from Schlichting and Truckenbrodt (1969). Positive pitching moment coefficients (D) indicate a nose-down pitching moment about the center of mass, whereas negative pitching coefficients indicate a nose-up pitching moment about the center of mass.

View larger version (20K): [in a new window]   Fig. 14. Lift forces acting on a smooth trunkfish model measured using a force balance (filled circles) and DPIV (open circles) plotted as a function of angle of attack. Values are means ± 1 S.D. In the force balance measurements, S.D. bars are often smaller than the symbols used to denote values.

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