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Fluid dynamics of flapping aquatic flight in the bird wrasse: three-dimensional unsteady computations with fin deformation

Ravi Ramamurti¹, William C. Sandberg¹, Rainald Löhner², Jeffrey A. Walker³ and Mark W. Westneat⁴

¹ Laboratory for Computational Physics and Fluid Dynamics, Naval Research Laboratory, Washington, DC 20375-5344, USA
² Computational Sciences and Informatics Department, George Mason University, Fairfax, VA 22030, USA
³ Department of Biological Sciences, University of Southern Maine, Portland, ME 04103, USA
⁴ Department of Zoology, Field Museum of Natural History, Chicago, IL 60605-2496, USA

View larger version (145K): [in a new window]   Fig. 1. Computational surface mesh for body and pectoral fin.

View larger version (83K): [in a new window]   Fig. 2. Pectoral fin and markers during (A) mid-phase and (B) late phase of downstroke.

View larger version (78K): [in a new window]   Fig. 3. Steady-state flow past the pectoral fin. The position of the fin corresponds to t=0.15 s. (A) Velocity vectors on the surface of the pectoral fin. The vectors are colored according to the magnitude of velocity and are of constant length. The velocity vector is non-dimensionalized with respect to the swimming velocity. (B) Particle traces past a fully extended pectoral fin. Particles are released along a rake parallel to and just upstream of the leading edge of the fin. These particle traces are colored according to the magnitude of velocity.

View larger version (31K): [in a new window]   Fig. 4. Pectoral fin location at various times t throughout the stroke cycle. (A) Downstroke (abduction). (B) Upstroke (adduction).

View larger version (19K): [in a new window]   Fig. 5. Variation of thrust and lift forces. (A) Steady state computations. (B) Quasi-steady state computations.

View larger version (24K): [in a new window]   Fig. 6. Time variation of unsteady (A) lift and (B) thrust forces.

View larger version (105K): [in a new window]   Fig. 7. Velocity vectors on the surface of the bird wrasse at five instants during the fin oscillation. The swimming velocity is 45 cm s-1. (A) t=1.065 s (84% downstroke). (B—F) Close-up view of the fin and body junction. (B) t=0.963 s (32% downstroke), (C) t=1.065 s (84% downstroke), (D) t=1.104 s (8% upstroke), (E) t=1.140 s (43% upstroke) and (F) t=1.167 s (68% upstroke). Velocity vectors are colored according to the magnitude of velocity (cm s-1) and are of constant length.

View larger version (75K): [in a new window]   Fig. 8. Surface pressure contours (N m-2) on the pectoral fin at three instants when the peak in the thrust occurs. (A,C,E) Front, (B,F) back, (D) ventral view. (A,B) t=0.963 s (32% downstroke); maximum and minimum pressure occur below and above the leading edge of the fin, respectively, producing maximum thrust (-x direction) and lift (+y direction). (C,D) t=1.065 s (84% downstroke); maximum and minimum pressure occur above and below the leading edge, respectively, in the outer half span of the fin, producing minimum thrust. (E,F) t=1.167 s (68% upstroke); high-pressure region extends for more than half the dorsal side of the fin while the pressure on the ventral side is almost uniform, with a region of minimum pressure near the outer leading edge, producing a maximum thrust.

View larger version (94K): [in a new window]   Fig. 9. (A) The orientation of the pectoral fin showing the leading and distal edges and the z=1.5 cm plane, for which the in-plane velocity components (cm s-1) are shown. The swimming velocity of the fish (45 cm s-1) is subtracted from the x component of the velocity to reveal the vortical structures. (B) Two counter-rotating vortices are observed at t-0.906 s, just after stroke reversal. These are shed from the distal edge on the previous upstroke. (C) A large vortex spans the entire chord at t=1.065 s, when the thrust is minimum. (D) A vortex is shed from the trailing edge midway during the upstroke, t=1.14 s, leading to a momentary increase in lift force. (E) At t=1.167 s, 68% upstroke, the TEV is convected downstream. (F) At t=1.197 s, prior to stroke reversal, two vortices are shed from the distal edge. UDEV, upper distal edge vortex; LDEV, lower distal edge vortex; LEV, leading edge vortex; TEV, trailing edge vortex.

View larger version (55K): [in a new window]   Fig. 10. Instantaneous particle traces are released from (A) a rake of rectangular grid of points in a plane 0.75 cm away from the leading edge of the pectoral fin and parallel to it. Using the instantaneous velocity field, the positions of theses particles were obtained by integrating the velocity at these points until the length of these traces exceeded a specified length, or the particles ended on a solid boundary, or exited the computational domain. These particle traces are colored according to the magnitude of velocity (in cm s-1) at that location. (B) Middle of the downstroke, t=1.064 s. (C) Beginning of the upstroke, t=1.1017 s.

View larger version (21K): [in a new window]   Fig. 11. Time variation of (A) fore—aft acceleration ax and (B) dorso—ventral acceleration ay.