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First published online December 28, 2007
Journal of Experimental Biology 211, 196-205 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.005629

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Flow patterns of larval fish: undulatory swimming in the intermediate flow regime

Ulrike K. Müller^*, Jos G. M. van den Boogaart and Johan L. van Leeuwen

Experimental Zoology Group, Wageningen Institute of Animal Sciences (WIAS), Wageningen University, Marijkeweg 40, 6709 PG Wageningen, The Netherlands

View larger version (40K): [in this window] [in a new window]   Fig. 1. C-start of a zebrafish larva (age 5 d.p.f., body length L=4.2 mm). Swimming kinematics. (A) During the preparatory stroke the body, represented by its midlines, adopts a C shape. Silhouettes (left, time step 10 ms) and midlines (right, time step 1 ms) of a fish larva. Black arrow, path of the centre of mass (dark red dot); blue arrow, path of head; red arrow, path of tail. (B) During the propulsive stroke the body straightens and the tail completes the first tail-beat cycle. Silhouettes (right, time step 10 ms) and path of the centre of mass are shown for preparatory plus propulsive stroke; midlines (left, time step 1 ms) are shown for the propulsive stroke only. White arrow, path of the centre of mass (dark red dot); blue arrow, path of head; red arrow, path of tail. (C) Curvature of the larval midline during a C-start. Body curvature increases steadily during the preparatory stroke; the propulsive stroke commences when the total concave curvature (red) reaches its maximum and the first body wave begins to form, visible as a convex curvature (blue) band that travels down the full length of the body. (Same sequence as Fig. 2.)

View larger version (53K): [in this window] [in a new window]   Fig. 2. Vorticity field (colour map) and flow velocities (black arrows) generated during the preparatory (left columns) and propulsive stroke (right columns) of a larval C-start (age 5 d.p.f., body length L=4.4 mm). The sketches beside the vorticity colour maps highlight the most relevant flow features. Over the entire C-start, the larva sheds two vortex pairs, one during the preparatory (vortices 1 and 2), and one during the propulsive stroke (vortices 2b and 3). By the time, the second pair is shed, the first pair has moved from its initial shedding position and has almost disappeared (70 ms, vorticity field). Grey arrow, jet into concave body bend; white arrows, other jets; blue circles: clockwise vortices; ochre circles, counter-clockwise vortices. (Same sequence as Fig. 1.)

View larger version (54K): [in this window] [in a new window]   Fig. 3. Kinematics of a cyclically swimming zebrafish larva (age 3 d.p.f., body length L=3.8 mm). (A) The larva generates a body wave travelling down its body with a roughly constant tail-beat frequency and amplitude. Blue, path of the head, red, path of tail. (B) The body wave becomes prominent behind the stiffer anterior body and travels as a wave of curvature with a roughly constant speed along the posterior body. (Same sequence as Fig. 4.)

View larger version (65K): [in this window] [in a new window]   Fig. 4. Flow generated during a tail beat of a cyclically swimming zebrafish larva (age 3 d.p.f., body length L=3.8 mm). (Left) Vorticity field (colour map) and velocity vector field (black arrows) adjacent to a fish larva. (Right) Sketch of most relevant flow features. The drag wake of the anterior body (elongate ochre area in sketch) is prominent in the vorticity field throughout the tail-beat cycle. The two main propulsive features of the flow along the larva are (1) the jet into the concave bend of the body, which gradually reorients more caudally as it travels down the body (black arrows); (2) several smaller patches of vorticity along the posterior body, which are shed as two vortex pairs per tail-beat cycle (blue and ochre circles). (Same sequence as Fig. 3.)

View larger version (53K): [in this window] [in a new window]   Fig. 5. Three-dimensional reconstruction of the wake behind the cyclically swimming zebrafish larva (age 3 d.p.f.) (overview panel; letters correspond to flow diagrams A–C). The vortex rings (red) shown in the overview panel take time to develop, so the ring immediately behind the tail has not yet fully formed (blue broken line), as is also evident in C. Transverse cross sections through the larval flow field (A) in front of and (B) behind the larva. (C) Horizontal cross-section through the larval wake. The stronger vortices are due to a slight turn (Fig. 3).

View larger version (75K): [in this window] [in a new window]   Fig. 6. Transition from cyclic swimming to coasting in a zebrafish larva (age 4 d.p.f., body length L=4.0 mm). (A) Amplitude envelope narrows, tail-beat frequency and stride length drop, as towards the end of an active swimming bout. (B) Peak curvature also decreases. Curvature of the body midline during the last four tail beats of a swimming bout. (C) The vorticity field (colour map) and velocity vector field (black arrows) adjacent to the larva show how the boundary layer increasingly engulfs the entire decelerating larva. Shown are the last two times that the tail reaches a lateral extreme (67 and 84 ms) and a coast flow field (105 ms). The times correspond to the time axis of B.