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Quantification of the wake of rainbow trout (Oncorhynchus mykiss) using three-dimensional stereoscopic digital particle image velocimetry

Jennifer C. Nauen and George V. Lauder^*

Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA

View larger version (41K): [in a new window]   Fig. 2. A schematic view of stereo-DPIV image processing and calculation methods using data from a trout 21.5 cm in total body length (BL) swimming at 1.2 BL s-1 with a freestream velocity in the x direction, U, of 25.8 cm s-1. Images of the three-dimensional calibration grid (A) recorded from the two cameras show distortion of the two-dimensional views caused by the camera arrangement and Scheimpflüg configuration (Fig. 1). The uniform, symmetrical calibration grid appears slanted, with a decreased vertical distance between rows on the inner sides of both images. Image alignment and distortion are corrected using polynomial equation mapping functions created using a least-squares method and the calibration grid points. Each of the two cameras (Fig. 1) collects two-dimensional images of the wake from which two-dimensional velocity vectors (dimensions scaled in pixels, B) are calculated. Note that freestream U has not been subtracted from these calculations; the high value of U results in a downstream trajectory for both sets of two-dimensional vectors (unlike the diagram in Fig. 1), and that vector density was decreased for viewing clarity. The orientation of the trout caudal fin relative to the light sheet is depicted as a small icon below B. The two-dimensional vectors are used to calculate three-dimensional flow fields (scaled in m s-1; C,D). Vector color in C and D indicates the magnitude of W (the lateral or z velocity component); note that free-stream flow has not been subtracted. Orange boxes connected by broken lines represent the alignment between areas of the calibration images (A), two-dimensional velocity vectors calculated from DPIV images scaled with the calibration images (B) and the final three-dimensional velocity vectors (viewed in the parasagittal plane in C, and viewed in three dimensions in D by rotating the parasagittal plane counterclockwise). The vector calculated for the image area identified by the orange boxes in A, B and C is identified by a black arrow in D, with the magnitude of its U, V and W components given. Rotating C counterclockwise shows strong lateral jet flow (emphasized here by the small scale of the z axis for ease of viewing) that alternates to the right (blue vectors) and left (red vectors) sides of the fish.

View larger version (37K): [in a new window]   Fig. 3. Stereo-DPIV measurements of the wake of a 16.5 cm BL fish, where BL is total body length, swimming at 1.2 BL s-1 with free-stream flow subtracted to reveal wake structure. The caudal fin of the fish was positioned immediately upstream of the wake flow (i.e. to the left of the vector plot). Vector length indicates flow magnitude; vector color indicates the magnitude of W (m s-1). The alternating areas of blue, red and blue vectors visible in the parasagittal plane (A) are clearly visible as regions of jet flow to the right and left of the fish, respectively, when viewed from above (B). Note that the lateral component of jet flow, emphasized here by the small scale of the z-axis for ease of viewing, is 10-60% greater in magnitude (on average) than that of U (see Fig. 4A). Rotating A counterclockwise also shows the alternating pattern of strong lateral jet flows. Ten vectors from the jet flow of 6-8 strokes for each individual were sampled to determine U, V and W magnitudes, where U, V and W are flow velocities in the downstream (x), vertical (y) and lateral (z) directions, respectively.

View larger version (18K): [in a new window]   Fig. 1. Equipment configuration for stereo-DPIV flow visualization viewed from above (xz plane). The laser light sheet (shown in blue) is positioned in the center of the flow tank. Two cameras are placed at a wide angle relative to the laser light sheet (A). The thick black arrow (A) represents wake flow, which is shown with a relatively large lateral trajectory angle (i.e. high magnitude of W, which is flow in the z dimension) to illustrate differences between the field of view of the two cameras. The red and green dotted lines and arrows for the left and right cameras, respectively, represent the different fields of view of each camera and the resulting two-dimensional views of flow movement in opposite directions. Each camera's lens is tilted relative to the camera (B) in the Scheimpflüg configuration so that the light sheet plane, the image plane and the lens principal plane intersect at a common line (depicted here as an orange circle), and the plane of best focus is the light sheet plane. The Scheimpflüg configuration results in a clear and sharp image of particles illuminated by the light sheet, despite the large camera angles. See Materials and methods for more details.

View larger version (13K): [in a new window]   Fig. 4. The magnitudes (means ± S.E.M., N=60-80) of U and W wake flows, and the magnitude and direction (relative to the x-axis) of V flows as a function of individual (A). Ratio of U/total wake flow as a function of individual (B). Symbols represent means ± S.E.M. (error bars are smaller than the symbols), N=60-80. Freestream flow has been subtracted from U. U, V and W are flow velocities in the downstream (x), vertical (y) and lateral (z) directions, respectively.