D1 Flow around the Fish (PIV)

Topic

Particle Image Velocimetry (PIV) is the standard experimental method for measuring the fluid velocity field around a swimming fish. Its physical principle involves tracking the movement of tracer particles suspended in the water—such as small hollow glass spheres ranging from ten to fifty micrometers in diameter or fluorescent microspheres—illuminated by a pulsed laser sheet fired twice in rapid succession.

This pulsed laser sheet illuminates the tracer particles at two moments separated by a very brief time interval—ranging from one to one thousand microseconds, depending on the speed of the fluid being measured—and a camera captures an image of the tracer particles at each of these two moments. By comparing the two images within small "interrogation windows" using cross-correlation, the technique determines the average displacement of the group of tracer particles contained in each window during that time interval.

This cross-correlation between the two images in each interrogation window produces a correlation peak; its position—measured in pixels, converted to a real-world distance using the image's scale factor, and divided by the time interval between the two images—yields the local fluid velocity vector for that interrogation window. By repeating this calculation across all interrogation windows covering the entire image, the technique reconstructs the two-dimensional fluid velocity field on the plane illuminated by the laser, with a typical spatial resolution of between half a millimeter and five millimeters; if two cameras are used in a stereoscopic configuration, this same velocity field can be reconstructed in three dimensions.

Based on this fluid velocity field, the technique allows for the calculation—via spatial differentiation—of the flow's vorticity and rate of deformation; And by integrating this same vorticity, it is possible to calculate the flow's hydraulic impulse and the thrust force generated by the fish as it swims, without needing to measure that force directly on the fish's body.

Thanks to this ability to calculate vorticity and hydraulic impulse, the particle image velocimetry technique directly quantifies the structure of the wake left by the fish during propulsion—a vortex street—as well as the circulation of each individual vortex shed by the fish while swimming; based on this circulation, and by applying the theorem relating fluid impulse to vortex circulation, the technique determines the fish's average propulsive force—again, without the need to measure any force directly on its body.

The typical behavior revealed by this technique in swimming fish is a street of counter-rotating vortices—that is, vortices spinning alternately in opposite directions—forming what is known as a reverse von Kármán vortex street; both the spatial separation between these vortices and their circulation are proportional to the fish's swimming speed and the frequency at which it beats its caudal fin. Thus, the very propulsive wake that particle image velocimetry allows us to visualize—described earlier in this model as the velocity field surrounding the fish—ultimately reveals both how fast the fish is swimming and the frequency at which it moves its tail to achieve that speed.

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