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Steady streaming in oscillatory flows has been studied for more than a century, yet our understanding of this flow at moderate Reynolds numbers is still quite limited. Steady streaming was visualized using phase-averaged particle path lines for spheroids of aspect ratio ARϵ a / b ͑a and b are the half-dimensions of the body parallel and normal to its axis of symmetry, respectively͒ oscillating along their ͑vertical͒ axes of symmetry at frequency and amplitude s. Estimates of the extent of the inner region of this flow T, defined here as the average distance from the body surface to the off-body stagnation points SP L , SP R and SP B ͓Fig. 1͑a͔͒, suggest that the results for several different spheroid geometries ͓Figs. 1͑a͒-1͑d͔͒; all images at the same magnification͔ are consistent for a body length scale L ϵ͑AR͒R eq , where R eq is the equivalent radius of the spheroid. Based on Fig. 1͑e͒, T / L Ϸ 40Re −1 , where the Reynolds number Reϵ L 2 / . The data are for different s / L values, implying that T is independent of s.Here T decreases as Re increases until the inner region extends beyond the field of view ͓Fig. 1͑f͔͒. Oscillating at 45°shifts the angular position of the surface stagnation point and leads to an off-surface stagnation point ͓Fig. 1͑g͔͒. FIG. 1.

The ears of fishes are remarkable sensors for the small acoustic disturbances associated with underwater sound. For example, each ear of the Atlantic cod (Gadus morhua) has three dense bony bodies (otoliths) surrounded by fluid and tissue, and detects sounds at frequencies from 30 to 500 Hz. Atlantic cod have also been shown to localize sounds. However, how their ears perform these functions is not fully understood. Steady streaming, or time-independent, flows near a 350% scale model Atlantic cod otolith immersed in a viscous fluid were studied to determine if these fluid flows contain acoustically relevant information that could be detected by the ear's sensory hair cells. The otolith was oscillated sinusoidally at various orientations at frequencies of 8-24 Hz, corresponding to an actual frequency range of 280-830 Hz. Phase-locked particle pathline visualizations of the resulting flows give velocity, vorticity, and rate of strain fields over a single plane of this mainly two-dimensional flow. Although the streaming flows contain acoustically relevant information, the displacements due to these flows are likely too small to explain Atlantic cod hearing abilities near threshold. The results, however, may suggest a possible mechanism for detection of ultrasound in some fish species.

Fish sense their acoustic environment using ears that are typically able to detect sounds of O(10–103 Hz) at 80–130 dB re 1 μPa (for the Atlantic cod Gadus morhua, for example). Each ear contains three stone-like masses (the “otoliths”) embedded in a fluid filled membrane. The sulcus, a groove on one side of the otolith, is lined with O(104) sensory hair cells which presumably hear by detecting the acoustically induced motion of the fluid and tissue relative to the otolith. The “auditory retina hypothesis” suggests that the fish ear uses the fluid flow patterns, sensed by the array of hair cells, to characterize incident sounds. Although the time-independent steady streaming flow patterns have been shown to encode the frequency and direction of the oscillation (and hence incident sounds), the hair cell cilia displacements due to such flows are probably too small to be sensible. This experimental study focuses instead on the unsteady flows near a 350% model cod otolith oscillating in an otherwise still fluid. Results are presented for an otolith oscillating at different orientations (corresponding to the excitation from sounds from different directions) at frequencies of 3–25 Hz and amplitudes of 0.1–0.5 mm. [Work supported by ONR.]