(a) Whisker material
Measurements were performed on six single hairs, three harbour seal vibrissae (P. vitulina; labelled as PvV1, PvV2, PvV3) and three vibrissae of a California sea lion (Zalophus californianus; labelled as ZcV1, ZcV2, ZcV3). Vibrissae used in this study stem from animals that had died from natural causes about a year before the study was implemented. The whiskers of a juvenile harbour seal were provided by the Research Centre Büsum (University of Kiel, Germany) and the sea lion whiskers were obtained from the Natural History Museum Münster, Germany. For each species, vibrissae of different sizes were used, taken from comparable positions on the vibrissal pads (row D, columns 1, 2 and 3 in the harbour seal and columns 2, 4 and 6 in the sea lion). The sea lion whiskers measured 93.6 mm (ZcV1), 71.9 mm (ZcV2) and 45.1 mm (ZcV3) in length with a bending angle of 9–15°. The lengths of the seal's vibrissae were 85 mm (PvV1), 66.5 mm (PvV2) and 50.8 mm (PvV3), with bending angles ranging from 20° to 35°. All whiskers were kept under dry conditions and therefore immersed in water for 2 h before starting the measurement.
(b) Experimental set-up
The experimental set-up consisted of two basic components: a round fluid tank (diameter 124 cm) and a steel mounting rack to which the measuring devices were attached and which served to fixate the whiskers. To avoid heterodyning of the measuring signals with external vibrations (e.g. from the drive), both components were decoupled mechanically from each other using heavy weights and vibration dampers. The fluid tank was filled with water to a level of 20 cm and was centred with respect to the rack. A 300 W DC motor served to rotate the tank around its vertical axis, leading to a rotation of the fluid at a constant angular speed after an initial break-in phase. Flow velocity in the flume depended on the radial distance. Angular speed was surveyed throughout the experiments by an optical sensor at the tank's fringe. An adjustable holder was attached to the rack and placed above the flume to mount the vibrissae and to allow the immersion of the whisker into the water at variable distances from the axis of rotation. This way the whisker could be exposed to varying flow speeds without any further break-in intervals, as it would occur in a linear tank. Radial variation of flow velocity within the diameter of the whiskers as well as within the diameter of the disturbing cylinders was below 1 per cent.
The whisker was fixed in a hollow piezoceramic cylinder, which transformed mechanical vibrations into corresponding electric charge fluctuations. The transducer was coupled at the base of the hair shaft in order to incorporate all structural and material parameters of the whisker during the measurement. The transducer output was connected to a charge amplifier that generated a voltage proportional to the momenta present at the root of the hair shaft. In order to assess comparative measurements, the voltage signal was not necessarily calibrated to applied absolute forces. The vibration signal of each whisker was recorded by a data acquisition card and analysed with the data analysis software LabVIEW (both: National Instruments, Austin, TX, USA). All whiskers were submerged in the tank for about two-thirds of their total length. Disturbing effects caused by the air–water interface along the hairshaft would have appeared as additional noise contribution to the measured signals in both hair types and thus both whisker signals were equally biased.
During hydrodynamic as well as haptic reception, harbour seals and sea lions protract their whiskers and then usually keep the hairs in the most forward position. This way, most whiskers in the harbour seal face a flow field right in front of the animal with their narrow side, while in the sea lion, the wide side of the whiskers is directed towards the flow field. In our experimental set-up, the orientation of the single whiskers was in accordance with this in situ situation.
(c) Flow measurements
After passing a critical Reynolds number (Re), vortices detach, alternating from the right and the left side of a cylindrical object in the flowing fluid. This phenomenon is called a Kármán vortex street. The generation of artificial and reproducible hydrodynamic disturbances was achieved by immersing aluminium cylinders in the flow tank at a depth of 10 cm in front of the vibrissae at a distance of 5 cm. The cylinders were 100 cm in length and were either hollow cylinders with a cross section of 16 mm or solid cylinders with diameters of 8 and 4 mm. Within a Reynolds number range of 300–10 000, the Strouhal number is constant (St = 0.2). With the knowledge of the characteristic width (cylinder diameter) D and flow speed U∞, the frequency of vortex shedding from the cylinder fVS was calculated using the equation St = fVS×D/U∞. The Kármán vortex street behind a cylinder is suitable to serve as a model for alternating patterns of water movements as generated by fish, although it differs from the hydrodynamic trail of a swimming fish in that it is not three dimensional, and rotation direction is inverted. For additional measurements with sea lion whiskers, a flat, rectangular profile (40 mm wide, 2 mm thick and 50 mm long) was used to generate a hydrodynamic event causing the collapse of the vibrissal self-oscillation.
Each of the six vibrissae was used to detect the vortex-shedding frequency fVS of the Kármán vortex streets generated by the different cylinders. Every measurement was repeated at three different flow speeds within the maximum range of the flume from 15 to 55 cm s–1. Data were collected over a time interval of approximately 120 s. The first 60 s served to record the wanted signal including noise with the cylinder fixed upstream of the vibrissae. Then the cylinder was removed. Continuous monitoring of the vibrissal signal allowed us to wait until the residual wake of the cylinder was attenuated. After a delay of usually 10–20 s this way, only the noise was recorded for another 40–50 s.
A quantitative comparison of sensors, in our case the two different whisker types, can be achieved by calculating their SNRs. The SNR describes the quality of the transmission of a wanted signal that is overlaid by background noise. It can be defined as the ratio of the mean power of wanted and noise signals. The mean power of wanted and noise signals was determined by the root mean square (RMS) of the voltage output of the charge amplifier.
(d) Data analysis
For signal conditioning, a notch filter blocked the 50 Hz noise of the mains electricity in the whisker signal. Then the whisker signal passed through a high-pass filter (fifth-order Butterworth), which blocked additionally all frequencies below 70 Hz. Finally, the maximum frequency and its amplitude were extracted out of the filtered whisker signal by means of a fast Fourier transformation (FFT) algorithm (sampling rate: 10 kHz, sample length: 1024, frequency resolution less than 1 Hz, window: Hanning). This frequency is caused by VIVs, which were identified and characterized that way.
In parallel, but before high-pass filtering, the signal was fed into a low-pass filter (fifth-order Butterworth), which blocked all frequencies above an adjustable threshold (usually 20 Hz). Hence, this extracted signal reflects the comparatively low frequency of vortex shedding from the cylinder (fVS). Every frequency and amplitude values for further processing were obtained by automatic averaging over 20 samples of single values.
To determine the SNR, the signal was tapped before and after the low-pass filter. The effective amplitudes (RMS) of the signal parts in the time domain were used to calculate the SNR. The SNR can be calculated in two different ways. If the signal is large and the noise is comparatively small (S
N), the wanted signal usually contains the noise, which can be neglected (S + N ≈ S, when S
N). In this case, the noise value has to be measured with no signal present, which means without disturbing the cylinder in the flow tank. This procedure was used with seal whiskers. However, if the noise level is higher than the signal (S
N), the signal has to be filtered out by a band-pass filter. Then, for the determination of the SNR, the noise can be provided by using the unfiltered signal, which also contains the wanted signal (N ≈ N + S, when N
S). This procedure was used with sea lion whiskers.