Relative changes in free bulge wave speed owing to the reduction in distensibility caused by longitudinal curvature in bulges (solid line), and owing to the presence of surrounding water (dashed line) α=0.45.
(a) Amplitudes of pressure in separate bulge wave components, as functions of normalized frequency. Superscripts+and−indicate the direction of travel. Subscripts denote the wave speed: w for the water wave, b for the free bulge wave. Thick line shows the pressure amplitude at the PTO. (b) Power converted in the PTO with an impedance that matches the tube. The length of the tube matches the water wavelength when ω=ω0.
(a) Galinstan strain gauge under test. (b) Tube in the water. A Galinstan gauge can be seen bridging a section of rubber between two fabric strips. The wire gauge above it was not used in the present tests. (Online version in colour.)
Cross-sectional areas of the tube inferred from static measurements of hoop strain at various internal pressures. Different symbols refer to measurements made on different occasions over the duration of the test programme. The solid line represents equation (2.1). The dashed line indicates the gradient dS/dp that corresponds to a bulge wave speed of 3.20 m s−1. The operating internal pressure is indicated by an arrow on the pressure axis.
(a) Time series of extensions recorded by hoop strain gauges over the length of the tube from the bow (top) to the stern. (b) Water surface elevation in the PTO is in quadrature with air pressure. Series 2: T=2.26 s, a=30 mm.
Internal particle velocities (a) inferred from measurements, and (b) calculated from one-dimensional theory, plotted over the length of the tube at 16 instants over one wave period; (c,d) corresponding total internal pressures; (e) forward- and backward-travelling bulge wave components, expressed in terms of corresponding particle velocity amplitudes and ; (f) measured and predicted phases of the forward-travelling bulge wave, plotted alongside the water wave phase shifted by 90°; (g) power in the form of capture width in diameters (Cg is the group celerity). Series 2: T=2.26 s, a=30 mm, A=29 mm.
(i) Measured amplitudes of total internal pressure and (ii) phases over the length of the tube, plotted as points. Solid lines represent the sum of three bulge wave components with amplitudes computed by least squares. Dashed lines represent the measured phase of the water waves with a shift of 90°. (a) Series 2: T=1.90 s, a=26 mm; (b) series 2: T=4.0 s, a=46 mm; (c) series 7: Z=0.64, a=30 mm; (d) series 7: Z=3.4, a=30 mm.
Amplitudes of the three constituent bulge waves in series 2 tests plotted as functions of relative wave period. Symbols represent the amplitudes obtained from pressures inferred from measurements; lines show the amplitudes of the same component waves obtained from equation (2.10) for the experimental conditions.
Points show measured (filled circles and open circles) pressures and amplitudes of motion in the PTO from tests in (a) series 6 (T/T0=0.91) and (b) series 7 (T/T0=1.03) as functions of PTO impedance. At Z=1, the PTO impedance matches the tube impedance. Lines represent results computed from the one-dimensional theory, §2d: δ=9°.