Attenuation of progressive surface gravity waves by floating spheres

Abstract

Laboratory experiments were performed to investigate the attenuation of progressive deep-water waves by a mono-layer of loose- and close-packed floating spheres. We measured the decay distance of waves having different incident wave frequency and steepness. The attenuation of waves was strong if the surface concentration of particles was close-packed, with the decay distance being shorter for incident waves with higher frequency and steepness. The amplitude of the highest-frequency (2.0 Hz) and largest amplitude incident waves (with steepness 0.25) decayed by half over a distance of approximately 3 wavelengths. Theoretical models used previously in the study of surface wave damping by sea ice do not capture correctly the physics of wave attenuation by floating spheres. We developed a new theory that estimates the influence upon wave attenuation of turbulent dissipation resulting from oscillatory flow under a close-packing of spheres. This theory predicts that the wave amplitude decays as a power law, and gives a correct order-of-magnitude estimate of the observed decay distance. We explore the potential implications of these findings for the attenuation of progressive waves by (pancake) sea ice and for the indirect detection of marine plastic pollution from space.

Figure 1

Side view (top image) and top view (bottom image) of the set-up of the experimental flume tank with top and side camera positions indicated. The measurement zone was situated between 10 m and 20 m from the wave maker.

Figure 2

Snapshots taken from the overhead camera looking down the length of the tank for four experiments in quasi-steady state, all with incident wave steepness . In (a–c) there is an initial close-packed (100%) concentration of particles and the wave frequency is (a)  Hz, (b)  Hz and (c)  Hz. In (d) the initial area concentration is 71% and the wave frequency is 1.8 Hz. Red arrows in point to selected bands of brighter yellow regions where waves consolidate particles at wave crests. The blue arrows in (b,c) point to where the particles are close-packed and the surface has become undisturbed by waves that have fully attenuated.

Figure 3

Image from a side-camera of the experiment shown in Fig. 2c) illustrating that the close-packed spheres attenuate the rightward propagating incident wave to near zero amplitude over a horizontal distance of 3.5 m.

Figure 4

Comparison of the free surface displacement, (dashed lines), and amplitude, A, (solid lines) measured by a wave gauge at  m from the wave maker (red) and at the same location as recorded by a side camera (black).

Figure 5

Relative amplitude versus distance across the observation window measured by wave gauges in experiments with fixed steepness and different incident wave frequencies, as indicated in the legend. The amplitude is normalized by the amplitude measured in experiments with the same forcing amplitude and frequency, but no floating spheres.

Figure 6

As in Fig. 5, but showing relative amplitude versus downstream distance as measured by side cameras in experiments with relatively high-frequency incident waves and . Here downstream distance is measured with respect to the location, , at which the wave decay begins, and amplitude is normalised by the amplitude at this location, . Where the black horizontal line crosses each curve gives the decay distance, .

Figure 7

Spatial decay distance with errors estimated for all experiments as a function of wave frequency f [Hz] for different values of steepness , as denoted by the legend. The black line with open circle markers are from wave gauge measurements. The rest are based on measurements using cameras.

Figure 8

As in Fig. 5, but showing relative amplitude versus distance in experiments with fixed steepness and frequency  Hz and different area concentrations of particles, as indicated in the legend.

Figure 9

Data in Fig. 7 replotted as versus frequency. The horizontal solid and dashed black lines indicate the best-fit mean and standard deviation of the non-dimensional constant .

Figure 10

SAR image of the Atlantic Ocean taken by Sentinel-1 on 10 June 2014 showing dark bands (inside the box), which may show the presence of plastic because these bands cannot be explained by either ice, algae blooms, or oil (which are normally attributed to such results). [Image provided courtesy of the European Space Agency (ESA).].