An idealised experimental model of ocean surface wave transmission by an ice floe
Introduction
Ocean surface waves penetrate up to hundreds of kilometres into the sea ice-covered ocean (e.g. Squire and Moore, 1980, Kohout et al., 2014). The region occupied by waves is known as the marginal ice zone (miz). Waves have a profound impact on the ice cover in the miz. They (i) fracture large floes into smaller, more mobile and vulnerable floes (Langhorne et al., 1998), (ii) herd floes (Wadhams, 1983), (iii) introduce warm water and overwash the floes, thus accelerating ice melt (Wadhams et al., 1979, Massom and Stammerjohn, 2010), and (iv) cause the floes to collide, which erodes the floes and influences the large-scale deformation of the ice field via momentum transfer (Shen et al., 1987, Martin and Becker, 1987, Martin and Becker, 1988). Kohout et al., 2014 recently identified a negative correlation between trends in local wave activity and trends in regional ice extent in the Antarctic miz, which is conjectured to result from impacts of large-amplitude storm waves on the ice cover.
Interactions between waves and the ice cover cause wave energy to reduce with distance travelled into the miz. Moreover, the ice cover reduces the energy of short-period waves more rapidly than longer-period waves (Wadhams et al., 1988, Meylan et al., 2014). Incident wave spectra, therefore, skew towards long periods as they propagate deeper into the miz, in addition to a reduction of energy held by each spectral component.
The ice cover in the miz is composed of ice floes with diameters on the order of metres to hundreds of metres. The ratio of the prevailing floe diameters to the incident wavelengths determines the form of the wave-ice interactions, and, hence, the mechanisms responsible for reducing wave energy. In particular, waves perceive a field of floes with diameters much smaller than their wavelength, for example, pancake ice, as an effective medium. In this regime, wave energy is reduced with penetration distance due to viscous losses (e.g. Keller, 1998, de Carolis and Desiderio, 2002, Wang and Shen, 2011, Zhao and Shen, 2013).
In contrast, waves distinguish individual floes with diameters comparable to their wavelength, for example, floes produced by wave-induced fracture. The individual floes reflect a proportion of the incident wave energy, dissipate a proportion and transmit the remaining proportion. Theoretical and numerical methods have been developed to predict the rate at which wave energy reduces in a large field of floes by combining transmission properties of individual floes (e.g. Masson and LeBlond, 1989, Meylan et al., 1997, Bennetts et al., 2010, Bennetts and Squire, 2012a, Bennetts and Squire, 2012b). The models have recently been used to parameterise wave propagation in the miz in large-scale ocean wave and sea ice models (Doble and Bidlot, 2013, Williams et al., 2013a, Williams et al., 2013b).
The present investigation focusses on modelling transmission of waves by a solitary ice floe. A sum of processes involved in wave-floe interactions determine the proportion of wave energy transmitted. Floes bend and flex in response to wave motion, in addition to responding in the standard six rigid-body degrees of motion. Waves experience drag (form and skin) travelling around the floe (Kohout et al., 2011). The floes are also susceptible to drift. Further, the small freeboards of floes permit waves of moderate amplitude to overwash the floes, and the shallow draughts permit energetic waves to slam floes against the ocean surface.
A series of mathematical models of wave interactions with an ice floe, and hence transmission, have been developed (e.g. Masson and LeBlond, 1989, Meylan, 2002, Bennetts and Williams, 2010). Thin plates are used to model the floes. The models are conservative, i.e. no energy dissipation, and assume all motions are proportional to the incident wave amplitude, i.e. the proportion of wave energy transmission does not depend on the incident amplitude. They neglect wave overwash of the floes by waves, slamming, drag and drift.
An idealised experimental model of wave transmission by an ice floe is presented here. Consistent with the mathematical models, thin plastic plates were used to model the floe. Regular (monochromatic) incident waves, ranging from gently-sloping to storm-like, were used. The transmitted wave field was measured by a wave gauge.
Kohout et al., 2007, Huang et al., 2011, Montiel et al., 2013b, Montiel et al., 2013a, McGovern and Bai, 2014 recently used closely related experimental models to investigate wave-induced motions of ice floes. However, the present investigation is the first to study transmission of waves by an ice floe.
Field measurements of wave energy at discrete points in the miz exist (e.g. Squire and Moore, 1980, Wadhams et al., 1988, Meylan et al., 2014). Wave transmission by a large collection of floes can be inferred from these measurements. However, the measurements are not accompanied by detailed information of floe properties. Field measurements of transmission of waves by an individual floe of known properties do not exist.
The experimental model is used to gain understanding of how a floe affects wave propagation, with respect to floe and incident wave properties. The study focusses on the proportion of wave energy transmitted by the floe, i.e. the transmission coefficient. The effect of the floes on the full wave spectrum is also analysed for a subset of the tests conducted. Further, the transmission is related to the properties of the overwash, which were measured by a specifically designed wave gauge mounted on the model floe.
Section snippets
Experimental model
The experimental model was implemented in the wave basin at the Coastal Ocean And Sediment Transport (coast) laboratories of Plymouth University, U.K. Fig. 1 shows a schematic plan view of the wave basin and experimental set-up. The basin is 10 m wide, 15.5 m long and was filled with fresh water m in depth. The room and water temperatures were approximately 20 °C and 16 °C, respectively.
At the left-hand end of the basin, a wave maker, consisting of twenty individually controlled active
Detailed results for 5 mm thickness floes
Detailed results are given here for the thinnest floes, with thickness 5 mm. The behaviours shown are broadly representative of the thicker floes tested.
Fig. 2 shows the wave-induced drift of the polypropylene floe for an incident wavelength, nondimensionlised with respect to the floe length, of , and the most gentle steepness, (left-hand panel), and most storm-like steepness, (right). In both cases, the floe undergoes an oscillatory surge motion of period
Summary and discussion
An idealised experimental model of transmission of ocean waves by a solitary ice floe has been reported. The experimental tests were conducted in a wave basin, using regular incident waves with different wave periods, amplitudes and steepnesses. The incident waves ranged from gently-sloping to storm-like. Thin plastic plates were used to model the floe. Two different plastics and three different thicknesses were tested. A wave gauge was used to measure the wave elevation in the lee of the floe.
Acknowledgments
Experiments were supported by the Small Research Grant Scheme of the School of Marine Science and Engineering of Plymouth University and performed when AA and AT were appointed at Plymouth University. The authors thank Peter Arber for technical support during the experiments. LGB acknowledges funding support from the Australian Research Council (DE130101571) and the Australian Antarctic Science Grant Program (Project 4123). MHM and AVB acknowledge funding support for the U.S. Office of Naval
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