The effect of submergence on wave scattering across a transition between two floating flexible plates

Williams, Timothy; Squire, Vernon A.

doi:10.1016/j.wavemoti.2007.07.003

Cited by 19 publications

(22 citation statements)

References 26 publications

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“…For the 20 m wide ridge the minimum (caused by resonance; see ) gets progressively deeper as the number of modes is increased. The slightly different slopes of the curves at high periods is the remaining point of departure of our results from those Williams & Squire (2008) and does not improve with higher number of modes. For the 100 m wide ridge, results are similar, but there the positions of resonance minima are shifted.…”

Section: (B) Verification Of the Modelcontrasting

confidence: 79%

“…That the comparisons are so good provides us with confidence in our model. Williams & Squire (2008) Here, a comparison is made with results from Williams & Squire (2008), who describe a model in which Archimedean draught may be optionally accommodated. For a 1 m thick ice sheet punctuated by a 2 m thick ridge, and for two different ridge widths, results are shown in figure 3, in which the inclusion and non-inclusion of draught have been examined.…”

Section: (B) Verification Of the Modelmentioning

confidence: 99%

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The decay of flexural-gravity waves in long sea ice transects

2009

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Flexural oscillations of floating sea ice sheets induced by ocean waves travelling at the boundary between the ice and the water below can propagate great distances. But, by virtue of scattering, changes of ice thickness and other properties encountered during the journey affect their passage, notwithstanding attenuation arising from several other naturally occurring agencies. We describe here a two-dimensional model that can simulate wave scattering by long (approx. 50 km) stretches of inelastic sea ice, the goal being to replicate heterogeneity accurately while also assimilating supplementary processes that lead to energy loss in sea ice at scales that are amenable to experimental validation. In work concerned with scattering from solitary or juxtaposed stylized features in the sea ice canopy, reflection and transmission coefficients are commonly used to quantify scattering, but on this occasion, we use the attenuation coefficient as we consider that it provides a more helpful description when dealing with long sequences of adjoining scatterers. Results show that scattering and viscosity both induce exponential decay and we observe three distinct regimes: (i) low period, where scattering dominates, (ii) high period, where viscosity dominates, and (iii) a transition regime. Each regime's period range depends on the sea ice properties including viscosity, which must be included for the correct identification of decay rate.

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Section: (B) Verification Of the Modelcontrasting

confidence: 79%

Section: (B) Verification Of the Modelmentioning

confidence: 99%

The decay of flexural-gravity waves in long sea ice transects

2009

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“…While the justification for the zero submergence approximation is defensible, namely that ocean wavelengths are very long compared with the vertical length scale associated with ice thickness so that effects owing to draught will be negligible, the approximation needs to be tested. This was done by Williams & Squire [15] by solving an integral equation arising from a formulation based on Green's functions. Bennetts et al [16] also included Archimedean draught but the focus is mainly on solitary floes.…”

Section: (I) Single Featuresmentioning

confidence: 99%

Past, present and impendent hydroelastic challenges in the polar and subpolar seas

Squire

2011

Phil. Trans. R. Soc. A.

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Current and emergent advances are examined on the topic of hydroelasticity theory applied to natural sea ice responding to the action of ocean surface waves and swell, with attention focused on methods that portray sea ice more faithfully as opposed to those that oversimplify interactions with a poor imitation of reality. A succession of authors have confronted and solved by various means the demanding applied mathematics associated with ocean waves (i) entering a vast sea-ice plate, (ii) travelling between plates of different thickness, (iii) impinging on a pressure ridge, (iv) affecting a single ice floe with arbitrarily specified physical and material properties, and (v) many such features or mixtures thereof. The next step is to embed simplified versions of these developments in an oceanic general circulation model for forecasting purposes. While targeted on specific sea-ice situations, many of the reported results are equally applicable to the interaction of waves with very large floating structures, such as pontoons, floating airports and mobile offshore bases.

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“…It may be noted that the eigenfunctions f 1n (y), n = 0, I, I I and L(ξ, y) satisfy the orthogonal mode-coupling relation defined in (12) with h → ∞ (see [20,Sect. 3.2]), which yields L(ξ, y), f 1n (y) = 0 for ξ > 0 ( B 5 )…”

Section: Appendix a Energy Density And Energy Relationmentioning

confidence: 99%

“…Sturova [11] studied the effect of periodic surface pressure on a rectangular elastic plate floating on shallow-water and found that elastic plates floating on shallow water can possess wave properties in the case of non-zero immersion. Williams and Squire [12] used a Green's function technique to study the effect of submergence on wave scattering across a transition between two floating elastic plates. Further, they developed a method based on a wide-spacing approximation, which provides the scattering coefficients when submergence is included.…”

Section: Introductionmentioning

confidence: 99%

Oblique flexural gravity-wave scattering due to changes in bottom topography

2009

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Oblique flexural gravity-wave scattering due to an abrupt change in water depth in the presence of a compressive force is investigated based on the linearized water-wave theory in the case of finite water depth and shallow-water approximation. Using the results for a single step, wide-spacing approximation is used to analyze wave transformation by multiple steps and submerged block. An energy relation for oblique flexural gravity-wave scattering due to a change in bottom topography is derived using the argument of wave energy flux and is used to check the accuracy of the computation. The changes in water depth significantly contribute to the change in the scattering coefficients. In the case of oblique wave scattering, critical angles are observed in certain cases. Further, a resonating pattern in the reflection coefficients is observed due to change in the water depth irrespective of the presence of a compressive force in the case of a submerged block.

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The effect of submergence on wave scattering across a transition between two floating flexible plates

Cited by 19 publications

References 26 publications

The decay of flexural-gravity waves in long sea ice transects

The decay of flexural-gravity waves in long sea ice transects

Past, present and impendent hydroelastic challenges in the polar and subpolar seas

Oblique flexural gravity-wave scattering due to changes in bottom topography

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