Oblique scattering of plane flexural–gravity waves by heterogeneities in sea–ice

Abstract

Ocean waves propagating beneath a sea-ice sheet encounter a variety of inhomogeneities, which normally arise because of the dynamic nature of the ice veneer over large physical scales. Zones of thinner, thicker, rougher or ridged ice, changes of material property, and abrupt transitions into and from open water, for example, each have their own distinctive scattering kernel that modifies the incoming wave energy spectrum as it progresses further into the ice cover. Here we present a theoretical analysis of wave propagation beneath sea-ice, where the ice is allowed to vary spatially. Isolated irregularities such as pressure ridges, rafted regions, ice islands that have become trapped in the sea-ice, open and refrozen leads, etc., are considered, as well as groups of such features, with their peripheries either welded to the surrounding ice sheet or separated from it by a free crack. Reflection and transmission coefficients, plotted as functions of wave period or wavelength, reveal considerable fine structure, including in some cases a comb of wave frequencies at which perfect transmission occurs. The work generalizes and extends work by Squire & Dixon, Williams & Squire and Evans & Porter, which all deal with abrupt transitions, to properly allow for inhomogeneity in the ice cover. For the multiple, randomly shaped, oriented and spaced irregularities observed in a real ice sheet, good agreement is found between the full solution, a wide-spacing approximation that neglects the evanescent parts of the wave field in subsequent interactions, and a simple serial approach where interactions between features are neglected and the effect of each irregularity is computed in sequence.

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

“…Williams & Squire [11,14], also go on to consider wave propagation through many such features. To date, however, the most ambitious attempt to achieve this, due to Vaughan et al [8] and Squire et al [2], interfuses the model of Bennetts et al [16] as its kernel.…”

“…Williams & Squire [11] incorporated a region of variable properties, expressed through the flexural rigidity and density, in an otherwise uniform ice sheet (figure 3), by redefining the operator (2.6) as…”

“…Here, we non-dimensionalize length with respect to the natural length L = 5 D/ru 2 and time with t = 8 D/rg 5 , which has the advantage of simultaneously assimilating the properties of both the ice floe and the wave and of furnishing a dispersion relation in terms of a single parameter (see [11]). Defining Open water waves impinge obliquely onto a compliant ice sheet that is either semi-infinite or of finite length d in the x-direction, but extends to ±∞ in the y-direction.…”

A higher order FEM for time-domain hydroelastic analysis of large floating bodies in an inhomogeneous shallow water environment

“…The analysis and simulation of ocean wave-ice interaction poses a significant and challenging problem, due to its direct association with sea ice distribution and global climate change [1][2][3]. In fact, climate change has triggered wind intensification, as well as a significant increase in wave height and storm intensity over the last 20 years [4].…”

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

“…The leads, polynyas, cracks and pressure ridges that cause sea ice to be heterogeneous partially transmit and partially reflect the incoming waves. To a degree, this has been investigated in the past by simulating how isolated features such as these scatter the incoming wave train, for example, by cracks (Squire & Dixon 2000), leads (Chung & Linton 2005), ridges (Williams & Squire 2004) and by sequences of such features. However, natural sea ice is rarely this simple and this observation led Vaughan & Squire (2008a) to simulate scattering by sea ice transects sampled from data collected using upward-pointing sonar during submarine voyages (NSIDC 2006).…”