Impingement of surface waves on the edge of compressed ice

Abstract

The impingement of small-amplitude surface waves on the edge of a solid compressed ice sheet in a basin of finite constant depth is considered. The influence of the cylindrical rigidity and the value of the compressing force on the dependence of the amplitude coefficients of reflection and transmission on the incident wave period is analyzed.

Dynamics of flexural gravity waves: from sea ice to Hawking radiation and analogue gravity

“…In the earlier study of [18,49,54], although the critical value of compressive force for which group and phase velocities vanish was determined, a detailed analysis of wave blocking in this trapped energy zone was missing. Further, in this trapped energy zone, the occurrence of three real positive roots and their coalescence is contrary to the earlier assumption that the dispersion relation in equation (3.5) has a single positive real root (as in [18,49]). A similar phenomenon in the case of capillary gravity waves was observed in [45] where, under the action of opposing current on capillary-gravity waves, a similar pitchfork bifurcation occurs to produce two blocking points.…”

“…Moreover, for Q < Q cg , two of the positive real roots disperse into a complex plane to provide four complex roots and one real root. In the earlier study of [18,49,54], although the critical value of compressive force for which group and phase velocities vanish was determined, a detailed analysis of wave blocking in this trapped energy zone was missing. Further, in this trapped energy zone, the occurrence of three real positive roots and their coalescence is contrary to the earlier assumption that the dispersion relation in equation (3.5) has a single positive real root (as in [18,49]).…”

“…Liu & Mollo-Christensen [17] analysed the effect of wave refraction at the ice-pack edge and the effect of a compressive force on the wave propagation and stability of the ice-pack. Bukatov & Zav'yalov [18] studied the wave scattering by a compressed floating ice sheet and for practical purposes limited all their analysis within certain limiting value of compressive force to avoid fracture in the ice sheet. The combined effects of current speed and compression on plane flexural gravity wave motion was studied by analysing the dispersion relation, phase and group velocities in [19].…”

Effect of compression on wave diffraction by a floating elastic plate

“…The effect of compressive force on floating ice sheet is studied in the context of moving load on floating ice sheet (see Kerr, 1983;Squire et al, 1996 and the literature cited therein). Bukatov and Zav'yalov (1995) studied the impingement of surface waves on the edge of compressed ice in a basin of constant depth based on conjugate gradient method. Although, Bukatov and Zav'yalov considered the effect of compression in the ice sheet, free edge boundary conditions are used in the analysis without adding the compressive force term in the edge condition.…”

Scattering of flexural-gravity waves by a crack in a floating ice sheet due to mode conversion during blocking

“…Further details on the buckling of a floating ice sheet can be found in Kerr (1983), where the connection between the critical compressive force for which buckling occurs is related to the vanishing of the phase velocity. Subsequent progress on this aspect includes the works of Davys, Hosking & Sneyd (1985), Schulkes, Hosking & Sneyd (1987), Liu & Mollo-Christensen (1988), Bukatov & Zav'yalov (1995), Squire et al (2012) and Collins, Rogers & Lund (2017). One fundamental change observed in the presence of compression is due to the occurrence of wave blocking (Das, Sahoo & Meylan 2018b).…”