Crack formation and breakout of shore fast sea ice in Mordvinova Bay, south-east Sakhalin Island

Highlights

• Wave observations conducted using bottom-mounted pressure sensors in Mordvinova Bay on Sakhalin Island are discussed.

• 2 s to 20 min waves were detected and analysed, with the main focus being swells and leaky modes up to about 7 min period

• Whilst sometimes detected in open water bays, the authors believe leaky modes have not been reported under sea ice before.

• Swells and leaky wave modes acting together is suggested as a novel mechanism by which shore fast ice can be fractured.

Abstract

Recognizing that cyclical flexural fluctuations in sea ice sheets stimulated by waves can potentially initiate and perpetuate cracks that may ultimately lead to the destruction of an ice cover, we discuss some winter observations collected beneath the fast ice cover of Mordvinova Bay in the south-east of Sakhalin Island during 2018–2019 when a large crack formed that subsequently detached the offshore sea ice from the inshore ice plate by a wide lead. Energy density spectra show the ramifications of surface-gravity waves from the open ocean—primarily at swell frequencies—penetrating far into the ice from offshore, together with comparatively long, resonant leaky wave modes that gradually dissipate as they propagate alongshore but present a diminishing standing wave envelope of antinodes perpendicular to the coast. By evaluating amplitudes over different ranges of period, three swell wave events are assessed to determine whether they alone could have induced enough bending in the sea ice plate to cause breakage, acknowledging that this would normally occur much closer to the peripheral ice edge where the stresses are largest or as the swells run ashore. The foreshortened seaward standing curvature profile of leaky wave antinodes is also considered as a prospective source of cracking. Whilst neither pathway is found conclusively to be independently responsible for breaking the ice in this case, it is conjectured that the combined influence of swell and leaky waves acting together could cause the observed crack to form. In this case, fracture would occur at a distance of less than about four or so kilometres from the shore, where the antinodal curvatures induced by the standing leaky modes are sufficient. Conceding that the unrelenting flexing of the ice plate by waves and swell could affect the longevity of the sea ice as well, fatigue-precipitated weakening is explored. By determining the value of the mechanical stress at which an ensuing rupture of the fast ice could happen, it is shown that ice destruction can eventuate approximately 17 h after the swell first arrives at the ice edge from the Sea of Okhotsk, appreciating that breakup will depend on prevailing and prior meteorological conditions, the form and state of the sea ice including any preexisting defects, and the specific periods of swell waves that infiltrate the Mordvinova Bay ice sheet.

Introduction

Although a proportion of the energy in surface-gravity waves incident on a continuous sheet of sea ice from the open ocean is reflected at the ice edge, appreciable energy can still pass beneath the sea ice as flexural-gravity waves that cause the ice to bend rhythmically over time. Underscoring that because of refraction at the edge, flexural-gravity waves will only align with their open-water surface-gravity wave source when the latter enters the ice cover at normal incidence, we will notionally associate the coordinate x with the direction of propagation of a flexural-gravity wave in the ice sheet. Loosely speaking, the amount of energy entering the ice depends primarily on the ratio of wavelength λ to ice thickness h; the passage of long waves into ice-covered sea being favoured over shorter waves (Fox and Squire, 1990, Fox and Squire, 1994). Nonetheless, mindful that open sea wavelengths commonly span some 50 to 500 m and that sea ice is rarely more than a small number of metres thick, a good proportion of the inbound wave energy finishes up beneath the ice. Indeed, long swells can travel into modest ice covers with hardly any reflection at all; they simply do not “see” or “feel” most sea ice sheets and their properties under ice are almost indistinguishable from their open-water lineage. As a matter of fact, fluctuations at swell periods are found hundreds of kilometres from open water (Robin, 1963; Squire et al., 1995; Squire, 2007, Squire, 2020; Squire et al., 2009; Vaughan et al., 2009), having suffered negligible dissipation en route and only nominal attrition as they pass through interfaces between water and ice, and vice versa.

The strain ε(x) at the surface of the ice sheet at a point x is the fractional extension of the ice in that direction. If the displacement generated by a passing wave train of amplitude ζ is small, ε(x) is related to the local radius of curvature of the thin, uniform ice sheet in the vertical plane, i.e. the reciprocal of the curvature κ(x), by

$$\epsilon \left(x\right)=-\frac{h}{2}\kappa \left(x\right)\approx -\frac{h}{2}\left(\frac{d^2\zeta }{{\mathit{dx}}^2}\right),$$

(see, e.g., Fox and Squire, 1994). Substantial bending of the ice plate can occur if the wave height 2ζ and especially the steepness 2ζ/λ, are sufficient, but an assumption of linearity underlies the above approximation (1). No geometric nonlinearity in flexural-gravity waves, i.e. trochoidal wave profiles, has ever been detected to the authors' knowledge, so a linear, time-harmonic framework is satisfactory. Mid-range wave periods are the most effective at deforming the ice plate, as most of the very short wave energy is attenuated or reflected at the ice edge whereas the slope of long swells is small. When the bending moments (proportional to strain ε) generated exceed those that the ice can withstand, numerous observations suggest that the ice sheet within a few wavelengths of the ice edge can fracture into separate ice floes which dissociate from the main sheet to form a new ice edge that is systematically eroded with the inevitable result that a large proportion of the ice sheet can eventually be destroyed. The progressive demolition of an ice sheet from where its outer edge meets the open sea has been witnessed many times with sequenced time-lapse photography and video illustrating the phenomenon—although few quantitative in situ data have been able to be collected because of the destructive nature of the process. A number of papers are devoted to these investigations (Squire, 1993a; Squire et al., 1995; Langhorne et al., 1998; Shuchman et al., 2004; Squire, 2007; Broström and Christensen, 2008). Furthermore, results of some of the measurements reported in the present paper, made in the fast ice zone of the Sea of Okhotsk near the settlement of Okhotskoe, Sakhalin Island (see Fig. 1), supplement these studies.

These works notwithstanding, the emergence of major cracks within the body of a fast ice sheet between where it abuts the shore and its outermost ice edge is also of interest. A prominent crack can develop and expand into a wide lead that splits the fast ice sheet at some distance from the shore rather than along the coastline itself, especially when fast ice connects pivotally to the coast (invariably, although not universally, via a tide crack). Measurements in Mordvinova Bay, Sakhalin Island, show that such cracks do form and can rapidly expand into a wide lead or even a broad polynya when winds are offshore. Moreover, if the fast ice is not constrained by an array of ice floes and cakes on its outermost edge, the liberated seaward ice plate can be advected away into the Sea of Okhotsk under the continued action of offshore winds and currents.

A tangible precedent unfolded some 4 km seaward from the work settlement of Okhotskoe in Mordvinova Bay on 25th February 2017, when the fast ice sheet cracked and 20 fishermen were stranded. On 8th March 2017, farther north in Dolinsky district near the Vzmor'ye settlement village, an ice floe carried away over 100 fishermen. Whilst the State Ministry of Emergency Situations successfully coordinated the rescue, the potential for appreciable loss of life and the considerable cost of operations in ice-infested seas reinforces a sense of urgency in understanding crack formation and how sea ice is ravaged by Nature. Acknowledging that the capacity to forecast the destruction of coastal sea ice is a worthwhile goal throughout the polar and subpolar regions, it is of singular practical importance to Sakhalin Island where fishermen regularly congregate on local fast ice and employees of Hydrometeorological Services are located in the winter to conduct meteorological and oceanographic measurements. Fig. 2 shows a comparable lead to those of 2017, which opened up on 30th January 2019 and extended in both directions from the place of observation.

Mordvinova Bay is shallow, deepening gradually seawards to reach a depth of 200 m but not until about 50 km offshore. Consequently, although incoming ocean wave trains customarily do damage in the vicinity of the ice edge, as discussed above, the impact of the continuous shoaling on waves and swell approaching the coast cannot be ignored—especially those prevailing swells with wavelengths as large as 400 m which, in open water, would start to feel the effect of the sea floor some 50 km from the coast. Shoaling will turn the waves towards normal incidence, cause a reduction in wavelength λ while frequency remains constant, and increase wave amplitude ζ. As a result, the steepness of wave trains increases along with their curvature d²ζ/dx², raising the possibility that the area of sea ice adjoining the land will break up regardless of whether the sea ice ruptures farther out—especially if the ice plate is rigidly welded to the shore and is incapable of relieving stress by pivoting. In this case, the sea ice tends to be fragmentized into a mélange of individual ice cakes and brash, rather than a smooth crack being created followed by a wide open-water lead like the one illustrated in Fig. 2.