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Observations of Flexural Waves on the Erebus Ice Tongue, Mcmurdo Sound, Antarctica, and Nearby Sea Ice

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Observations of Flexural Waves on the Erebus Ice Tongue, Mcmurdo Sound, Antarctica, and Nearby Sea Ice Journal of Glaciology, Vo!. 40, No. 135, 1994 Observations of flexural waves on the Erebus Ice Tongue, McMurdo Sound, Antarctica, and nearby sea ice VERNON A. SQUIRE, Department of Mathematics and Statistics, Universiry of Otago, Dunedin, New Zealand WILLIAM H. ROBINSON, New Zealand Institute for Industrial Research and Development, Lower Hull, Wellington, New Zealand MICHAEL MEYLAN, Department of Mathematics and Statistics, Universiry of Otago, Dunedin, New Zealand TIMOTHY G. HASKELL New Zealand Institute for Industrial Research and Development, Lower Hull, Wellington, New Zealand ABSTRACT. New strain data relating to flexural oscillations of the Erebus Glacier Tongue (EGT), McMurdo Sound, Antarctica, are presented and are analysed in the frequency domain. The data were collected during November 1989, just 3 months prior to the most recent calving of the ice tongue which occurred in March 1990. A broad-band oscillation centred on 50 s is found in both the strain measurements collected on the EGT and those collected on the sea ice nearby. The oscillation is shown, at least in part, to be propagating with a phase velocity of approximately 65 m S- 1 in a direction away from the snout towards the grounding line, rather than being wholly due to a standing-wave pattern in the EGT. A coupling model between the sea ice and the EGT is proposed and is shown to compare reasonably well with the data. 3794 INTRODUCTION MOUNT ER EBUS The Erebus Glacier Tongue (EGT) flows from the western side of Mount Erebus into McMurdo Sound, ROSS ISLAND about 20 km north of New Zealand's Scott Base and the Cape Evans nearby United States base, McMurdo (Fig. I). Its close Inaccessible proximity to excellent logistical support has meant that Island C=> Tent /Sland the EGT has been the focus of a number of experimental Q and theoretical studies to map its geometry and structure (Holdsworth, 1982), and to understand its dynamics (Holdsworth, 1969, 1974; Goodman and Holdsworth, 1978; Holdsworth and Holdsworth, 1978; Holdsworth Sea Ice and Glynn, 1981; Vinogradov and Holdsworth, 1985; Gui and Squire, 1989). The EGT is known to have calved at least three times since the turn of the cen tury: in March 1911 members of S COtl Base Scott's British Antarctic (Terra Nova ) Expedition ob­ (NZ) served a major calving event and the formation of an 2 approximately 4 km tabular iceberg weighing more than Ross Ice Shelf 6 100 x 10 tonnes; a similar calving was deduced by 1 5 10 , !' !, , ! , , , ! Holdsworth (1974) to have occurred in the 1940s and km he suggested another calving was imminent. The last calving occurred on I March 1990 (Robinson and Fig. 1. Map showing Erebus Glacier Tongue in relation to Haskell, 1990), 3 months after the measurements that New Zealand's Scott Base and the U.S. McMurdo are reported in this paper were collected. Station. Downloaded from https://www.cambridge.org/core. 24 Sep 2021 at 11:52:10, subject to the Cambridge Core terms of use. 377 Journal of Claciology These calvings and many others in similar ice tongues the EGT's snout. The EGT grows at the rate of about took place at some distance from the grounding line, 150 m year-I (DeLisle and others, 1989). Most of the year where one might expect the bending moments and stresses it is surrounded by sea ice of 1-3 m thickness and it is only to be largest. This has led to the suggestion that the for a short time at the height of summer that the sea ice calving is due to the build-up of standing waves in the melts around the tongue (Robinson and Haskell, 1992). tongue and that these are of sufficient amplitude to The results of Robinson and Haskell (1992) suggest produce fatigue failure of the ice after many cycles. All that the strains in the EGT are due to length-wise flexural theoretical studies have assumed that the waves are waves, and in the rest of this paper we shall assume that standing. Various groups have measured strain or tilt on this is the case. the EGT (e.g. Goodman and Holdsworth, 1978; Holds­ worth and Holdsworth, 1978) and have attributed the observed oscillations in strain to standing flexural waves. FLEXURAL WAVES In 1984, the New Zealand Department of Scientific and Industrial Research (DSIR) Physical Sciences buried A commonly used model for a floating ice sheet which is sensitive strain gauges in the EGT to monitor oscillations flexing under the action of small-amplitude waves is that and to observe a calving event, noting that one was of a perfectly elastic, thin plate on a fluid foundation. The overdue. Strains were measured daily from October 1984 alternative use of a thick-plate model, which includes the to 1989, and were telemetered to Scott Base where they effect of rotatory inertia and transverse shear, has been were recorded on floppy disk. Initially, two strain gauges investigated by Fox and Squire (1991 a) and it has been were buried lengthways either side of the tongue, 3.5 km shown to be unnecessary except in the case of very short from the snout. The strains from these two instruments waves or very thick ice. For example, Fox and Squire were in phase and of similar amplitudes, which is (1991 a) found the thin- and thick-plate models agreed for consistent with a lengthwise flexure of the tongue periods greater than 20 s with 200 m thick ice. Thus, the (Robinson and Haskell, 1992). A rosette of three strain present geometries for either the EGT or the sea ice of gauges was used to investigate further the mode of McMurdo Sound do not call for this more complicated vibration. The major principal strain was found to lie theory; a thin-plate theory is quite adequate. along the length of the tongue and the minor principal strain was found to be approximately - ~ of the major The ice-plate Jnodel and dispersion relation principal strain (Robinson and Haskell, 1992) . This was additional evidence th a t the strains were due to The dispersion relation for a thin sea-ice plate of thickness lengthwise flexure of the ice tongue. Since, at this time, h and density pi is derived by assuming an homogeneous it was not possible to distinguish between standing and ice sheet occupying -00 < x < 00, -00 < y < 00, travelling waves, two more stra in gauges were placed at o < z < h floating on inviscid, irrotational water of distances of 180 and 1700 m towards the snout. Results depth H and density p (Fig. 2) . Then, for no downward from the three strain gauges suggested that flexural waves load, it is straightforward to derive a linearized surface­ were travelling from the snout towards the grounding boundary condition for the ice sheet as follows (Fox and line at a phase speed of approximately 70 ± 10 ms-I Squire, 199Ib): (Robinson and Haskell, 1992) . To clarify further these observations, which were quite L\14"., + p' h7]tt = -pcPtlz=o - P911 (1) sparse, the present intensive study was staged during where 7](x, y, t) represents a small vertical displacement of November 1989. It is the analysis of these 1989 data that the ice sheet, and compressive stresses have been is the subject of this paper. The long data set telemetered neglected. The effective flexural rigidity of the ice from Scott Base during 1984-89 is deficient in several L = Eh3/12(1 - if), where E is the effective Young's respects, mainly because oflimitations in the band width modulus and v is Poisson's ratio. The dispersion relation of the telemetry system. The 1984-89 data set cannot, for for uniform plane waves of wave number k and angular example, be used for spectral analysis because the length frequency w travelling in the positive x-direction is found of the data records transmitted is too short for meaningful statistical interpretation. It was intended for, and is therefore more suited to, climatological work; for instance, looking for long-term changes preceding a calving even t. The N ovem ber 1989 experiment, on the other hand, only took place over a few days but the records were collected with the aim of interpreting the data fully. Unfortunately, the long-awaited EGT calving event of March 1990 took place after all the DSIR strain gauges had been uplifted. H The most recent measurements of the dimensions of the EGT were made in December 1985 (DeLisle and others, 1989). Its length was 15 km, of which the last Sea floor at z ; -H 13.5km were floating, and its thickness varied from 50m at the snout to 300 m at the grounding line. Its width varied from 0.5 to 2 km with many large bays along its Fig. 2. Schematic showing ice sheet or beam of thickness h sides. The depth of McMurdo Sound is about 300 m at floating on water depth H. Downloaded37 from8 https://www.cambridge.org/core. 24 Sep 2021 at 11:52:10, subject to the Cambridge Core terms of use. Squire and others: Flexural waves on the Erebus Ice Tongue, Antarctica by assuming that the surface displacement TJ is every­ For both the sea· ice and the EGT, we may write the where proportional to ei(kx-wt). Then, using the kine­ displacement amplitude in terms of the principal surface matic boundary condition strains using Expressions (5) and (6): TJt = 4>zlz=o = ktanh(kH)<J1lz=o (2) 2fo TJo = hk2 (7) we substitute Equation (2) into Equation (I), to get where 5 for the sea ice 2 Lk /p + gk w = --':"":"'--"-- (3) kh' + cothkH for the ice tongue.
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