Ice shelf flexures modeled with a 2-D elastic flow line model

Abstract. Ice shelf flexures modeling was performed using a 2-D finite-difference elastic model, which takes into account sub-ice-shelf sea water flow. The sub-ice water flow was described by the wave equation for the sub-ice-shelf pressure perturbations (Holdsworth and Glynn, 1978). In the model ice shelf flexures result from variations in ocean pressure due to changes in prescribed sea levels. The numerical experiments were performed for a flow line down one of the fast flowing ice streams of the Academy of Sciences Ice Cap. The profile includes a part of the adjacent ice shelf. The numerical experiments were carried out for harmonic incoming pressure perturbations P' and the ice shelf flexures were obtained for a wide spectrum of the pressure perturbations frequencies, ranging from tidal periods down to periods of a few seconds (0.004..0.02 Hz). The amplitudes of the ice shelf deflections obtained by the model achieve a maxima at about T &approx; 165 s in concordance with previous investigations of the impact of waves on Antarctic ice shelves (Bromirski et al., 2010). The explanation of the effect is found in the solution of the corresponding eigenvalue problem revealing the existence of a resonance at these high frequencies.

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Ice-shelf forced vibrations modelled with a full 3-D elastic model

The Cryosphere Discussions ◽

10.5194/tcd-8-6059-2014 ◽

2014 ◽

Vol 8 (6) ◽

pp. 6059-6078

Author(s):

Y. V. Konovalov

Keyword(s):

Thin Plate ◽

High Frequency ◽

Numerical Experiments ◽

Wide Spectrum ◽

Forced Vibrations ◽

Elastic Model ◽

Ice Shelf ◽

Plate Vibrations ◽

The Impact ◽

Pressure Perturbations

Abstract. Ice-shelf forced vibrations modelling was performed using a full 3-D finite-difference elastic model, which takes into account sub-ice seawater flow. The sub-ice seawater flow was described by the wave equation, so the ice-shelf flexures result from the hydrostatic pressure perturbations in sub-ice seawater layer. The numerical experiments were performed for idealized ice-shelf geometry, which was considered in the numerical experiments in Holdsworth and Glynn (1978). The ice-plate vibrations were modelled for harmonic ingoing pressure perturbations and for a wide spectrum of the ocean swell periodicities, ranging from infragravity wave periods down to periods of a few seconds (0.004–0.2 Hz). The spectrums for the vibration amplitudes were obtained in this range and are published in this manuscript. The spectrums contain distinct resonant peaks, which corroborate the ability of resonant-like motion in suitable conditions of the forcing. The impact of local irregularities in the ice-shelf geometry to the amplitude spectrums was investigated for idealized sinusoidal perturbations of the ice surface and the sea bottom. The results of the numerical experiments presented in this manuscript, are approximately in agreement with the results obtained by the thin-plate model in the research carried out by Holdsworth and Glynn (1978). In addition, the full model allows to observe 3-D effects, for instance, vertical distribution of the stress components in the plate. In particular, the model reveals the increasing in shear stress, which is neglected in the thin-plate approximation, from the terminus towards the grounding zone with the maximum at the grounding line in the case of considered high-frequency forcing. Thus, the high-frequency forcing can reinforce the tidal impact to the ice-shelf grounding zone additionally exciting the ice fracture there.

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The effect of the blocking of impact ocean waves by the crevasse-ridden ice shelf

10.5194/egusphere-egu2020-9665 ◽

2020 ◽

Author(s):

Yuri Konovalov

Keyword(s):

Band Gap ◽

Numerical Experiments ◽

Amplitude Spectrum ◽

Ocean Waves ◽

Band Gaps ◽

Elastic Model ◽

Ice Shelf ◽

Impact Wave ◽

Wide Range ◽

The Impact

The propagation of high-frequency elastic-flexural waves through an ice shelf was modeled by a full 3-D elastic model, which also takes into account sub-ice seawater flow. The sea water flow is described by the wave equation. Numerical experiments were undertaken both for an intact ice shelf free of crevasses, which has idealized rectangular geometry, and for a crevasse-ridden ice shelf. The crevasses were modeled as triangle/rectangular notches into the ice shelf. The obtained dispersion spectra (the dispersion curves describing the wavenumber/periodicity relation) are not continuous. The spectra reveal gaps that provide the transition from n-th mode to (n+1)-th mode. These gaps are observed both for an intact ice shelf free of crevasses and for a crevasse-ridden ice shelf. They are aligned with the minimums in the amplitude spectrum. That is the ice shelf essentially blocks the impact wave at this transition. However, the dispersion spectrum obtained for a crevasse-ridden ice shelf, has a qualitatively difference from that obtained for an intact ice shelf free of crevasses. Moreover, the dispersion spectrum obtained for a crevasse-ridden ice shelf reveals the band gap &#8211; the zone there no eigenmodes exist (Freed-Brown and others, 2012). The numerical experiments with the crevasse-ridden ice tongue that is 16 km in longitudinal extent, 0.8km width and 100m thick, were undertaken for a wide range of the periodicities of the incident wave: from 5 s to 250 s. The obtained dispersion spectra reveal two band gaps in this range: the first band gap at about 20 s and the second band gap at about 7 s for 1km spatial periodicity of the crevasses. The width of the band gap significantly increases when the crevasses depth increases too. Respectively, the amplitude spectra reveal significantly increasing area of periodicities/frequencies where the ice shelf blocks the impact wave.ReferencesFreed-Brown, J., Amundson, J., MacAyeal, D., & Zhang, W. (2012). Blocking a wave: Frequency band gaps in ice shelves with periodic crevasses. Annals of Glaciology, 53(60), 85-89. doi:10.3189/2012AoG60A120Konovalov, Y.V. (2019). Ice-shelf vibrations modeled by a full 3-D elastic model. Annals of Glaciology, 1-7. doi:10.1017/aog.2019.9

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Ice-shelf vibrations modeled by a full 3-D elastic model

Annals of Glaciology ◽

10.1017/aog.2019.9 ◽

2019 ◽

Vol 60 (79) ◽

pp. 68-74 ◽

Cited By ~ 2

Author(s):

Yuri V. Konovalov

Keyword(s):

Thin Plate ◽

Sea Water ◽

Elastic Model ◽

Ice Shelf ◽

Incoming Wave ◽

Plate Vibrations ◽

Wide Range ◽

Pressure Perturbations ◽

D Model ◽

Vibration Modeling

ABSTRACTForced ice-shelf vibration modeling is performed using a full 3-D finite-difference elastic model, which also takes into account sub-ice seawater flow. The sea water flow is described by the wave equation. Ice-shelf flexure therefore results from hydrostatic pressure perturbations in the sub-ice seawater layer. Numerical experiments were undertaken for idealized rectangular ice-shelf geometry. The ice-plate vibrations were modeled for harmonic incoming pressure perturbations and for a wide range of incoming wave frequencies. The spectra showed distinct resonant peaks, which demonstrate the ability of the model to simulate a resonant-like motion. The spectra obtained by the full 3-D model are compared with exact solutions for the elastic thin plate with two fixed edges and two free edges. The spectra are also compared with the spectra modeled by the thin-plate Holdsworth and Glynn model (1978).

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Viscous and elastic buoyancy stresses as drivers of ice-shelf calving

Journal of Glaciology ◽

10.1017/jog.2020.35 ◽

2020 ◽

Vol 66 (258) ◽

pp. 643-657 ◽

Cited By ~ 1

Author(s):

Cyrille Mosbeux ◽

Till J. W. Wagner ◽

Maya K. Becker ◽

Helen A. Fricker

Keyword(s):

Ice Sheet ◽

Elastic Model ◽

Ice Shelf ◽

Ice Shelves ◽

Bending Stresses ◽

Iceberg Calving ◽

Basal Melting ◽

The Antarctic ◽

The Impact ◽

Maximum Stresses

AbstractThe Antarctic Ice Sheet loses mass via its ice shelves predominantly through two processes: basal melting and iceberg calving. Iceberg calving is episodic and infrequent, and not well parameterized in ice-sheet models. Here, we investigate the impact of hydrostatic forces on calving. We develop two-dimensional elastic and viscous numerical frameworks to model the ‘footloose’ calving mechanism. This mechanism is triggered by submerged ice protrusions at the ice front, which induce unbalanced buoyancy forces that can lead to fracturing. We compare the results to identify the different roles that viscous and elastic deformations play in setting the rate and magnitude of calving events. Our results show that, although the bending stresses in both frameworks share some characteristics, their differences have important implications for modeling the calving process. In particular, the elastic model predicts that maximum stresses arise farther from the ice front than in the viscous model, leading to larger calving events. We also find that the elastic model would likely lead to more frequent events than the viscous one. Our work provides a theoretical framework for the development of a better understanding of the physical processes that govern glacier and ice-shelf calving cycles.

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Thermal Regime of George VI Ice Shelf, Antarctic Peninsula (Abstract)

Annals of Glaciology ◽

10.1017/s0260305500006650 ◽

1988 ◽

Vol 11 ◽

pp. 206 ◽

Cited By ~ 1

Author(s):

J. G. Paren ◽

S. Cooper

Keyword(s):

Sea Level ◽

Thermal Regime ◽

Sea Water ◽

Water Movement ◽

Freezing Point ◽

Flow Line ◽

Layer Structure ◽

Hot Water ◽

Lake Area ◽

Ice Shelf

New data on the thermal regime of George VI Ice Shelf have been obtained by thermistor chains installed through the use of a hot-water drill. Twenty thermistors are used at each site, spaced close together at sea-level and at the base of the ice shelf, and farther apart elsewhere in the ice shelf and in the sea beneath. Based on earlier observations (Bishop and Walton 1981, fig. 7) that the 10 m temperature warms from around −10°C in the central melt-lake area of the ice shelf (from 70°45′ to 71°45′S) to around −2°C near the northern ice front (70°00′S), the thermistor chains were deployed at three sites (70°00′, 70°15′ and 70°30′S) along a presumed flow line. The observations show that as ice flows towards the northern ice front of George VI Ice Shelf, it becomes more temperate in character. Heat from the sea and from the percolation of melt water at the upper surface progressively warms the ice shelf. At mid-depth (the coldest level in the ice shelf) the recorded temperatures were −6°C off Moore Point (70°30′S), −4°C off Carse Point (70°15′S) and, near the northern ice front (70°00′S), between −1.6° and −1.8°C depending on the time of year. The ice-shelf temperatures near the ice front, warmer in mid-summer than the freezing point of fully saline sea-water, are most unusual. The only explanation of the high, fluctuating temperatures found 1 year after drilling is that the hole through the ice shelf was open, allowing unimpeded water movement. This implies that the ice shelf is also warmed by the percolation of sea-water, whose presence was confirmed by ice-core drilling to below sea-level. Confirmation of the presence of brine below sea-level in the ice shelf comes from geo-electrical investigations. A Schlumberger georesistivity array modelled the ice shelf as a simple two-layer structure, with ordinary glacier overlying highly conductive ice. This is consistent with the fact that no radio echoes have been received from the bottom of George VI Ice Shelf to the north of 70°09′S. A detailed analysis of the ice-shelf / ocean-temperature profiles was undertaken. This included an analysis of the fluctuation observed in mid-summer at the warmest site and the subsequent transition to a stable isothermal profile through the submerged part of the ice shelf.

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Computing marine-ice thickness at an ice-shelf base

Journal of Glaciology ◽

10.3189/172756502781831674 ◽

2002 ◽

Vol 48 (160) ◽

pp. 9-19 ◽

Cited By ~ 5

Author(s):

David M. Holland

Keyword(s):

Numerical Method ◽

Ocean Circulation ◽

Sea Water ◽

Model Simulation ◽

Accumulation Rate ◽

Ocean Model ◽

Ice Thickness ◽

Ice Shelf ◽

The Impact ◽

Shelf Flow

AbstractThe freezing of sea water to the base of an ice shelf can give rise to large patches of accumulated ice, a phenomenon known as marine ice. In this study a numerical method is presented for calculating the thickness of the marine-ice layer using an ice- shelf-ocean model. The present-day modeling paradigm of ice-shelf–ocean interaction usually involves the fixed specification of the ice-shelf geometry while the ocean circulation in the cavity beneath the ice shelf evolves freely. This approach relies on several assumptions, such as steady-state ice-shelf thickness and ice-shelf flow fields, in order to make reasonable quantitative estimates of the thermodynamic exchange processes occurring at the ice-shelf base. This paper discusses the impact of these and other assumptions on the estimation of the thickness of the marine-ice layer. Model simulation results are presented for an idealized ice-shelf–ocean configuration as a demonstration of the feasibility of the numerical method. A sensitivity analysis is given so as to quantify the relative uncertainty in the marine-ice thickness that arises from uncertainties in the model input parameters, these being principally the ice-shelf flow field, the basal accumulation rate and the ice-shelf thickness field.

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Thermal Regime of George VI Ice Shelf, Antarctic Peninsula (Abstract)

Annals of Glaciology ◽

10.3189/s0260305500006650 ◽

1988 ◽

Vol 11 ◽

pp. 206-206

Author(s):

J. G. Paren ◽

S. Cooper

Keyword(s):

Sea Level ◽

Thermal Regime ◽

Sea Water ◽

Water Movement ◽

Freezing Point ◽

Flow Line ◽

Layer Structure ◽

Hot Water ◽

Lake Area ◽

Ice Shelf

New data on the thermal regime of George VI Ice Shelf have been obtained by thermistor chains installed through the use of a hot-water drill. Twenty thermistors are used at each site, spaced close together at sea-level and at the base of the ice shelf, and farther apart elsewhere in the ice shelf and in the sea beneath. Based on earlier observations (Bishop and Walton 1981, fig. 7) that the 10 m temperature warms from around −10°C in the central melt-lake area of the ice shelf (from 70°45′ to 71°45′S) to around −2°C near the northern ice front (70°00′S), the thermistor chains were deployed at three sites (70°00′, 70°15′ and 70°30′S) along a presumed flow line.The observations show that as ice flows towards the northern ice front of George VI Ice Shelf, it becomes more temperate in character. Heat from the sea and from the percolation of melt water at the upper surface progressively warms the ice shelf. At mid-depth (the coldest level in the ice shelf) the recorded temperatures were −6°C off Moore Point (70°30′S), −4°C off Carse Point (70°15′S) and, near the northern ice front (70°00′S), between −1.6° and −1.8°C depending on the time of year.The ice-shelf temperatures near the ice front, warmer in mid-summer than the freezing point of fully saline sea-water, are most unusual. The only explanation of the high, fluctuating temperatures found 1 year after drilling is that the hole through the ice shelf was open, allowing unimpeded water movement. This implies that the ice shelf is also warmed by the percolation of sea-water, whose presence was confirmed by ice-core drilling to below sea-level. Confirmation of the presence of brine below sea-level in the ice shelf comes from geo-electrical investigations. A Schlumberger georesistivity array modelled the ice shelf as a simple two-layer structure, with ordinary glacier overlying highly conductive ice. This is consistent with the fact that no radio echoes have been received from the bottom of George VI Ice Shelf to the north of 70°09′S.A detailed analysis of the ice-shelf / ocean-temperature profiles was undertaken. This included an analysis of the fluctuation observed in mid-summer at the warmest site and the subsequent transition to a stable isothermal profile through the submerged part of the ice shelf.

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The eigenvalue problem for ice-shelf vibrations: comparison of a full 3-D model with the thin plate approximation

Earth System Dynamics Discussions ◽

10.5194/esdd-6-1605-2015 ◽

2015 ◽

Vol 6 (2) ◽

pp. 1605-1633 ◽

Cited By ~ 1

Author(s):

Y. V. Konovalov

Keyword(s):

Thin Plate ◽

High Frequency ◽

Elastic Model ◽

Full Model ◽

Ice Shelf ◽

Frequency Spectra ◽

Plate Vibrations ◽

Pressure Perturbations ◽

D Model ◽

The Vertical Distribution

Abstract. Ice-shelf forced vibration modelling is performed using a full 3-D finite-difference elastic model, which also takes into account sub-ice seawater flow. The ocean flow in the cavity is described by the wave equation; therefore, ice-shelf flexures result from hydrostatic pressure perturbations in sub-ice seawater layer. Numerical experiments have been carried out for idealized rectangular and trapezoidal ice-shelf geometries. The ice-plate vibrations are modelled for harmonic ingoing pressure perturbations and for high-frequency spectra of the ocean swells. The spectra show distinct resonance peaks, which demonstrate the ability to model a resonant-like motion in the suitable conditions of forcing. The spectra and ice-shelf deformations obtained by the developed full 3-D model are compared with the spectra and the deformations modelled by the thin-plate Holdsworth and Glynn model (1978). The main resonance peaks and ice-shelf deformations in the corresponding modes, derived by the full 3-D model, are in agreement with the peaks and deformations obtained by the Holdsworth and Glynn model. The relative deviation between the eigenvalues (periodicities) in the two compared models is about 10 %. In addition, the full model allows observation of 3-D effects, for instance, the vertical distribution of the stress components in the plate. In particular, the full model reveals an increase in shear stress, which is neglected in the thin-plate approximation, from the terminus towards the grounding zone with a maximum at the grounding line in the case of the considered high-frequency forcing. Thus, the high-frequency forcing can reinforce the tidal impact on the ice-shelf grounding zone causing an ice fracture therein.

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Coastal Tourism and the Ocean Fringe

The Impact of Tourism on the Marine Environment ◽

10.23912/9781911635574-4461 ◽

2020 ◽

Author(s):

Professor John Swarbrooke

Keyword(s):

Marine Environment ◽

Coastal Erosion ◽

Sea Water ◽

Coastal Tourism ◽

Tourism Impact ◽

Sea Levels ◽

Rising Sea Levels ◽

The Impact

This focus of this book is on the marine environment, but one cannot understand the impact of tourism on the marine environment without looking at the ocean fringe, the interface between the land and the ocean. In this chapter we will concentrate on how things that happen on land in relation to tourism impact on the marine environment. However, it is also important to note that this relationship is two-way and that tourism on land is affected by the ocean in terms of coastal erosion, for example, as well as being impacted by changes in the temperature of sea water and rising sea levels.

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Characterization of stony soils' hydraulic conductivity using laboratory and numerical experiments

SOIL Discussions ◽

10.5194/soild-2-1103-2015 ◽

2015 ◽

Vol 2 (2) ◽

pp. 1103-1133

Author(s):

M. Pichault ◽

E. Beckers ◽

A. Degré ◽

S. Garré

Keyword(s):

Hydraulic Conductivity ◽

Water Flow ◽

Numerical Experiments ◽

Saturated Hydraulic Conductivity ◽

Rock Fragments ◽

Hydraulic Behaviour ◽

Unsaturated Hydraulic Conductivity ◽

The One ◽

The Impact

Abstract. Determining soil hydraulic properties is of major concern in various fields of study. Though stony soils are widespread across the globe, most studies deal with gravel-free soils so that the literature describing the impact of stones on soil's hydraulic conductivity is still rather scarce. Most frequently, models characterizing the saturated hydraulic conductivity of stony soils assume that the only effect of rock fragments is to reduce the volume available for water flow and therefore they predict a decrease in hydraulic conductivity with an increasing stoniness. The objective of this study is to assess the effect of rock fragments on the saturated and unsaturated hydraulic conductivity. This was done by means of laboratory and numerical experiments involving different amounts and types of coarse fragments. We compared our results with values predicted by the aforementioned models. Our study suggests that considering that stones only reduce the volume available for water flow might be ill-founded. We pointed out several drivers of the saturated hydraulic conductivity of stony soils, not considered by these models. On the one hand, the shape and the size of inclusions may substantially affect the hydraulic conductivity. On the other hand, the presence of rock fragments can counteract and even overcome the effect of a reduced volume in some cases. We attribute this to the creation of voids at the fine earth-stone interface. Nevertheless, these differences are mainly important near to saturation. However, we come up with a more nuanced view regarding the validity of the models under unsaturated conditions. Indeed, under unsaturated conditions, the models seem to represent the hydraulic behaviour of stones reasonably well.

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