Analytical Solutions Describing Zonal
and Circular Wind Drift of Sea Ice
with Elastic-Plastic Rheology
Aleksey Marchenko
Introduction
Modelling of large scale dynamics of drifting ice is based on the consideration of
ice rheology at scales of several tens kilometres and greater. Since experiments are
not possible over such scales, the rheological properties are formulated using
intuitive ideas, results of field measurements, and analysis of satellite data. A model
with elastic-plastic rheology was considered in AIDJEX project (e.g., [1]), and a
model with viscous-plastic rheology was formulated by Hibler [2]. Both of the
models use normal flow rule with closed yield curve transforming in self-similar
manner depending on the ice thickness and compactness. In the elastic-plastic
model, the ice is considered as an isotropic elastic continuum when the stresses are
inside the yield curve. In the viscous-plastic model the ice is modelled as a linear
compressible viscous continuum when the stresses are inside the yield curve.
A comprehensive review of sea ice rheological models is performed by Lepparanta [6]. He also analysed analytical steady-state solutions describing ice drift
along the coastal boundaries of rectilinear and circular shapes within the
viscous-plastic model of Hibler [2]. The ice thickness, compactness profiles, and
drift velocity were analysed depending on the wind direction and distance to the
shoreline. Axially symmetric solutions describing the drift of floating ice with
elastic-plastic rheology were investigated by Schwaegler and Pritchard [11]
numerically for the validation of rheological characteristics of drifting ice in the
Arctic and for the investigation of quasi-steady-state response of an axisymmetric
A. Marchenko ( ✉ )
The University Centre in Svalbard, Longyearbyen, Norway
e-mail: aleksey.marchenko@unis.no
A. Marchenko
Sustainable Arctic Marine and Coastal Technology (SAMCoT),
Centre for Research-Based Innovation (CRI), Norwegian University of Science
and Technology, Trondheim, Norway
© Springer International Publishing AG, part of Springer Nature 2018
M. G. Velarde et al. (eds.), The Ocean in Motion, Springer Oceanography,
https://doi.org/10.1007/978-3-319-71934-4_34
539
and Circular Wind Drift of Sea Ice
with Elastic-Plastic Rheology
Aleksey Marchenko
Introduction
Modelling of large scale dynamics of drifting ice is based on the consideration of
ice rheology at scales of several tens kilometres and greater. Since experiments are
not possible over such scales, the rheological properties are formulated using
intuitive ideas, results of field measurements, and analysis of satellite data. A model
with elastic-plastic rheology was considered in AIDJEX project (e.g., [1]), and a
model with viscous-plastic rheology was formulated by Hibler [2]. Both of the
models use normal flow rule with closed yield curve transforming in self-similar
manner depending on the ice thickness and compactness. In the elastic-plastic
model, the ice is considered as an isotropic elastic continuum when the stresses are
inside the yield curve. In the viscous-plastic model the ice is modelled as a linear
compressible viscous continuum when the stresses are inside the yield curve.
A comprehensive review of sea ice rheological models is performed by Lepparanta [6]. He also analysed analytical steady-state solutions describing ice drift
along the coastal boundaries of rectilinear and circular shapes within the
viscous-plastic model of Hibler [2]. The ice thickness, compactness profiles, and
drift velocity were analysed depending on the wind direction and distance to the
shoreline. Axially symmetric solutions describing the drift of floating ice with
elastic-plastic rheology were investigated by Schwaegler and Pritchard [11]
numerically for the validation of rheological characteristics of drifting ice in the
Arctic and for the investigation of quasi-steady-state response of an axisymmetric
A. Marchenko ( ✉ )
The University Centre in Svalbard, Longyearbyen, Norway
e-mail: aleksey.marchenko@unis.no
A. Marchenko
Sustainable Arctic Marine and Coastal Technology (SAMCoT),
Centre for Research-Based Innovation (CRI), Norwegian University of Science
and Technology, Trondheim, Norway
© Springer International Publishing AG, part of Springer Nature 2018
M. G. Velarde et al. (eds.), The Ocean in Motion, Springer Oceanography,
https://doi.org/10.1007/978-3-319-71934-4_34
539