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−
 
 
−
[[Image:MIZ1.JPG|thumb|right|600px|[[Vernon Squire]]]]
 
−
 
 
−
The marginal ice zone (MIZ) is an interfacial region that forms at the boundary of the
 
−
open and frozen oceans. Essentially it is a the region which is neither open ocean
 
−
or frozen ocean, consisting of a patchwork of ice floes and open water. Wave processes are very
 
−
important in the MIZ because waves facture the continuous ice and simultaneously
 
−
the region of broken ice scatters wave energy protecting the interior of the ice from
 
−
further wave induced fracture.
 
−
The major way in which
 
−
the open ocean interacts
 
−
with the continuous ice is through wave induced breaking,
 
−
and it is this process which produces the MIZ.
 
−
However, wave action does not break up the continuous ice over an infinite
 
−
distance. Instead, the wave energy is dissipated by scattering from the ice
 
−
floes which have formed in the MIZ. The MIZ is thus formed by wave
 
−
induced breaking of the continuous ice and simultaneously shields the
 
−
continuous ice from breaking. There are two aspects which need to be
 
−
understood to model this process: the first is the wave induced breaking of
 
−
the continuous ice, and the second is the wave scattering in the MIZ
 
−
[[Squire_Duggan_Wadhams_Rottier_Liu_1995a|Squire et. al. 1995]].  
 
−
 
 
−
The experimental studies of
 
−
wave propagation in the MIZ reported in \cite{directional86} and
 
−
\cite{attenuation88} have shown the following features.
 
−
There is strong exponential attenuation of energy, which decreases as
 
−
the wave period increases. From a narrow directional spectrum at
 
−
the ice edge the
 
−
wave field broadens and becomes isotropic as it evolves with increasing
 
−
distance into the MIZ.
 
−
 
 
−
= Structure of the MIZ =
 
−
 
 
−
The MIZ is generally tens to hundreds of kilometers deep. The structure varies
 
−
dramatically depending on incident wave energy, wind, ice structure etc.
 
−
Generally is can be divided into bands with floe size increasing with penetration
 
−
depth into the MIZ.
 
−
 
 
−
= Models for Wave Scattering =
 
−
 
 
−
== Mass Loading Model ==
 
−
 
 
−
The [[Mass Loading Model of Ice]] simply includes the effect of the ice cover by adding an additional mass term.
 
−
 
 
−
== Eddy Viscosity Model ==
 
−
 
 
−
Model proposed by [[Weber 1987]] is based on a two layer fluid (this ice being the second layer). The top layer is a viscous Newtonian fluid.
 
−
 
 
−
== Floe Collision Models ==
 
−
 
 
−
Models based on floe collisions have been proposed by [[Shen and Squire]]
 
−
 
 
−
== Elastic Plate Models ==
 
−
 
 
−
Large ice floes can be modelled as a [[:Category:Floating Elastic Plate|Floating Elastic Plate]] see [[Ice as a Thin Elastic Plate]] for more details, (this idea goes back
 
−
more than 100 years). For this reason much of the study of wave-interaction with floating thin plates
 
−
has been motivated by the application to ice floes. However, there is a discussion of this
 
−
problem in [[Stoker_1957| Stoker 1957]] in relation to breakwaters and more recently there has been a very large
 
−
study of this problem (especially, but by no means exclusively in Japan) motivated by the
 
−
marine engineering application to [[VLFS]].
 
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The problem of wave scattering by a floating elastic plate of shallow draft is well understood
 
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and the major challenge in geophysics is to try and understand the scattering of wave energy
 
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and how this is related to the small scale scattering. The problem can be divided into
 
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two and three-dimensional models.
 
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== Two Dimensional Model ==
 
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[[Image:SetPlatesTheta.jpg|thumb|right|600px|Figure 1]]
 
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Figure 1: Schematic diagram of a wave propagating through a set of elastic plates.
 
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Two dimensional wave scattering models in the MIZ have generally been studied in the context of a two-dimensional fluid covered by a finite number of elastic plates of possibly different properties. The problem is assumed to be invariant in the y direction, therefore reducing the problem to the dimensions in the x and z directions (Figure 1). The simplest problem to consider is one where there are only two semi-infinite plates of identical properties separated by a crack. A related problem in acoustics was considered by [[Kouzov_1963a|Kouzov 1963]] who used an integral representation of the problem to solve it explicitly using the Riemann-Hilbert technique. Recently the crack problem has been considered by [[Squire_Dixon_2000A|Squire and Dixon 2000]] and [[Williams_Squire_2002A|Williams and Squire 2002]] using a Green function method applicable to infinitely deep water and they obtained simple expressions for the reflection and transmission coefficients. [[Squire_Dixon_2001a|Squire and Dixon 2001]] extended the single crack problem to a multiple crack problem in which the semi-infinite regions are separated by a region consisting of a finite number of plates of finite size with all plates having identical properties. 
 
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[[Evans_Porter_2005a|Evans and Porter 2005]] further considered the multiple crack problem for finitely deep water and provided an explicit solution.
 
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In parallel to the crack problem, the more challenging problem of two semi-infinite plates
 
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of different properties was considered. The first significant work on this problem was by [[evans_davies_1968a|Evans and Davies 1968]] who present a solution method for evaluating the transmission and reflection of waves, in finitely deep water, propagating from a semi-infinite region of open water into a semi-infinite region of a floating elastic plate.
 
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Although much simpler,  the two-dimensional models have a number of advantages over the three-dimensional models, the most important being that it is much less computationally demanding. We also believe that a simple model is the best place to begin to make comparisons with data and to test and debug the more sophisticated models.
 
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[[Two-Dimensional Multiple Elastic Plate MIZ Wave Scattering Model]]
 
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== Three Dimensional Models ==
 
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The most through study of this problem
 
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was by [[Masson_LeBlond_1989a| Masson and LeBlond 1989]] who used transport theory to derive
 
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and equation for energy transport. [[Meylan_Squire_Fox_1997a | Meylan, Squire  and Fox 1997]] independently derived a method
 
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based on the [[Linear Boltzmann Equation]] and an adhoc arguement. [[Meylan_Masson_2006a | Meylan and Masson 2006]] have shown
 
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that these two methods are nearly identical and have derived a [[Linear Boltzmann Model for Wave Scattering in the MIZ]]
 
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[[Category:Polar Regions]]
 

Revision as of 01:47, 21 July 2007

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Pages in category "Wave Scattering in the Marginal Ice Zone"

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