The shallow ice approximation for anisotropic ice : Formulation and limits
The shallow ice approximation for anisotropic ice : Formulation and limits
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DOI：
10.1029/97jb02539
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发表时间：
1998-01
影响因子：
--
通讯作者：
A. Mangeney;F. Califano
中科院分区：
文献类型：
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作者：
A. Mangeney;F. Califano
冰盖流动模拟通常基于为各向同性冰开发的浅冰近似（SIA）。我们将这种近似扩展到各向异性冰，并通过将二阶SIA的结果与从模型求解全套力学方程获得的结果进行比较，检查其有效性。该理论是为描述牛顿和非牛顿行为的本构关系而开发的，但数值结果仅显示牛顿行为。在稳态条件下的等温冰的平面流动的结果进行了比较。SIA给出了一个很好的代表性的牛顿流的各向同性冰盖和各向异性的情况下，一个很好的描述。零阶近似足以精确描述冰流在平坦基岩，各向异性和各向同性的情况下，甚至接近冰鸿沟。对于不均匀基岩，二阶SIA对各向同性冰给出了良好的结果，对各向异性冰给出了可接受的结果。最后，我们量化了引入的误差，使用增强因子来表示各向异性时，考虑纵向应力。
Ice sheet flow modeling is generally based on the shallow ice approximation (SIA) developed for isotropic ice. We extend this approximation to anisotropic ice and check its validity for both the isotropic and anisotropic cases by comparing the results of up to second-order SIA with those obtained from a model solving the full set of mechanical equations. The theory is developed for a constitutive relation describing Newtonian and non-Newtonian behavior, but numerical results are shown only for a Newtonian behavior. The results are compared for plane flow of isothermal ice under steady state conditions. SIA gives an excellent representation of the Newtonian flow of an isotropic ice sheet and a good description for the anisotropic case. The zero-order approximation is sufficient to describe ice flow precisely over flat bedrock, for the anisotropic and isotropic cases, even close to an ice divide. For uneven bedrock, the second-order SIA gives excellent results for isotropic ice and acceptable results for anisotropic ice. Finally, we quantify the error introduced by using an enhancement factor to represent the anisotropy when longitudinal stresses are taken into account.