海冰动力学正则化方程的线性适定性

IF 0.5 4区 数学 Q3 MATHEMATICS
Soufiane Chatta, B. Khouider, M. Kesri
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引用次数: 0

摘要

Hibler粘塑性方程(VPE) [J]。地球物理学。Res. 82(27), 3932-3938(1977)]被广泛采用并用于地球系统模型中,以表示海面风、洋流和内应力引起的海冰漂移。然而,据不同的研究者报道,至少在一个空间维度上,Hibler的原始方程及其使用压力替换的变体在不同的流动状态下都是不适定的。特别是Guba等人。理论物理。Oceanogr. 43(10), 2185-2199(2013)]表明,当流动散度超过最小阈值时,这两种变体都是病态的,并且当使用拉伸截止时,它们的结果似乎扩展到二维。特别是,Hibler使用Heaviside函数截断VPE的粘度系数,以避免在无穷远处出现奇点。[J]。第一版。数学学报(自然科学版),2013(5):526 - 544(2012)。在这里,我们证明了,对于周期性数据,线性化的一维正则化VPE,其中Heaviside函数被双曲正切取代,在Hibler原始方程的情况下是很好的。此外,我们证明了正则化方程的线性化过程是一致的,即在适当的范数下,残差收敛于零,解的扰动趋于零。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Linear well posedness of regularized equations of sea-ice dynamics
The viscous–plastic equations (VPE) of Hibler [J. Geophys. Res. 82(27), 3932–3938 (1977)] are widely adopted and used in Earth system models to represent sea-ice drift due to surface winds, ocean currents, and internal stresses. However, it has been reported by various investigators, at least in one space dimension, that both Hibler’s original equations and their variant using a pressure replacement are ill posed in divergent flow regimes. Especially, Guba et al. [J. Phys. Oceanogr. 43(10), 2185–2199 (2013)] shows that both variants are ill-posed when the flow divergence exceeds a minimum threshold and their results seem to extend to two dimensions when a tensile cut-off is used. In particular, Hibler uses a Heaviside function cut-off for the viscosity coefficients of the VPE’s to avoid a singularity at infinity. Lemieux et al. [J. Comput. Phys. 231(17), 5926–5944 (2012)] regularized the Heaviside function by a hyperbolic tangent for numerical efficiency. Here, we show that, for periodic data, the linearized one-dimensional regularized VPE’s, in which the Heaviside function is replaced with a hyperbolic tangent, is well posed in the case of Hibler’s original equations. Moreover, we prove that the linearization procedure, for the regularized equations, is consistent, in the sense that the residual converges to zero that the perturbation of the solutions goes to zero, in suitable norms.
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来源期刊
CiteScore
0.70
自引率
20.00%
发文量
18
审稿时长
>12 weeks
期刊介绍: Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects: mathematical problems of modern physics; complex analysis and its applications; asymptotic problems of differential equations; spectral theory including inverse problems and their applications; geometry in large and differential geometry; functional analysis, theory of representations, and operator algebras including ergodic theory. The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.
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