发表机构
Graduate School of Science and Technology, Gunma University（群马大学理工学研究科）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究表面准地转方程解的大时间行为，通过抛物型尺度唯一确定非线性剖面，揭示科里奥利力产生的细微旋转流，并指出其非线性效应弱于同尺度其他方程。
AI 中文摘要
准地转方程是众所周知的高纬度地区低压系统周围位温预测模型。当该方程加入扩散效应后，它可作为海面位温的模型。在两种情形下，非线性项代表科里奥利力的效应。本文给出了表面准地转方程解中的非线性剖面。该剖面从解的大时间行为角度被唯一确定。解的各个分量按照抛物型尺度从慢衰减到快衰减依次排列。随后，这样的展开被唯一确定。由于在大时间效应背景下方程是次临界的，主要分量呈现线性特征。非线性特征出现在对解影响较小的分量中。从时空变量相关性的角度来看，非线性剖面表现出与线性剖面截然不同的特征。此外，由于该方程的空间结构，其非线性效应预计弱于具有相同尺度的其他方程。主要定理揭示了由科里奥利力产生的细微但独特的旋转流。
英文摘要
The quasi-geostrophic equation is well known as a model for predicting potential temperature around low-pressure systems in high-latitude regions. When diffusion effects are added to this equation, it serves as a model for potential temperature at the sea surface. In either case, the nonlinear term represents the effect of the Coriolis force. This paper yields nonlinear profile in solutions to the surface quasi-geostrophic equation. This profile is determined uniquely from the perspective of large-time behavior of solutions. Components of solutions are arranged sequentially from slow to fast decay based on the parabolic scale. Then such an expansion is determined uniquely. Since the equation is subcritical in the context of large-time effects, the main components exhibit linear features. Nonlinear characteristics appear in components that have a smaller effect on solutions. From the perspective of the correlation between spacetime variables, nonlinear profiles exhibit characteristics that are distinctly different from those of linear profiles. Moreover, the nonlinear effects of this equation are expected to be weaker than those of other equations with the same scale due to their spatial structure. The main theorem publishes minute, but unique rotational flow arising from the Coriolis force.
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