相干流体力学系统的动力学和蒙日流形上的几何学

Qeios Pub Date : 2024-05-22 DOI:10.32388/bpyaz1

Nikolay Fimin

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摘要

为流体动力学涡旋系统引入了蒙日势流形上的度量概念。根据给定流形上大地线的偏差，提出了连续旋涡结构的一致性概念。建立了涡旋连续系统的衰减和崩溃标准。

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Dynamics of Coherent Hydrodynamic Systems and Geometry on the Monge Manifolds

The concept of a metric on the manifold of Monge potentials is introduced for hydrodynamic vortex system. The concept of coherence of continuous vortex structures is formulated in terms of the deviation of geodesic lines on a given manifold. Criteria of decay and collapse of a vortex continual system are established.

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Qeios

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