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arXiv · 1701.06647

Geometric Structure of Pseudo-plane Quadratic Flows

Che Sun
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Abstract

Quadratic flows have the unique property of uniform strain and are commonly used in turbulence modeling and hydrodynamic analysis. While previous application focused on two-dimensional homogeneous fluid, this study examines the geometric structure of three-dimensional quadratic flows in stratified fluid by solving a steady-state pseudo-plane flow model. The complete set of exact solutions reveals that steady quadratic flows have invariant conic type in non-rotating frame and non-rotatory vertical structure in rotating frame. Three baroclinic solutions with vertically non-aligned structure disprove an earlier conjecture. The rich topology of quadratic flows stands in contrast to the depleted geometry of high-degree polynomial flows. A paradox in the steady solutions of shallow-water reduced-gravity models is also explained.

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Che Sun. 2017-01-18. Geometric Structure of Pseudo-plane Quadratic Flows. https://doi.org/10.1063/1.4979089

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