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Earth and Space Sciences · 术语表

什么是 f-plane and β-plane？

又称： f-plane · beta-plane

Definition 19.1 University Earth and Space Sciences — Year 3 · 第 19 章 — Geophysical Fluid Dynamics

Near a reference latitude φ0\varphi_0, the ff-plane approximation takes the Coriolis parameter as constant, f=f0=2Ωsin⁡φ0f = f_0 = 2\Omega\sin\varphi_0. The β\beta-plane approximation keeps its first-order change with the northward distance yy: f=f0+βyf = f_0 + \beta y, with β=df/dy=2Ωcos⁡φ0/a\beta = \mathrm df/\mathrm dy = 2\Omega \cos\varphi_0/a.

Left, the local frame at latitude : z along the local vertical, y northward in the tangent plane, x eastward into the page. The rotation vector splits into about the vertical, which turns horizontal motion, and about the northward axis, dropped for thin flows. Right, the Coriolis parameter and its -plane tangent at 45: close over a band of latitude, far from it near the equator and the pole.
Left, the local frame at latitude : z along the local vertical, y northward in the tangent plane, x eastward into the page. The rotation vector splits into about the vertical, which turns horizontal motion, and about the northward axis, dropped for thin flows. Right, the Coriolis parameter and its -plane tangent at 45: close over a band of latitude, far from it near the equator and the pole.
Left, the local frame at latitude φ\varphi: zz along the local vertical, yy northward in the tangent plane, xx eastward into the page. The rotation vector splits into Ωsin⁡φ\Omega\sin\varphi about the vertical, which turns horizontal motion, and Ωcos⁡φ\Omega\cos\varphi about the northward axis, dropped for thin flows. Right, the Coriolis parameter and its β\beta-plane tangent at 45∘45{}^{\circ}: close over a band of latitude, far from it near the equator and the pole.
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