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Earth and Space Sciences · 术语表

什么是 Ekman layer, Ekman transport, Ekman spiral？

又称： Ekman layer · Ekman transport · Ekman spiral · sverdrup (unit)

Definition 29.3 University Earth and Space Sciences — Year 1 · 第 29 章 — The Circulation of the Ocean

The Ekman layer is the thin surface layer of the ocean, at most a few hundred metres thick, in which the stress of the wind is carried down by turbulent friction and balanced by the Coriolis force. The Ekman transport is the mass of water that the layer carries per second across a vertical strip 1 m1\,\mathrm{m} wide, from the surface down to below the layer:

M⃗=∫−d0ρ v⃗ dz(kg m−1 s−1);\vec M = \int_{-d}^{0} \rho\,\vec v\,\mathrm dz \quad (\mathrm{kg}\,\mathrm{m}^{-1}\,\mathrm{s}^{-1});

divided by the density, it is a volume transport per metre, in m2 s−1\mathrm{m}^{2}\,\mathrm{s}^{-1}. The Ekman spiral is the turning and weakening of the current with depth in the layer. Ocean transports are counted in sverdrups: 1 Sv1\,\mathrm{Sv} =106 m3 s−1= 10^{6}\,\mathrm{m}^{3}\,\mathrm{s}^{-1}.

Ekman’s spiral under a wind of 10\, m/ s blowing towards the north at 35 N, with Ekman’s constants. Left: the current seen from above at the surface and every tenth of the Ekman depth D_E down to D_E (blue arrows), the grey curve joining their tips; the surface current is 45 to the right of the wind, the deeper ones are weaker and turned further right. The transport of the whole layer (green; direction only) is at 90 to the right of the wind. Right: the two components against depth.
Ekman’s spiral under a wind of 10 m/s10\,\mathrm{m}/\mathrm{s} blowing towards the north at 35∘35{}^{\circ} N, with Ekman’s constants. Left: the current seen from above at the surface and every tenth of the Ekman depth DED_E down to DED_E (blue arrows), the grey curve joining their tips; the surface current is 45∘45{}^{\circ} to the right of the wind, the deeper ones are weaker and turned further right. The transport of the whole layer (green; direction only) is at 90∘90{}^{\circ} to the right of the wind. Right: the two components against depth.

示例

Example 29.5 (The transport under a fresh breeze)

A wind of 10 m/s10\,\mathrm{m}/\mathrm{s} blowing towards the north at 35∘35{}^{\circ} N exerts T=0.170 PaT = 0.170\,\mathrm{Pa}. With f=2Ωsin⁡35∘=8.365×10−5 s−1f = 2\Omega\sin35{}^{\circ} = 8.365 \times 10^{-5}\,\mathrm{s}^{-1}, the Ekman transport is 0.170/(8.365×10−5)=2036 kg m−1 s−10.170/(8.365 \times 10^{-5}) = 2036\,\mathrm{kg}\,\mathrm{m}^{-1}\,\mathrm{s}^{-1}, towards the east. With ρ=1027 kg m−3\rho = 1027\,\mathrm{kg}\,\mathrm{m}^{-3}, this is 1.98 m3 s−11.98\,\mathrm{m}^{3}\,\mathrm{s}^{-1} for each metre measured across the transport: across a line 1000 km1000\,\mathrm{km} long, about 2 Sv2\,\mathrm{Sv}.

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