The region on the core—mantle boundary where a geostrophic velocity field can be determined from frozen-flux magnetic data
The region on the core—mantle boundary where a geostrophic velocity field can be determined from frozen-flux magnetic data
复制标题
地核-地幔边界上的区域，可以通过冻结通量磁数据确定地转速度场
DOI：
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发表时间：
1986
期刊：
影响因子：
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通讯作者：
J. Mouël
中科院分区：
文献类型：
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作者：
G. Backus;J. Mouël
总结
在核幔边界层正下方的球面S上，设u为核幔流体速度，Br为径向磁场，θ为余纬度，φ=Br sec θ。在通量冻结且u为切向地转的近似中，u可以由S上所有通过φ的水平线连接到地理赤道的点的Br和Δ tBr确定。在S的其它点上，u仅在φ的水平线附近有未知的任意切向地转环流时由Br和λ tBr决定。冻结通量 * 近似在近似宽度的“漏带”中总是失败的。|ν β 2（rBr）|/|2011年1月1日（布鲁）|以“漏曲线”为中心的弧度，其中λ 1·（Bru）= 0。这里ν是核心的磁扩散率，r−1 <$1是S上的表面梯度。漏磁带包括零通量曲线出现或消失的那些点。在以地理赤道为中心的狭窄地带，地转近似总是失效的。这两种故障都不影响由Br和φtBr确定u，除非带宽度比u的水平刻度宽。利用S上地转运动空间的显式完全基，可以由Br和φtBr数值计算u。基场是一个、两个或三个表面矢量球谐函数的线性组合，正如本顿所预测的那样，它们迫使地理赤道总是由相同的流体粒子组成。每一个基本场和每一个切向地转流都在地理赤道上产生恒定的核心流体压力。
Summary
On the spherical surface S just below the core-mantle boundary layer, let u be the core-fluid velocity, Br the radial magnetic field, θ the colatitude, and φ=Br sec θ. In the approximation where the flux is frozen and u is tangentially geostrophic, u can be determined from Br and ∂tBr at all points of S which are connected to the geographical equator by level lines of φ. At the other points of S, u is determined by Br and ∂tBr only up to an unknown arbitrary tangentially geostrophic circulation around the level lines of φ. The frozen flux*** approximation will always fail in a ‘leaky belt’ of approximate width | ν▿2 (rBr) |/| ▿1▿1· (Bru) | radians centred on the ‘leaky curve’ where ▿1· (Bru) = 0. Here ν is the magnetic diffusivity of the core and r−1▿1 is the surface gradient on S. The leaky belt includes those points at which null-flux curves appear or disappear. The geostrophic approximation will always fail in a narrow belt centred on the geographical equator. Neither failure interferes with the determination of u from Br and φtBr unless the belt widths are wider than the horizontal scale of u. Numerical calculation of u from Br and φtBr can be carried out using an explicit complete basis for the space of geostrophic motions on S. The basis fields are linear combinations of one, two or three surface vector spherical harmonics, and as predicted by Benton, they force the geographical equator to consist always of the same fluid particles. Each basis field, and every tangentially geostrophic flow, produces constant core fluid pressure on the geographical equator.