Dynamic topography and gravity anomalies for fluid layers whose viscosity varies exponentially with depth
Dynamic topography and gravity anomalies for fluid layers whose viscosity varies exponentially with depth
复制标题
粘度随深度呈指数变化的流体层的动态地形和重力异常
DOI：
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发表时间：
1987
期刊：
影响因子：
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通讯作者：
B. Parsons
中科院分区：
文献类型：
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作者：
J. Revenaugh;B. Parsons
总结
我们推导出边界地形和温度之间的解析积分关系作为波数的函数的流体层的粘度随深度呈指数变化。重力和温度之间的关系也得到了类似的。结果表明，当粘性随层深变化不大（小于一个数量级）时，表面和底部边界的形貌核与等粘性情况下的形貌核相似，在中间波长（λ =层深的两倍）处差异更为明显。在这些波长下，重力核的极值可以改变多达30%，在该层的深度上粘度增加或减少两倍。在波长小于层的深度，有依赖于粘度的增长率和表面边界条件，后者的依赖性消失在等粘的情况下。对于更大的粘度变化（几个数量级），地形和重力内核在所有波长的强烈影响。粘度随深度迅速增加可以近似刚性下边界条件，导致用自由下边界条件计算的重力核对于显著范围的源深度为负。对于非常迅速变化的粘度，附近的层边界的扰动压力的符号可以从等粘性的情况下，在地形内核，导致一些源深度是负的。
Summary
We have derived analytic integral relations between boundary topography and temperature as a function of wavenumber for a fluid layer whose viscosity varies exponentially with depth. Similar relations between gravity and temperature are also derived. It is found that when the viscosity changes little over the depth of the layer (less than an order of magnitude), the topography kernels for both the surface and bottom boundaries are similar to those for the isoviscous case, the differences being more pronounced at intermediate wavelengths (λ∼ twice the layer depth). At these wavelengths, the extrema of the gravity kernel can be altered by as much as 30 per cent for a factor of two increase or decrease in viscosity over the depth of the layer. At wavelengths less than the layer depth, there are dependences on both the rate of growth of viscosity and the surface boundary condition, the latter dependency vanishing in the isoviscous case. For greater viscosity variation (several orders of magnitude), topography and gravity kernels at all wavelengths are strongly affected. Viscosity increasing rapidly with depth can approximate a rigid lower boundary condition, causing gravity kernels calculated with a free lower boundary condition to be negative for a significant range of source depths. For very rapidly varying viscosity, the sign of the perturbation pressure near the layer boundaries can be reversed from the isoviscous case, resulting in topography kernels that are negative for some source depths.