Limitations of a linear model for the hurricane boundary layer
Limitations of a linear model for the hurricane boundary layer
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DOI：
10.1002/qj.390
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发表时间：
2009-04
影响因子：
8.9
通讯作者：
S. Vogl;Roger K. Smith
中科院分区：
文献类型：
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作者：
S. Vogl;Roger K. Smith
本文从运动方程的详细尺度分析出发，导出了快速旋转轴对称旋涡定常边界层的线性模型。对于飓风尺度和强度的涡旋，重新评估了先前已知的解析解。通过从解中计算近似中被忽略的非线性项与保留的项相比的大小，研究了这种涡旋的线性近似的内部一致性。结果表明，非线性项是不可忽略的小，在一个大的区域的涡，一个功能是一致的尺度分析。我们认为，边界层问题是适定的，只有在外半径有下沉到层。在有上升的内半径处，只能规定径向压力梯度，而不能规定边界层顶部的风分量，但在这种情况下，线性问题不能求解。我们研究的半径，在边界层顶部的垂直流动的变化标志不同的切向风剖面相关的飓风，并表明，这是几百公里的漩涡中心。这一特点进一步限制了应用于飓风的线性模型。虽然本分析假设轴对称，但同样的限制可能适用于线性模型的非轴对称扩展。版权所有© 2009皇家气象学会
The linear model for the steady boundary layer of a rapidly rotating axisymmetric vortex is derived from a detailed scale analysis of the full equations of motion. The previously known analytic solution is re‐appraised for vortices of hurricane scale and strength. The internal consistency of the linear approximation is investigated for such a vortex by calculating from the solution the magnitude of the nonlinear terms that are neglected in the approximation compared with the terms retained. It is shown that the nonlinear terms are not negligibly small in a large region of the vortex, a feature that is consistent with the scale analysis. We argue that the boundary‐layer problem is well‐posed only at outer radii where there is subsidence into the layer. At inner radii, where there is ascent, only the radial pressure gradient may be prescribed and not the wind components at the top of the boundary layer, but the linear problem cannot be solved in these circumstances. We examine the radius at which the vertical flow at the top of the boundary layer changes sign for different tangential wind profiles relevant to hurricanes and show that this is several hundred kilometres from the vortex centre. This feature represents a further limitation of the linear model applied to hurricanes. While the present analysis assumes axial symmetry, the same limitations presumably apply to non‐axisymmetric extensions to the linear model. Copyright © 2009 Royal Meteorological Society