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首页> 外文期刊>Journal of Physical Oceanography >A Geosolitary Wave Solution on an f Plane
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A Geosolitary Wave Solution on an f Plane

机译：f平面上的地球孤波解

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摘要

This paper presents an exact solution for nonlinear shallow-water waves on an f plane. It is a long wave satisfying the hydrostatic balance. It is also a solitary wave maintained by the balance of a dispersion effect of Coriolis force and the nonlinear effect of advection and finite wave amplitude. It satisfies the conservation of potential vorticity. It has a negative wave height, a negative (positive) relative vorticity in the Northern (Southern) Hemisphere, and a propagation speed smaller than that of the shallow-water wave. It propagates upstream, as a consequence of the conservation of potential vorticity, with a speed of (1 - |a|/h)[gh(1 - |a|/h]~(1/2), where a is the wave height (a < 0). The trough of the surface elevation is a singular point where the first-order derivative approaches infinity. However, the region of this singularity is very small for such a wave on earth. For instance, with a 1-m amplitude, the horizontal length scale of the wave is several hundred kilometers but the large derivative region is only a fraction of a centimeter. In reality, if this wave exists, friction and surface tension would erase the sharp surface gradient on such a small scale. The wave profile and its horizontal length scale do not depend on water depth at the first-order approximation. The length scale is proportional to the square root of the product of amplitude and gravity and is inversely proportional to the Coriolis parameter, which can be expressed as L ～ 10(g |a|)~(1/2)/f.
机译：本文提出了f平面上非线性浅水波的精确解。是满足静水力平衡的长波。它也是通过科里奥利力的色散效应与对流和有限波振幅的非线性效应之间的平衡所保持的孤立波。它满足了潜在涡度的守恒。它具有负波高度，在北（南）半球具有负（正）相对涡度，并且传播速度小于浅水波的传播速度。由于保持了潜在的涡度，它以（1--| a | / h）[gh（1-| a | / h]〜（1/2）的速度向上游传播，其中a是波高度（a <0）。表面高程的波谷是一阶导数接近无穷大的奇异点。但是，对于地球上的这种波，这种奇异性的区域非常小。例如，具有1-在振幅上，波浪的水平长度尺度为几百公里，但较大的导数区域仅为一厘米的几分之一，实际上，如果存在该波浪，则摩擦和表面张力会在如此小的尺度上消除尖锐的表面梯度一阶近似时，波廓及其水平长度尺度不取决于水深，长度尺度与振幅和重力乘积的平方根成正比，而与科里奥利参数成反比。表示为L〜10（g | a |）〜（1/2）/ f。

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  • 来源
    《Journal of Physical Oceanography》 |2004年第4期|p.856-864|共9页
  • 作者

    CHUNYAN LI;

  • 作者单位

    Skidaway Institute of Oceanography, 10 Ocean Science Circle, Savannah, GA 31411;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 海洋学;
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