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Meanders and Eddies from Topographic Transformation of Coastal-Trapped Waves

机译：沿海陷波地形变换的曲折和涡流

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摘要

This paper describes how topographic variations can transform a small-amplitude, linear, coastal-trapped wave (CTW) into a nonlinear wave or an eddy train. The dispersion relation for CTWs depends on the slope of the shelf. Provided the cross-shelf slope varies sufficiently slowly along the shelf, the local structure of the CTW adapts to the local geometry and the wave transformation can be analyzed by the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) method. Two regions of parameter space are straightforward: adiabatic transmission (where, at the incident wave frequency, a long wave exists everywhere along the shelf) and short-wave reflection (where somewhere on the shelf no long wave exists at the incident frequency, but the stratification is sufficiently weak that a short reflected wave can coexist with the incident wave). This paper gives the solutions for these two cases but concentrates on a third parameter regime, which includes all sufficiently strongly stratified flows, where neither of these behaviors is possible and the WKBJ method fails irrespective of how slowly the topography changes. Fully nonlinear integrations of the equation for the advection of the bottom boundary potential vorticity show that the incident wave in this third parameter regime transforms into a nonlinear wave when topographic variations are gradual or into an eddy train when the changes are abrupt.
机译：本文介绍了地形变化如何将小幅度的线性线性沿海波（CTW）转换为非线性波或涡流。 CTW的色散关系取决于架子的斜率。如果跨架子的坡度沿架子足够缓慢地变化，则CTW的局部结构适应于局部几何形状，并且可以通过Wentzel-Kramers-Brillouin-Jeffreys（WKBJ）方法来分析波的转换。参数空间的两个区域很简单：绝热透射（在入射波频率处，在架子上各处都存在长波）和短波反射（在货架上的某处，入射频率处不存在长波，但是分层足够弱，短反射波可以与入射波共存。本文给出了这两种情况的解决方案，但着重于第三种参数方案，该方案包括所有足够强的分层流，其中两种行为均不可能发生，并且WKBJ方法失败，而与地形变化的速度无关。对底部边界势涡度的平流方程的完全非线性积分表明，当地形变化是逐渐变化时，该第三参数方案中的入射波转换为非线性波，或当变化突然时转换为涡流。

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  • 来源
    《Journal of Physical Oceanography》 |2014年第4期|1133-1150|共18页
  • 作者

    J. T. Rodney; E. R. Johnson;

  • 作者单位

    Department of Mathematics, Gower St., London, WC1E 6BT, United Kingdom;

    Department of Mathematics, University College London, London, United Kingdom;

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