Near-inertial wave dispersion by geostrophic flows
Near-inertial wave dispersion by geostrophic flows
复制标题
地转流的近惯性波色散
DOI：
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发表时间：
2017
影响因子：
3.7
通讯作者：
O. Bühler
中科院分区：
文献类型：
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作者：
Jim Thomas;K. S. Smith;O. Bühler
我们从理论和数值上研究了较大幅度地转平衡平均流对近惯性波的调制。由于激发波最初被困在混合层中，它投射到广泛的垂直模式上，每个模式$n$由Burger数$Bu_{n}$表征，与模式垂直尺度的平方成正比。通过对Boussinesq方程在给定的平衡背景流下线性化的数值模拟表明，波场的演化强烈依赖于$Bun}$相对于平衡流的Rossby数$Unicode[STIX]{x1D716}$的频谱，相对较小的$Bun}$导致波场的水平尺度较小，反气旋中波幅积累更快，波能向深海传播更快。这种不同的波动行为可以通过分别考虑每种模式下的动力学来理解；将线性化的静力Boussinesq方程投影到模式上，得到一组线性浅水方程，其中$Bun}$起到减重的作用。波模分为两个渐近区域，由标度数$Bu_(N)sim O(1)$定义为低模，$Bu_{n}sim O(Unicode[STIX]{x1D716})$标度定义为高模。导出的振幅方程表明，在低模情况下，垂直传播很弱。高模体制是Young&Ben Jellul(《市场研究》，第55卷，1997年，第735-766页)理论的基础。将这一理论推广到$O(UNICODE[STIX]{x1D716}^{2})$，由此导出了$Bu_(n})SIMO(UNICODE[STIX]{x1D716}^{1/2})$和$BU_{n}SIMO(UNICODE[STIX]{x1D716}^{2})$的振幅方程。通过将相应的振幅方程的数值解与相同情况下的线性化浅水方程的模拟结果进行比较，证明了每种近似的精度。我们强调，由于惯性波能量和切变是跨垂直模式分布的，它们的整体调制是由于每个区域中波场的集体行为。对这些制度的统一处理是这项工作的一个新特点。
We investigate theoretically and numerically the modulation of near-inertial waves by a larger-amplitude geostrophically balanced mean flow. Because the excited wave is initially trapped in the mixed layer, it projects onto a broad spectrum of vertical modes, each mode $n$ being characterized by a Burger number, $Bu_{n}$ , proportional to the square of the vertical scale of the mode. Using numerical simulations of the hydrostatic Boussinesq equations linearized about a prescribed balanced background flow, we show that the evolution of the wave field depends strongly on the spectrum of $Bu_{n}$ relative to the Rossby number of the balanced flow, $unicode[STIX]{x1D716}$ , with smaller relative $Bu_{n}$ leading to smaller horizontal scales in the wave field, faster accumulation of wave amplitude in anticyclones and faster propagation of wave energy into the deep ocean. This varied behaviour of the wave may be understood by considering the dynamics in each mode separately; projecting the linearized hydrostatic Boussinesq equations onto modes yields a set of linear shallow water equations, with $Bu_{n}$ playing the role of the reduced gravity. The wave modes fall into two asymptotic regimes, defined by the scalings $Bu_{n}sim O(1)$ for low modes and $Bu_{n}sim O(unicode[STIX]{x1D716})$ for high modes. An amplitude equation derived for the former regime shows that vertical propagation is weak for low modes. The high-mode regime is the basis of the Young & Ben Jelloul (J. Mar. Res., vol. 55, 1997, pp. 735–766) theory. This theory is here extended to $O(unicode[STIX]{x1D716}^{2})$ , from which amplitude equations for the subregimes $Bu_{n}sim O(unicode[STIX]{x1D716}^{1/2})$ and $Bu_{n}sim O(unicode[STIX]{x1D716}^{2})$ are derived. The accuracy of each approximation is demonstrated by comparing numerical solutions of the respective amplitude equation to simulations of the linearized shallow water equations in the same regime. We emphasize that since inertial wave energy and shear are distributed across vertical modes, their overall modulation is due to the collective behaviour of the wave field in each regime. A unified treatment of these regimes is a novel feature of this work.
影响因子：
3.7
作者：
Jin-Han Xie;J. Vanneste
通讯作者：
Jin-Han Xie;J. Vanneste
影响因子：
3.7
作者：
Eric Danioux;J. Vanneste;O. Bühler
通讯作者：
Eric Danioux;J. Vanneste;O. Bühler