Particle dispersion by random waves in the rotating Boussinesq system
Particle dispersion by random waves in the rotating Boussinesq system
复制标题
旋转 Boussinesq 系统中随机波的粒子色散
DOI：
10.1017/s0022112010005240
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发表时间：
2011
影响因子：
3.7
通讯作者：
R. Ferrari
中科院分区：
文献类型：
--
作者：
Miranda C. Holmes;O. Bühler;R. Ferrari
我们对三维旋转分层布辛涅斯克系统中随机波引起的水平粒子弥散进行了理论和数值研究，该模型可作为研究内波场在海洋中示踪剂弥散的简单模型。具体来说，泰勒意义上的有效单粒子扩散率（Proc. Lond. Math. Soc.，第 20 卷，1921 年，第 196 页）是针对小幅度内部重力波场计算的，该波场被建模为稳态均匀且水平各向同性高斯随机场，其频谱远离零。该系统中的色散并不像表面重力波那样仅仅由于斯托克斯漂移效应而产生，而且它还受到线性速度场的非线性二阶校正的驱动，可以使用波均相互作用理论的方法进行计算。提出了作为随机波场频谱函数的单粒子扩散率的公式。结果表明，这种扩散率比基于斯托克斯漂移或赝动量大小的启发式论证所预期的要小得多。这似乎源于斯托克斯漂移和二阶速度场的某些不可压缩性约束。最后，该理论应用于典型模型波谱、加勒特-蒙克波谱以及北大西洋示踪剂释放实验的详细现场观测所描述的海洋条件。
We present a theoretical and numerical study of horizontal particle dispersion due to random waves in the three-dimensional rotating and stratified Boussinesq system, which serves as a simple model to study the dispersion of tracers in the ocean by the internal wave field. Specifically, the effective one-particle diffusivity in the sense of Taylor (Proc. Lond. Math. Soc., vol. 20, 1921, p. 196) is computed for a small-amplitude internal gravity wave field modelled as a stationary homogeneous and horizontally isotropic Gaussian random field whose frequency spectrum is bounded away from zero. Dispersion in this system does not arise simply because of a Stokes drift effect, as in the case of surface gravity waves, but in addition it is driven by the nonlinear, second-order corrections to the linear velocity field, which can be computed using the methods of wave–mean interaction theory. A formula for the one-particle diffusivity as a function of the spectrum of the random wave field is presented. It is shown that this diffusivity is much smaller than might be expected from heuristic arguments based on the magnitude of the Stokes drift or the pseudomomentum. This appears to stem from certain incompressibility constraints for the Stokes drift and the second-order velocity field. Finally, the theory is applied to oceanic conditions described by a typical model wave spectrum, the Garrett–Munk spectrum, and also by detailed field observations from the North Atlantic tracer release experiment.