内波吸引子的数值模拟

王刚; 乔方利

内波吸引子的数值模拟

王刚,
乔方利

国家海洋局第一海洋研究所,山东青岛 266061; 海洋环境科学和数值模拟国家海洋局重点实验室,山东青岛 266061

基金项目: 国家高技术研究发展计划(863)(2008AA09A402);自然科学基金重点项目(40730842);国家海洋局第一海洋研究所基本科研业务经费(GY02-2009G08);中国科学院海洋环流与波动重点实验室开放基金项目(KLOCAW0905)。

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出版历程
- 收稿日期: 2010-05-30
- 修回日期: 2010-06-22

Numerical simulation on internal wave attractors

First Institute of Oceanography,State Oceanic Administration,Qingdao 266061,China; Key Lab of Marine Science and Numerical Modeling, State Oceanic Administration, Qingdao 266061, China

摘要

摘要: 密度稳定层结的流体中产生的内波沿着由内波固有频率、流体浮力频率等因素所确定的特征线(或内波射线)传播。边界上的反射不改变内波的频率,从而也不改变反射后的内波特征线与重力方向所成的夹角。侧边界倾斜的封闭容器内,内波能量沿特征线传播的过程中经侧壁、表面和底面的反射可能会集中在一个封闭的轨道上,形成内波吸引子。该现象已经得到水槽试验、线性理论和数值试验的验证。本文利用非线性非静压的环流模式MITgcm,模拟了二维封闭区域中(1,1)-吸引子和(2,1)-吸引子的形成过程,并讨论初值条件对它们的影响。稳定的(1,1)-吸引子其极限环两侧流速出现很强的剪切流。当减小地形的坡度时,由于线性因素的增加,吸引子的结构不变,但吸引子厚度在相空间中的收缩速度加快。对于(2,1)-吸引子,由于轨道所成的两个环中间的节点耗散了部分能量,吸引子的收敛速度较慢。节点处,流体速度始终为0,但存在强烈混合,流体浮力频率呈现振幅较大的周期变化。
- 内波吸引子 /
- MITgcm /
- 非静压 /
- 内波特征线 /
- 均匀层结
Abstract: Internal waves in the steady stratified fluid propagate along the characteristic, whose angle with the vertical direction is determined by the wave frequency, float frequency and some other factors. The characteristics being reflected at boundaries keep the wave frequency as well as the angle with the vertical direction. In a closed container with one oblique boundary, the energy of the internal waves concentrate or diverse due to the reflections of characteristic by the boundaries. A limited circle, which is called internal wave attractor, might be formed in the concentrating case. This phenomenon has been observed in the water tank experiment, and verified by linear theory and numerical simulation. In this paper, we simulate the (1, 1) and (2, 1)-attractors using a nonlinear non-hydrostatic circulation model, MITgcm, and discuss the dependence of their characteristics on initial conditions. For a stable (1, 1)-attractor, strong shear current was generated around the limit circle. When reducing the slop of oblique boundary in a range, the structure of the attractor will not change greatly, but induce a quicker shrinkage of phase space due to the increase of linearity. For a (2, 1)-attractor, a part of the wave energy dissipated at the node between the two circuits and thus convergence of it needs more time. At the position of the node, current velocity is always zero. But the mixing is strong, and the buoyancy oscillates periodically with large amplitude.
- internal wave attractor /
- MITgcm /
- non-hydrostatic /
- wave beam /
- uniform stratification

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