On the opposing roles of the Boussinesq and non‐Boussinesq baroclinic torques in surface gravity wave propagation
On the opposing roles of the Boussinesq and non‐Boussinesq baroclinic torques in surface gravity wave propagation
复制标题
布辛涅斯克和非布辛涅斯克斜压力矩在表面重力波传播中的相反作用
DOI：
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发表时间：
2019
影响因子：
8.9
通讯作者：
A. Guha
中科院分区：
文献类型：
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作者：
E. Heifetz;Ronnie Maor;A. Guha
在这里，我们提出了一个替代的理解的表面重力波传播机制的基础上的斜压扭矩，它的操作来翻译的界面涡度异常的空气-水界面。我们演示了斜压扭矩的非Boussinesq项如何与Boussinesq项作用以阻碍波的传播。通过标准涡量反演和镜像成像，我们展示了底边界的存在如何影响这两种类型的扭矩。由于相反的非Boussinesq扭矩仅由镜像产生，因此它在深水极限中消失，其大小是浅水极限中Boussinesq扭矩的一半。这表明Boussinesq近似在深水极限是有效的，即使空气和水之间的密度差异很大。斜压扭矩的Boussinesq和非Boussinesq部分所起的机械作用在标准导数中仍然模糊不清，其中使用了含时伯努利方程而不是界面涡度方程。最后，我们注意到，表面重力波的维里定理可以得到单独的考虑在空气-水界面的动力学。
Here we suggest an alternative understanding of the surface gravity wave propagation mechanism based on the baroclinic torque, which operates to translate the interfacial vorticity anomalies at the air–water interface. We demonstrate how the non‐Boussinesq term of the baroclinic torque acts against the Boussinesq one to hinder wave propagation. By standard vorticity inversion and mirror imaging, we then show how the existence of the bottom boundary affects the two types of torque. Since the opposing non‐Boussinesq torque results solely from the mirror image, it vanishes in the deep‐water limit and its magnitude is half of the Boussinesq torque in the shallow‐water limit. This reveals that the Boussinesq approximation is valid in the deep‐water limit, even though the density contrast between air and water is large. The mechanistic roles played by the Boussinesq and non‐Boussinesq parts of the baroclinic torque remain obscured in the standard derivation where the time‐dependent Bernoulli equation is implemented instead of the interfacial vorticity equation. Finally, we note on passing that the Virial theorem for surface gravity waves can be obtained solely from considerations of the dynamics at the air–water interface.
非 Boussinesq 状态下的分层剪切流不稳定性
影响因子：
4.6
作者：
Heifetz E
通讯作者：
Heifetz E