Maximization of inertial waves focusing in linear and nonlinear regimes

IF 2.5 3区 物理与天体物理 Q2 PHYSICS, FLUIDS & PLASMAS
A. Mohamed, A. Delache, F. S. Godeferd, J. Liu, M. Oberlack, Y. Wang
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Abstract

We study the propagation of inertial waves (IWs) generated by an axisymmetric torus oscillating at frequency ωf in a rotating fluid. Inertial waves are emitted from the torus and propagate at an angle θf that depends on the ratio of the rotation frequency of the fluid to the forcing frequency of the torus. The waves focus in a neighborhood of the apex of the propagation cone. Using direct numerical simulations, we characterize the flow in this region, within a linear approximation or in the regime where nonlinear interactions between waves produce a turbulent patch. Forcing by the torus is modeled in two ways. The first model represents the effect of the oscillating torus as a local volume force in the form of a Dirac delta function, called the Dirac ring. The second approach aims at a more realistic three-dimensional model of a torus represented by a volume penalization technique. We observe the appearance of a mean flow composed of a central vortex produced by the nonlinear interaction of the IWs. We show that this phenomenon is in agreement with the theory of Davidson et al. [J. Fluid Mech. 557, 135 (2006)] for a rotating fluid. Using Dirac ring forcing in the linear regime, we obtain the dependence on the propagation angle of the vertical kinetic energy at the focal point, which reaches a maximum for θf=35, in agreement with the linear theory developed by Liu et al. [Phys. Fluids 34, 086601 (2022)]. A similar angle is observed in the 3D torus forcing case for both linear and nonlinear simulations: the angle θf=30 maximizes the vertical velocity and dissipation, attesting an optimal energy transfer from the oscillating source to the focal region. In the nonlinear regime, we obtain the detailed spectral distribution of the kinetic energy in the focal zone, and we develop a spatiotemporal analysis of the velocity field that shows a wide presence of IWs in the flow. Moreover, we identify triadic resonances of IWs that lead to the production of the turbulent patch and of a large-scale mode similar to the geostrophic mean flow.

Abstract Image

线性和非线性状态下惯性波聚焦的最大化
我们研究了在旋转流体中以 ωf 频率振荡的轴对称环所产生的惯性波(IWs)的传播。惯性波从环上发出并以一定角度θf传播,该角度取决于流体旋转频率与环的强迫频率之比。波聚焦在传播锥顶点附近。通过直接的数值模拟,我们描述了这一区域的流动特征,包括线性近似或波浪之间的非线性相互作用产生湍流补丁的情况。环流的作用有两种模式。第一种模型将振荡环的效应表示为狄拉克三角函数形式的局部体积力,称为狄拉克环。第二种方法旨在通过体积惩罚技术建立一个更真实的环状三维模型。我们观察到由 IWs 非线性相互作用产生的中心漩涡组成的平均流的出现。我们发现这一现象与 Davidson 等人[J. Fluid Mech. 557, 135 (2006)]关于旋转流体的理论一致。利用线性机制中的狄拉克环强迫,我们得到了焦点处垂直动能对传播角度的依赖性,在 θf=35∘ 时达到最大值,这与 Liu 等人[Phys. Fluids 34, 086601 (2022)]提出的线性理论一致。在线性和非线性模拟的三维环形强迫情况下,也观察到了类似的角度:角度θf=30∘使垂直速度和耗散最大化,证明了从振荡源到焦点区域的最佳能量转移。在非线性系统中,我们获得了焦点区动能的详细频谱分布,并对速度场进行了时空分析,结果表明流动中广泛存在 IWs。此外,我们还确定了导致产生湍流斑块和类似于地转平均流的大尺度模式的 IWs 三元共振。
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来源期刊
Physical Review Fluids
Physical Review Fluids Chemical Engineering-Fluid Flow and Transfer Processes
CiteScore
5.10
自引率
11.10%
发文量
488
期刊介绍: Physical Review Fluids is APS’s newest online-only journal dedicated to publishing innovative research that will significantly advance the fundamental understanding of fluid dynamics. Physical Review Fluids expands the scope of the APS journals to include additional areas of fluid dynamics research, complements the existing Physical Review collection, and maintains the same quality and reputation that authors and subscribers expect from APS. The journal is published with the endorsement of the APS Division of Fluid Dynamics.
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