瑞利-泰勒不稳定性对声学脉冲的感受性:脉冲传播的理论解释

IF 2.3 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Physics Letters A Pub Date : 2024-10-24 DOI:10.1016/j.physleta.2024.130004
Tapan K. Sengupta , Bhavna Joshi , Prasannabalaji Sundaram
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引用次数: 0

摘要

Sengupta 等人(2022 年)[35] 报道了雷利-泰勒不稳定性(RTI)的直接数值模拟(DNS),使用了超过 40 亿个点,初始时间步长为 7.69 ×10-8s。该装置由静止的重(冷)流体和轻(热)流体组成,最初由一个绝缘隔板隔开。移除隔板会在界面的法线方向产生声脉冲,这就为 RTI 提供了接受瞬态声脉冲的途径,这些脉冲的频率分布在几兆赫兹范围内,远远超过超声波频率。DNS 及其分析表明脉冲被严重衰减,这无法用经典波方程来解释。在本研究中,在展示了 DNS 结果的特征之后,我们详细报告了基于纳维-斯托克斯方程的损耗波方程的理论发展,该方程在静态环境下没有斯托克斯假设。除了这个改变了的波方程的物理特性外,我们还获得了它的数值解。扰动在频谱平面上传播的支配偏微分方程(PDE)提供了耗散介质中波长和圆周频率之间的频散关系,并考虑了粘性损耗。所做的分析利用全局频谱分析(GSA)提供了物理特性。这表明远场扰动要么以衰减波的形式传播,要么严格以扩散的方式传播,具体取决于波长。该 PDE 采用高精度紧凑方案和四级 Runge-Kutta 方案进行数值求解。结果表明,计算结果不仅与理论分析相吻合,而且在计算流场真正代表静态环境时,还解释了早期 RTI 的 DNS 结果。
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Receptivity of Rayleigh-Taylor instability to acoustic pulses: Theoretical explanation of pulse propagation
Direct numerical simulation (DNS) of Rayleigh-Taylor instability (RTI) has been reported in Sengupta, et al. (2022) [35] using more than 4 billion points with initial time steps of 7.69 ×108s. The set-up consists of quiescent heavy (cold) fluid atop lighter (hot) fluid initially separated by an insulated partition. Removal of this partition creates acoustic pulses in the directions normal to the interface, which provides the receptivity route of RTI to transient acoustic pulses spread over several mega-Hz frequencies, far in excess of ultrasonic frequencies. The DNS and its analysis reveal the pulses to be severely attenuated, which cannot be explained by the classical wave equation. In the present research, after demonstrating the features of the DNS results, we report in detail, the theoretical development of a wave equation incorporating losses based on the Navier-Stokes equation without Stokes' hypothesis for a quiescent ambience. Apart from the physical properties of this altered wave equation, the numerical solution of the same is obtained. The governing partial differential equation (PDE) for the propagation of disturbances in the spectral plane, provides the dispersion relation between wavenumber and circular frequency in the dissipative medium accounting for viscous losses. The presented analysis provides physical properties using the global spectral analysis (GSA). This shows the far-field perturbation to propagate either as attenuated waves or strictly in a diffusive manner depending upon the wavenumber. The PDE is solved numerically by a high-accuracy compact scheme and the four-stage, Runge-Kutta scheme for time advancement. The computed solution is shown to match not only with the developed theoretical analysis but also explains the DNS results for RTI at early times when the computed flow field truly represents the quiescent ambience.
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来源期刊
Physics Letters A
Physics Letters A 物理-物理:综合
CiteScore
5.10
自引率
3.80%
发文量
493
审稿时长
30 days
期刊介绍: Physics Letters A offers an exciting publication outlet for novel and frontier physics. It encourages the submission of new research on: condensed matter physics, theoretical physics, nonlinear science, statistical physics, mathematical and computational physics, general and cross-disciplinary physics (including foundations), atomic, molecular and cluster physics, plasma and fluid physics, optical physics, biological physics and nanoscience. No articles on High Energy and Nuclear Physics are published in Physics Letters A. The journal''s high standard and wide dissemination ensures a broad readership amongst the physics community. Rapid publication times and flexible length restrictions give Physics Letters A the edge over other journals in the field.
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