Tapan K. Sengupta , Bhavna Joshi , Prasannabalaji Sundaram
{"title":"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","authors":"Tapan K. Sengupta , Bhavna Joshi , Prasannabalaji Sundaram","doi":"10.1016/j.physleta.2024.130004","DOIUrl":null,"url":null,"abstract":"<div><div>Direct numerical simulation (DNS) of Rayleigh-Taylor instability (RTI) has been reported in Sengupta, et al. (2022) <span><span>[35]</span></span> using more than 4 billion points with initial time steps of 7.69 <span><math><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>8</mn></mrow></msup><mi>s</mi></math></span>. 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.</div></div>","PeriodicalId":20172,"journal":{"name":"Physics Letters A","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Receptivity of Rayleigh-Taylor instability to acoustic pulses: Theoretical explanation of pulse propagation\",\"authors\":\"Tapan K. Sengupta , Bhavna Joshi , Prasannabalaji Sundaram\",\"doi\":\"10.1016/j.physleta.2024.130004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Direct numerical simulation (DNS) of Rayleigh-Taylor instability (RTI) has been reported in Sengupta, et al. (2022) <span><span>[35]</span></span> using more than 4 billion points with initial time steps of 7.69 <span><math><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>8</mn></mrow></msup><mi>s</mi></math></span>. 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.</div></div>\",\"PeriodicalId\":20172,\"journal\":{\"name\":\"Physics Letters A\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2024-10-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physics Letters A\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0375960124006984\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physics Letters A","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0375960124006984","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
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 . 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.
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.