Pulse propagation in the quiescent environment during direct numerical simulation of Rayleigh-Taylor instability: Solution by Bromwich contour integral method
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2024
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| _version_ | 1866913381862080512 |
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| author | Sengupta, Tapan K. Joshi, Bhavna Sundaram, Prasannabalaji |
| author_facet | Sengupta, Tapan K. Joshi, Bhavna Sundaram, Prasannabalaji |
| contents | In: {\it "Three-dimensional direct numerical simulation (DNS) of Rayleigh-Taylor instability (RTI) trigerred by acoustic excitation -- Sengupta et al. {\bf 34},054108 (2022)"} the receptivity of RTI to pressure pulses have been established. It has also been shown that at the onset of RTI these pulses are one-dimensional and the dissipation of the pressure pulses are governed by a dissipative wave equation. The propagation of these infrasonic to ultrasonic pressure pulses have been studied theoretically and numerically by a high fidelity numerical procedure in the physical plane. The numerical results are consistent with the theoretical analysis and the DNS of RTI noted above. The properties of pulse propagation in a quiescent dissipative ambience have been theoretically obtained from the linearized compressible Navier-Stokes equation, without Stokes' hypothesis. This analysis is extended here for a special class of excitation, with combination of wavenumbers and circular frequencies for which the phase shift results in an imposed time period is integral multiple of $π$, and the signal amplification is by a real factor. Here, the governing partial differential equation (PDE) for the free-field propagation of pulses is solved by the Bromwich contour integral method in the spectral plane. This method, for an input Gaussian pulse excited at a fixed frequency, is the so-called signal problem. Responses for the specific phase shifts integral multiple of $π$ can reinforce each other due to the phase coherence. It is shown that these combinations occur at a fixed wavenumber, with higher frequencies attenuated more in such a sequence. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_05164 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pulse propagation in the quiescent environment during direct numerical simulation of Rayleigh-Taylor instability: Solution by Bromwich contour integral method Sengupta, Tapan K. Joshi, Bhavna Sundaram, Prasannabalaji Fluid Dynamics In: {\it "Three-dimensional direct numerical simulation (DNS) of Rayleigh-Taylor instability (RTI) trigerred by acoustic excitation -- Sengupta et al. {\bf 34},054108 (2022)"} the receptivity of RTI to pressure pulses have been established. It has also been shown that at the onset of RTI these pulses are one-dimensional and the dissipation of the pressure pulses are governed by a dissipative wave equation. The propagation of these infrasonic to ultrasonic pressure pulses have been studied theoretically and numerically by a high fidelity numerical procedure in the physical plane. The numerical results are consistent with the theoretical analysis and the DNS of RTI noted above. The properties of pulse propagation in a quiescent dissipative ambience have been theoretically obtained from the linearized compressible Navier-Stokes equation, without Stokes' hypothesis. This analysis is extended here for a special class of excitation, with combination of wavenumbers and circular frequencies for which the phase shift results in an imposed time period is integral multiple of $π$, and the signal amplification is by a real factor. Here, the governing partial differential equation (PDE) for the free-field propagation of pulses is solved by the Bromwich contour integral method in the spectral plane. This method, for an input Gaussian pulse excited at a fixed frequency, is the so-called signal problem. Responses for the specific phase shifts integral multiple of $π$ can reinforce each other due to the phase coherence. It is shown that these combinations occur at a fixed wavenumber, with higher frequencies attenuated more in such a sequence. |
| title | Pulse propagation in the quiescent environment during direct numerical simulation of Rayleigh-Taylor instability: Solution by Bromwich contour integral method |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2406.05164 |