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| Autori principali: | , , , |
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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2503.20204 |
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| _version_ | 1866908617644441600 |
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| author | Nakamura, Yuto Kuroda, Yuma Sato, Shintaro Ohnishi, Naofumi |
| author_facet | Nakamura, Yuto Kuroda, Yuma Sato, Shintaro Ohnishi, Naofumi |
| contents | We derive a phase-averaged representation of transient flows based on the eigenmodes of a data-driven linear operator that approximates the Navier-Stokes dynamics. In performing phase averaging, it is assumed that, at each instant during the transient evolution, the eigenmode amplitude remains invariant, while only the complex phase angle differs among distinct realizations of the transient process. From this modal-phase perspective, the linear operator is defined as the best-fit operator that represents phase-different transient evolutions. By introducing a time-varying dynamic mode decomposition with a phase-control strategy formulated from this modal-phase perspective, time-varying eigenmodes are extracted from numerical simulations. In this formulation, the transient process is decomposed into time-varying eigenmodes, phase-shift angles, and amplitude coefficients. Furthermore, by averaging the Navier-Stokes equations over the phase-shift angle, a frequency-domain form of the equations can be derived at any given instant, assuming that the phase-shift angle is time-independent. This frequency-domain representation reveals the instantaneous energy budget and the presence of energy transfer through triadic interactions. The proposed analysis is demonstrated using a canonical example of two-dimensional flow around a circular cylinder transitioning from a steady to an unsteady state. The time-varying dynamic mode decomposition with phase control is shown to capture the transient evolution of the frequency components accurately. In addition, the temporal evolution of the energy budget and transfer distribution reveals that transient growth processes exhibit different time-dependent characteristics of energy transfer, even in cylinder flows at Reynolds numbers that eventually lead to a periodic state. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20204 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Energy transfer and budget analysis for transient process with phase-averaged reduced-order model Nakamura, Yuto Kuroda, Yuma Sato, Shintaro Ohnishi, Naofumi Fluid Dynamics We derive a phase-averaged representation of transient flows based on the eigenmodes of a data-driven linear operator that approximates the Navier-Stokes dynamics. In performing phase averaging, it is assumed that, at each instant during the transient evolution, the eigenmode amplitude remains invariant, while only the complex phase angle differs among distinct realizations of the transient process. From this modal-phase perspective, the linear operator is defined as the best-fit operator that represents phase-different transient evolutions. By introducing a time-varying dynamic mode decomposition with a phase-control strategy formulated from this modal-phase perspective, time-varying eigenmodes are extracted from numerical simulations. In this formulation, the transient process is decomposed into time-varying eigenmodes, phase-shift angles, and amplitude coefficients. Furthermore, by averaging the Navier-Stokes equations over the phase-shift angle, a frequency-domain form of the equations can be derived at any given instant, assuming that the phase-shift angle is time-independent. This frequency-domain representation reveals the instantaneous energy budget and the presence of energy transfer through triadic interactions. The proposed analysis is demonstrated using a canonical example of two-dimensional flow around a circular cylinder transitioning from a steady to an unsteady state. The time-varying dynamic mode decomposition with phase control is shown to capture the transient evolution of the frequency components accurately. In addition, the temporal evolution of the energy budget and transfer distribution reveals that transient growth processes exhibit different time-dependent characteristics of energy transfer, even in cylinder flows at Reynolds numbers that eventually lead to a periodic state. |
| title | Energy transfer and budget analysis for transient process with phase-averaged reduced-order model |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2503.20204 |