Singular value decomposition analysis of Kelvin-Helmholtz instability in two-phase flow: Temporal mode dynamics and coherent structures
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https://doi.org/10.15625/0866-7136/23272Keywords:
Kelvin–Helmholtz instability, singular value decomposition, temporal modes, extrema-based harmonic fitting, two-phase flow, coherent structuresAbstract
We investigate the spatio-temporal organization of a two-phase Kelvin–Helmholtz (K–H) instability using singular value decomposition (SVD) of the solid-phase vertical velocity field \(w_s\). The analysis quantifies modal energy and reveals that the dominant coherent dynamics are governed by a principal rotating pair. To mitigate coarse snapshot sampling, we introduce an extrema-based harmonic fitting that preserves amplitude and phase while smoothing jitter, enabling clear phase portraits and robust interpretation of modal interactions. We focus on temporal modes \(a_1\)–\(a_6\), report their periods, amplitudes, and phase shifts, and relate these to the emergence and saturation of K–H billows. The results support a low-dimensional, reduced-order description for two-phase shear flows.
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Blanco, D. C. P., Martini, E., Sasaki, K., & Cavalieri, A. V. G. (2022). Improved convergence of spectral proper orthogonal decomposition through time shifting. Journal of Fluid Mechanics, 950, A9. https://doi.org/10.1017/jfm.2021.1099
Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2016). Extracting spatial--temporal coherent patterns in large-scale numerical simulations of fluid flows using dynamic mode decomposition. Journal of Computational Dynamics, 2(2), 155–164. https://doi.org/10.3934/jcd.2016005
Cavagna, L., & Razzak, A. (2012). Two-phase flow instabilities: theory and experiments. International Journal of Multiphase Flow, 43, 62–78. https://doi.org/10.1016/j.ijmultiphaseflow.2012.03.001
Elghobashi, S. (1994). On predicting particle-laden turbulent flows. Applied Scientific Research, 52, 309–329. https://doi.org/10.1007/BF00936835
Ferrante, A., & Elghobashi, S. (2004). On the physical mechanisms of two-phase turbulence. Physics of Fluids, 16(12), 4386–4399. https://doi.org/10.1063/1.1811979
Guala, M., Hommema, S. E., & Adrian, R. J. (2006). Large-scale and very-large-scale motions in turbulent pipe flow. Journal of Fluid Mechanics, 554, 521–542. https://doi.org/10.1017/S0022112006009308
He, G., Wang, L., & Liu, T. (2009). PIV measurements of two-phase turbulent channel flow. International Journal of Multiphase Flow, 35(2), 161–173. https://doi.org/10.1016/j.ijmultiphaseflow.2008.11.002
Lohse, D. (2010). Particle-laden flows: from laboratory experiments to full-scale turbulence. Annual Review of Fluid Mechanics, 42, 335–364. https://doi.org/10.1146/annurev-fluid-121108-145610
Nguyen, D. H., Guillou, S., Nguyen, K. D., Pham Van Bang, D., & Chauchat, J. (2012). Simulation of dredged sediment releases into homogeneous water using a two-phase model: Application to environmental flow problems. Advances in Water Resources, 48, 102–112. https://doi.org/10.1016/j.advwatres.2012.03.009
Pagano, A. (2022). Two‑phase flow characterization through recurrence quantification analysis coupled with SVD. Journal of Hydraulic Research. https://doi.org/10.1080/00221686.2022.2081537
Popinet, S. (2018). Numerical models of surface tension. Annual Review of Fluid Mechanics, 50, 49–75. https://doi.org/10.1146/annurev-fluid-122316-045034
Rowley, C. W., Colonius, T., & Murray, R. M. (2004). On the dynamics of large-scale structures in turbulent boundary layers. Journal of Fluid Mechanics, 497, 1–12. https://doi.org/10.1017/S0022112003006693
Schmid, P. J. (2010). Dynamic mode decomposition of numerical and experimental data. Journal of Fluid Mechanics, 656, 5–28. https://doi.org/10.1017/S0022112010001217
Shin, S., & Juric, D. (2017). A modal analysis of interfacial instabilities in multiphase flows. Physics of Fluids, 29(8), 082104. https://doi.org/10.1063/1.4999303
Sujudi, D., & Haimes, R. (1995). Identification of swirling flow in 3D vector fields. Proc. AIAA Computational Fluid Dynamics Conference, 95–1715.
Taira, K., Hemati, M. S., Brunton, S. L., Sun, Y., Duraisamy, K., Bagheri, S., Dawson, S. T. M., & Yeh, C. (2017). Modal analysis of fluid flows: An overview. AIAA Journal, 55(12), 4013–4041. https://doi.org/10.2514/1.J056060
Towne, A., Schmidt, O. T., & Colonius, T. (2018). Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. Journal of Fluid Mechanics, 847, 821–867. https://doi.org/10.1017/jfm.2018.283
Tryggvason, G., Scardovelli, R., & Zaleski, S. (2011). Direct Numerical Simulations of Multiphase Flows. Cambridge University Press. https://doi.org/10.1017/CBO9780511975264
Wang, Z. H., Zhang, G. Y., Huang, H. K., Xu, H., & Sun, T. Z. (2023). Joint proper orthogonal decomposition: A novel perspective for feature extraction from multivariate cavitation flow fields. Ocean Engineering, 288, 116003. https://doi.org/10.1016/j.oceaneng.2023.116003
Xu, J., Dong, M., Zhou, J., Liang, Y., & Lu, J. (2024). Fast reconstruction of physical fields via POD and conditional deep convolutional GANs. International Journal of Green Energy. https://doi.org/10.1080/15435075.2024.2322950
Yeo, H., & Lee, S. (2010). Stability of gas–liquid two-phase flows. International Journal of Multiphase Flow, 36(6), 482–491. https://doi.org/10.1016/j.ijmultiphaseflow.2010.02.007
Zhang, Y. (2023). Forecasting through deep learning and modal decomposition in two‑phase concentric jets. Expert Systems with Applications, 232, 120817. https://doi.org/10.1016/j.eswa.2023.120817
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