- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Regime maps for sloshing in horizontal cylindrical tanks under vertical acceleration

Francisco Monteiro1,2,*, Tommaso De Maria1,3, Samuel Ahizi1,2, Ramon Abarca4, Giuseppe C. A. Caridi1, and Miguel A. Mendez1,2,5

  • *Contact author: francisco.monteiro@vki.ac.be
PDF

Phys. Rev. Fluids 11, 084804 – Published 28 August, 2026

DOI: https://doi.org/10.1103/t48x-53br

Abstract

Vertical excitation of partially filled horizontal cylindrical tanks can induce large-amplitude sloshing, particularly when the forcing frequency approaches twice the fundamental sloshing frequency, leading to parametric resonance. Under these conditions, parametric resonance can trigger exponential growth of free-surface perturbations, leading to large-amplitude waves, interface breakup, and enhanced mixing. In this work, we experimentally investigate the sloshing regimes associated with this primary parametric instability. Experiments are conducted in a transparent horizontal cylindrical tank (D=134.5mm, L=336.3mm) over a range of fill ratios and excitation conditions. A data-driven, image-based methodology is developed to identify and classify sloshing regimes directly from high-speed visualizations. The approach combines multiscale proper orthogonal decomposition for feature extraction with prototype-based clustering and support vector machine classification. The results are summarized in a dimensionless regime map across three fill ratios (Hl/D∈[0.40;0.67]), distinguishing stable free-surface conditions, dominant longitudinal modes, and mixed or mode-interaction regimes. The map provides a structured characterization of the flow responses in the vicinity of the primary parametric resonance.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (82)

  1. H. N. Abramson, The Dynamic Behavior of Liquids in Moving Containers: With Applications to Space Vehicle Technology, 1st ed. (Southwest Research Institute, San Antonio, TX, 1981).
  2. N. Kobayashi, T. Mieda, H. Shibata, and Y. Shinozaki, A study of the liquid slosh response in horizontal cylindrical tanks, J. Pressure Vessel Technol. 111, 32 (1989).
  3. H. C. Mayer and R. Krechetnikov, Walking with coffee: Why does it spill? Phys. Rev. E 85, 046117 (2012).
  4. F. T. Dodge, The New “Dynamic Behavior of Liquids in Moving Containers,” 1st ed. (Southwest Research Institute, San Antonio, TX, 2000).
  5. O. M. Faltinsen and A. N. Timokha, Sloshing, 1st ed. (Cambridge University Press, Cambridge, UK, 2009).
  6. R. A. Ibrahim, Liquid Sloshing Dynamics: Theory and Applications, 1st ed. (Cambridge University Press, Cambridge, UK, 2005).
  7. F. Monteiro, P. Marques, A. Simonini, L. Carbonnelle, and M. A. Mendez, Experimental characterization of non-isothermal sloshing in microgravity, Exp. Therm. Fluid Sci. 166, 111473 (2025).
  8. A. V. Bazilevskii, V. A. Kalinichenko, and A. N. Rozhkov, Effect of fluid viscosity on the Faraday surface waves, Fluid Dyn. 53, 750 (2018).
  9. T. Arndt, Sloshing of Cryogenic Liquids in a Cylindrical Tank Under Normal Gravity Conditions, 1st ed. (Cuvillier Verlag, Göttingen, 2012).
  10. A. van Foreest, Modeling of Cryogenic Sloshing Including Heat and Mass Transfer, 1st ed. (Cuvillier Verlag, Göttingen, 2014).
  11. P. Marques, S. Ahizi, and M. A. Mendez, Real-time data assimilation for the thermodynamic modeling of cryogenic storage tanks, Energy 302, 131739 (2024).
  12. P. Marques, A. Simonini, L. Peveroni, and M. A. Mendez, Experimental analysis of heat and mass transfer in non-isothermal sloshing using a model-based inverse method, Appl. Therm. Eng. 231, 120871 (2023).
  13. J. Miles, Resonantly forced surface waves in a circular cylinder, J. Fluid Mech. 149, 15 (1984).
  14. A. Royon-lebeaud, E. J. Hopfinger, and A. Cartellier, Liquid sloshing and wave breaking in circular and square-base cylindrical containers, J. Fluid Mech. 577, 467 (2007).
  15. E. J. Hopfinger and V. Baumbach, Liquid sloshing in cylindrical fuel tanks, Prog. Propul. Phys. 1, 279 (2009).
  16. P. Guthrie, F. Gambioli, A. Chamos, S. Jones, J. Webb, J. Levenhagen, P. Behruzi, F. Mastroddi, A. Malan, S. Longshaw, A. Skillen, J. Cooper, L. Gonzalez, and S. Marrone, Sloshing wing dynamics—Project overview, in Proceedings of the Transport Research Arena Conference (, 2020).
  17. S. Marrone, A. Colagrossi, J. Calderon-Sanchez, and J. Martinez-Carrascal, Numerical study on the dissipation mechanisms in sloshing flows induced by violent and high-frequency accelerations. II. Comparison against experimental data, Phys. Rev. Fluids 6, 114802 (2021).
  18. S. Marrone, A. Colagrossi, F. Gambioli, and L. González-Gutiérrez, Numerical study on the dissipation mechanisms in sloshing flows induced by violent and high-frequency accelerations. I. Theoretical formulation and numerical investigation, Phys. Rev. Fluids 6, 114801 (2021).
  19. L. Constantin, J. De Courcy, B. Titurus, T. C. S. Rendall, and J. E. Cooper, Analysis of damping from vertical sloshing in a SDOF system, Mech. Syst. Sig. Process. 152, 107452 (2021).
  20. L. Constantin, J. De Courcy, B. Titurus, T. C. S. Rendall, and J. E. Cooper, Nonlinear damping effects in vertically vibrating systems with violently sloshing liquid, J. Sound Vib. 544, 117405 (2023).
  21. HASTA Project, Hasta project—The hydrogen aircraft sloshing tank advancement (2025), https://hasta-project.eu/, accessed: 2025-04-30.
  22. M. Faraday, On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces, Philos. Trans. R. Soc. London 121, 299 (1831).
  23. J. W. S. L. Rayleigh, On the convection currents in a horizontal layer of fluid when the higher temperature is on the under side, Philos. Mag. 32, 529 (1916).
  24. R. A. Ibrahim, Recent advances in physics of fluid parametric sloshing and related problems, J. Fluids Eng. 137, 090801 (2015).
  25. F. T. Dodge, D. D. Kana, and H. N. Abramson, Liquid surface oscillations in longitudinally excited rigid cylindrical containers, AIAA J. 3, 685 (1965).
  26. R. P. Brand and W. L. Nyborg, Parametrically excited surface waves, J. Acoust. Soc. Am. 37, 509 (1965).
  27. L. Chang, Y. J. Jian, J. Su, R. Na, Q. S. Liu, and G. W. He, Nonlinear interfacial waves in a circular cylindrical container subjected to a vertical excitation, Wave Motion 51, 804 (2014).
  28. L. Yu, M.-A. Xue, and Z. Jiang, Experimental investigation of parametric sloshing in a tank with vertical baffles, Ocean Eng. 213, 107783 (2020).
  29. T. B. Benjamin and F. Ursell, The stability of the plane free surface of a liquid in vertical periodic motion, Proc. R. Soc. London A 225, 505 (1954).
  30. J. Miles and D. Henderson, Parametrically forced surface waves, Annu. Rev. Fluid Mech. 22, 143 (1990).
  31. J. Woodward, Fluid motion in a cylindrical tank of sector-annular cross section when subjected to a longitudinal excitation, Ph.D. Thesis, Georgia Institute of Technology, 1966.
  32. S. Ciliberto and J. P. Gollub, Chaotic mode competition in parametrically forced surface waves, J. Fluid Mech. 158, 381 (1985).
  33. S. Ciliberto and J. P. Gollub, Pattern competition leads to chaos, Phys. Rev. Lett. 52, 922 (1984).
  34. Y. O. El-Dib, Nonlinear Mathieu equation and coupled resonance mechanism, Chaos Solitons Fractals 12, 705 (2001).
  35. J. B. Frandsen, Sloshing motions in excited tanks, J. Comput. Phys. 196, 53 (2004).
  36. V. A. Kalinichenko, Breaking of Faraday waves and jet launch formation, Fluid Dyn. 44, 577 (2009).
  37. L. Jiang, M. Perlin, and W. W. Schultz, Period tripling and energy dissipation of breaking standing waves, J. Fluid Mech. 369, 273 (1998).
  38. H. Hashimoto and S. Sudo, Violent liquid sloshing in vertically excited cylindrical containers, Exp. Therm. Fluid Sci. 1, 159 (1988).
  39. L. Kayal and R. Dasgupta, Jet from a very large, axisymmetric, surface-gravity wave, J. Fluid Mech. 975, A22 (2023).
  40. S. Ciliberto and J. P. Gollub, Phenomenological model of chaotic mode competition in surface waves, Il Nuovo Cimento D 6, 309 (1985).
  41. Z. C. Feng and P. R. Sethna, Symmetry-breaking bifurcations in resonant surface waves, J. Fluid Mech. 199, 495 (1989).
  42. F. Simonelli and J. P. Gollub, Surface wave mode interactions: Effects of symmetry and degeneracy, J. Fluid Mech. 199, 471 (1989).
  43. S. P. Das and E. J. Hopfinger, Parametrically forced gravity waves in a circular cylinder and finite-time singularity, J. Fluid Mech. 599, 205 (2008).
  44. S. P. Das and E. J. Hopfinger, Mass transfer enhancement by gravity waves at a liquid–vapour interface, Int. J. Heat Mass Transf. 52, 1400 (2009).
  45. H. Luo, W. Wu, B. Jiang, S. Guo, L. Huang, and B. Yue, Experiments and analysis of dynamic characteristics of liquid sloshing in horizontal Cassini tank, Phys. Scr. 98, 075007 (2023).
  46. E. L. Grotle and V. Æsøy, Dynamic modelling of the thermal response enhanced by sloshing in marine LNG fuel tanks, Appl. Therm. Eng. 135, 512 (2018).
  47. A. L. Martín López, Estudio teórico experimental de la estabilidad lateral en vehículos cisterna. Metodología para la determinación del umbral de vuelco, Ph.D. Thesis, Universidad Politécnica de Madrid, 2013.
  48. S. M. Hasheminejad and H. Soleimani, An analytical solution for free liquid sloshing in a finite-length horizontal cylindrical container filled to an arbitrary depth, Appl. Math. Modell. 48, 338 (2017).
  49. Y. Han, X. Zhu, T. Li, W. Guo, and L. Pan, A semi-analytical study of the three-dimensional liquid sloshing in a horizontal cylindrical tank with an arbitrary liquid depth, Ocean Eng. 238, 109722 (2021).
  50. S. W. Colville, Y.-M. Scolan, F. Gambioli, D. Greaves, E. Ransley, and Y. C. Lee, Faraday waves and period tripling in a horizontal circular tank, J. Fluid Mech. 1006, A4 (2025).
  51. F. Saltari, M. Pizzoli, M. T. Migliorino, A. Binni, G. Coppotelli, F. Mastroddi, T. Pagliaroli, F. D. Duchetto, F. Gambioli, and R. Abarca, Experimental methodological investigations of sloshing-induced mass transfer coefficients for aircraft tanks, J. Thermophys. Heat Transfer 39, 386 (2025).
  52. M. Pizzoli, F. Saltari, M. T. Migliorino, F. Mastroddi, and F. Gambioli, Modeling non-isothermal vertical sloshing via experimentally-driven Froude-dependent Nusselt number, Nonlinear Dyn. 114, 443 (2026).
  53. T. Pagliaroli, F. Gambioli, F. Saltari, and J. Cooper, Proper orthogonal decomposition, dynamic mode decomposition, wavelet and cross wavelet analysis of a sloshing flow, J. Fluids Struct. 112, 103603 (2022).
  54. D. Gligor, P. A. Marques, P. Salgado Sánchez, J. Porter, M. A. Méndez, and J. M. Ezquerro, Experiments on sloshing mitigation using tuned oscillating baffles, Phys. Fluids 36, 092122 (2024).
  55. C. Chen, O. Li, D. Tao, A. Barnett, C. Rudin, and J. K. Su, This looks like that: Deep learning for interpretable image recognition, in Advances in Neural Information Processing Systems 32 (NeurIPS 2019), edited by H. M. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alché-Buc, E. Fox, and R. Garnett (Curran Associates, Inc., Red Hook, NY, 2019), pp. 8930–8941.
  56. P. Perner, Prototype-based classification, Appl. Intell. 28, 238 (2008).
  57. M. Biehl, B. Hammer, and T. Villmann, Prototype-based models in machine learning, WIREs Cognit. Sci. 7, 92 (2016).
  58. J.-W. Jang, A. Alaniz, L. Yang, J. Powers, and C. Hall, Mechanical slosh models for rocket-propelled spacecraft, in Proceedings of the AIAA Guidance, Navigation and Control Conference (, 2013).
  59. E. A. Cerda and E. L. Tirapegui, Faraday's instability in viscous fluid, J. Fluid Mech. 368, 195 (1998).
  60. E. A. Cerda and E. L. Tirapegui, Faraday's instability for viscous fluids, Phys. Rev. Lett. 78, 859 (1997).
  61. S. A. Ahizi, F. Monteiro, R. Abarca, and M. A. Mendez, Real-time identification of parametric sloshing-induced heat and mass transfer in a horizontally oriented cylindrical tank, Int. J. Heat Mass Transf. 264, 128707 (2026).
  62. E. W. Lemmon, I. H. Bell, M. L. Huber, and M. O. McLinden, NIST standard reference database 23: Reference fluid thermodynamic and transport properties-REFPROP, version 10.0, National Institute of Standards and Technology (2018), https://www.nist.gov/srd/refprop.
  63. G. Bradski, The OpenCV library, Dr. Dobb's J. Software Tools 25, 120 (2000).
  64. M. J. Casiano, Extracting Damping Ratio from Dynamic Data and Numerical Solutions, NASA Technical Memorandum NASA/TM–2016–218227 (NASA, Marshall Space Flight Center, Huntsville, AL, 2016).
  65. U. Tosun, R. Aghazadeh, C. Sert, and M. B. Özer, Tracking free surface and estimating sloshing force using image processing, Exp. Therm. Fluid Sci. 88, 423 (2017).
  66. M.-R. Jiang, W.-J. Zhong, J.-X. Yu, P.-L. Liu, H.-J. Yin, S.-D. Wang, and Y.-X. Ma, Experimental study on sloshing characteristics in the elastic tank based on Morlet wavelet transform, China Ocean Eng. 32, 400 (2018).
  67. J. Slavič, I. Simonovski, and M. Boltežar, Damping identification using a continuous wavelet transform: Application to real data, J. Sound Vib. 262, 291 (2003).
  68. S. Hans, E. Ibraim, S. Pernot, C. Boutin, and C.-H. Lamarque, Damping identification in multi-degree-of-freedom system via a wavelet-logarithmic decrement—Part 2: Study of a civil engineering building, J. Sound Vib. 235, 375 (2000).
  69. M. A. Mendez, M. T. Scelzo, and J.-M. Buchlin, Multiscale modal analysis of an oscillating impinging gas jet, Exp. Therm. Fluid Sci. 91, 256 (2018).
  70. M. A. Mendez, D. Hess, B. B. Watz, and J.-M. Buchlin, Multiscale proper orthogonal decomposition (mPOD) of TR-PIV data—A case study on stationary and transient cylinder wake flows, Meas. Sci. Technol. 31, 094014 (2020).
  71. R. Poletti, L. Schena, D. Ninni, and M. A. Mendez, Modulo: A Python toolbox for data-driven modal decomposition, J. Open Source Software 9, 6753 (2024).
  72. M. A. Mendez, Generalized and multiscale modal analysis, in Data-Driven Fluid Mechanics (Cambridge University Press, Cambridge, UK, 2023) pp. 153–181.
  73. A. M. Ikotun, A. E. Ezugwu, L. Abualigah, B. Abuhaija, and J. Heming, K-means clustering algorithms: A comprehensive review, variants analysis, and advances in the era of big data, Inf. Sci. 622, 178 (2023).
  74. W. M. Rand, Objective criteria for the evaluation of clustering methods, J. Am. Stat. Assoc. 66, 846 (1971).
  75. C. Cortes and V. Vapnik, Support-vector networks, Mach. Learn. 20, 273 (1995).
  76. K. Crammer and Y. Singer, On the algorithmic implementation of multiclass kernel-based vector machines, J. Mach. Learn. Res. 2, 265 (2001).
  77. C.-W. Hsu and C.-J. Lin, A comparison of methods for multiclass support vector machines, IEEE Trans. Neural Networks 13, 415 (2002).
  78. T. Arndt and M. Dreyer, Damping behavior of sloshing liquid in laterally excited cylindrical propellant vessels, J. Spacecr. Rockets 45, 1085 (2008).
  79. H. N. Abramson, Space vehicle design criteria (structures): Slosh suppression, Tech. Rep. NASA SP-8031, NASA, Washington, D.C., 1969.
  80. H. Yang, R. Purandare, J. Peugeot, and J. West, Prediction of liquid slosh damping using a high resolution CFD tool, in Proceedings of the 48th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit (, 2012).
  81. P. Marques, S. Ahizi, F. Monteiro, B. Scheid, and M. Méndez, On the scaling of heat and mass transfer in cryogenic propellant tanks: A model-based and experimental analysis under static conditions and lateral sloshing, Appl. Therm. Eng. 279, 127751 (2025).
  82. T. De Maria, F. Monteiro, S. Ahizi, G. C. A. Caridi, R. Abarca, and M. A. Mendez, Experimental analysis of sloshing-induced thermal mixing in horizontally oriented cylindrical tanks subjected to vertical acceleration, in Proceedings of the 11th European Conference for Aeronautics and Aerospace Sciences (, 2025).

Outline

Information

Phys. Rev. Fluids 11, 084804– Published 28 August, 2026
  • Received 2 December 2025
  • Accepted 4 August 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation