Characteristics of nonbuoyant jets in a wave environment investigated numerically by SPH

  • Diana De PadovaEmail author
  • Michele Mossa
  • Stefano Sibilla
Original Article


Numerical experiments of plane jets are performed to investigate their behaviour into a still ambient and into a flow field of regular waves. SPH simulations are obtained by a pseudo-compressible XSPH scheme with pressure smoothing; turbulent stresses are represented by a two-equation k-ε model. The SPH model is validated by comparing the obtained results with experimental measurements and analytical solutions. The main fluid mechanical characteristics of jets discharged either in still water or transversally to regular wave trains characterized by different heights are compared. The study focuses specifically on the role played by the wave heights on the velocity distribution.


Jets Wave Jet-wave interaction Smoothed particle hydrodynamics models 



  1. 1.
    Albertson ML et al (1950) Diffusion of submerged jets. Trans ASCE 115:639–697Google Scholar
  2. 2.
    Antuono M, Colagrossi A, Marrone S (2012) Numerical diffusive terms in weakly-compressible SPH schemes. Comput Phys Commun 183:2570–2580CrossRefGoogle Scholar
  3. 3.
    Aristodemo F, Marrone S, Federico I (2015) SPH modeling of plane jets into water bodies through an inflow/outflow algorithm. Ocean Eng 105:160–175CrossRefGoogle Scholar
  4. 4.
    Aristodemo F, Tripepi G, Meringolo DD, Veltri P (2017) Solitary wave-induced forces on horizontal circular cylinders: laboratory experiments and SPH simulations. Coast Eng 129:17–35CrossRefGoogle Scholar
  5. 5.
    Capone T, Panizzo A, Monaghan JJ (2010) SPH modelling of water waves generated by submarine landslides. J Hydraul Res 48:80–84CrossRefGoogle Scholar
  6. 6.
    Chen YP, Li CW, Zhang CK (2008) Numerical modeling of a round jet discharged into random waves. Ocean Eng 35(1):77–89CrossRefGoogle Scholar
  7. 7.
    Chen YP, Li CW, Zhang CK, Xu ZS (2012) Numerical study of a round buoyant jet under the effect of JONSWAP random waves. China Ocean Eng. 26(2):235–250CrossRefGoogle Scholar
  8. 8.
    Chyan JM, Hwung HH (1993) On the interaction of a turbulent jet with waves. J Hydraul Res 31(6):791–810CrossRefGoogle Scholar
  9. 9.
    Dai HC, Wang LL (2005) Numerical study of submerged vertical plane jets under progressive water surface waves. China Ocean Eng 19(3):433–442Google Scholar
  10. 10.
    Dalrymple RA, Rogers BD (2006) Numerical modelling of waves with the SPH method. Coast Eng 53:131–147CrossRefGoogle Scholar
  11. 11.
    De Chowdhury S, Sannasiraj SA (2013) SPH Simulation of shallow water wave propagation. Ocean Eng 60(2013):41–52CrossRefGoogle Scholar
  12. 12.
    De Padova D, Mossa M, Sibilla S, Torti E (2013) 3D SPH modelling of hydraulic jump in a very large channel. J Hydraul Res 51:158–173CrossRefGoogle Scholar
  13. 13.
    De Padova D, Dalrymple RA, Mossa M (2014) Analysis of the artificial viscosity in the smoothed particle hydrodynamics modelling of regular waves. J Hydraul Res 52:836–848CrossRefGoogle Scholar
  14. 14.
    De Padova D, Mossa M, Sibilla S (2016) SPH numerical investigation of the velocity field and vorticity generation within a hydrofoil-induced spilling breaker. Environ Fluid Mech 16:267–287CrossRefGoogle Scholar
  15. 15.
    De Padova D, Mossa M, Sibilla S (2017) SPH modelling of hydraulic jump oscillations at an abrupt drop. Water 9(10):790. CrossRefGoogle Scholar
  16. 16.
    De Padova D, Mossa M, Sibilla S (2018) SPH numerical investigation of characteristics of hydraulic jumps. Environ Fluid Mech. CrossRefGoogle Scholar
  17. 17.
    De Padova D, Mossa M, Sibilla S (2018) SPH numerical investigation of the characteristics of an oscillating hydraulic jump at an abrupt drop. J Hydrodyn 30(1):106–113CrossRefGoogle Scholar
  18. 18.
    De Padova D, Brocchini M, Buriani F, Corvaro S, De Serio F, Mossa M, Sibilla S (2018) Experimental and numerical investigation of pre-breaking and breaking vorticity within a plunging breaker. Water 10:387. CrossRefGoogle Scholar
  19. 19.
    De Padova D, Mossa M, Sibilla S (2019) Numerical investigation of the behaviour of jets in a wave environment. J Hydraul Res. CrossRefGoogle Scholar
  20. 20.
    De Padova D, Ben Meftah M, De Serio F, Mossa M, Sibilla S (2019) Characteristics of breaking vorticity in spilling and plunging waves investigated numerically by SPH. Environ Fluid Mech. CrossRefGoogle Scholar
  21. 21.
    Espa P, Sibilla S, Gallati M (2008) SPH simulations of a vertical 2-D liquid jet introduced from the bottom of a free-surface rectangular tank. Adv Appl Fluid Mech 3:105–140Google Scholar
  22. 22.
    Federico I, Marrone S, Colagrossi A, Aristodemo F, Antuono M (2012) Simulating 2D open-channel flows through an SPH model. Eur J Mech B/Fluids 34:35–46CrossRefGoogle Scholar
  23. 23.
    Fischer HB, List EG, Koh RCY, Imberger J, Brooks NH (1979) Mixing in inland and coastal waters. Academic Press, New York, p 483Google Scholar
  24. 24.
    Gomez-Gesteira M, Rogers BD, Darlymple RA, Crespo AJC (2010) State-of-the-art of classical SPH for free-surface flows. J Hydraul Res 48:6–27CrossRefGoogle Scholar
  25. 25.
    Gotoh H, Shibihara T, Sakai T (2001) Sub-particle-scale model for the MPS method—Lagrangian flow model for hydraulic engineering. Comput Fluid Dyn J 9(4):339–347Google Scholar
  26. 26.
    Gotoh H, Shao S, Memita T (2004) SPH_LES model for numerical investigation of wave interaction with partially immersed breakwater. Coast Eng J 46(1):39–63CrossRefGoogle Scholar
  27. 27.
    Hasselbrink EF, Mungal MG (2001) Transverse jets and jet flames. part 1. Scaling laws for strong transverse jets. J Fluid Mech 443:1–25CrossRefGoogle Scholar
  28. 28.
    Hsiao SC, Hsu TW, Lin JF, Chang KA (2011) Mean and turbulence properties of a neutrally buoyant round jet in a wave environment. J Waterway Port Coast Ocean Eng 137(3):109–122CrossRefGoogle Scholar
  29. 29.
    Jirka GH, Harleman DRF (1979) “Stability and mixing of a vertical plane buoyant jet in confined depth. J Fluid Mech 94(2):275–304CrossRefGoogle Scholar
  30. 30.
    Koole R, Swan C (1994) Measurements of a 2-D non-buoyant jet in a wave environment. Coast Eng 24:151–169CrossRefGoogle Scholar
  31. 31.
    Launder BE, Spalding DB (1974) The numerical computation of turbulent flows. Comput Methods Appl Mech Eng 3:269–289CrossRefGoogle Scholar
  32. 32.
    Lo E, Shao S (2002) Simulation of near-shore solitary wave mechanics by an incompressible SPH method. Appl Ocean Res 24:275–286CrossRefGoogle Scholar
  33. 33.
    Manenti S, Pierobon E, Gallati M, Sibilla S, D’Alpaos L, Macchi EG, Todeschini S (2016) Vajont disaster: smoothed particle hydrodynamics modeling of the post-event 2D experiments. J Hydraul Eng 142(05015007):1–11Google Scholar
  34. 34.
    Makris CV, Memos CD, Krestenitis YN (2016) Numerical modeling of surf zone dynamics under weakly plunging breakers with SPH method. Ocean Model 98:12–35CrossRefGoogle Scholar
  35. 35.
    Marrone S, Colagrossi A, Park JS, Campana EF (2017) Challenges on the numerical prediction of slamming loads on LNG tank insulation panels. Ocean Eng 141:512–530CrossRefGoogle Scholar
  36. 36.
    Meringolo DD, Colagrossi A, Marrone S, Aristodemo F (2017) On the filtering of acoustic components in weakly-compressible SPH simulations. J Fluids Struct 70:1–23CrossRefGoogle Scholar
  37. 37.
    Monaghan JJ (1992) Smoothed particle hydrodynamics. Annu Rev Astron Astrophys 30:543–574CrossRefGoogle Scholar
  38. 38.
    Mori N, Chang KA (2003) Experimental study of a horizontal jet in a wavy environment. J Eng Mech 129(10):1149–1155CrossRefGoogle Scholar
  39. 39.
    Mossa M (2004) Experimental study on the interaction of non-buoyant jets and waves. J Hydraul Res 42(1):13–28CrossRefGoogle Scholar
  40. 40.
    Mossa M (2004) Behavior of Nonbuoyant Jets in a Wave Environment. J Hydraul Eng 130(7):704–717CrossRefGoogle Scholar
  41. 41.
    Muppidi S, Mahesh K (2005) Study of trajectories of jets in crossflow using direct numerical simulations. J Fluid Mech 530:81–100CrossRefGoogle Scholar
  42. 42.
    Papanicolaou PN, List EJ (1988) Investigation of round vertical turbulent buoyant jets. J Fluid Mech 195:341–391CrossRefGoogle Scholar
  43. 43.
    Rajaratnam N (1976) Turbulent jets. Elsevier, AmsterdamGoogle Scholar
  44. 44.
    Randles PW, Libersky LD (1996) Smoothed particle hydrodynamics: some recent improvements and applications. Comput Methods Appl Mech Eng 139(1–4):375–408CrossRefGoogle Scholar
  45. 45.
    Ryu Y, Chang KA, Mori N (2005) Dispersion of neutrally buoyant horizontal round jet in wave environment. J Hydraul Eng 131(12):1088–1097CrossRefGoogle Scholar
  46. 46.
    Shao S (2006) Incompressible SPH simulation of wave breaking and overtopping with turbulence modelling. Int J Num Method Fluids 50(5):597–621CrossRefGoogle Scholar
  47. 47.
    Shao S (2006) Simulation of breaking wave by SPH method coupled with k–ε model. J Hydraul Res 40(3):338–349CrossRefGoogle Scholar
  48. 48.
    Sibilla S (2015) An algorithm to improve consistency in smoothed particle hydrodynamics. Comput Fluids 118:148–158CrossRefGoogle Scholar
  49. 49.
    Subramanya K, Porey PD (1984) Trajectory of a turbulent cross jet. J Hydraul Res 22(5):343–354CrossRefGoogle Scholar
  50. 50.
    Ulrich C, Leonardi M, Rung T (2013) Multi-physics SPH simulation of complex marine-engineering hydrodynamic problems. Ocean Eng 64:109–121CrossRefGoogle Scholar
  51. 51.
    Violeau D (2012) Fluid mechanics and the SPH method: theory and applications. Oxford University Press, OxfordCrossRefGoogle Scholar
  52. 52.
    Violeau D, Issa R (2007) Numerical modelling of complex turbulent free-surface flows with the SPH method: an overview. Int J Numer Methods Fluids 53:277–304CrossRefGoogle Scholar
  53. 53.
    Wood IR, Bell RG, Wilkinson DL (1993) Ocean disposal of wastewater. Advances series on ocean engineering. World Scientific, Singapore, p 425CrossRefGoogle Scholar
  54. 54.
    Xu Z, Chen Y, Wang Y, Zhang C (2017) Near-field dilution of a turbulent jet discharged into coastal waters: effect of regular waves. Ocean Eng 140:29–42CrossRefGoogle Scholar
  55. 55.
    Yuan LL, Street RL (1998) Trajectory and entrainment of a round jet in crossflow. Phys Fluids 10(9):2323–2335CrossRefGoogle Scholar
  56. 56.
    Zijnem BG, Der Hegge Van (1958) Measuremnts at turbulence in a plane jet of air by the diffusion methos by the hot wire method. Appl Sci Res A 7:293–313Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Diana De Padova
    • 1
    Email author
  • Michele Mossa
    • 1
  • Stefano Sibilla
    • 2
  1. 1.Department of Civil Environmental, Land, Building Engineering and Chemistry (DICATECh)Polytechnic University of BariBariItaly
  2. 2.Department of Civil Engineering and Architecture (DICAr)University of PaviaPaviaItaly

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