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Interaction between waves and gravity currents: description of turbulence in a simple numerical model

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Abstract

Effects of surface waves on gravity current propagation are studied by means of a numerical model. The adopted modeling approach couples a Boussinesq-type of model for surface waves and a gravity current model for stratified flows. In particular two different turbulence closure models are introduced which take into account subgrid turbulence and an additional depth-constant eddy-viscosity. The turbulence parameters are calibrated by means of experimental data on the time evolution of the heavy front, obtained both in the absence and in the presence of regular surface waves. Velocity fields, heavy and light front position, shear stresses, vorticity and entrainment calculated by the model are analyzed. The turbulence closure which includes both uniform and Smagorinsky type eddy viscosity allows a better description of the actual gravity current propagation. In particular, the results highlight the fact that the presence of the oscillatory motion causes, simultaneously, a reduction in turbulence and an increase in the mixing of heavy and light fluids. Such a result is in agreement with the experimental observations.

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References

  1. Briganti R, Musumeci RE, Bellotti G, Brocchini M, Foti E (2004) Boussinesq modeling of breaking waves: description of turbulence. J Geophys Res 109:C07015

    Article  Google Scholar 

  2. Cavallaro L, Scandura P, Foti E (2011) Turbulence-induced steady streaming in an oscillating boundary layer: on the reliability of turbulence closure models. Coast Eng 58:290–304. doi:10.1016/j.coastaleng.2010.10.001

    Article  Google Scholar 

  3. Chowdhury M, Testik F (2014) A review of gravity currents formed by submerged single-port discharges in inland and coastal waters. Environ Fluid Mech 14:265–293. doi:10.1007/s10652-014-9334-7

    Article  Google Scholar 

  4. Dean R, Dalrymple R (1991) Water wave mechanics for engineers and scientists. World Scientific, Singapore

    Book  Google Scholar 

  5. Germano M, Piomelli U, Moin P, Cabot WH (1991) A dynamic subgrid scale eddy viscosity model. Phys Fluids A 3:1760–1765. doi:10.1063/1.857955

    Article  Google Scholar 

  6. Hallworth MA, Phillips JC, Huppert HE, Sparks RSJ (1993) Entrainment in turbulent gravity currents. Nature 362:829–831. doi:10.1038/362829a0

    Article  Google Scholar 

  7. Härtel C, Meiburg E, Necker F (2000) Analysis and direct numerical simulation of the flow at a gravity-current head. Part 1. Flow topology and front speed for slip and no-slip boundaries. J Fluid Mech 418:189–212

    Article  Google Scholar 

  8. Huppert HE, Simpson JE (1980) The slumping of gravity currents. J Fluid Mech 99(4):785–799

    Article  Google Scholar 

  9. La Rocca M, Adduce C, Lombardi V, Sciortino G, Hinkelmann R (2012) Development of a lattice boltzmann method for two-layer shallow-water flow. Int J Numer Methods Fluids 70:1048–1072. doi:10.1002/fld.2742

    Article  Google Scholar 

  10. La Rocca M, Adduce C, Sciortino G, Pinzon AB (2008) Experimental and numerical simulation of the three-dimensional gravity currents on smooth and rough bottom. Phys Fluids 20:106603. doi:10.1063/1.3002381

    Article  Google Scholar 

  11. La Rocca M, Montessori A, Prestininzi P, Musumeci RE (2015) Influence of surface waves on the propagation of a gravity current. In: Proceedings of the twenty-fifth (2015) International Ocean and Polar Engineering Conference, vol 3. International Society of Offshore and Polar Engineers (ISOPE), p 476

  12. Lo Re C, Musumeci RE, Foti E (2012) A shoreline boundary condition for a highly nonlinear boussinesq model for breaking waves. Coast Eng 60:41–52. doi:10.1016/j.coastaleng.2011.08.003

    Article  Google Scholar 

  13. Lodahl C, Sumer B, Fredsøe J (1998) Turbulent combined oscillatory flow and current in a pipe. J Fluid Mech 373:313–348

    Article  Google Scholar 

  14. Longuet-Higgins MS (1953) Mass transport in water waves. Philos Trans R Soc Lond A Math Phys Eng Sci 245(903):535–581. doi:10.1098/rsta.1953.0006

    Article  Google Scholar 

  15. Longuet-Higgins MS (1970) Longshore currents generated by obliquely incident sea waves, 1. J Geophys Res 75:6778–6801

    Article  Google Scholar 

  16. Madsen PA, Schäffer HA (1998) Higher-order boussinesq-type equations for surface gravity waves: derivation and analysis. Philos Trans R Soc Lond A 356:3123–3184

    Article  Google Scholar 

  17. Mei CC, Stiassnie M, Yue DKP (2005) Theory and aapplication of ocean surface waves. Part 2: nonlinear aspects. World Scientific, Singapore

    Google Scholar 

  18. Musumeci R, Cavallaro L, Foti E, Scandura P, Blondeaux P (2006) Waves plus currents crossing at right angle: experimental investigation. J Geophys Res 111(C07019):1–19

    Google Scholar 

  19. Musumeci RE, Svendsen IA, Veeramony J (2005) The flow in the surf zone: a fully nonlinear boussinesq-type of approach. Coast Eng 52:565–598

    Article  Google Scholar 

  20. Musumeci RE, Viviano A, Foti E (2017) Influence of regular surface waves on the propagation of gravity currents: experimental and numerical modelling. J Hydraul Eng. doi:10.1061/(ASCE)HY.1943-7900.0001308

    Google Scholar 

  21. Ng C-O, Fu S-C (2002) On the propagation of a two-dimensional viscous density current under surface waves. Phys Fluids 14(3):970–984. doi:10.1063/1.1448348

    Article  Google Scholar 

  22. Nogueira HIS, Adduce C, Alves E, Franca MJ (2013) Analysis of lock-exchange gravity currents over smooth and rough beds. J Hydraul Res 51(4):417–431

    Article  Google Scholar 

  23. Nogueira HIS, Adduce C, Alves E, Franca MJ (2014) Dynamics of the head of gravity currents. Environ Fluid Mech 14:519–540. doi:10.1007/s10652-013-9315-2

    Article  Google Scholar 

  24. Ooi S, Costantinescu G, Weber L (2007) A numerical study of intrusive compositional gravity currents. Phys Fluids 19:076,602-1–076,602-14

    Article  Google Scholar 

  25. Ooi SK, Constantinescu G, Weber LJ (2007) 2D large-eddy simulation of lock-exchange gravity current flows at high Grashof numbers. J Hydraul Eng 133(9):1037–1047. doi:10.1061/(ASCE)0733-9429(2007)133:9(1037)

    Article  Google Scholar 

  26. Ottolenghi L, Adduce C, Inghilesi R, Armenio V, Roman F (2016) Entrainment and mixing in unsteady gravity currents. J Hydraul Res 54(5):541–557. doi:10.1080/00221686.2016.1174961

    Article  Google Scholar 

  27. Ottolenghi L, Adduce C, Inghilesi R, Roman F, Armenio V (2016) Mixing in lock-release gravity currents propagating up a slope. Phys Fluids 28(5):056604. doi:10.1063/1.4948760

    Article  Google Scholar 

  28. Press WH, Flannery BP, Teukolsky SA, Vetterling WT (1992) Numerical recipes in Fortran, 2nd edn. Cambridge University Press, Cambridge

    Google Scholar 

  29. Prestininzi P, Sciortino G, La Rocca M (2013) On the effect of the intrinsic viscosity in a two-layer shallow water lattice boltzmann model of axisymmetric density currents. J Hydraul Res 51(6):668–680. doi:10.1080/00221686.2013.819532

    Article  Google Scholar 

  30. Robinson TO, Eames I, Simons R (2013) Dense gravity currents moving beneath progressive free-surface water waves. J Fluid Mech 725:588–610

    Article  Google Scholar 

  31. Smagorinsky J (1964) Implications of dynamical modelling of the general circulation on long-range forecasting. In: WMO-IUGG symposium on research and development aspects of long-range forecasting, WMO Technical Note 62, vol 62, pp 131–137

  32. Stancanelli LM, Musumeci RE, Cavallaro L, Foti E (2017) A small scale pressure retarded osmosis power plant: dynamics of the brackish effluent discharge along the coast. Ocean Eng 130:417–428. doi:10.1016/j.oceaneng.2016.11.045

    Article  Google Scholar 

  33. Svendsen IA, Madsen PA, Hansen JB (1978) Wave characteristics in the surf zone. In: Proceedings of 16th coastal engineering conference, vol I (Chap 29), pp 520–539 Hamburg

  34. Ungarish M (2009) An introduction to gravity currents and intrusions. CRC Press, Boca Raton

    Book  Google Scholar 

  35. van Dongeren AR, Svendsen IA (1997) Absorbing-generating boundary condition for shallow water models. J Waterw Port Coast Ocean Eng 123(6):303–313

    Article  Google Scholar 

  36. Veeramony J, Svendsen IA (2000) The flow in the surf-zone waves. Coast Eng 39:93–122

    Article  Google Scholar 

  37. Viviano A, Musumeci RE, Foti E (2015) A nonlinear rotational, quasi-2DH numerical model for spilling wave propagation. Appl Math Model 39:1099–1118. doi:10.1016/j.apm.2014.07.030

    Article  Google Scholar 

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Acknowledgements

This work has been partly funded by the Italian Ministry of Education, Universities and Research MIUR through the Research projects of significant national interest—PRIN 2010–2011—project name HYDROCAR (cod. \(20104J2Y8M\_003\)) and the PRIN 2012 Project ”Hydro-morphodynamics modelling of coastal processes for engineering purposes” (cod. 2012BYTPR5), through the PO FESR SICILIA 2007–2013 Axis IV Operational Objective 4.1.2 Intervention lines 4.1.2.A project MedNETNA and through the EU funded project HYDRALAB PLUS (Proposal Number 64110).

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Authors and Affiliations

  1. Department Civil Engineering and Architecture, University of Catania, Catania, Italy

    Antonino Viviano, Rosaria E. Musumeci & Enrico Foti

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  1. Antonino Viviano
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  2. Rosaria E. Musumeci
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  3. Enrico Foti
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Correspondence to Antonino Viviano.

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Viviano, A., Musumeci, R.E. & Foti, E. Interaction between waves and gravity currents: description of turbulence in a simple numerical model. Environ Fluid Mech 18, 117–148 (2018). https://doi.org/10.1007/s10652-017-9527-y

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  • DOI: https://doi.org/10.1007/s10652-017-9527-y

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