Hostname: page-component-7b9c58cd5d-wdhn8 Total loading time: 0 Render date: 2025-03-15T08:10:10.309Z Has data issue: false hasContentIssue false
  • English
  • Français

High-fidelity simulations of bubble, droplet and spray formation in breaking waves

Published online by Cambridge University Press:  03 March 2016

Zhaoyuan Wang ,
Jianming Yang  and
Frederick Stern
Zhaoyuan Wang
Affiliation:
IIHR-Hydroscience and Engineering, University of Iowa, Iowa City, IA 52242, USA
Jianming Yang
Affiliation:
IIHR-Hydroscience and Engineering, University of Iowa, Iowa City, IA 52242, USA
Frederick Stern*
Affiliation:
IIHR-Hydroscience and Engineering, University of Iowa, Iowa City, IA 52242, USA
*
†Email address for correspondence: frederick-stern@uiowa.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

High-fidelity simulations of wave breaking processes are performed with a focus on the small-scale structures of breaking waves, such as bubble/droplet size distributions. Very large grids (up to 12 billion grid points) are used in order to resolve the bubbles/droplets in breaking waves at the scale of hundreds of micrometres. Wave breaking processes and spanwise three-dimensional interface structures are identified. It is speculated that the Görtler type centrifugal instability is likely more relevant to the plunging wave breaking instabilities. Detailed air entrainment and spray formation processes are shown. The bubble size distribution shows power-law scaling with two different slopes which are separated by the Hinze scale. The droplet size distribution also shows power-law scaling. The computational results compare well with the available experimental and computational data in the literature. Computational difficulties and challenges for large grid simulations are addressed.

JFM classification

Mathematical Foundations: Computational methods Drops and Bubbles: Drops and Bubbles Waves/Free-surface Flows: Wave breaking
Type
Papers
Information
Journal of Fluid Mechanics , Volume 792 , 10 April 2016 , pp. 307 - 327
Check for updates
Copyright
© 2016 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Andreas, E. L. 1998 A new sea spray generation function for wind speeds up to 32 m s $^{-1}$ . J. Phys. Oceanogr. 28, 2175–2184.2.0.CO;2>CrossRefGoogle Scholar
Aulisa, E., Manservisi, S., Scardovelli, R. & Zaleski, S. 2003 A geometrical area-preserving volume-of-fluid advection method. J. Comput. Phys. 192, 355–364.CrossRefGoogle Scholar
Brocchini, M. & Peregrine, D. H. 2001 The dynamics of strong turbulence at free surfaces. Part 1. Description. J. Fluid Mech. 449, 225–254.CrossRefGoogle Scholar
Brucker, K. A., O’Shea, T. T., Dommermuth, D. G. & Adams, P. 2010 Three-dimensional simulations of deep-water breaking waves. In 28th Symposium on Naval Hydrodynamics, Pasadena, CA, U.S. Office of Naval Research (ONR).Google Scholar
Cartmill, J. & Su, M. 1993 Bubble size distribution under saltwater and freshwater breaking waves. Dyn. Atmos. Oceans 20, 25–31.CrossRefGoogle Scholar
Chen, G., Kharif, C., Zaleski, S. & Li, J. 1999 Two-dimensional Navier–Stokes simulation of breaking waves. Phys. Fluids 11, 121–133.CrossRefGoogle Scholar
Choi, H. & Moin, P. 1994 Effects of the computational time step on numerical solutions of turbulent flow. J. Comput. Phys. 113, 1–4.CrossRefGoogle Scholar
Clift, R., Grace, J. R. & Webber, M. E. 1978 Bubbles, Drops, and Particles. Academic.Google Scholar
Deane, G. B. & Stokes, M. D. 2002 Scale dependency of bubble creation mechanisms in breaking waves. Nature 418, 839–844.CrossRefGoogle ScholarPubMed
Derakhti, M. & Kirby, J. T. 2014 Bubble entrainment and liquid–bubble interaction under unsteady breaking waves. J. Fluid Mech. 761, 464–506.CrossRefGoogle Scholar
Drazen, D. A., Melville, W. K. & Lenain, L. 2008 Inertial scaling of dissipation in unsteady breaking waves. J. Fluid Mech. 611, 307–332.CrossRefGoogle Scholar
Duncan, J. H. 1981 An experimental investigation of breaking waves produced by a towed hydrofoil. Proc. R. Soc. Lond. A 377 (1770), 331–348.Google Scholar
Falgout, R. D., Jones, J. E. & Yang, U. M. 2006 The design and implementation of hypre, a library of parallel high performance preconditioners. In Numerical Solution of Partial Differential Equations on Parallel Computers (ed. Bruaset, A. & Tveito, A.), Lecture Notes in Computational Science and Engineering, vol. 51, pp. 267–294. Springer.CrossRefGoogle Scholar
Garrett, C., Li, M. & Farmer, D. 2000 The connection between bubble size spectra and energy dissipation rates in the upper ocean. J. Phys. Oceanogr. 30, 2163–2171.2.0.CO;2>CrossRefGoogle Scholar
Gui, L., Yoon, H. & Stern, F.2014a Experimental and theoretical investigation of instabilities for flow over a bump in a shallow water flume with steady downstream wave train. Tech. Rep. 487. IIHR, The University of Iowa.Google Scholar
Gui, L., Yoon, H. & Stern, F. 2014b Techniques for measuring bulge-car pattern of free surface deformation and related velocity distribution in shallow water flow over a bump. Exp. Fluids 55 (4), 1721.CrossRefGoogle Scholar
Herrmann, M. 2010 A parallel Eulerian interface tracking/Lagrangian point particle multi-scale coupling procedure. J. Comput. Phys. 229 (3), 745–759.CrossRefGoogle Scholar
Hinze, J. O. 1955 Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J. 1 (3), 289–295.CrossRefGoogle Scholar
Iafrati, A. 2009 Numerical study of the effects of the breaking intensity on wave breaking flows. J. Fluid Mech. 622, 371–411.CrossRefGoogle Scholar
Iafrati, A. 2010 Air–water interaction in breaking wave events: quantitative estimates of drops and bubbles. In 28th Symposium on Naval Hydrodynamics, Pasadena, CA, U.S. Office of Naval Research (ONR).Google Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Jiang, G.-S. & Shu, C.-W. 1996 Efficient implementation of weighted {ENO} schemes. J. Comput. Phys. 126 (1), 202–228.CrossRefGoogle Scholar
Kang, D., Ghosh, S., Reins, G., Koo, B., Wang, Z. & Stern, F. 2012 Impulsive plunging wave breaking downstream of a bump in a shallow water flume. Part I. Experimental observations. J. Fluids Struct. 32, 104–120.CrossRefGoogle Scholar
Kiger, K. T. & Duncan, J. H. 2012 Air entrainment mechanisms in plunging jets and breaking waves. Annu. Rev. Fluid Mech. 44, 563–596.CrossRefGoogle Scholar
Koo, B., Wang, Z., Yang, J. & Stern, F. 2012 Impulsive plunging wave breaking downstream of a bump in a shallow water flume. Part II. Numerical simulations. J. Fluids Struct. 32, 121–134.CrossRefGoogle Scholar
Leonard, B. P. 1979 A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Meth. Appl. Mech. Engng 19 (1), 59–98.CrossRefGoogle Scholar
Lhuissier, H. & Villermaux, E. 2012 Bursting bubble aerosols. J. Fluid Mech. 696, 5–44.CrossRefGoogle Scholar
Li, X., Arienti, M., Soteriou, M. C. & Sussman, M. M.2010 Towards an efficient, high-fidelity methodology for liquid jet atomization computations. AIAA Paper 2010-210.Google Scholar
Loewen, M. R., ODor, M. A. & Skafel, M. G. 1996 Bubbles entrained by mechanically generated breaking waves. J. Geophys. Res. 101, 20759–20820.CrossRefGoogle Scholar
Longuet-Higgins, M. 1995 On the disintegration of the jet in a plunging breaker. J. Phys. Oceanogr. 25, 2458–2462.2.0.CO;2>CrossRefGoogle Scholar
Lubin, P. & Glockner, S. 2015 Numerical simulations of three-dimensional plunging breaking waves: generation and evolution of aerated vortex filaments. J. Fluid Mech. 767, 364–393.CrossRefGoogle Scholar
Lubin, P., Vincent, S., Abadie, S. & Caltagirone, J. P. 2006 Three-dimensional large eddy simulation of air entrainment under plunging breaking waves. Coast. Engng 53, 631–655.CrossRefGoogle Scholar
Mori, N. & Kakuno, S. 2008 Aeration and bubble measurements of coastal breaking waves. Fluid Dyn. Res. 40 (7–8), 616–626.CrossRefGoogle Scholar
Saric, W. S. 1994 Görtler vortices. Annu. Rev. Fluid Mech. 26, 379–409.CrossRefGoogle Scholar
Saruwatari, A., Watanabe, Y. & Ingram, D. M. 2009 Scarifying and fingering surfaces of plunging jets. Coast. Engng 56 (1112), 1109–1122.CrossRefGoogle Scholar
Scardovelli, R. & Zaleski, S. 2003 Interface reconstruction with least-square fit and split Eulerian–Lagrangian advection. Intl J. Numer. Meth. Fluids 41, 251–274.CrossRefGoogle Scholar
Soloviev, A. & Lukas, R. 2006 The Near-Surface Layer of the Ocean: Structure, Dynamics and Applications. Springer.Google Scholar
Suh, J., Yang, J. & Stern, F. 2011 The effect of air–water interface on the vortex shedding from a vertical circular cylinder. J. Fluids Struct. 27, 1–22.CrossRefGoogle Scholar
Tavakolinejad, M.2010 Air bubble entrainment by breaking bow waves simulated by a $2d+t$ technique. PhD thesis, University of Maryland.Google Scholar
Towle, D. M.2014 Spray droplet generation by breaking water waves. Master’s thesis, University of Maryland.Google Scholar
Veron, F., Hopkins, C., Harrison, E. L. & Mueller, J. A. 2012 Sea spray spume droplet production in high wind speeds. Geophys. Res. Lett. 39 (16), l16602.CrossRefGoogle Scholar
Wang, Z., Suh, J., Yang, J. & Stern, F.2012b Sharp interface LES of breaking waves by an interface piercing body in orthogonal curvilinear coordinates. AIAA Paper 2012-1111.CrossRefGoogle Scholar
Wang, Z., Yang, J., Koo, B. & Stern, F. 2009a A coupled level set and volume-of-fluid method for sharp interface simulation of plunging breaking waves. Intl J. Multiphase Flow 35, 227–246.CrossRefGoogle Scholar
Wang, Z., Yang, J. & Stern, F. 2009b An improved particle correction procedure for the particle level set method. J. Comput. Phys. 228 (16), 5819–5837.CrossRefGoogle Scholar
Wang, Z., Yang, J. & Stern, F.2012a High-fidelity simulations of bubble, droplet, and spray formation in breaking waves. HPC Insights, Fall Issue, 5–7.Google Scholar
Wang, Z., Yang, J. & Stern, F. 2012c A new volume-of-fluid method with a constructed distance function on general structured grids. J. Comput. Phys. 231, 3703–3722.CrossRefGoogle Scholar
Wang, Z., Yang, J. & Stern, F. 2012d A simple and conservative operator-splitting semi-Lagrangian volume-of-fluid advection scheme. J. Comput. Phys. 231, 4981–4992.CrossRefGoogle Scholar
Watanabe, Y. & Saeki, H. 2002 Velocity field after wave breaking. Intl J. Numer. Meth. Fluids 39, 607–637.CrossRefGoogle Scholar
Watanabe, Y., Saeki, H. & Hosking, R. 2005 Three-dimensional vortex structures under breaking waves. J. Fluid Mech. 545, 291–328.CrossRefGoogle Scholar
Yang, J., Bhushan, S., Suh, J., Wang, Z., Koo, B., Sakamoto, N. & Xing, T. 2008 Large-eddy simulation of ship flows with wall-layer models on cartesian grids. In 27th Symposium on Naval Hydrodynamics, Seoul, Korea, U.S. Office of Naval Research (ONR).Google Scholar
Yang, J. & Stern, F.2007 A sharp interface method for two-phase flows interacting with moving bodies. AIAA Paper 2007-4578.CrossRefGoogle Scholar
Yang, J. & Stern, F. 2009 Sharp interface immersed-boundary/level-set method for wave–body interactions. J. Comput. Phys. 228, 6590–6616.CrossRefGoogle Scholar
Zhou, Z., Sangermano, J., Hsu, T.-J. & Ting, F. C. K. 2014 A numerical investigation of wave-breaking-induced turbulent coherent structure under a solitary wave. J. Geophys. Res. 119 (10), 6952–6973.CrossRefGoogle Scholar

Wang et al. supplementary movie

Simulation of Stokes wave breaking process using 3.2 billion grid points.

Download Wang et al. supplementary movie(Video)
Video 10.7 MB

Wang et al. supplementary movie

Simulation of Stokes wave breaking process using 3.2 billion grid points.

Download Wang et al. supplementary movie(Video)
Video 4 MB