Research Papers: Offshore Technology

A Numerical Study on Stratified Shear Layers With Relevance to Oil-Boom Failure

[+] Author and Article Information
David Kristiansen

SINTEF Fisheries and Aquaculture AS,
Trondheim 7465, Norway
e-mail: david.kristiansen@sintef.no

Odd M. Faltinsen

Centre for Autonomous Marine Operations
and Systems (AMOS),
Department of Marine Technology,
Trondheim 7491, Norway

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received June 15, 2014; final manuscript received April 29, 2015; published online May 28, 2015. Assoc. Editor: Sergio H. Sphaier.

J. Offshore Mech. Arct. Eng 137(4), 041301 (Aug 01, 2015) (8 pages) Paper No: OMAE-14-1062; doi: 10.1115/1.4030527 History: Received June 15, 2014; Revised April 29, 2015; Online May 28, 2015

Interface dynamics of two-phase flow, with relevance for leakage of oil retained by mechanical oil barriers, is studied by means of a two-dimensional (2D) lattice-Boltzmann method (LBM) combined with a phase-field model for interface capturing. A multirelaxation-time (MRT) model of the collision process is used to obtain a numerically stable model at high Reynolds number flow. In the phase-field model, the interface is given a finite but small thickness, where the fluid properties vary continuously across a thin interface layer. Surface tension is modeled as a volume force in the transition layer. The numerical model is implemented for simulations with the graphic processing unit (GPU) of a desktop personal computer. Verification tests of the model are presented. The model is then applied to simulate gravity currents (GCs) obtained from a lock-exchange configuration, using fluid parameters relevant for those of oil and water. Interface instability phenomena are observed, and obtained numerical results are in good agreement with theory. This work demonstrates that the numerical model presented can be used as a numerical tool for studies of stratified shear flows with relevance to oil-boom failure.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Fingas, M., 2001, The Basics of Oil Spill Cleanup, 2 ed., CRC Press LCC, Boca Raton, Chap. 6.
Delvigne, G. A. L., 1989, “Barrier Failure by Critical Accumulation of Viscous Oil,” Int. Oil Spill Conf. Proc., 1989(1), pp. 143–148 [CrossRef].
Leibovich, S., 1976, “Oil Slick Instability and Entrainment Failure of Oil Containment Booms,” ASME J. Fluids Eng., 98(1), pp. 98–103. [CrossRef]
Thorpe, S. A., 1969, “Experiments on the Instability of Stratified Shear Flows: Immiscible Fluids,” J. Fluid Mech., 39(1), pp. 25–48. [CrossRef]
Holmboe, J., 1962, “On the Behavior of Symmetric Waves in Stratified Shear Layers,” Geophys. Publ., 24, pp. 67–113.
Browand, F. K., and Winant, C. D., 1973, “Laboratory Observations of Shear-Layer Instability in a Stratified Fluid,” Boundary-Layer Meteorol., 5(1–2), pp. 67–77. [CrossRef]
Lawrence, G. A., Browand, F. K., and Redekopp, L. G., 1991, “The Stability of a Sheared Density Interface,” Phys. Fluids, A3(10), pp. 2360–2370 [CrossRef].
Pouliquen, O., Chomaz, J., and Huerre, P., 1994, “Propagating Holmboe Waves at the Interface Between Two Immiscible Fluids,” J. Fluid Mech., 266, pp. 277–302. [CrossRef]
Smyth, W. D., and Moum, J. N., 2000, “Length Scales of Turbulence in Stably Stratified Mixing Layers,” Phys. Fluids, 12(6), pp. 1327–1342. [CrossRef]
Grilli, S. T., Hu, Z., Spalding, M. L., and Liang, D., 1997, “Numerical Modeling of Oil Containment by a Boom/Barrier System: Phase II,” Department of Ocean Engineering, University of Rhode Island, Kingston, RI.
He, X., and Luo, L.-S., 1997, “Lattice Boltzmann Model for the Incompressible Navier–Stokes Equation,” J. Stat. Phys., 88(3–4), pp. 927–944. [CrossRef]
Bhatnagar, P. L., Gross, E. P., and Krook, M., 1954, “A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems,” Phys. Rev., 94(3), pp. 511–525. [CrossRef]
Lallemand, P., and Luo, L.-S., 2000, “Theory of the Lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability,” NASA Langley Research Center, Hampton, VA, Technical Report No. 2000-17.
Brackbill, J. U., Kothe, D. B., and Zemack, C., 1992, “A Continuum Method for Modeling Surface Tension,” J. Comput. Phys., 100(2), pp. 335–354. [CrossRef]
Jacqmin, D., 1999, “Calculation of Two-Phase Navier–Stokes Flows Using Phase-Field Modeling,” J. Comput. Phys., 155(1), pp. 96–127. [CrossRef]
Cahn, J. W., and Hilliard, J. E., 1958, “Free Energy of a Nonuniform System. I. Interfacial Free Energy,” J. Chem. Phys., 28(2), pp. 258–267. [CrossRef]
Huang, J. J., Shu, C., and Chew, Y. T., 2009, “Mobility-Dependent Bifurcations in Capillarity-Driven Two-Phase Fluid Systems by Using a Lattice Boltzmann Phase-Field Model,” Int. J. Numer. Methods Fluids, 60(2), pp. 203–225. [CrossRef]
Fakhari, A., and Rahimian, M. H., 2010, “Phase-Field Modeling by the Method of Lattice Boltzmann Equations,” Phys. Rev. E, 81(3 Pt. 2), p. 036707. [CrossRef]
Shao, J. Y., Shu, C., and Chew, Y. T., 2012, “A Hybrid Phase-Field Based Lattice-Boltzmann Method for Contact Line Dynamics,” Int. J. Mod. Phys.: Conf. Ser., 19, pp. 50–61 [CrossRef].
He, X., Shan, X., and Doolen, G., 1998, “Discrete Boltzmann Equation Model for Nonideal Gases,” Phys. Rev., 57(1), pp. 13–16 [CrossRef].
He, X., Chen, S., and Zhang, R., 1999, “A Lattice Boltzmann Scheme for Incompressible Multiphase Flow and Its Application in Simulation of Rayleigh-Taylor Instability,” J. Comput. Phys., 152(2), pp. 642–663. [CrossRef]
He, X., and Luo, L.-S., 1997, “Theory of the Lattice Boltzmann Method: From the Boltzmann Equation to the Lattice Boltzmann Equation,” Phys. Rev., 56(6), pp. 6811–6817 [CrossRef].
Pooley, C. M., and Furtado, K., 2008, “Eliminating Spurious Velocities in the Free-Energy Lattice Boltzmann Method,” Phys. Rev. E, 77(4), p. 046702. [CrossRef]
Schlichting, H., and Gersten, K., 2000, Boundary Layer Theory, Springer, Berlin, pp. 126–128 [CrossRef].
Lamb, H., 1932, Hydrodynamics, 6th ed., Dover Publications, New York, pp. 461–462.
Lowe, R. J., Rottman, J. W., and Linden, P. F., 2005, “The Non-Boussinesq Lock-Exchange Problem. Part 1. Theory and Experiments,” J. Fluid Mech., 537, pp. 101–124. [CrossRef]
Härtel, C., Eckart, M., and 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, pp. 189–212. [CrossRef]
Benjamin, T. B., 1968, “Gravity Currents and Related Phenomena,” J. Fluid Mech., 31(Pt. 2), pp. 209–248. [CrossRef]
Marino, B. M., Thomas, L. P., and Linden, P. F., 2005, “The Front Condition for Gravity Currents,” J. Fluid Mech., 536, pp. 49–78. [CrossRef]


Grahic Jump Location
Fig. 1

Stokes first problem. Comparison of velocity profile obtained from present numerical simulations with theoretical profile for nondimensional times T=tU2/ν.

Grahic Jump Location
Fig. 2

Pressure difference inside and outside a stationary bubble. Comparison between numerical simulations and theory.

Grahic Jump Location
Fig. 3

Wave celerity for gravity capillary waves. Comparison between numerical simulations and theory.

Grahic Jump Location
Fig. 4

Vorticity field in units of s-1 for different instability modes of stratified shear layers. The interface is shown as a solid line. (a) KH mode: J = 0.09 and β = −0.074, (b) symmetric Holmboe mode: J = 0.26 and β = −0.074, and (c) asymmetric Holmboe mode: J = 0.26 and β = −0.57.

Grahic Jump Location
Fig. 5

Interface profiles and vorticity field from numerical simulations of lock-exchange test with different density ratios γ and asymmetry parameter β. Results are shown at nondimensional times tg(1-γ)/H={0.586,1.17,1.76,2.34,2.93}: (a) γ = 0.993 and β = −0.074, (b) γ = 0.993 and β = −0.57, (c) γ = 0.950 and β = −0.074, (d) γ = 0.950 and β = −0.57, (e) γ = 0.870 and β = −0.074, and (f) γ = 0.870 and β = −0.57

Grahic Jump Location
Fig. 6

Froude number of GCs. Comparison between numerical simulations, experiments, and theory.




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In