Booms are often used to contain oil spills prior to various oil removal techniques. Under certain conditions, the oil droplets can leave the oil slick and enter the water. A simple balance of hydrodynamic forces on a droplet results in an instability criterion which determines whether the droplet will be swept past the boom or not. For viscous flows, it is shown here that the instability criterion consists of a term proportional to the pressure gradient along the boom, as in the potential-flow case, and a term that is inversely proportional to the Reynolds number, although the magnitude of this new term is found to be very small. The solution of viscous flow past an oil boom is obtained using the fractional-step method in a curvilinear coordinate system and the instability criterion is estimated. The influence of the approximate free-surface conditions, such as the rigid-lid no-slip, rigid-lid free-slip, and the exact free-surface condition, the instability criterion is also investigated. The different approximations of free-surface conditions are shown to influence the pressure distributions, thus resulting in different neutral stability curves.

1.
Ananthakrishnan, P., 1991, “Surface Waves Generated by a Translating Two-dimensional Body: Effects of Viscosity,” Ph.D. dissertation, University of California, Berkeley, CA.
2.
Chorin
A. J.
,
1968
, “
Numerical Solution of the Navier-Stokes Equations
,”
Mathematics of Computation
, Vol.
22
, No.
104
, pp.
745
762
.
3.
Ertekin, R. C., and Sundararaghavan, H., 1994, “Potential and Viscous Flows Past an Oil Boom: The Instability Problem,” Proceedings, 13th International Conference of Offshore Mechanics and Arctic Engineering, ASME, Vol. I, pp. 189–197.
4.
Ertekin
R. C.
, and
Sundararaghavan
H.
,
1995
, “
The Calculation of the Instability Criterion for a Uniform Viscous Flow Past an Oil Boom
,”
ASME Journal of Offshore Mechanics and Arctic Engineering
, Vol.
117
, pp.
24
29
.
5.
Fletcher, C. A. J., 1991, Computational Techniques for Fluid Dynamics, 2nd Edition, Vol. II, Springer-Verlag, Berlin, Germany.
6.
Grosenbaugh
M. A.
, and
Yeung
R. W.
,
1989
, “
Nonlinear Free-Surface Flow at a Two-Dimensional Bow
,”
Journal of Fluid Mechanics
, Vol.
209
, pp.
57
75
.
7.
Jones
W. T.
,
1972
, “
Instability at an Interface Between Oil and Floating Water
,”
ASME, Journal of Basic Engineering
, Vol.
94
, pp.
874
878
.
8.
Kordyban
E.
,
1990
, “
The Behavior of the Oil-Water Interface at a Planar Boom
,”
ASME JOURNAL OF ENERGY RESOURCES TECHNOLOGY
, Vol.
112
, pp.
90
95
.
9.
Kordyban
E.
,
1992
, “
The Effect of Waves on the Oil Slick at a Retention Boom
,”
ASME JOURNAL OF ENERGY RESOURCES TECHNOLOGY
, Vol.
114
, pp.
31
37
.
1.
Leibovich
S.
,
1976
, “
Oil Slick Instability and the Entrainment Failure of Oil Containment Booms
,”
ASME Journal of Fluids Engineering
, Vol.
98
, pp.
98
103
.
2.
Discussion
,
ASME Journal of Fluids Engineering
, Vol.
98
, pp.
103
105
.
1.
Shapiro
R.
,
1975
, “
Linear Filtering
,”
Mathematics of Computation
, Vol.
29
, No.
132
, pp.
1094
1097
.
This content is only available via PDF.
You do not currently have access to this content.