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Underwater sand bed erosion and internal jump formation by travelling plane jets

Published online by Cambridge University Press:  08 January 2008

A. T. H. PERNG  and
H. CAPART
A. T. H. PERNG
Affiliation:
Department of Civil Engineering and Hydrotech Research Institute, National Taiwan University, Taiwan
H. CAPART
Affiliation:
Department of Civil Engineering and Hydrotech Research Institute, National Taiwan University, Taiwan
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Abstract

Theory and experiments are used to investigate the water and sediment motion induced along a sea bed by travelling plane jets. Steadily moving jets are considered, and represent an idealization of the tools mounted on ships and remotely operated vehicles (ROVs) for injection dredging and trenching. The jet-induced turbulent currents simultaneously suspend sand from the bed and entrain water from the ambient. To describe these processes, a shallow-flow theory is proposed in which the turbulent current is assumed stratified into sediment-laden and sediment-free sublayers. The equations are written in curvilinear coordinates attached to the co-evolving bed profile. A sharp interface description is then adopted to account rigorously for mass and momentum exchanges between the bed, current and ambient, including their effects on the balance of mechanical energy. Travelling-wave solutions are obtained, in which the jet-induced current scours a trench of permanent form in a frame of reference moving with the jetting tool. Depending on the operating parameters, it is found that the sediment-laden current may remain supercritical throughout the trench, or be forced to undergo an internal hydraulic jump. These predictions are confirmed by laboratory experiments. For flows with or without jump in which the current remains attached to the bed, bottom profiles computed by the theory compare favourably with imaging measurements.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 595 , 25 January 2008 , pp. 1 - 43
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Abbott, M. B. 1979 Computational Hydraulics. Elements of the Theory of Free Surface Flows. Pitman.Google Scholar
Aderibigbe, O. O. & Rajaratnam, N. 1996 Erosion of loose beds by submerged circular impinging vertical turbulent jets. J. Hydraul. Res. 34, 19–33.Google Scholar
Bagnold, R. A. 1966 An approach to the sediment transport problem from general physics. US Geol. Surv. Prof. Paper 422-I.Google Scholar
Baines, P. G. 1995 Topographic Effects in Stratified Flows. Cambridge University Press.Google Scholar
Bakhmeteff, B. A. 1932 Hydraulics of Open Channels. McGraw-Hill.Google Scholar
Bombardelli, F. A. & Gioia, G. 2006 Scouring of granular beds by jet-driven axisymmetric turbulent cauldrons. Phys. Fluids 18, art. 088101, 1–4.Google Scholar
Chen, C. J. & Rodi, W. 1980 Vertical Buoyant Jets: A Review of Experimental Data. Pergamon.Google Scholar
Chen, H., Crosta, G. B. & Lee, C. F. 2006 Erosional effects on runout of fast landslides, debris flows and avalanches: a numerical investigation. Géotechnique 56 (5), 305–322.CrossRefGoogle Scholar
Crowe, C. T. 2000 On models for turbulence modulation in fluid–particle flows. Intl J. Multiphase Flow 26, 719–727.Google Scholar
Dronkers, J. 2005 Dynamics of Coastal Systems. World Scientific.Google Scholar
Durbin, P. A. & Pettersson Reif, B. A. 2001 Statistical Theory and Modeling for Turbulent Flows. Wiley.Google Scholar
Ellison, T. H. & Turner, J. S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6, 423–448.CrossRefGoogle Scholar
Fraccarollo, L. & Capart, H. 2002 Riemann wave description of erosional dam-break flows. J. Fluid Mech. 461, 183–228.Google Scholar
Fredsøe, J. & Deigaard, R. 1992 Mechanics of Coastal Sediment Transport. World Scientific.CrossRefGoogle Scholar
Gioia, G. & Bombardelli, F. A. 2005 Localized turbulent flows on scouring granular beds. Phys. Rev. Lett. 95, art. 014501, 1–4.Google Scholar
Guy, H. P., Simons, D. B., & Richardson, E. V. 1966 Summary of alluvial channel data from flume experiments, 1956–1961, Geol. Surv. Prof. Paper 462-I.Google Scholar
Hoffman, A. L. 1967 A single fluid model for shock formation in MHD shock tubes. J. Plasma Phys. 1, 193–207.CrossRefGoogle Scholar
Hogg, A. J., Huppert, H. E. & Dade, W. B. 1997 Erosion by planar turbulent wall jets. J. Fluid Mech. 338, 317–340.Google Scholar
Hopfinger, E. J., Kurniawan, A., Graf, W. H. & Lemmin, U. 2004 Sediment erosion by Görtler vortices: the scour-hole problem. J. Fluid Mech. 520, 327–342.Google Scholar
Hsu, T.-J., Jenkins, J. T. & Liu, P. L.-F. 2003 On two-phase sediment transport: dilute flow. J. Geophys. Res. 108 (C3), art. 3057, 1–14.Google Scholar
Hydon, P. E. 2000 Symmetry Methods for Differential Equations. Cambridge University Press.Google Scholar
Jirka, G. H. 2006 Integral model for turbulent buoyant jets in unbounded stratified flows. Part 2: Plane jet dynamics resulting from multiport diffuser jets. Environ. Fluid Mech. 6 (1), 43–100.Google Scholar
Knox, D., Krumholz, D. J. & Clausner, J. E. 1994 Water injection dredging in the United States. In Proc. Second Intl Conf. on Dredging and Dredged Material Placement (ed. McNair, E. Clark Jr,), pp. 847–856, ASCE.Google Scholar
Kobayashi, N. & Johnson, B. D. 2001 Sand suspension, storage, advection, and settling in surf and swash zones. J. Geophys. Res. 106 (C5), 9363–9376.Google Scholar
Kobayashi, N. & Tega, Y. 2002 Sand suspension and transport on equilibrium beach. ASCE J. Waterways, Port, Coastal, Ocean Engng 128 (6), 239–248.Google Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Dokl. Akad. Nauk SSSR 30, 301–305. [English translation Proc. R. Soc. Lond. A (1991) 434, 9–13.]Google Scholar
Kostic, S. & Parker, G. 2007 Conditions under which a supercritical turbidity current traverses an abrupt transition to vanishing bed slope without a hydraulic jump. J. Fluid Mech. 586, 119–145.Google Scholar
Machin, J. 2001 Recent Research on Cable Jet Burial. Perry Slingsby Systems, Jupiter, Florida.Google Scholar
Mastbergen, D. R. & Van den Berg, J. H. 2003 Breaching in fine sands and the generation of sustained turbidity currents in submarine canyons. Sedimentology 50, 625–637.Google Scholar
Mathieu, J. & Scott, J. 2000 An Introduction to Turbulent Flow. Cambridge University Press.CrossRefGoogle Scholar
Mazurek, K. A., Rajaratnam, N. & Sego, D. C. 2003 Scour of a cohesive soil by submerged plane turbulent wall jets. J. Hydraul. Res. 41 (2), 195–206.Google Scholar
van Melkebeek, E. 2002 Pre-trenching, pre-sweeping and backfilling for the 36” offshore pipeline project in Taiwan. Terra Aqua 87 (3), 19–25.Google Scholar
Mohamed, M. S. & McCorquodale, J. A. 1992 Short-term local scour. J. Hydraul. Res. 30 (5), 685–699.Google Scholar
Panchapakesan, N. R. & Lumley, J. L. 1993 Turbulence measurements in axisymmetric jets of air and helium. Part 1. Air jet. J. Fluid Mech. 246, 197–223.CrossRefGoogle Scholar
Parker, G., Fukushima, Y. & Pantin, H. M. 1986 Self-accelerating turbidity currents. J. Fluid Mech. 171, 145–181.Google Scholar
Perng, A. T. H. 2006 Trenching of underwater sand beds by steadily moving jets. PhD thesis, Graduate Institute of Civil Engineering, National Taiwan University.Google Scholar
Rajaratnam, N. 1981 Erosion by plane turbulent jets. J. Hydraul. Res. 19, 339–358.Google Scholar
Raubenheimer, B., Elgar, S. & Guza, R. T. 2004 Observations of swash zone velocities: a note on friction coefficients. J. Geophys. Res. 109 (C1), C01027, 1–8.Google Scholar
Richardson, J. F. & Zaki, W. N. 1954 Sedimentation and fluidisation, Part 1. Trans. Instn Chem. Engrs 32, 35–53.Google Scholar
van Rijn, L. C. 1984 Sediment transport, part II: suspended load transport. J. Hydraul. Engng ASCE 110 (11), 1613–1641.Google Scholar
Rouse, H. 1937 Modern conceptions of the mechanics of fluid turbulence. Trans. ASCE 102, 532–536.Google Scholar
Rouse, H. 1940 Criteria for similarity in the transportation of sediment. Proc. Hydraul. Conf., Univ. of Iowa Studies in Engineering, Bulletin 20, pp. 32–49.Google Scholar
Stein, O. R., Julien, P. Y. & Alonso, C. V. 1993 Mechanics of jet scour downstream of a headcut. J. Hydraul. Res. 31, 723–738.CrossRefGoogle Scholar
Stoker, J. J. 1957 Water waves. Interscience.Google Scholar
Strang, G. 1988 Linear Algebra and its Applications. Brooks/Cole.Google Scholar
Sumer, B. M., Kozakiewicz, A., Fredsøe, J. & Deigaard, R. 1996 Velocity and concentration profiles in sheet-flow layer of movable bed. J. Hydraul. Engng ASCE 122, 549–558.Google Scholar
Ten Cate, A., Derksen, J. J., Portela, L. M. & Van den Akker, H. E. A. 2004 Fully resolved simulations of colliding monodisperse spheres in forced isotropic turbulence. J. Fluid Mech. 519, 233–271.Google Scholar
Ungarish, M. 1993 Hydrodynamics of Suspensions. Springer.Google Scholar
Van den Berg, J. H., VanGelder, A. Gelder, A. & Mastbergen, D. R. 2002 The importance of breaching as a mechanism of subaqueous slope failure in fine sand. Sedimentology 49, 81–95.CrossRefGoogle Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.Google Scholar
Wilson, K. C. 1989 Mobile-bed friction at high shear stress. J. Hydraul. Engng ASCE 115, 825–830.CrossRefGoogle Scholar
Zanker, K. J. & Bonnington, S. T. 1967 Recent research development in hydraulic dredging. In Dredging (ed. Williams, J. T., Hargreaves, G. L. & Palmer, J. E. G.) pp. 81–96. Institution of Civil Engineers London.Google Scholar