Numerical Investigation of Turbulence Modulation by Sediment-Induced Stratification and Enhanced Viscosity in Oscillatory Flows
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 140, Issue 2
Abstract
Recent turbulence-resolving simulations of fine sediment transport in the oscillatory bottom boundary layer (OBBL) revealed the existence of a diverse range of flow regimes over muddy seabeds. Transitions between these flow regimes are caused by different degrees of sediment-induced stable density stratification in the OBBL. These transitions have critical implications for the role of wave resuspension in the delivery of fine sediment and hydrodynamic dissipation over muddy seabeds. This study further investigates the effect of Newtonian rheology, parameterized as a concentration-dependent effective viscosity, on turbulence modulation and the transition from turbulent to laminar states. Assuming small particle Stokes number, the equilibrium approximation is adopted to simplify the Eulerian two-phase flow governing equations. The resulting simplified equations are solved with a high-accuracy hybrid scheme in an idealized OBBL. A sixth-order centered compact finite difference is implemented in the vertical direction to solve the governing equations with a flow-dependent viscosity while the pseudospectral method is retained for two horizontal directions. At Stokes Reynolds number , simulations reveal that when rheology is incorporated, the enhanced effective viscosity can further attenuate the flow turbulence in addition to the well-known sediment-induced stable density stratification. Through the enhanced viscosity, the velocity gradient very near the bed is significantly reduced, which leads to much weaker turbulent production and the onset of laminarization. Although the sediment-induced stable density stratification is known to cause laminarization of bottom boundary layer flows, our preliminary finding that the enhanced viscosity via rheological stresses encourages the flow laminarization may be useful in explaining the field-observed large wave dissipation rate over muddy seabeds during the waning stage of a storm.
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Acknowledgments
This study is supported by U.S. Office of Naval Research (N00014-11-1-0270) and National Science Foundation (OCE-1130217) to the University of Delaware and National Science Foundation (OCE-1131016) to the University of Florida. Simulations presented in this paper are carried out on Chimera at the University of Delaware with funding supported by the National Science Foundation (CNS-0958512) and the Extreme Science and Engineering Discovery Environment, which is supported by National Science Foundation Grant No. TG-OCE100015.
References
Amoudry, L. O., and Souza, A. J. (2011). “Deterministic coastal morphological and sediment transport modeling: A review and discussion.” Rev. Geophys., 49(RG2002), 1–21.
Balachandar, S., and Eaton, J. K. (2010). “Turbulent dispersed multiphase flow.” Annu. Rev. Fluid Mech., 42, 111–133.
Cantero, M. I., Balachandar, S., Cantelli, A., Pirmez, C., and Parker, G. (2009). “Turbidity current with a roof: Direct numerical simulation of self-stratified turbulent channel flow driven by suspended sediment.” J. Geophys. Res. Oceans, 114(C3).
Cantero, M. I., Balachandar, S., and Garcia, M. H. (2008). “An Eulerian-Eulerian model for gravity currents driven by inertial particles.” Int. J. Multiphase Flow, 34(5), 484–501.
Cantero, M. I., Lee, J. R., Balachandar, S., and Garcia, M. H. (2007). “On the front velocity of gravity currents.” J. Fluid Mech., 586, 1–39.
Chakraborty, P., Balachandar, S., and Adrian, R. J. (2005). “On the relationship between local vortex identification schemes.” J. Fluid Mech., 535, 189–214.
Cortese, T., and Balachandar, S. (1995). “High performance spectral simulation of turbulent flows in massively parallel machines with distributed memory.” Int. J. Supercomput. Appl., 9(3), 187–204.
Dalrymple, R. A., and Liu, P. L. (1978). “Wave over soft mud beds: A two layer fluid mud model.” J. Phys. Oceanogr., 8(6), 1121–1131.
Eckelmann, H. (1974). “The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow.” J. Fluid Mech., 65(3), 439–459.
Einstein, A. (1906). “Eine neue bestimmung der moleküldimensionen.” Ann. Phys., 324(2), 298–306.
Ferry, J., and Balachandar, S. (2001). “A fast Eulerian method for disperse two phase flow.” Int. J. Multiphase Flow, 27(7), 1199–1226.
Hill, P. S., Milligan, T. G., and Geyer, W. R. (2000). “Controls on effective settling velocity in the Eel river flood plume.” Cont. Shelf Res., 20(16), 2095–2111.
Hino, M., Sawamoto, M., and Takasu, S. (1976). “Experiments on transition to turbulence in an oscillatory pipe flow.” J. Fluid Mech., 75(2), 193–207.
Kim, J., Moin, P., and Moser, R. (1987). “Turbulence statistics in fully developed channel at low Reynolds number.” J. Fluid Mech., 177, 133–166.
Kineke, G. C., Sternberg, R. W., Trowbridge, J. H., and Geyer, W. R. (1996). “Fluid-mud processes on the Amazon continental shelf.” Cont. Shelf Res., 16(5–6), 667–696.
Krieger, I. M., and Dougherty, T. J. (1959). “A mechanism for non-Newtonian flow in suspensions of rigid spheres.” Trans. Soc. Rheol., 3(1), 137–152.
Lele, S. K. (1992). “Compact finite difference schemes with spectral-like resolution.” J. Comput. Phys., 103(1), 16–42.
McAnally, M. H., et al. (2007). “Management of fluid mud in estuaries, bays and lakes. I: Present state of understanding on character and behavior.” J. Hydraul. Eng., 9–22.
Mehta, A. J. (1991). “Understanding fluid mud in a dynamic environment.” Geo-Mar. Lett., 11(3–4), 113–118.
Ozdemir, C. E., Hsu, T.-J., and Balachandar, S. (2010a). “A numerical investigation of fine particle laden flow in oscillatory channel: The role of particle-induced density stratification.” J. Fluid Mech., 665, 1–45.
Ozdemir, C. E., Hsu, T.-J., and Balachandar, S. (2010b). “Simulation of fine sediment transport in oscillatory boundary layer.” J. Hydro-environ. Res., 3(4), 247–259.
Ozdemir, C. E., Hsu, T.-J., and Balachandar, S. (2011). “A numerical investigation of lutocline dynamics and saturation of fine sediment in the oscillatory boundary layer.” J. Geophys. Res., 116(C9).
Sahin, C., Safak, I., Sheremet, A., and Mehta, A. J. (2011). “Observations on cohesive bed reworking by waves: Atchafalaya shelf, Louisiana.” J. Geophys. Res., 117(C9).
Sanford, L. P. (2008). “Modeling a dynamically varying mixed sediment bed with erosion, deposition, bioturbation, consolidation, and armoring.” Comput. Geosci., 34(10), 1263–1283.
Sherement, A., Jaramillo, S., Su, S.-F., Allison, M. A., and Holland, K. T. (2011). “Wave-mud interaction over the muddy Atchafalaya subaqueous clinoform, Louisiana, United States: Wave processes.” J. Geophys. Res., 116(C6).
Sherement, A., and Stone, G. W. (2003). “Observations of nearshore wave dissipation over muddy sea beds.” J. Geophys. Res., 108(C11).
Shukla, R. K., and Zhong, X.-L. (2005). “Derivation of high order compact finite difference schemes for non-uniform grid using polynomial interpolation.” J. Comput. Phys., 204(2), 404–429.
Spalart, P., and Baldwin, B. (1988). “Direct simulation of a turbulent oscillating boundary layer.” Turbulent shear flows, J. Andre, et al., eds., Vol. 6, Springer, New York, 417–440.
Traykovski, P. (2012). “Mechanisms of surface wave energy dissipation over a high concentration sediment suspension.” J. Geophys. Res., in press.
Traykovski, P., Geyer, W. R., Irish, J. D., and Lynch, J. F. (2000). “The role of wave-induced fluid mud flows for cross-shelf transport on the Eel river continental shelf.” Cont. Shelf Res., 20(16), 2113–2140.
Traykovski, P., Wiberg, P., and Geyer, W. R. (2007). “Observations and modeling of wave-supported sediment gravity flows on the Po prodelta and comparison to prior observations from the Eel shelf.” Cont. Shelf Res., 27(3–4), 375–399.
Vinzon, S. B., and Mehta, A. J. (2000). “Boundary layer effects due to suspended sediment in the Amazon river estuary.” Proc. Mar. Sci., 3, 359–372.
Wells, J. T., and Coleman, J. M. (1981). “Physical processes and fine grained sediment dynamics, coast of surinam, South America.” J. Sediment. Petrol., 51(4), 1069–1075.
Winterwerp, J. C. (1998). “A simple model for turbulence induced flocculation of cohesive sediment.” J. Hydraul. Res., 36(3), 309–326.
Winterwerp, J. C. (2001). “Stratification effects by cohesive and non-cohesive sediment.” J. Geophys. Res., 106(C10), 22559–22574.
Winterwerp, J. C., Manning, A. J., Martens, C., de Mulder, T., and Vanlede, J. (2006). “A heuristic formula for turbulence-induced flocculation of cohesive sediment.” Estuarine Coastal Shelf Sci., 68(1–2), 195–207.
Winterwerp, J. C., and van Kesteren, W. G. M. (2004). Introduction to the physics of cohesive sediment in the marine environment, Elsevier, New York.
Winterwerp, J. C., van Kesteren, W. G. M., van Prooijen, B., and Jacobs, W. (2012). “A conceptual frame work for shear flow induced erosion of soft cohesive sediment beds.” J. Geophys. Res., 117(C10), 1–17.
Wright, L. D., and Friedrichs, C. T. (2006). “Gravity-driven sediment transport on continental shelves: A status report.” Cont. Shelf Res., 26(17–18), 2092–2107.
Yu, X., Hsu, T.-J., and Balachandar, S. (2012). “A hybrid spectral-compact scheme for turbulence resolving simulation of fine sediment transport in the bottom boundary layer.” Rep. No. CACR-12-07, Center for Applied Coastal Research, Univ. of Delaware, Newark, DE.
Yu, X., Hsu, T.-J., and Balachandar, S. (2013). “A spectral-like turbulence-resolving scheme for fine sediment transport in bottom boundary layer.” Comput. Geosci., 61, 11–22.
Zhou, J., Adrian, R. J., Balachandar, S., and Kendall, T. M. (1999). “Mechanisms for generating coherent packets of hairpin vortices in channel flow.” J. Fluid Mech., 387, 353–396.
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 140 • Issue 2 • March 2014
Pages: 160 - 172
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Dec 15, 2012
Accepted: Aug 7, 2013
Published online: Aug 10, 2013
Published in print: Mar 1, 2014
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