Hostname: page-component-7479d7b7d-pfhbr Total loading time: 0 Render date: 2024-07-15T20:12:44.240Z Has data issue: false hasContentIssue false
  • English
  • Français

A numerical investigation of acceleration-skewed oscillatory flows

Published online by Cambridge University Press:  04 November 2016

Pietro Scandura ,
Carla Faraci  and
Enrico Foti
Pietro Scandura*
Affiliation:
Department of Civil Engineering and Architecture, University of Catania, Via Santa Sofia 64, 95123 Catania, Italy
Carla Faraci
Affiliation:
Department of Engineering, University of Messina, Contrada Di Dio (S. Agata), 98166 Messina, Italy
Enrico Foti
Affiliation:
Department of Civil Engineering and Architecture, University of Catania, Via Santa Sofia 64, 95123 Catania, Italy
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Numerical simulations of wall-bounded acceleration-skewed oscillatory flows are here presented. The relevance of this type of boundary layer arises in connection with coastal hydrodynamics and sediment transport, as it is generated at the bottom of sea waves in shallow water. Because of the acceleration skewness, the bed shear stress during the onshore half-cycle is larger than in the offshore half-cycle. The asymmetry in the bed shear stress increases with increasing acceleration skewness, while an increase of the Reynolds number from the laminar regime causes the asymmetry first to decrease and then increase. Low- and high-speed streaks of fluid elongated in the streamwise direction emerge near the wall, shortly after the beginning of each half-cycle, at a phase that depends on the flow parameters. Such flow structures strengthen during the first part of the accelerating phase, without causing a significant deviation of the streamwise wall shear stress from the laminar values. Before the occurrence of the peak of the free stream velocity, the low-speed streaks break down into small turbulent structures causing a large increase in wall shear stress. The ratio of the root-mean-square (r.m.s.) of the fluctuations to the mean value (relative intensity) of the wall shear stress is approximately 0.4 throughout a relatively wide interval of the flow cycle that begins when breaking down of the streaks has occurred in the entire fluid domain. The acceleration skewness and the Reynolds number determine the phase at which this time interval begins. Both the skewness and the flatness coefficients of the streamwise wall shear stress are large when elongated streaks are present, while values of approximately 1.1 and 5.4 respectively occur just after breaking has occurred. The trend of both the relative intensity and the flatness of the spanwise wall shear stress are qualitatively similar to those of the wall shear in the streamwise direction. As a result of the acceleration skewness, the period-averaged Reynolds stress does not vanish. Consequently, an offshore directed steady streaming is generated which persists into the irrotational region.

JFM classification

Geophysical and Geological Flows: Coastal engineering Waves/Free-surface Flows: Surface gravity waves Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 808 , 10 December 2016 , pp. 576 - 613
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

van der A, D. A., O’Donoghue, T., Davies, A. & Ribberink, J. S. 2011 Experimental study of the turbulent boundary layer in acceleration-skewed oscillatory flow. J. Fluid Mech. 684, 251–283.Google Scholar
van der A, D. A., O’Donoghue, T., Davies, A. & Ribberink, J. S. 2010 Measurements of sheet flow transport in acceleration-skewed oscillatory flow and comparison with practical formulations. Coast. Engng 57, 331–342.Google Scholar
Abreu, T., Michallet, H., Silva, P., Sancho, F., van der A, D. A. & Ruessink, B. 2013 Bed shear stress under skewed and asymmetric oscillatory flows. Coast. Engng 73, 1–10.Google Scholar
Alfredsson, P. H. & Johansson, A. 1988 The fluctuating wall-shear stress and the velocity field in the viscous sublayer. Phys. Fluids 32 (5), 1026–1033.Google Scholar
Blondeaux, P., Vittori, G., Lalli, F. & Pesarino, V. 2012 Steady streaming and sediment transport at the bottom of sea waves. J. Fluid Mech. 697, 115–149.Google Scholar
Calantoni, J. & Puleo, J. 2006 Role of pressure gradient in sheet flow of coarse sediments under sawtooth waves. J. Geophys. Res. Oceans 111, C01010.Google Scholar
Carstensen, S., Sumer, B. M. & Fredsøe, J. 2010 Coherent structures in wave boundary layers. Part 1. Oscillatory motion. J. Fluid Mech. 646, 169–206.Google Scholar
Cavallaro, L., Scandura, P. & Foti, E. 2011 Turbulence-induced steady streaming in an oscillating boundary layer. Coast. Engng 58, 290–304.Google Scholar
Corino, E. R. & Brodkey, R. S. 1969 A visual investigation of the wall region in turbulent flow. J. Fluid Mech. 37, 1–39.Google Scholar
Costamagna, P., Vittori, G. & Blondeaux, P. 2003 Coherent structures in oscillatory boundary layers. J. Fluid Mech. 474, 1–33.Google Scholar
Dibajnia, M. & Watanabe, A. 1998 Transport rate under irregular sheet flow conditions. Coast. Engng 35, 167–183.Google Scholar
Dong, L., Sato, S. & Liu, H. 2013 A sheetflow sediment transport model for skewed-asymmetric waves combined with strong opposite currents. Coast. Engng 71, 87–101.Google Scholar
Drake, T. & Calantoni, J. 2001 Discrete particle model for sheet flow sediment transport in the nearshore. J. Geophys. Res. Oceans 106 (C9), 19859–19868.Google Scholar
Durst, F., Jovanovic, J. & Sender, J. 1995 LDA measurments in the near-wall region of a turbulent pipe flow. J. Fluid Mech. 295, 305–335.Google Scholar
Elgar, S., Guza, R.-T. & Freilich, M. 1988 Eulerian measurements of horizontal accelerations in shoaling gravity waves. J. Geophys. Res. 93, 9261–9269.Google Scholar
Fishler, L. S. & Brodkey, R. S. 1991 Transition, turbulence and oscillating flow in a pipe. Exp. Fluids 11, 388–398.Google Scholar
Fuhrman, D. R., Fredsøe, J. & Sumer, B. 2009 Bed slope effects on turbulent wave boundary layers: 2. Comparison with skewness, asymmetry, and other effects. J. Geophys. Res. 114, 19.Google Scholar
Hamilton, J., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317–348.Google Scholar
Holmedal, L. & Myrhaugh, D. 2006 Boundary layer flow and net sediment transport beneath asymmetrical waves. Coast. Engng 26, 252–268.Google Scholar
Hsu, T. & Hanes, D. 2004 Effects of wave shape on sheet flow sediment transport. J. Geophys. Res. Oceans 109 (C05025), 15.Google Scholar
Jensen, B. L., Sumer, B. M. & Fredsøe, J. 1989 Turbulent oscillatory boundary layers at high Reynolds numbers. J. Fluid Mech. 206, 265–297.Google Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–74.Google Scholar
Johnson, N., Kotz, S. & Balakrishnan, N. 1995 Continuous Univariate Distributions, vol. 2. Wiley.Google Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–323.Google Scholar
King, D.1990 Studies in oscillatory flow bed load sediment transport. PhD thesis, University of California, San Diego.Google Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layer. J. Fluid Mech. 30, 741–773.Google Scholar
Madsen, O. 1974 Stability of a sand bed under breaking waves. In Proc. 14th Conf. on Coastal Engineering, pp. 776–794. ASCE.Google Scholar
Moin, P. & Mahesh, K. 1998 Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech. 30, 539–578.Google Scholar
Nielsen, P. & Callaghan, D. 2003 Shear stress and sediment transport calculations for sheet flow under waves. Coast. Engng 47, 347–354.Google Scholar
Obi, S., Inoue, K., Furukawa, T. & Masuda, S. 1996 Experimental study on the statistics of wall shear stress in turbulent channel flow. Intl J. Heat Fluid Flow 17, 187–192.Google Scholar
O’Donoghue, T. & Wright, S. 2004 Flow tunnel measurements of velocities and sand flux in oscillatory sheet flow for well-sorted and graded sands. Coast. Engng 51, 1163–1184.Google Scholar
Ozdemir, C. E., Hsu, T. J. & Balachandar, S. 2014 Direct numerical simulations of transition and turbulence in smooth-walled Stokes boundary layer. Phys. Fluids 26, 25.Google Scholar
Pedocchi, F., Cantero, M. & Garcia, M. 2011 Turbulent kinetic energy balance of an oscillatory boundary layer in the transition to the fully turbulent regime. J. Turbul. 12 (32), 1–27.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Ribberink, J. & Al-Salem, A. 1995 Sheet flow and suspension of sand in oscillatory boundary layers. Coast. Engng 25, 205–225.Google Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639.Google Scholar
Salon, S., Armenio, V. & Crise, A. 2007 A numerical investigation of the Stokes boundary layer in the turbulent regime. J. Fluid Mech. 570, 253–296.Google Scholar
Scandura, P. 2007 Steady streaming in a turbulent oscillating boundary layer. J. Fluid Mech. 571, 265–280.Google Scholar
Scandura, P. 2013 Two-dimensional vortex structures in the bottom boundary layer of progressive and solitary waves. J. Fluid Mech. 728, 340–361.Google Scholar
Scandura, P. & Foti, E. 2011 Measurements of wave-induced steady currents outside the surf zone. J. Hydraul. Res. 49 (S1), 64–71.Google Scholar
Scandura, P., Foti, E. & Faraci, C. 2012 Mass transport under standing waves over a sloping beach. J. Fluid Mech. 701, 460–472.Google Scholar
Schoppa, W. & Hussain, F. 2002 Coherent structures generation in the near-wall turbulence. J. Fluid Mech. 453, 57–108.Google Scholar
Silva, P., Abreu, T., van der A, D. A., Sancho, F., Ruessink, B., van der Werf, J. & Ribberink, J. S. 2011 Sediment transport in nonlinear skewed oscillatory flows: Transkew experiments. J. Hydraul. Res. 49, 72–80.Google Scholar
Trowbridge, J. & Madsen, O. 1984 Turbulent wave boundary layer 2: second order theory and mass transport. J. Geophys. Res. Oceans 89 (C5), 7999–8007.Google Scholar
Vittori, G. & Verzicco, R. 1998 Direct simulation of transition in an oscillatory boundary layer. J. Fluid Mech. 371, 207–232.Google Scholar
Watanabe, A. & Sato, S. 2004 A sheet-flow transport rate formula for asymmetric forward-leaning waves and currents. In Proc. 19th Coastal Engng Conf., pp. 1703–1714. ASCE.Google Scholar
Yevjevich, V. 1982 Probability and Statistics in Hydrology. Water Resources Publications.Google Scholar