Skip to main content Accessibility help
×
Home

A numerical investigation of acceleration-skewed oscillatory flows

  • Pietro Scandura (a1), Carla Faraci (a2) and Enrico Foti (a1)

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.

Copyright

Corresponding author

Email address for correspondence: pscandu@dica.unict.it

References

Hide All
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, 251283.
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, 331342.
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, 110.
Alfredsson, P. H. & Johansson, A. 1988 The fluctuating wall-shear stress and the velocity field in the viscous sublayer. Phys. Fluids 32 (5), 10261033.
Blondeaux, P., Vittori, G., Lalli, F. & Pesarino, V. 2012 Steady streaming and sediment transport at the bottom of sea waves. J. Fluid Mech. 697, 115149.
Calantoni, J. & Puleo, J. 2006 Role of pressure gradient in sheet flow of coarse sediments under sawtooth waves. J. Geophys. Res. Oceans 111, C01010.
Carstensen, S., Sumer, B. M. & Fredsøe, J. 2010 Coherent structures in wave boundary layers. Part 1. Oscillatory motion. J. Fluid Mech. 646, 169206.
Cavallaro, L., Scandura, P. & Foti, E. 2011 Turbulence-induced steady streaming in an oscillating boundary layer. Coast. Engng 58, 290304.
Corino, E. R. & Brodkey, R. S. 1969 A visual investigation of the wall region in turbulent flow. J. Fluid Mech. 37, 139.
Costamagna, P., Vittori, G. & Blondeaux, P. 2003 Coherent structures in oscillatory boundary layers. J. Fluid Mech. 474, 133.
Dibajnia, M. & Watanabe, A. 1998 Transport rate under irregular sheet flow conditions. Coast. Engng 35, 167183.
Dong, L., Sato, S. & Liu, H. 2013 A sheetflow sediment transport model for skewed-asymmetric waves combined with strong opposite currents. Coast. Engng 71, 87101.
Drake, T. & Calantoni, J. 2001 Discrete particle model for sheet flow sediment transport in the nearshore. J. Geophys. Res. Oceans 106 (C9), 1985919868.
Durst, F., Jovanovic, J. & Sender, J. 1995 LDA measurments in the near-wall region of a turbulent pipe flow. J. Fluid Mech. 295, 305335.
Elgar, S., Guza, R.-T. & Freilich, M. 1988 Eulerian measurements of horizontal accelerations in shoaling gravity waves. J. Geophys. Res. 93, 92619269.
Fishler, L. S. & Brodkey, R. S. 1991 Transition, turbulence and oscillating flow in a pipe. Exp. Fluids 11, 388398.
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.
Hamilton, J., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317348.
Holmedal, L. & Myrhaugh, D. 2006 Boundary layer flow and net sediment transport beneath asymmetrical waves. Coast. Engng 26, 252268.
Hsu, T. & Hanes, D. 2004 Effects of wave shape on sheet flow sediment transport. J. Geophys. Res. Oceans 109 (C05025), 15.
Jensen, B. L., Sumer, B. M. & Fredsøe, J. 1989 Turbulent oscillatory boundary layers at high Reynolds numbers. J. Fluid Mech. 206, 265297.
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6974.
Johnson, N., Kotz, S. & Balakrishnan, N. 1995 Continuous Univariate Distributions, vol. 2. Wiley.
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308323.
King, D.1990 Studies in oscillatory flow bed load sediment transport. PhD thesis, University of California, San Diego.
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layer. J. Fluid Mech. 30, 741773.
Madsen, O. 1974 Stability of a sand bed under breaking waves. In Proc. 14th Conf. on Coastal Engineering, pp. 776794. ASCE.
Moin, P. & Mahesh, K. 1998 Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech. 30, 539578.
Nielsen, P. & Callaghan, D. 2003 Shear stress and sediment transport calculations for sheet flow under waves. Coast. Engng 47, 347354.
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, 187192.
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, 11631184.
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.
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), 127.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Ribberink, J. & Al-Salem, A. 1995 Sheet flow and suspension of sand in oscillatory boundary layers. Coast. Engng 25, 205225.
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601639.
Salon, S., Armenio, V. & Crise, A. 2007 A numerical investigation of the Stokes boundary layer in the turbulent regime. J. Fluid Mech. 570, 253296.
Scandura, P. 2007 Steady streaming in a turbulent oscillating boundary layer. J. Fluid Mech. 571, 265280.
Scandura, P. 2013 Two-dimensional vortex structures in the bottom boundary layer of progressive and solitary waves. J. Fluid Mech. 728, 340361.
Scandura, P. & Foti, E. 2011 Measurements of wave-induced steady currents outside the surf zone. J. Hydraul. Res. 49 (S1), 6471.
Scandura, P., Foti, E. & Faraci, C. 2012 Mass transport under standing waves over a sloping beach. J. Fluid Mech. 701, 460472.
Schoppa, W. & Hussain, F. 2002 Coherent structures generation in the near-wall turbulence. J. Fluid Mech. 453, 57108.
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, 7280.
Trowbridge, J. & Madsen, O. 1984 Turbulent wave boundary layer 2: second order theory and mass transport. J. Geophys. Res. Oceans 89 (C5), 79998007.
Vittori, G. & Verzicco, R. 1998 Direct simulation of transition in an oscillatory boundary layer. J. Fluid Mech. 371, 207232.
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. 17031714. ASCE.
Yevjevich, V. 1982 Probability and Statistics in Hydrology. Water Resources Publications.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

A numerical investigation of acceleration-skewed oscillatory flows

  • Pietro Scandura (a1), Carla Faraci (a2) and Enrico Foti (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed