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Direct numerical simulations of instability and boundary layer turbulence under a solitary wave

  • Celalettin E. Ozdemir (a1), Tian-Jian Hsu (a1) and S. Balachandar (a2)

Abstract

A significant amount of research effort has been made to understand the boundary layer instability and the generation and evolution of turbulence subject to periodic/oscillatory flows. However, little is known about bottom boundary layers driven by highly transient and intermittent free-stream flow forcing, such as solitary wave motion. To better understand the nature of the instability mechanisms and turbulent flow characteristics subject to solitary wave motion, a large number of direct numerical simulations are conducted. Different amplitudes of random initial fluctuating velocity field are imposed. Two different instability mechanisms are observed within the range of Reynolds number studied. The first is a short-lived, nonlinear, long-wave instability which is observed during the acceleration phase, and the second is a broadband instability that occurs during the deceleration phase. Transition from a laminar to turbulent state is observed to follow two different breakdown pathways: the first follows the sequence of $K$ -type secondary instability of a near-wall boundary layer at comparatively lower Reynolds number and the second one follows a breakdown path similar to that of free shear layers. Overall characteristics of the flow are categorized into four regimes as: (i) laminar; (ii) disturbed laminar; (iii) transitional; and (iv) turbulent. Our categorization into four regimes is consistent with earlier works. However, this study is able to provide more specific definitions through the instability characteristics and the turbulence breakdown process.

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Corresponding author

Current Address: Applied Ocean Physics & Engineering Department, Woods Hole Oceanographic Institution, 02543, Woods Hole, MA, USA. Email address for correspondence: cozdemir@whoi.edu

References

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Apel, J. R., Byrne, H. M., Proni, J. R. & Charnell, R. L. 1975 Observations of oceanic internal and surface waves from the earth resources technology satellite. J. Geophys. Res. 80 (6), 865881.
Blondeaux, P. & Vittori, G. 2012 RANS modelling of the turbulent boundary layer under a solitary wave. Coast. Engng 60, 110.
Blondeaux, P., Pralits, J. & Vittori, G. 2012 Transition to turbulence at the bottom of a solitary wave. J. Fluid Mech. 709, 396407.
Bogucki, D. J., Rodekopp, L. G. & Barth, J. 2005 Internal solitary waves in the coastal mixing and optics 1996 experiment: multimodal structure and resuspension. J. Geophys. Res. 110, C02024.
Cantero, M. I., Balachandar, S. & Garcia, M. 2008 An Eulerian–Eulerian model for gravity currents driven by inertial particles. Intl J. Multiphase Flow 34, 484501.
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1987 Spectral Methods in Fluid Dynamics. Springer.
Cortese, T. & Balachandar, S. 1995 High performance spectral simulation of turbulent flows in massively parallel machines with distributed memory. Intl J. Supercomput. Appl. 9 (3), 187204.
Dawson, A. G. & Shi, S. 2000 Tsunami deposits. Pure Appl. Geophys. 157, 875897.
Diamessis, P. J. & Rodekopp, L. G. 2006 Numerical investigation of solitary internal wave-induced global instability in shallow water benthic boundary layers. J. Phys. Oceanogr. 36, 784812.
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Grimshaw, R. 1971 The solitary wave in water of variable depth. J. Fluid Mech. 46, 611622.
Kachanov, Y. S., Kozlov, V. V. & Levchenko, V. Y. 1977 Nonlinear development of a wave in a boundary layer. Fluid Dyn. 12, 383390.
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.
Lin, Y. & Rodekopp, L. G. 2011 The wave-induced boundary layer under long internal waves. Ocean Dyn. 61, 10451065.
Liu, P. L.-F. & Orfilia, A. 2004 Viscous effects on transient long-wave propagation. J. Fluid Mech. 520, 8392.
Liu, P. L.-F., Park, Y. S. & Cowen, E. A. 2007 Boundary layer flow and bed shear stress under a solitary wave. J. Fluid Mech. 574, 449463.
Negretti, M. E. & Socolofsky, S. A. 2005 Stabilization of cylinder wakes in shallow water flows by means of roughness elements: an experimental study. Exp. Fluids 38, 403414.
Seol, D. G. & Jirka, G. H. 2010 Quasi-tow dimensional properties of single shallow vortex with high initial Reynolds numbers. J. Fluid Mech. 665, 274299.
Son, S., Lynett, P. J. & Kim, D.-H. 2011 Nested and multi-physics modelling of tsunami evolution from generation to inundation. Ocean Model. 38 (1–2), 96113.
Spalart, & Baldwin, 1989 Direct simulation of a turbulent oscillating boundary layer. In Turbulent Shear Flows 6 (ed. Andre, J. C.), pp. 417440. Springer.
Stastna, M. & Lamb, K. G. 2002 Vortex shedding and sediment resuspension associated with the interaction of an internal solitary wave and the bottom boundary layer. Geophys. Res. Lett. 29 (11), 7-17-3.
Sumer, B. M., Jensen, P. M., Søerensen, L. B., Fredsøe, J. & Liu, P. L. F. 2010 Coherent structures in wave boundary layers. Part 2. Solitary motion. J. Fluid Mech. 646, 207231.
Synolakis, C. E., E. N., Bernard, Titov, V. V., Kânoğlu, U. & González, F. I. 2008 Validation and verification of tsunami numerical models. Pure Appl. Geophys. 165 (11–12), 21972228.
Tonkin, S., Yeh, H., Kato, F. & Sato, S. 2003 Tsunami scour around a cylinder. J. Fluid Mech. 496, 165192.
Vittori, G. & Blondeaux, P. 2008 Turbulent boundary layer under a solitary wave. J. Fluid Mech. 615, 433443.
Vittori, G. & Blondeaux, P. 2011 Characteristics of the boundary layer at the bottom of a solitary wave. Coast. Engng 58, 206213.
Voit, S. S. 1987 Tsunamis. Annu. Rev. Fluid Mech. 19, 217236.
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353396.
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Direct numerical simulations of instability and boundary layer turbulence under a solitary wave

  • Celalettin E. Ozdemir (a1), Tian-Jian Hsu (a1) and S. Balachandar (a2)

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