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Receptivity and transition in a solitary wave boundary layer over random bottom topography

Published online by Cambridge University Press:  10 February 2021

Asim Önder Open the ORCID record for Asim Önder [Opens in a new window]  and
Philip L.-F. Liu Open the ORCID record for Philip L.-F. Liu [Opens in a new window]
Asim Önder*
Affiliation:
Department of Civil and Environmental Engineering, National University of Singapore, Singapore117576, Republic of Singapore
Philip L.-F. Liu
Affiliation:
Department of Civil and Environmental Engineering, National University of Singapore, Singapore117576, Republic of Singapore School of Civil and Environmental Engineering, Cornell University, Ithaca, NY14850, USA Institute of Hydrological and Oceanic Sciences, National Central University, Jhongli, Taoyuan320, Taiwan
*
†Email address for correspondence: [email protected]
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Abstract

Direct numerical simulations are conducted to study the receptivity and transition mechanisms in a solitary wave boundary layer developing over randomly organized wave-like bottom topography. The boundary layer flow shows a selective response to broadband perturbations from the bottom, and develops streamwise-elongated streaks. When the streaks reach high amplitudes, they indirectly amplify streamwise-elongated vortices through modulating small-scale fluctuations and pressure fields. These stronger vortices in turn stir the boundary layer more effectively and further intensify streaks via the lift-up mechanism. This nonlinear feedback loop increases the sensitivity of the boundary layer to the roughness level and yields dramatic variations among cases sharing the same Reynolds number with differing roughness height. Three different local breakdown scenarios are observed depending on the amplitude of the streaks: (i) two-dimensional wave instabilities in the regions with weak streaks; (ii) inner shear-layer instabilities in the regions with moderate-amplitude streaks; and (iii) rapidly growing outer shear-layer instabilities in the regions with highly elevated high-amplitude streaks. Inner instabilities have the slowest growth rate among all transition paths, which confirms the previous predictions on the stabilising role of moderate-amplitude streaks (Önder & Liu, J. Fluid. Mech., vol. 896, 2020, A20).

JFM classification

Boundary Layers: Boundary layer stability Boundary Layers: Boundary layer receptivity Waves/Free-surface Flows: Solitary waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 912 , 10 April 2021 , A21
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Andersson, P., Brandt, L., Bottaro, A. & Henningson, D.S. 2001 On the breakdown of boundary layer streaks. J.Fluid Mech. 428, 29–60.CrossRefGoogle Scholar
Biau, D. 2016 Transient growth of perturbations in Stokes oscillatory flows. J.Fluid Mech. 794, R4.CrossRefGoogle Scholar
Blondeaux, P., Pralits, J. & Vittori, G. 2012 Transition to turbulence at the bottom of a solitary wave. J.Fluid Mech. 709, 396–407.CrossRefGoogle Scholar
Boyd, J.P. 2001 Chebyshev and Fourier Spectral Methods. Courier Corporation.Google Scholar
Busse, A., Lützner, M. & Sandham, N.D. 2015 Direct numerical simulation of turbulent flow over a rough surface based on a surface scan. Comput. Fluids 116, 129–147.CrossRefGoogle Scholar
Busse, A., Thakkar, M. & Sandham, N.D. 2017 Reynolds-number dependence of the near-wall flow over irregular rough surfaces. J.Fluid Mech. 810, 196–224.CrossRefGoogle Scholar
Butler, K.M. & Farrell, B.F. 1992 Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids 4 (8), 1637–1650.Google Scholar
Cantwell, C.D., et al. . 2015 Nektar++: an open-source spectral/hp element framework. Comput. Phys. Commun. 192, 205–219.CrossRefGoogle Scholar
Carstensen, S., Sumer, B.M. & Fredsøe, Jørgen 2012 A note on turbulent spots over a rough bed in wave boundary layers. Phys. Fluids 24 (11), 115104.CrossRefGoogle Scholar
Cossu, C. & Brandt, L. 2002 Stabilization of Tollmien–Schlichting waves by finite amplitude optimal streaks in the Blasius boundary layer. Phys. Fluids 14 (8), L57–L60.CrossRefGoogle Scholar
Durbin, P.A. 2017 Perspectives on the phenomenology and modeling of boundary layer transition. Flow Turbul. Combust. 99 (1), 1–23.CrossRefGoogle Scholar
Hunt, J.C.R., Wray, A.A. & Moin, P. 1988 Eddies, streams, and convergence zones in turbulent flows. In Center for Turbulence Research, Proceedings of the 1988 Summer Program, pp. 193–208, NASA Ames.Google Scholar
Karniadakis, G.E. 1990 Spectral element-Fourier methods for incompressible turbulent flows. Comput. Meth. Appl. Mech. Engng 80 (1), 367–380.CrossRefGoogle Scholar
Karniadakis, G.E. & Sherwin, S.J. 2005 Spectral/hp Methods for Computational Fluid Dynamics. Oxford University Press.CrossRefGoogle Scholar
Kirby, R.M. & Sherwin, S.J. 2006 Aliasing errors due to quadratic nonlinearities on triangular spectral/hp element discretisations. J.Engng Maths 56 (3), 273–288.CrossRefGoogle Scholar
Landahl, M.T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J.Fluid Mech. 98, 243–251.CrossRefGoogle Scholar
Liu, P.L.F. & Orfila, A. 2004 Viscous effects on transient long-wave propagation. J.Fluid Mech. 520, 83–92.CrossRefGoogle Scholar
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, 449–463.CrossRefGoogle Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J.Fluid Mech. 628, 311–337.CrossRefGoogle Scholar
Mazzuoli, M. & Vittori, G. 2016 Transition to turbulence in an oscillatory flow over a rough wall. J.Fluid Mech. 792, 67–97.CrossRefGoogle Scholar
Mazzuoli, M. & Vittori, G. 2019 Turbulent spots in an oscillatory flow over a rough wall. Eur. J. Mech. B/Fluids 78, 161–168.CrossRefGoogle Scholar
Munk, W.H. 1949 The solitary wave theory and its application to surf problems. Ann. N.Y. Acad. Sci. 51 (3), 376–424.CrossRefGoogle Scholar
Önder, A. & Liu, P.L.-F. 2020 Stability of the solitary wave boundary layer subject to finite-amplitude disturbances. J.Fluid Mech. 896, A20.CrossRefGoogle Scholar
Önder, A. & Meyers, J. 2018 On the interaction of very-large-scale motions in a neutral atmospheric boundary layer with a row of wind turbines. J.Fluid Mech. 841, 1040–1072.CrossRefGoogle Scholar
Önder, A. & Yuan, J. 2019 Turbulent dynamics of sinusoidal oscillatory flow over a wavy bottom. J.Fluid Mech. 858, 264–314.CrossRefGoogle Scholar
Ozdemir, C.E., Hsu, T.-J. & Balachandar, S. 2013 Direct numerical simulations of instability and boundary layer turbulence under a solitary wave. J.Fluid Mech. 731, 545–578.CrossRefGoogle Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Sadek, M.M., Parras, L., Diamessis, P.J. & Liu, P.L.F. 2015 Two-dimensional instability of the bottom boundary layer under a solitary wave. Phys. Fluids 27 (4), 044101.CrossRefGoogle Scholar
Scandura, P. 2013 Two-dimensional vortex structures in the bottom boundary layer of progressive and solitary waves. J.Fluid Mech. 728, 340–361.CrossRefGoogle Scholar
Serson, D, Meneghini, J.R. & Sherwin, S.J. 2016 Velocity-correction schemes for the incompressible Navier–Stokes equations in general coordinate systems. J.Comput. Phys. 316 (C), 243–254.CrossRefGoogle Scholar
Sumer, B.M., Jensen, P.M., Sørensen, L.B., Fredsøe, J., Liu, P.L.F. & Carstensen, S. 2010 Coherent structures in wave boundary layers. Part 2. Solitary motion. J.Fluid Mech. 646, 207–231.CrossRefGoogle Scholar
Trefethen, L.N., Trefethen, A.E., Reddy, S.C. & Driscoll, T.A. 1993 Hydrodynamic stability without eigenvalues. Science 261 (5121), 578–584.CrossRefGoogle ScholarPubMed
Vaughan, N.J. & Zaki, T.A. 2011 Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks. J.Fluid Mech. 681, 116–153.CrossRefGoogle Scholar
Verschaeve, J.C.G., Pedersen, G.K. & Tropea, C. 2017 Non-modal stability analysis of the boundary layer under solitary waves. J.Fluid Mech. 836, 740–772.CrossRefGoogle Scholar
Vittori, G. & Blondeaux, P. 2008 Turbulent boundary layer under a solitary wave. J.Fluid Mech. 615, 433–443.Google Scholar
Vittori, G. & Verzicco, R. 1998 Direct simulation of transition in an oscillatory boundary layer. J.Fluid Mech. 371, 207–232.CrossRefGoogle Scholar
Vos, P.E.J., Eskilsson, C., Bolis, A., Chun, S., Kirby, R.M. & Sherwin, S.J. 2011 A generic framework for time-stepping partial differential equations (PDEs): general linear methods, object-oriented implementation and application to fluid problems. Intl J. Comput. Fluid Dyn. 25 (3), 107–125.CrossRefGoogle Scholar
Waleffe, F. 1995 Hydrodynamic stability and turbulence: beyond transients to a self-sustaining process. Stud. Appl. Maths 95 (3), 319–343.CrossRefGoogle Scholar
Xiong, C., Qi, X., Gao, A., Xu, H., Ren, C. & Cheng, L. 2020 The bypass transition mechanism of the Stokes boundary layer in the intermittently turbulent regime. J.Fluid Mech. 896, A4.CrossRefGoogle Scholar

Önder and Liu supplementary movie 1

Development of streamwise streaks in case h0.06. Contours show the distribution of the streamwise velocity at height z=0.5 (normalized with the Stokes length). The velocity at each time instant is normalized by the respective free-stream velocity.

Download Önder and Liu supplementary movie 1(Video)
Video 7.7 MB

Önder and Liu supplementary movie 2

Orderly transition in case h0.01. Contours show the magnitude of the vertical velocity at height z=1.3. The levels are normalized by the maximum free-stream velocity and span the interval [0.0022, 0.165].

Download Önder and Liu supplementary movie 2(Video)
Video 14.6 MB

Önder and Liu supplementary movie 3

Bypass transition in case h0.06. Contours show the magnitude of the vertical velocity at height z=1.3. The levels are normalized by the maximum free-stream velocity and span the interval [0.012, 0.144].

Download Önder and Liu supplementary movie 3(Video)
Video 28.5 MB

Önder and Liu supplementary movie 4

Mixed transition in case h0.055. Contours show the magnitude of the vertical velocity at height z=1.3. The levels are normalized by the maximum free-stream velocity and span the interval [0.002, 0.101].

Download Önder and Liu supplementary movie 4(Video)
Video 14 MB