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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

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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