Turbulent dynamics of sinusoidal oscillatory flow over a wavy bottom

Abstract

A direct numerical simulation study is conducted to investigate sinusoidal oscillatory flow over a two-dimensional wavy wall. The height and wavelength of the bottom profile, and the period and amplitude of the free-stream oscillation, are selected to mimic a wave-driven boundary layer over vortex ripples on a sandy seabed. Two cases with different Reynolds numbers $(Re)$ are considered, and the higher-$Re$ case achieves a fully developed turbulent state with a wide separation between the energy-containing and dissipative scales. The oscillatory flow is characterized by coherent columnar vortices, which are the main transport agents of turbulent kinetic energy and enstrophy. Two classes of coherent vortices are observed: (i) a primary vortex formed at the lee side of the ripple by flow separation at the crest; (ii) a secondary vortex formed beneath the primary vortex by vortex-induced separation. When the free-stream velocity weakens, these vortices form a counter-rotating vortex dipole and eject themselves over the crest with their mutual induction. Turbulence production peaks twice in a half-cycle; during the formation of the primary vortex and during the ejection of the vortex dipole. The intensity of the former peak remains low in the lower-$Re$ case, as the vortex dipole follows a higher altitude trajectory limiting its interactions with the bottom, and leaving minimal residual turbulence around the ripples for the subsequent half-cycle. Flow snapshots and spectral analysis reveal two dominant three-dimensional features: (i) an energetic vortex mode with a preferred spanwise wavelength close to the ripple wavelength; (ii) streamwise vortical structures in near-wall regions with a relatively shorter spanwise spacing influenced by viscous effects. The vortex mode becomes strong when the cores of the vortices are strained to an elliptical form while moving towards the crest. Following the detachment of the vortices from the ripple, the vortex mode in the higher-$Re$ case breaks down the spanwise coherence of the columnar vortices and decomposes them into intermittent patches of turbulent vortex clusters. The distribution of wall shear stress over the ripple is also analysed in detail. The peak values are observed near the ripple crest around the ejection of the vortex dipole and the maximum free-stream velocity. In the former, both the vortex mode and streamwise vortices have strong footprints on the wall, yielding a bimodal wall-shear-stress spectrum with two distinctive peaks. In the second high-stress regime, decaying coherent vortices impose strong inhomogeneity on the wall shear stress as their wall-attached parts sweep the ripples. These spanwise variations in the wall shear provide insights into the instability of two-dimensional sand ripples.

An Experimental Investigation of Acceleration‐Skewed Oscillatory Flow Over Vortex Ripples

“…Beneath the primary negative lee vortex, there is a secondary vortex with positive vorticity that also develops with time. This phenomenon was documented by the numerical modeling of Blondeaux and Vittori () and recently confirmed by the DNS work of Önder and Yuan (). This secondary vortex is produced by the adverse pressure gradient along the ripple surface, and it forms a vortex dipole with the primary vortex.…”

“…During this period, the flow turbulence embedded within the coherent vortex increases, and the highest turbulence intensity (in terms of magnitude and spatial coverage) occurs around the phase of maximum vortex strength, for example, (Figure d). The DNS work of Önder and Yuan () showed that shear production of turbulence mainly occurs within the separated shear layer in the immediate wake behind the ripple crest, where the local shear strain is very strong. They also showed that the produced turbulence is advected into the coherent vortex, where most of the turbulence dissipation occurs.…”

“…Alternatively, some modelers solved the Reynolds‐averaged flow with the aid of various turbulence‐closure models, such as the model (e.g., Sato et al, ) and the model (e.g., Fredsøe et al, ; van der Werf et al, ). There are also some attempts using the large‐eddy‐simulation technique (e.g., Grigoriadis et al, ; Zedler & Street, ) or even direct numerical simulation (DNS) (e.g., Blondeaux et al, ; Önder & Yuan, ; Scandura et al, ).…”

Large‐Eddy Simulation of Turbulent Oscillatory Flow Over Three‐Dimensional Transient Vortex Ripple Geometries in Quasi‐Equilibrium

“…The latter is directly associated to the increase of bed resistance and its effect on the dissipation of nonbreaking waves in shallow waters. Finally, direct numerical simulations over 2-D vortex ripples, having a shape created by the superposition of two sinusoidal functions with ripple steepness of 0.167, were performed by Önder and Yuan (2019) at Re = 2,500 and 10,000. They found that turbulence production and wall shear stress peaked at maximum free-stream velocity and during flow reversal.…”

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

“…This mapping transforms the physical domain with undulated bottom to a rectangular box, which is suitable for a mixed discretization, where a bi-dimensional spectral-element discretization (Karniadakis & Sherwin 2005) can be combined with Fourier expansions (Karniadakis 1990). The mixed representation allows significant cost reduction and was employed in previous DNS works on bottom boundary layers (Önder & Yuan 2019;Önder & Liu 2020;Xiong et al 2020). We employ a bi-dimensional modified Legendre basis (Karniadakis & Sherwin 2005) in the streamwise-wall normal (x-z) plane, and Fourier expansions are defined in the spanwise (ȳ) direction.…”