Zixuan Yang

To investigate the spanwise length scales of turbulent motions essential for sustaining near-wall turbulence, we perform numerical experiments in direct numerical simulations of full-scale turbulent channel flows by filtering out motions wider than a prescribed cutoff wavelength lamda Subscript z f λ z f $\lambda _{zf}$ . As lamda Subscript z f λ z f $\lambda _{zf}$ decreases, near-wall short vortical structures are suppressed, while long streaks are amplified. When lamda Subscript z f λ z f $\lambda _{zf}$ is reduced to approximately 200 wall units, the flow relaminarises, indicating that at least turbulent motions twice those of near-wall coherent structures are necessary. To elucidate the underlying mechanism, we derive transport equations for Reynolds shear stresses associated separately with long streaks and short vortical structures, and decompose nonlinear transport terms into contributions from spanwise-wide motions, long streaks, short vortical structures and their interactions. Spanwise-wide motions enhance the energy production of short vortical structures by supplying energy, via nonlinear interactions, to vertical velocity fluctuations; thus, their removal suppresses these structures. Conversely, nonlinear interactions involving spanwise-wide motions act as a major energy sink for long streamwise fluctuations, so their absence amplifies streaks. However, long streaks ultimately depend on short vortical structures, as their energy is extracted from the mean shear by vertical velocity fluctuations, which draw energy from spanwise velocity fluctuations sustained by nonlinear interactions involving both short structures and spanwise-wide motions. Therefore, when short structures are strongly suppressed at sufficiently small lamda Subscript z f λ z f $\lambda _{zf}$ , the flow relaminarises. These findings highlight the central role of short vortical structures and their dependence on ‘inactive’ spanwise-wide turbulent motions, and reveal multiple interconnected energy cycles governing near-wall coherent structures.

Free-surface response to flow past a fully submerged circular cylinder is known to be governed by the Froude number italic Fr Fr $\textit{Fr}$ and the gap ratio upper G G $G$ . However, most previous work has primarily examined this combined dependence in two-dimensional configurations at low Reynolds numbers. Here, three-dimensional high-resolution numerical simulations are conducted to investigate turbulent two-phase free-surface flow past a fully submerged circular cylinder at high Froude numbers ( 0.8 less than or slanted equals italic Fr less than or slanted equals 2.0 0.8 ⩽ Fr ⩽ 2.0 $0.8 \leqslant \textit{Fr} \leqslant 2.0$ ) and small gap ratios ( 0.025 less than or slanted equals upper G less than or slanted equals 0.4 0.025 ⩽ G ⩽ 0.4 $0.025 \leqslant G \leqslant 0.4$ ), at a Reynolds number italic Re equals 2000 Re = 2000 $\textit{Re} = 2000$ and a Weber number italic We equals 1000 We = 1000 $\textit{We} = 1000$ , corresponding to a fully turbulent regime and small surface tension. The investigated parameter space corresponds to a flow regime where wake-induced interface disruption generates bubbles over a broad range of scales. This mechanism is of practical significance for engineering applications involving naval and offshore structures. The upstream and downstream free-surface flow patterns are classified. Free-surface breaking upstream of the cylinder is reported for 1.1 less than or slanted equals italic Fr less than or slanted equals 1.4 1.1 ⩽ Fr ⩽ 1.4 $1.1 \leqslant \textit{Fr} \leqslant 1.4$ , and its physical mechanism and occurrence condition are discussed. Downstream, as the breaking pattern transitions from spilling to plunging with increasing Froude number, the bubble number density spectrum exhibits distinct scaling behaviour. While a combined negative 4.3 − 4.3 $-4.3$ and negative 5.83 − 5.83 $-5.83$ power-law regime persists over a range of conditions, a negative 10 divided by 3 − 10 / 3 $-10/3$ scaling emerges under stronger plunging events with respect to the effective bubble radius. The frequency characteristics of the cylinder’s lift and drag coefficients associated with the transition from two-phase to single-phase flow are identified. Variations in mean statistical quantities with respect to italic Fr Fr $\textit{Fr}$ and upper G G $G$ confirm the coupled influence of these parameters, with increasing italic Fr Fr $\textit{Fr}$ or upper G G $G$ enhancing flow symmetry and promoting momentum transport within the jet-like flow above the cylinder. A combined analysis of vorticity transport, shear-layer dynamics, bubble statistics and turbulence properties elucidates how Froude number and gap ratio govern momentum exchange and air entrainment in high-Froude-number, small-gap-ratio flows. This study provides new mechanistic insight and numerical evidence for understanding interactions between highly deformable free surfaces and bluff-body wakes.

Direct numerical simulations of two-phase, free-surface flow past a fully submerged, fixed circular cylinder are conducted for transitional Reynolds numbers $400 \leqslant {\textit{Re}} \leqslant 2000$ , with Weber number ${\textit{We}} = 1000$ , Froude number ${\textit{Fr}} = 1$ and a fixed gap ratio $G = 0.5$ . This parameter combination corresponds to the gas entrainment regime characterised by the production of multiscale gas bubbles through interface breakup in the wake, which is of particular interest for its implications in enhancing gas transfer and mixing in environmental and engineering flows, such as air–water gas exchange processes in rivers and oceans, and the design and performance of naval and offshore structures. For ${\textit{Re}}= 400$ , the jet forced through the $0.5D$ gap where $D$ is the diameter of the cylinder, efficiently convects opposite-signed vorticity downstream, suppressing the classical von Kármán instability and yielding a quasisteady recirculation bubble. The jet’s stabilising influence, however, breaks down once ${\textit{Re}} \approx 500$ : periodic vortex shedding re-emerges and the wake becomes unsteady in spite of the continuing jet. The corresponding dimensionless shedding frequency Strouhal number $St$ grows with ${\textit{Re}}$ as $0.52-72.7{\textit{Re}}^{-1}$ . The onset of unsteadiness first shortens the mean separation length but then drives it towards a saturation plateau for higher ${\textit{Re}}$ values. Surface rupture in the turbulent wake fragments entrained air into a multiscale bubble population whose number density follows $S_b(R_{\textit{eff}}) \propto R_{\textit{eff}}^{-6}$ , consistent with gravity–capillary breakup in breaking waves, where $R_{\textit{eff}}$ represents the effective radii of the bubbles. Intermittency in entrainment corresponding to vortex shedding contrasts sharply with the finger-like structures observed under laminar conditions, underscoring the role of turbulent mixing. The coupled analysis of vorticity transport, shear-layer instability and bubble statistics elucidates how momentum exchange and air entrainment over a submerged body are governed under non-turbulent and turbulent conditions.

We perform simulations of a two-fluid–structure interaction problem involving liquid–gas flow past a fully submerged stationary circular cylinder. Interactions between the liquid–gas interface with finite surface tension and flow disturbances arising from the cylinder induce a variety of interfacial phenomena and wake structures. We map different interface regimes in a parameter space defined by the Bond number $Bo \in [100, 5000]$ and the submergence depth $h/D \in [1, 2.5]$ of the cylinder while keeping the Reynolds (Re) and Weber (We) numbers fixed at 150 and 1000, respectively. The emerging interface features are classified into three distinct regimes: interfacial waves generated by Strouhal vortices, the entrainment of multi-scale gas bubbles and the reduced deformation state. In the interfacial wave regime, we demonstrate that the frequency of transverse interface fluctuations at a specific streamwise location is identical to the vortex shedding frequency. Additionally, the wavelength of interfacial waves is determined by the size of vortex pairs consisting of alternating Strouhal vortices. In the gas entrainment regime at $ Bo = 1000$ , our bubble-size distributions reveal that the entrained bubbles have sizes ranging from one to two orders of magnitude smaller than the cylinder. These multi-scale bubbles are formed primarily through plunging and surfing breakers at $h/D = 2.5$ . In contrast, at $h/D = 1$ , smaller bubbles initially emerge from the breakup of a gas finger. Over time, some of these bubbles grow in size through coalescence cascades. The influence of $ Re \in [50, 150]$ and $ We \in [700, 1100]$ on gas entrainment is quantified in terms of mean bubble size and count. Lastly, we demonstrate how the deformability of the liquid–gas interface drives the hydrodynamic lift force acting on the cylinder. The net downward lift materializes only in the gas entrainment and reduced deformation regimes due to the broken symmetry of the front stagnation point. While our study focuses on two-dimensional simulations, we also provide insights into the three-dimensional gas entrainment mechanism for one of the extreme cases at $h/D = 1$ .

In this study, we conducted interface-capturing high-resolution simulations of a bubbly upflow in a vertical channel to investigate the bubble distribution and its interaction with surrounding turbulence, focusing on the effects of the density ratio. A bulk Reynolds number $Re_b=2300$ was used for all simulations. The influence of density ratio on vortex structures and turbulence statistics differed between the near-wall and core regions of the channel. Adding 5.43 $\%$ gas caused an increase in wall friction. By applying a generalised FIK identity to analyse wall friction, it was determined that the drag rise in the bubbly channel was mostly due to the near-wall region. Visualisation of the bubble and vortex structures showed that small bubbles near the wall induced larger magnitude of Reynolds shear stress and increased wall friction. Bubble behaviour near the wall region was similar for density ratios above 30, leading to wall friction saturation. In the core region, large deformable bubbles created wake vortices due to slip velocity between liquid and gas phases. Wake vortices help large bubbles absorb smaller bubbles and maintain their sizes. As the density ratio increased, the slip velocity increased owing to greater difference in the gravitational acceleration between liquid and gas phases, resulting in corresponding increase in wake intensity and velocity fluctuations. However, quadrant analysis showed that Q1 and Q3 events increased together with Q2 and Q4 events in the core region, cancelling out any net effect of wake vortices on Reynolds shear stress or wall friction.