We investigate the influence of smooth and ribletted shark skin on a turbulent boundary layer flow. Through laser Doppler anemometry (LDA) the role of riblets in combination with the shark skin denticle is established for the first time. Our results show that smooth denticles behave like a typical rough surface when exposed to an attached boundary layer. Drag is increased for the full range of tested dimensionless denticle widths, w ⁺ ≈ 25–80, where w ⁺ is the denticle width, w, scaled by the friction velocity, u _τ , and the kinematic viscosity, ν. However, when riblets are added to the denticle crown we demonstrate there is a significant reduction in drag, relative to the smooth denticles. We obtain a modest maximum drag reduction of 2% for the ribletted denticles when compared to the flat plate, but when compared to the smooth denticles the difference in drag is in excess of 20% for w ⁺ ≈ 80. This study enables a new conclusion that riblets have evolved as a mechanism to reduce or eliminate the skin friction increase due to the presence of scales (denticles). The combination of scales and riblets is hydrodynamically efficient in terms of skin-friction drag, while also acting to maintain flow attachment, and providing the other advantages associated with scales, e.g. anti-fouling, abrasion resistance, and defence against parasites.

We investigate the flow over smooth (non-ribletted) shark skin denticles in an open-channel flow using direct numerical simulation (DNS) and two Reynolds averaged Navier–Stokes (RANS) closures. Large peaks in pressure and viscous drag are observed at the denticle crown edges, where they are exposed to high-speed fluid which penetrates between individual denticles, increasing shear and turbulence. Strong lift forces lead to a positive spanwise torque acting on individual denticles, potentially encouraging bristling if the denticles were not fixed. However, DNS predicts that denticles ultimately increase drag by 58% compared to a flat plate. Good predictions of drag distributions are obtained by RANS models, although an underestimation of turbulent kinetic energy production leads to an underprediction of drag. Nevertheless, RANS methods correctly predict trends in the drag data and the regions contributing most to viscous and pressure drag. Subsequently, RANS models are used to investigate the dependence of drag on the flow blockage ratio (boundary layer to roughness height ratio), finding that the drag increase due to denticles is halved when the blockage ratio δ / h is increased from 14 to 45. Our results provide an integrated understanding of the drag over non-ribletted denticles, enabling existing diverse drag data to be explained.

A simulation of stably stratified plane Poiseuille flow at a moderate Reynolds number ( $\textit {Re}_\tau = 550$ ) and Richardson number ( $\textit {Ri}_\tau = 480$ ) is presented. For the first time, the dynamics in the channel core are shown to be described as a series of internal waves that approximately obey a linear wave dispersion relationship. For a given streamwise wavenumber $k_x$ there are two internal wave solutions, a dominant low frequency mode and a weaker-amplitude high-frequency mode, respectively corresponding to ‘backward’ and ‘forward’ propagating internal waves relative to the mean flow. Analysis of linearised equations shows that the dominant low-frequency mode appears to arise due to a particularly sensitive response of the mean flow profiles to incoherent forcing. Instantaneous visualisations reveal that hairpin vortices dominate the outer region of the channel flow, neighbouring the buoyancy dominated channel core. These hairpins are fundamentally different from those observed in canonical unstratified boundary layer flows, as they arise via quasi-linear local processes far from the wall, governed by background shear. Outer region ejection events are common and can be induced by high amplitude waves. Ejected hairpins are transported into the channel core, in turn ‘ringing’ the prevailing strong buoyancy gradient and thus generating high-amplitude internal waves, high dissipation and wave breaking, induced by spanwise vortex stretching and baroclinic vorticity generation. Such spontaneous and sustained generation of quasi-linear internal waves by wall-bounded sheared turbulence may provide novel idealised solutions for, and insight into, large-scale turbulent mixing in a wide range of environmental and industrial flows.

The sensitivity of a large range of turbulence closures to the near-wall grid resolution is assessed through analytical and numerical techniques. We determine model boundedness, limiting behaviour, and solution dependence of channel flow simulations to the near-wall cell size $y_1^{+}$. The sensitivity of present simulations to $y_1^{+}$ is strongly dependent on the choice of scale determining variable; $\epsilon$ and $\omega$ based models can lead to friction velocity errors of 1.5% and 4.74% at $y_1^{+}\approx 1$, the latter due to the singular behaviour of $\omega$ close to the wall. Here this is mitigated by adopting mathematically equivalent $k-{\omega }^{\mathrm{\prime }}$, $k-g$ or $k-\tau$ models, which reduce errors by an order of magnitude to $<0:1\mathrm{\%}$ at $y_1^{+}\approx 0.3$. The $k-\tau$ model is insensitive to $y_1^{+}$ motivating a new closure with updated coefficients and a cross diffusion term, with the aim to ensure its applicability to a wider range of flows.

We investigate a turbulent stratified plane Poiseuille flow using linear models and nonlinear simulations. We propose the first complete explanation for the prolific and coherent backward (BWs)- and forward-propagating waves (FWs), which have been observed in these flows. We demonstrate a significant presence of oblique waves in the channel core, particularly for the FWs. Critically, we show that neglect of spanwise structure leads to a distorted dispersion relation due to its strong dependence on the angle of obliquity. Interestingly, solutions to the Taylor–Goldstein equations show that wave dynamics is strongly dependent on shear, with only a weak dependence on buoyancy for the BWs at low and order-one wavenumbers, when the wavenumber is scaled by the channel half-height. As the wavenumber increases, waves transition from a shear-dominated regime to a buoyancy-dominated regime, with their dispersion relation tending towards that of idealised internal waves subject to a shear-free and constant-buoyancy-gradient flow, with a characteristic velocity and buoyancy frequency corresponding to respective centreline values in the channel. Finally, we show that the dominance of the BWs arises due to the external forcing of the system, whereby turbulent fluid ejected into the core has a lower momentum when compared with the local flow, therefore preferentially generating BWs in the channel. Qualitatively, channel-core dynamics can be reproduced with low-momentum forcing to a velocity profile with a velocity maximum and a corresponding negative second derivative intersecting a region of strong buoyancy gradient. This structure is inherent to a wide variety of jet-like environmental, atmospheric and industrial flows, suggesting that BWs are a critical control on dynamics of such flows.

Floating offshore wind turbine (FOWT) platforms are subject to a wide range of hydrodynamic loading and dynamic movement, making hydrodynamic force evaluation difficult. Amongst various floating platforms, submersible platforms are structurally complex, with multiple members held together by cross-braces. The influence of these members on hydrodynamic loading is poorly understood. An investigation of the effect of these members on loads is essential to optimise the design of FOWT platforms, mooring systems, and protective coatings, leading to a reduction in construction and maintenance costs. This paper numerically investigates the effect of structural members on the forces acting on a static semi-submersible platform in a unidirectional current flow of Reynolds number ($Re$) ranging from 2000 to 200,000, based on structural diameter and tidal velocity. The OC4 semi-submersible is chosen as the baseline platform. For each $Re$, this study is divided into three stages, such that in each stage, the number of members increased. These stages are as follows: (1) a finite cylinder (FC), (2) a finite cylinder with a heave plate (FCHP), (3) three cylinders with heave plates (TCHP) in an equilateral triangle arrangement, and (4) the OC4 semi-sub. The drag coefficient (${\overline{C}}_d$) increases with increasing structural members and weakly varies with increasing $Re$. However, the viscous drag coefficient (${\overline{C}}_f$) decreases with increasing $Re$, and a reverse trend is seen in the case of the pressure drag coefficient (${\overline{C}}_p$), with pressure drag dominating over friction drag. Further, the contribution of individual members is observed to vary with $Re$. The contribution of cylinders towards ${\overline{C}}_d$ is higher than heave plates, showing that contributions directly depend on the aspect ratio of members. In the case of TCHP and OC4, the contribution of the rear members is higher than that of the leading members due to the strong wake effect of the former. Also, the braces and pontoons of OC4 have contributed substantially towards total ${\overline{C}}_d$, unlike the central cylinder, which has experienced low drag due to the wake effect of the front cylinder and heave plate. Also, flow visualisation has shown vortex cores, and recirculating flows in the near wake of the cylinders and under the heave plates. Recirculation zones under the heave plates lead to vertical pressure on the structures. This vertical pressure increases with the number of structural members and the vertical pressure coefficient (${\overline{C}}_v$), varying with $Re$ due to three-dimensionality in the wake. Further, this pressure varies across the bottom surfaces of structures. Analyses of the streamwise pressure coefficient have shown it is highest on the front surfaces of cylinders. The highest friction is on the top and sides of the heave plates, and there is considerable friction on the sides of the cylinder.