Symmetry-breaking bifurcations, where a flow state with a certain symmetry undergoes a transition to a state with a different symmetry, are ubiquitous in fluid mechanics. Much can be understood about the nature of these transitions from symmetry alone, using the theory of groups and their representations. Here, we show how the extensive databases on groups in crystallography can be exploited to yield insights into fluid dynamical problems. In particular, we demonstrate the application of the crystallographic layer groups to problems in fluid layers, using thermal convection as an example. Crystallographic notation provides a concise and unambiguous description of the symmetries involved, and we advocate its broader use by the fluid dynamics community.

The actuator line method (ALM) is a commonly used technique to simulate slender lifting and dragging bodies such as wings or blades. However, the accuracy of the method is significantly reduced near the tip. To quantify the loss of accuracy, translating wings with various aspect and taper ratios are simulated using several methods: wall-resolved Reynolds-averaged Navier–Stokes (RANS) simulations, an advanced ALM with two-dimensional (2-D) mollification of the force, a lifting line method, a mollified lifting line method and a vortex lattice method. Significant differences in the lift and drag distributions are found on the part of the wing where the distance to the tip is smaller than approximately 3 chords and are identified to arise from both the forces mollification and the uneven induced velocity along the chord. Correction functions acting on the lift coefficient and effective angle of attack near the wing tip are then derived for rectangular wings of various aspect ratios. They are then also applied to wings of various taper ratios using the ‘effective dimensionless distance to the tip’ as the main parameter. The application of the correction not only leads to a much improved lift distribution, but also to a more consistent drag distribution. The correction functions are also obtained for various mollification sizes, as well as for ALM with three-dimensional (3-D) mollification. These changes mostly impact the correction for the effective angle of attack. Finally, the correction is applied to simulations of the NREL Phase VI wind turbine, leading to an enhanced agreement with the experimental data.

A new wall-wake law is proposed for the streamwise turbulence in the outer region of a turbulent boundary layer. The formulation pairs the logarithmic part of the profile (with a slope $A_1$ and additive constant $B_1$) to an outer linear part, and it accurately describes over 95 % of the boundary layer profile at high Reynolds numbers. Once the slope $A_1$ is fixed, $B_1$ is the only free parameter determining the fit. Most importantly, $B_1$ is shown to follow the same trend with Reynolds number as the wake factor in the wall-wake law for the mean velocity, which is tied to changes in scaling of the mean flow and the turbulence that occur at low Reynolds number.

We investigate flow of liquid which is partially filled in a cylindrical container horizontally rotating about its axis of symmetry. Even if the rotation is slow enough to keep the liquid–gas interface almost undeformed, convection cells whose circulation axis is perpendicular to the container's rotational axis can be sustained. We conduct experiments by particle image velocimetry and direct numerical simulations with the S-CLSVOF and immersed boundary methods to reveal the condition of the Reynolds number, the aspect ratio of the container and the filling ratio of liquid for the onset of these convection cells. When the filling ratio is not too large, as the Reynolds number increases, convection cells appear through a pitchfork bifurcation in an infinitely long cylinder. This bifurcation becomes imperfect in the case of a finite-length cylinder. In contrast, when the filling ratio is large enough, convection cells appear through a subcritical bifurcation. Through these investigations, it becomes evident that the axial wavelength of sustained convection cells is an increasing function of the filling ratio in an infinitely long cylinder. In practice, to sustain intense convection cells, we should use a cylinder with the length equal to an integer multiple of the wavelength of the most unstable mode in the infinite-length cylinder. Although we focus on the liquid-pool regime with small Froude numbers, the critical Reynolds number for the pitchfork bifurcation weakly depends on the Froude number. This dependence is explained by considering the changes in the effective filling ratio and the convection velocity.

Low Stokes number particles at dilute concentrations in turbulent flows can reasonably be approximated as passive scalars. The added presence of a drift velocity due to buoyancy or gravity when considering the transport of such passive scalars can reduce the turbulent dispersion of the scalar via a diminution of the eddy diffusivity. In this work, we propose a model to describe this decay and use a recently developed technique to accurately and efficiently measure the eddy diffusivity using Eulerian fields and quantities. We then show a correspondence between this method and standard Lagrangian definitions of diffusivity and collect data across a range of drift velocities and Reynolds numbers. The proposed model agrees with data from these direct numerical simulations, offers some improvement to previous models in describing other computational and experimental data and satisfies theoretical constraints that are independent of Reynolds number.

Dense mixtures of particles of varying size tend to segregate based on size during flow. Granular size segregation impacts many industrial and geophysical processes, but the development of coupled, continuum models capable of predicting the evolution of segregation dynamics and flow fields in dense granular media across different geometries remains a challenge. One reason is because size segregation stems from two driving forces: pressure gradients and shear-strain-rate gradients. Another reason is the challenge of integrating segregation models with rheological constitutive equations for dense granular flow. In this paper we develop a continuum model that accounts for pressure-gradient-driven and shear-strain-rate-gradient-driven segregation, coupled to rheological modelling of a dense granular medium across the quasi-static and dense inertial flow regimes. To calibrate and test the continuum model, we perform discrete element method (DEM) simulations of dense flow of bidisperse granular systems in two flow geometries in which both segregation driving forces are present: inclined plane flow and planar shear flow with gravity. Steady-state DEM data from inclined plane flow is used to determine the dimensionless material parameters in the pressure-gradient-driven segregation model for both spheres and disks. Then, predictions of the continuum model are tested against DEM data across different cases of inclined plane flow and planar shear flow with gravity, while varying parameters such as the size of the flow geometry, the flow speed and the initial conditions. We find that it is crucial to account for both driving forces to capture segregation dynamics across both flow geometries with a single set of parameters.

This paper gives, in the limit of infinite Froude number, a closed-form, analytical solution for steady, two-dimensional, irrotational, infinite-depth, free-surface, attached flow over a submerged tandem cascade of hydrofoils for arbitrary angle of attack, depth of submergence and interfoil separation. The multiply connected flow domain is conformally mapped to a concentric annulus in an auxiliary plane. The complex flow potential and its derivative, the complex velocity, are obtained in the auxiliary plane by considering their form at known special points in the flow and the required conformal mapping is determined by explicit integration, allowing accurate evaluation of various flow quantities including the lift on each foil. The circulation around the foils causes the foil array to act as a row of point vortices, or a shear layer, and so, for positive angles of attack, the flow speed at the free surface can substantially exceed the speed at depth, with the speeds simply related through the lift coefficient. Decreasing the interfoil separation decreases the disturbance to the free surface and greatly increases the lift per hydrofoil, thus allowing for the shallower operation of a hydrofoil array than of an isolated foil for a given lift requirement. Further, the flow over a hydrofoil array approaches its infinite depth form significantly more rapidly than that over an isolated foil. In contrast to the infinite-submergence case where a through-array flow can be imposed, in the finite submergence case, periodicity and the presence of the free surface mean that there is no net flow between the foils.

Turbulent boundary layers (TBLs) over surface perturbations like bumps with roughness – notably altering heat and mass transfer, drag, etc. – are prevalent in nature (mountains, dunes, etc.) and technology. We study a channel flow with a transverse bump on one wall superimposed with small-scale longitudinal grooves via direct numerical simulation (DNS) of incompressible flow. Turbulence statistics and dynamics are compared between grooved wall (GW) and smooth wall (SW) bumps. Streamwise spinning jets emanating from the crests’ corners alter the flow structure within the separation bubble (SB), extending the SB length by 30 % over that for SW, and have lingering effects far downstream. Grooves decrease skin friction but increase the bump's form drag by 25 %. In GW, the peaks of turbulence intensity and production decrease by 20 % and shift downstream, compared with SW. Three regions of negative production, found upstream as well as downstream of the bump, are explained in terms of two separate mechanisms: normal and shear productions. Separation upstream of the bump occurs always for GW, but intermittently for SW. Within the downstream SB, counter-rotating minibubbles form intermittently for SW but always for GW. Interestingly, a minibubble causes streamwise vorticity reversal of the upstream moving secondary flow around each crest corner. The wall pressure in GW is invariant in the spanwise direction and is explained in terms of its non-local nature and its connection with outer structures. The grooved bump unearths rich TBL flow physics – upstream separation, dynamics of the downstream minibubble, altered reattachment dynamics and negative production.