Macroscopic vortex rings are generated thermally in superfluid 4He, between 1.28 and 1.95 K, by applying a brief voltage pulse to a resistive heater located below a circular vertical tube 5 mm in diameter and 20 mm high. The rings form above the tube and propagate upward with velocities of the order of $10~\text{mm}~\text{s}^{-1}$, resulting in Reynolds numbers up to $10^{5}$. We visualize their cross-section, of size comparable with the tube diameter, by capturing the motions of relatively small solid deuterium particles, previously dispersed in the quiescent bath of superfluid 4He. We employ particle positions and velocities to compute the Lagrangian pseudovorticity, which can be seen as a measure of the ring strength and which allows us to identify and track these objects. We thus obtain time-dependent sizes, positions and velocities of the vortex rings. We show that, in the range of investigated parameters, these rings behave as if they were turbulent vortex rings moving in classical viscous fluids, at least in the direction of ring propagation. The outcome reinforces the view that the study of turbulent flows of superfluid 4He is not only interesting in its own right, but that it can also contribute to our current understanding of fluid turbulence in general.

The present paper uses the detailed flow data produced by direct numerical simulation (DNS) of a three-dimensional, spatially developing plane free shear layer to assess several commonly used turbulence models in compressible flows. The free shear layer is generated by two parallel streams separated by a splitter plate, with a naturally developing inflow condition. The DNS is conducted using a high-order discontinuous spectral element method (DSEM) for various convective Mach numbers. The DNS results are employed to provide insights into turbulence modelling. The analyses show that with the knowledge of the Reynolds velocity fluctuations and averages, the considered strong Reynolds analogy models can accurately predict temperature fluctuations and Favre velocity averages, while the extended strong Reynolds analogy models can correctly estimate the Favre velocity fluctuations and the Favre shear stress. The pressure–dilatation correlation and dilatational dissipation models overestimate the corresponding DNS results, especially with high compressibility. The pressure–strain correlation models perform excellently for most pressure–strain correlation components, while the compressibility modification model gives poor predictions. The results of an a priori test for subgrid-scale (SGS) models are also reported. The scale similarity and gradient models, which are non-eddy viscosity models, can accurately reproduce SGS stresses in terms of structure and magnitude. The dynamic Smagorinsky model, an eddy viscosity model but based on the scale similarity concept, shows acceptable correlation coefficients between the DNS and modelled SGS stresses. Finally, the Smagorinsky model, a purely dissipative model, yields low correlation coefficients and unacceptable accumulated errors.

We characterise the incompressible turbulence cascade in terms of the concurrent inter-scale and inter-space exchanges of the scale-by-scale energy, helicity and enstrophy. The governing equations for the scale-by-scale helicity and enstrophy are derived in a similar fashion to that of the second order structure function following Hill (J. Fluid Mech., vol. 468, 2002, pp. 317–326). We examine the instantaneous dynamics, applying these equations to forced periodic turbulence and a von Kármán flow focusing on scales in the dissipative range $r=2.5\eta$, the near-dissipative range $r=0.5\lambda$ and the onset inertial range $r=\lambda$ (where $\eta$ and $\lambda$ are the Kolmogorov and Taylor length scales, respectively). The signature of the random sweeping effect is observed in all three individual budgets and between the energy and enstrophy transfers. As in the energy cascade, the anti correlation of the pressure transport and non-linear transfer is identified also in the helicity cascade. Owing to its lack of positive definiteness, the helicity transfers are found to be decorrelated from the others. However a connection between the energy cascade and helicity is identified kinematically. This connection reveals the large-scale sweeping motions are a key element in the overall energy cascade and underpins previous observations of large-scale intermittency. Taken together, this work extends a classic framework to gain novel insight on turbulence dynamics that underlay the statistically steady state, and demonstrates how transfers are interconnected.

We study the inverse flux of waves in one of the simplest geophysical fluid dynamics models: one-dimensional rotating shallow water equations. Based on direct numerical integration of the governing equations, we find that waves injected at small scales get transferred upscale predominantly via resonant quartic interactions between wave modes. The waves’ upscale transfer is non-local and involves turbulent transfer between disparate scales of the flow. Our analysis reveals that the upscale transfer of waves is extremely intermittent and is a result of localized-in-time bursts in wave action flux. These intermittent events of flux bursts lead to shallower waves’ spectrum and relatively higher amplitude wave fields in physical space. On examining statistics of the flow fields, we find that low-energy high wavenumbers more or less comply with the assumptions used in wave turbulence theory, such as uniformly distributed wave phases and the Gaussian distribution of fields, while non-uniform distribution of wave phases and non-Gaussian statistics dominate at large scales or low wavenumbers that contain a major share of the flow energy. Our findings point out that the one-dimensional rotating shallow water equations, despite being a simple geophysical fluid dynamic model, harbour complex and intricate features associated with the upscale transfer of waves that have not been recognized in the past.

In this work, the dynamics of two-dimensional rotating Janus drops in shear flow is studied numerically using a ternary-fluid diffuse interface method. The rotation of Janus drops is found to be closely related to their deformation. A new deformation parameter $D$ is proposed to assess the significance of the drop deformation. According to the maximum value of $D$ ($D_{max}$), the deformation of rotating Janus drops can be classified into linear deformation ($D_{max}\le 0.2$) and nonlinear deformation ($D_{max}> 0.2$). In particular, $D_{max}$ in the former depends linearly on the Reynolds and capillary numbers, which can be interpreted by a mass–spring model. Furthermore, the rotation period $t_R$ of a Janus drop is found to be more sensitive to the drop deformation than to the aspect ratio of the drop at equilibrium. By introducing a corrected shear rate and an aspect ratio of drop deformation, a rotation model for Janus drops is established based on Jeffery's theory for rigid particles, and it agrees well with our numerical results.

We demonstrate a novel shear-induced mechanism for growth of concentration fluctuations in a bacterial suspension. Using a linear stability analysis, a homogeneous bacterial suspension, subject to a simple shear flow, is shown to be susceptible to exponentially growing layering perturbations in the shear rate and bacterial concentration. A semi-analytical expression for the growth rate of concentration perturbations is first obtained using the method of multiple scales, in the limit where the time scales characterizing the positional and orientation degrees of freedom are well separated. Next, the eigenspectrum obtained numerically from a full linear stability analysis is used to validate and extend the multiple scales result, and draw a contrast with the known orientation-shear instability. Finally, fully nonlinear simulations, but restricted to one-dimensional variations of the relevant fields (velocity, concentration and swimmer orientation distribution) show that the initial instability leads to gradient-banded velocity profiles, with a local depletion of bacteria at the interface between the homogeneous shear bands. Our results demonstrate that long-ranged hydrodynamic interactions serve as an alternate explanation for recent observations of shear bands in bacterial suspensions.

Turbulent Taylor–Couette flow between two concentric independently rotating cylinders with a radius ratio of $\eta = 0.1$ is studied experimentally. While the scope is to study the counter-rotating cases between both cylinders, the radial and azimuthal velocity components are recorded at different horizontal planes with high-speed particle image velocimetry. The parametric study considered a set of different shear Reynolds numbers in the range of $20\,000 \leq Re_s \leq 1.31 \times 10^5$, with different rotation ratios of $-0.06 \leq \mu \leq +0.008$. The observed flow fields had a clear dependence on the rotation ratio, where flow patterns evolved with a more pronounced axial dependence. The angular momentum transport is computed as a result of the recorded flow fields and given by a quasi-Nusselt number. The dependence of the Nusselt number on the different rotation ratios shows a maximum for the low counter-rotating case and $\mu _{max}$ is found between $-0.011 < \mu _{max} < -0.0077$. The Nusselt number decreases for stronger counter-rotation until a minimum is reached, where it tends to increase again for higher counter-rotation rates. The space–time behaviour of the turbulent flow showed the existence of patterns propagating from the inner region towards the outer region for all studied counter-rotating cases. In addition, patterns have been found that tend to propagate from the outer region towards the inner region with a novel character at high counter-rotation cases. These patterns enhance the angular momentum transport where a second maximum in the transport mechanism has to be expected.

Turbulent shear flows are abundant in geophysical and astrophysical systems and in engineering-technology applications. They are often riddled with large-scale secondary flows that drastically modify the characteristics of the primary stream, preventing or enhancing mixing, mass and heat transfer. Using experiments and numerical simulations, we study the possibility of modifying these secondary flows by using superhydrophobic surface treatments that reduce the local shear. We focus on the canonical problem of Taylor–Couette flow, the flow between two coaxial and independently rotating cylinders, which has robust secondary structures called Taylor rolls that persist even at significant levels of turbulence. We generate these structures by rotating only the inner cylinder of the system, and show that an axially spaced superhydrophobic treatment can weaken the rolls through a mismatching surface heterogeneity, as long as the roll size can be fixed. The minimum hydrophobicity of the treatment required for this flow control is rationalized, and its effectiveness beyond the Reynolds numbers studied here is also discussed.

We investigate the dynamics of a fluid layer subject to a bottom heat flux and a top monotonically increasing temperature profile driving horizontal convection (HC). We use direct numerical simulations and consider a large range of flux-based Rayleigh numbers $10^6 \leq Ra_F \leq 10^9$ and imposed top horizontal to bottom vertical heat flux ratios $0 \leq \varLambda \leq 1$. The fluid domain is a closed two-dimensional box with aspect ratio $4\leq \varGamma \leq 16$ and we consider no-slip boundaries and adiabatic side walls. We demonstrate a regime transition from Rayleigh–Bénard (RB) convection to HC at $\varLambda \approx 10^{-2}$, which is independent of $Ra_F$ and $\varGamma$. At small $\varLambda$, the flow is organised in multiple overturning cells with approximately unit aspect ratio, whereas at large $\varLambda$ a single cell is obtained. The RB-relevant Nusselt number scaling with $Ra_F$ and the HC-relevant Nusselt number scaling with the horizontal Rayleigh number $Ra_L=Ra_F\varLambda \varGamma ^4$ are in good agreement with previous results from classical RB convection and HC studies in the limit $\varLambda \ll 10^{-2}$ and $\varLambda \gg 10^{-2}$, respectively. We demonstrate that the system is multi-stable near the transition $\varLambda \approx 10^{-2}$, i.e. the exact number of cells not only depends on $\varLambda$ but also on the system's history. Our results suggest that subglacial lakes, which motivated this study, are likely to be dominated by RB convection, unless the slope of the ice–water interface, which controls the horizontal temperature gradient via the pressure-dependence of the freezing point, is greater than unity.

Nonlinearity of density stratification modulates buoyancy effects. We report results from a body-inclusive large eddy simulation of a wake in nonlinear stratification, specifically for a circular disk at diameter-based Reynolds number (${\it Re} $) of $5000$. Five density profiles are considered; the benchmark has linear stratification and the other four have hyperbolic tangent profiles of the same thickness to model a pycnocline. The disk moves inside the central core of the pycnocline in two of those four cases and, in the other two cases with a shifted density profile, the disk moves partially/completely outside the pycnocline. The maximum buoyancy frequency ($N_{max}$) for all the profiles is the same. The first part of the study investigates the centred cases. Non-uniform stratification results in increasing wake turbulence relative to the benchmark owing to reduced suppression of turbulence production as well as wave trapping in the pycnocline. Steady lee waves are also quantified to understand the limitations of linear theory. The second part pays attention to the effect of a relative shift between the pycnocline and the disk. The wake defect velocity decays substantially faster in the cases with a shift and the wake has higher turbulence level. The effect of disk location on the Kelvin wake waves (a family of steady waves within the pycnocline) and its modal form is obtained and explained by solving the Taylor–Goldstein equation. The family of unsteady internal gravity waves that are generated by the wake is also studied and the effect of disk shift is quantified.

Experiments to study the effect of edge undulation on vortex formation have been conducted on impulsively accelerated plates. Abstractions of propulsors found in nature are produced by imprinting undulatory features with varying wavelengths onto the circumferential vortex-forming edge of circular plates. The effects of the small-scale disturbances introduced by these modifications are accessed by means of force measurements and time-resolved particle image velocimetry. Investigations of four different geometries at two different Reynolds numbers reveal an insensitivity of the flow towards length scales smaller than or similar to the thickness of the feeding shear layer. However, the instabilities in the shear layer and the coherence of the vortex wake are influenced when the wavelength of the undulation exceeds the shear-layer thickness by a significant margin. This results in a force augmentation due to enhanced entrainment into the turbulent vortex core, and thus an associated faster vortex growth rate. Yet, contrary to prior expectations, the time of vortex pinch-off remains constant for all edge modifications. The cause–effect relationship behind the stability of the vortex wake is further investigated. While for small edge undulations a turbulent transition of the vortex core results in vortex pinch-off, for larger edge undulations the turbulent vortex core is found to be fed constantly with additional circulation from the shear layer.