The spectral eddy viscosity (SEV) concept is a handy tool for the derivation of large-eddy simulation (LES) turbulence models and for the evaluation of their performance in predicting the spectral energy transfer. We compute this quantity by filtering and truncating fully resolved turbulence data from direct numerical simulations (DNS) of neutrally and stably stratified homogeneous turbulence. The results qualitatively confirm the plateau–cusp shape, which is often assumed to be universal, but show a strong dependence on the test filter size. Increasing stable stratification not only breaks the isotropy of the SEV but also modifies its basic shape, which poses a great challenge for implicit and explicit LES methods. We find indications that for stably stratified turbulence it is necessary to use different subgrid-scale (SGS) models for the horizontal and vertical velocity components. Our data disprove models that assume a constant positive effective turbulent Prandtl number.

In Haller & Beron-Vera (J. Fluid Mech., vol. 731, 2013, R4) we developed a variational principle for the detection of coherent Lagrangian vortex boundaries. The solutions of this variational principle turn out to be closed null geodesics of the Lorentzian metric induced by a generalized Green–Lagrange strain tensor family. This metric interpretation implies a mathematical analogy between coherent Lagrangian vortex boundaries and photon spheres in general relativity. Here, we give an improved discussion of this analogy.

Turbulent jets and plumes are commonly encountered in industrial and natural environments; they are, for example, key processes during explosive eruptions. They have been the objects of seminal works on turbulent free shear flows. Their dynamics is often described with the concept of the so-called entrainment coefficient, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\alpha $ , which quantifies entrainment of ambient fluid into the turbulent flow. This key parameter is well characterized for axisymmetric jets and plumes, but data are scarcer for turbulent planar plumes and jets. The data tend to show that the Gaussian entrainment coefficient in plane pure plumes is about twice the value for plane pure jets. In order to confirm and to explain this difference, we develop a model of entrainment in turbulent plane jets and plumes taking into account the effect of buoyancy on entrainment, as a function of the shape of the velocity, buoyancy and turbulent shear stress profiles. We perform new experiments to better characterize the rate of entrainment in plane pure plumes and to constrain the values of the model parameters. Comparison between theory and experiments shows that the enhancement of entrainment in plane turbulent pure plumes relative to plane turbulent pure jets is well explained by the contribution of buoyancy.

We study magnetically induced interfacial instability of a thin ferrofluid film subjected to an applied uniform magnetic field and covered by a non-magnetizable passive gas. Governing equations are derived using the long-wave approximation of the coupled static Maxwell and Stokes equations. The contact angle is imposed via a disjoining/conjoining pressure model. Numerical simulations show the patterning resulting from unstable perturbations and dewetting of the ferrofluid film. We find that the subtle competition between the applied field and the van der Waals induced dewetting determines the appearance of satellite droplets. The results suggest a new route for generating self-assembled ferrofluid droplets from a thin film using an external magnetic field. An axisymmetric droplet on a surface is also studied, and we demonstrate the deformation of the droplet into a spiked cone, in agreement with experimental findings.

The coherent structures of a turbulent wake generated behind a bluff three-dimensional axisymmetric body are investigated experimentally at a diameter-based Reynolds number of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\sim }2\times 10^5$ . Proper orthogonal decomposition of base pressure measurements indicates that the most energetic coherent structures retain the structure of the symmetry-breaking laminar instabilities and are manifested as unsteady vortex shedding with azimuthal wavenumber $m={\pm }1$ . In a rotating reference frame, the shedding preserves the reflectional symmetry and is linked with a reflectionally symmetric mean pressure distribution on the base. Due to a slow rotation of the symmetry plane of the turbulent wake around the axis of the body, statistical axisymmetry is recovered in the time average. The ratio of the time scales associated with the slow rotation of the symmetry plane and the vortex shedding is of order 100.

The phenomenology of turbulent relative dispersion is revisited. A heuristic scenario is proposed, in which pairs of tracers undergo a succession of independent ballistic separations during time intervals whose lengths fluctuate. This approach suggests that the logarithm of the distance between tracers self-averages and performs a continuous-time random walk. This leads to specific predictions for the probability distribution of separations, which differ from those obtained using scale-dependent eddy-diffusivity models (e.g. in the framework of Richardson’s approach). These predictions are tested against high-resolution simulations and shed new light on the explosive separation between tracers.

In some specific conditions, a flying spinning ball deflects in a direction opposite to that predicted by the Magnus effect, which is known as the inverse Magnus effect. To elucidate when and why this effect occurs, we measure the variations of the drag and lift forces on a rotating sphere and the corresponding flow field with the spin ratio (the ratio of the rotational velocity to the translational one). This counterintuitive phenomenon occurs because the boundary layer flow moving against the surface of a rotating sphere undergoes a transition to turbulence, whereas that moving with the rotating surface remains laminar. The turbulence energizes the flow and thus the main separation occurs farther downstream, inducing faster flow velocity there and generating negative lift force. Empirical formulae are derived to predict the location where the flow separates as a function of the Reynolds number and the spin ratio. Using the formulae derived, the condition for the onset of the inverse Magnus effect is suggested based on the negative lift generation mechanism.

The edge of a stationary radially expanding liquid sheet and the receding rim bordering a plane sheet are naturally indented. It presents a collection of cusps at the extremity of which the liquid concentrates and is expelled. An experimental description of these cusps for a stationary flat inviscid Savart sheet is given. We identify the stable node–jet structure responsible for the deflection of the incoming flow at the rim and demonstrate how these cusps are the structures that accommodate for both mass and momentum conservation at the sheet edge. Their shape, their number around the sheet, and the residual momentum carried by the ejected liquid are computed.

One of the simplest geometries in which to study fluid flow between two soap films connected by a Plateau border is provided by a catenoid with a secondary film at its narrowest point. Dynamic variations in the spacing between the two rings supporting the catenoid lead to fluid flow between the primary and secondary films. When the rings are moved apart, while keeping their spacing within the overall stability regime of the films, after a rapid thickening of the secondary film the excess fluid in it starts to drain into the sloped primary film through the Plateau border at which they meet. This influx of fluid is accommodated by a local thickening of the primary film. Experiments described here show that after this drainage begins the leading edge of the gravity current becomes linearly unstable to a finite-wavelength fingering instability. A theoretical model based on lubrication theory is used to explain the mechanism of this instability. The predicted characteristic wavelength of the instability is shown to be in good agreement with experimental results. Since the gravity current advances into a film of finite, albeit microscopic, thickness this situation is one in which the regularization often invoked to address singularities at the nose of a thin film is physically justified.

A model of the total volume flux and entrainment occurring in two coalescing axisymmetric turbulent plumes is developed and compared with laboratory experiments. The dynamical evolution of the two plumes is divided into three regions. In region 1, where the plumes are separate, the entrainment in each plume is unaffected by the other plume, although the two plumes are drawn together due to the entrainment of ambient fluid between them. In region 2 the two plumes touch each other but are not yet merged. In this region the total entrainment is a function of both the dynamics of the touching plumes and the reduced surface area through which entrainment occurs. In region 3 the two plumes are merged and the entrainment is equivalent to that in a single plume. We find that the total volume flux after the two plumes touch and before they merge increases linearly with distance from the sources, and can be expressed as a function of the known total volume fluxes at the touching and merging heights. Finally, we define an ‘effective’ entrainment constant, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\alpha _{eff}$ , as the value of $\alpha $ needed to obtain the same total volume flux in two independent plumes as that occurring in two coalescing plumes. The definition of $\alpha _{eff}$ allows us to find a single expression for the development of the total volume flux in the three different dynamical regions. This single expression will simplify the representation of coalescing plumes in more complex models, such as in large-scale geophysical convection, in which plume dynamics are not resolved. Experiments show that the model provides an accurate measure of the total volume flux in the two coalescing plumes as they evolve through the three regions.

We present a continuum approach to predicting the electrophoretic mobility of a charged dielectric colloidal particle in a concentrated multivalent electrolyte. Our model takes into account steric (excluded volume) hindrance between ions via Bikerman’s approach (Philos. Mag., vol. 33, 1942, p. 384) and ion–ion electrostatic (Coulombic) correlations via the work of Bazant et al. (Phys. Rev. Lett., vol. 106, 2011, 046102). The latter can result in the prediction of an electrophoretic mobility reversal, that is, the migration velocity of a particle switches direction with increasing ion concentration. Our model predictions compare favourably with experiments that observe mobility reversals in multivalent electrolytes.

Path and wake instabilities of buoyancy-driven oblate spheroidal bubbles with a prescribed shape rising freely in a viscous fluid otherwise at rest are studied using global stability analysis, following the technique recently developed for a coupled fluid $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}+$ body system by Tchoufag, Fabre & Magnaudet (J. Fluid Mech. vol. 740, 2014, pp. 278–311). The essential role of the wake on the path instability is evidenced by comparing the shape of the global stability diagram with that obtained in the case of a fixed bubble. However, dramatic differences are also found, since the critical curve of the coupled system mostly involves low- and high-frequency oscillating modes, whereas that of a fixed bubble only involves stationary modes. Comparison of the present predictions with results obtained through direct numerical simulation is achieved in several regimes, confirming the predictions of the linear approach but also highlighting some of its limitations when the system successively encounters several unstable modes.

A new set of numerical simulations of turbulent plane Couette flow in a large box of dimension ( $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}20\pi h,\, 2h,\, 6\pi h$ ) at Reynolds number $(\mathit{Re}_{\tau }) =125$ , 180, 250 and 550 is described and compared with simulations at lower Reynolds numbers, Poiseuille flows and experiments. The simulations present a logarithmic near-wall layer and are used to verify and revise previously known results. It is confirmed that the fluctuation intensities in the streamwise and spanwise directions do not scale well in wall units. The scaling failure occurs both near to and away from the wall. On the contrary, the wall-normal intensity scales in inner units in the near-wall region and in outer units in the core region. The spectral ridge found by Hoyas & Jiménez (Phys. Fluids, vol. 18, 2003, 011702) for the turbulent Poiseuille flow can also be seen in the present flow. Away from the wall, very large-scale motions are found spanning through all the length of the channel. The statistics of these simulations can be downloaded from the webpage of the Chair of Fluid Dynamics.

Two-dimensional steady gravity waves with vorticity are considered on water of finite depth. The dispersion equation is analysed for general vorticity distributions, but under assumptions valid only for unidirectional shear flows. It is shown that for these flows (i) the general dispersion equation is equivalent to the Sturm–Liouville problem considered by Constantin & Strauss (Commun. Pure Appl. Math., vol. 57, 2004, pp. 481–527; Arch. Rat. Mech. Anal., vol. 202, 2011, pp. 133–175), (ii) the condition guaranteeing bifurcation of Stokes waves with constant wavelength is fulfilled. Moreover, a necessary and sufficient condition that the Sturm–Liouville problem mentioned in (i) has an eigenvalue is obtained.

This paper demonstrates that the shallow water semigeostrophic equations arise from a degenerate second-order Hamilton principle of very special structure. The associated Euler–Lagrange operator factors into a fast and a slow first-order operator; restricting to the slow part yields the geostrophic momentum approximation as balanced dynamics. While semigeostrophic theory has been considered variationally before, this structure appears to be new. It leads to a straightforward derivation of the geostrophic momentum approximation and its associated potential vorticity law. Our observations further affirm, from a different point of view, the known difficulty in generalizing the semigeostrophic equations to the case of a spatially varying Coriolis parameter.

We present an equilibrium solution of plane Couette flow that is exponentially localized in both the spanwise and streamwise directions. The solution is similar in size and structure to previously computed turbulent spots and localized, chaotically wandering edge states of plane Couette flow. A linear analysis of dominant terms in the Navier–Stokes equations shows how the exponential decay rate and the wall-normal overhang profile of the streamwise tails are governed by the Reynolds number and the dominant spanwise wavenumber. Perturbations of the solution along its leading eigenfunctions cause rapid disruption of the interior roll-streak structure and formation of a turbulent spot, whose growth or decay depends on the Reynolds number and the choice of perturbation.

We present results of direct numerical simulation of incompressible fluid flow over a thick bed of mobile spherically shaped particles. The algorithm is based upon the immersed-boundary technique for fluid–solid coupling and uses a soft-sphere model for the solid–solid contact. Two parameter points in the laminar flow regime are chosen, leading to the emergence of sediment patterns classified as ‘small dunes’, while one case under turbulent flow conditions leads to ‘vortex dunes’ with significant flow separation on the lee side. The wavelength, amplitude and propagation speed of the patterns extracted from the spanwise-averaged fluid–bed interface are found to be consistent with available experimental data. The particle transport rates are well represented by available empirical models for flow over a plane sediment bed in both the laminar and the turbulent regimes.

The instability of the hub vortex observed in wind turbine wakes has recently been studied by Iungo et al. (J. Fluid Mech., vol. 737, 2013, pp. 499–526) via local stability analysis of the mean velocity field measured through wind tunnel experiments. This analysis was carried out by neglecting the effect of turbulent fluctuations on the development of the coherent perturbations. In the present paper, we perform a stability analysis taking into account the Reynolds stresses modelled by eddy-viscosity models, which are calibrated on the wind tunnel data. This new formulation for the stability analysis leads to the identification of one clear dominant mode associated with the hub vortex instability, which is the one with the largest overall downstream amplification. Moreover, this analysis also predicts accurately the frequency of the hub vortex instability observed experimentally. The proposed formulation is of general interest for the stability analysis of swirling turbulent flows.

Taylor–Couette (TC) flow is used to probe the hydrodynamical (HD) stability of astrophysical accretion disks. Experimental data on the subcritical stability of TC flow are in conflict about the existence of turbulence (cf. Ji et al. (Nature, vol. 444, 2006, pp. 343–346) and Paoletti et al. (Astron. Astroph., vol. 547, 2012, A64)), with discrepancies attributed to end-plate effects. In this paper we numerically simulate TC flow with axially periodic boundary conditions to explore the existence of subcritical transitions to turbulence when no end plates are present. We start the simulations with a fully turbulent state in the unstable regime and enter the linearly stable regime by suddenly starting a (stabilizing) outer cylinder rotation. The shear Reynolds number of the turbulent initial state is up to $Re_s \lesssim 10^5$ and the radius ratio is $\eta =0.714$ . The stabilization causes the system to behave as a damped oscillator and, correspondingly, the turbulence decays. The evolution of the torque and turbulent kinetic energy is analysed and the periodicity and damping of the oscillations are quantified and explained as a function of shear Reynolds number. Though the initially turbulent flow state decays, surprisingly, the system is found to absorb energy during this decay.

On the basis of a two-point similarity analysis, the well-known power-law variations for the mean kinetic energy dissipation rate $\overline{\epsilon }$ and the longitudinal velocity variance $\overline{u^2}$ on the axis of a round jet are derived. In particular, the prefactor for $\overline{\epsilon } \propto (x-x_0)^{-4}$ , where $x_0$ is a virtual origin, follows immediately from the variation of the mean velocity, the constancy of the local turbulent intensity and the ratio between the axial and transverse velocity variance. Second, the limit at small separations of the two-point budget equation yields an exact relation illustrating the equilibrium between the skewness of the longitudinal velocity derivative $S$ and the destruction coefficient $G$ of enstrophy. By comparing the latter relation with that for homogeneous isotropic decaying turbulence, it is shown that the approach towards the asymptotic state at infinite Reynolds number of $S+2G/R_{\lambda }$ in the jet differs from that in purely decaying turbulence, although $S+2G/R_{\lambda } \propto R_{\lambda }^{-1}$ in each case. This suggests that, at finite Reynolds numbers, the transport equation for $\overline{\epsilon }$ imposes a fundamental constraint on the balance between $S$ and $G$ that depends on the type of large-scale forcing and may thus differ from flow to flow. This questions the conjecture that $S$ and $G$ follow a universal evolution with $R_{\lambda }$ ; instead, $S$ and $G$ must be tested separately in each flow. The implication for the constant $C_{\epsilon 2}$ in the $k-\overline{\epsilon }$ model is also discussed.