Focus issue on Turbulent Mixing and Beyond

Fractal grids have attracted attention as a new-type of turbulence-generating grid due to their unique characteristics. Recent studies have revealed that such uniqueness appears in the near field of regular grid-generated turbulence. Scalar transport in those flows is also of great interest as it is not yet fully understood. In this study, we investigate the scalar mixing in the near field of regular grid-generated turbulence with various grid configurations. Experiments have been carried out in liquid mixing layers with a Reynolds number of 5000 based on the mesh size of the grid and uniform velocity. Simultaneous measurements of two-component velocities and concentration have been performed by particle image velocimetry and a planar laser-induced fluorescence technique, respectively. The results show that the scaling law using the wake-interaction length scale is applicable for the turbulence intensity in the grid turbulence with different mesh sizes and the same thickness of the grid bar. The turbulence intensity increases as the thickness of the grid bar increases; thus, consequently increasing the scalar diffusion. The streamwise development of the scalar mixing layer thickness collapses onto a single curve by normalization based on the thickness of the grid bar.

Return-to-isotropy and kinetic-potential energy equipartition are two fundamental pressure-moderated energy redistributive processes in anisotropic compressible turbulence. Pressure-strain correlation tensor redistributes energy among various Reynolds stress components and pressure-dilatation is responsible for energy reallocation between dilatational kinetic and potential energies. The competition and interplay between these pressure-based processes are investigated in this study. Direct numerical simulations (DNS) of low turbulent Mach number dilatational turbulence are performed employing the hybrid thermal Lattice Boltzman method (HTLBM). It is found that a tendency towards equipartition precedes proclivity for isotropization. An evolution towards equipartition has a collateral but critical effect on return-to-isotropy. The preferential transfer of energy from strong (rather than weak) Reynolds stress components to potential energy accelerates the isotropization of dilatational fluctuations. Understanding of these pressure-based redistributive processes is critical for developing insight into the character of compressible turbulence.

Turbulent mixing is ubiquitous in both nature and industrial applications. Most of them concern different fluids, therefore with variable physical properties (density and/or viscosity). The focus here is on variable viscosity flows and mixing, involving density-matched fluids. The issue is whether or not these flows may be self-similar, or self-preserving. The importance of this question stands on the predictability of these flows; self-similar dynamical systems are easier tractable from an analytical viewpoint. More specifically, self-similar analysis is applied to the scale-by-scale energy transport equations, which represent the transport of energy at each scale and each point of the flow. Scale-by-scale energy budget equations are developed for inhomogeneous and anisotropic flows, in which the viscosity varies as a result of heterogeneous mixture or temperature variations. Additional terms are highlighted, accounting for the viscosity gradients, or fluctuations. These terms are present at both small and large scales, thus rectifying the common belief that viscosity is a small-scale quantity. Scale-by-scale energy budget equations are then adapted for the particular case of a round jet evolving in a more viscous host fluid. It is further shown that the condition of self-preservation is not necessarily satisfied in variable-viscosity jets. Indeed, the jet momentum conservation, as well as the constancy of the Reynolds number in the central region of the jet, cannot be satisfied simultaneously. This points to the necessity of considering less stringent conditions (with respect to classical, single-fluid jets) when analytically tackling these flows and reinforces the idea that viscosity variations must be accounted for when modelling these flows.

As fluid flows through a conventional wind or hydro turbine, it slows from losing energy to extraction from a turbine and spreads out to a wider area. This results in a loss of turbine efficiency. In order to exploit wind or water flow power more effectively, it was suggested to place the turbine inside a system of specially designed airfoils ('a flow booster'). One part of the booster ('a nozzle') improves the turbine performance by speeding up the flow acting on the turbine blades. The other part of the accelerating system ('a diffuser') creates a field of low pressure behind the turbine which helps to draw more mass flow to the turbine and avoid the loss of efficiency due to flow deceleration. The flow booster accumulates the kinetic energy of the flow (e.g. river flow or wind) in a small volume where the smaller turbine can be installed. Another possible application of the booster could be the improvement of wind turbine efficiency during low wind period. The present paper also discusses the possibility of kinetic energy accumulation by the use of several accelerating systems of different sizes—the smaller one can be installed inside the bigger one. It helps to accumulate even more kinetic energy on the turbine blades. We call this method the kinetic energy cumulation. Lab and field experiments and CFD simulations of shrouded turbine demonstrate significant increase in velocity in comparison of those for conventional (bare) turbines.

We consider a close relative of plane Couette flow called Waleffe flow in which the fluid is confined between two free-slip walls and the flow driven by a sinusoidal force. We use a reduced model of such flows constructed elsewhere to compute stationary exact coherent structures in this flow in periodic domains with a large spanwise period. The computations reveal the emergence of stationary states exhibiting strong amplitude and wavelength modulation in the spanwise direction. These modulated states lie on branches exhibiting complex dependence on the Reynolds number but no homoclinic snaking.

This paper presents a new theory on the behaviour of shear-thickening (dilatant) fluids under turbulent conditions. The structure of a dilatant colloidal fluid in turbulent motion may be characterized by (at least) four characteristic length scales: (i) the 'statistically largest' turbulent scale, ${\lambda }_{0}$, labeling the begin of the inertial part of the wavenumber spectrum; (ii) the energy-containing scale, ${ \mathcal L };$ (iii) Kolmogorov's micro-scale, ${\lambda }_{{ \mathcal K }}$, related with the size of the smallest vortices existing for a given kinematic viscosity and forcing; (iv) the inner ('colloidal') micro-scale, ${\lambda }_{i}$, typically representing a major stable material property of the colloidal fluid. In particular, for small ratios $r={\lambda }_{i}/{\lambda }_{{ \mathcal K }}\sim { \mathcal O }(1)$, various interactions between colloidal structures and smallest turbulent eddies can be expected. In the present paper we discuss particularly that for $\rho ={\lambda }_{0}/{\lambda }_{{ \mathcal K }}\to { \mathcal O }(1)$ turbulence (in the narrow, inertial sense) is strangled and chaotic but less mixing fluid motions remain. We start from a new stochastic, micro-mechanical turbulence theory without empirical parameters valid for inviscid fluids as seen in publications by Baumert in 2013 and 2015. It predicts e.g. von Karman's constant correctly as $1/\sqrt{2\;\pi }=0.399$. In its generalized version for non-zero viscosity and shear-thickening behavior presented in this contribution, it predicts two solution branches for the steady state: The first characterizes a family of states with swift (inertial) turbulent mixing and small ${\lambda }_{{ \mathcal K }}$, potentially approaching ${\lambda }_{i}$. The second branch characterizes a state family with $\rho \to { \mathcal O }(1)$ and thus strangled turbulence, $\rho \approx { \mathcal O }(1)$. Stability properties and a potential dynamic commuting between the two solution branches had to be left for future research.

Many systems in nature are out of equilibrium and irreversible. The non-detailed balance observable representation (NOR) provides a useful methodology for understanding the evolution of such non-equilibrium complex systems, by mapping out the correlation between two states to a metric space where a small distance represents a strong correlation [1]. In this paper, we present the first application of the NOR to a continuous system and demonstrate its utility in controlling chaos. Specifically, we consider the evolution of a continuous system governed by the Lorenz equation and calculate the NOR by following a sufficient number of trajectories. We then show how to control chaos by converting chaotic orbits to periodic orbits by utilizing the NOR. We further discuss the implications of our method for potential applications given the key advantage that this method makes no assumptions of the underlying equations of motion and is thus extremely general.

A nonlinear motion of vortex sheets with a non-uniform current is investigated using the vortex blob method. The fluid interface forms a double layered current-vortex sheet due to the boundary condition possessing the induction equation. We can prove that the current only flows on the interface and that does not appear in the bulk when we apply the initial magnetic field to be parallel to the interface. We show that the current induced on a vortex sheet leads to a strong amplification of the magnetic field, taking the motion of vortex sheets in magnetohydrodynamic Richtmyer–Meshkov instability as an example. When the initial Lorentz force term is large, an oscillation due to the Alfvén wave appears and the nonlinear growth is suppressed.

Previous research into three-dimensional numerical simulation of self-similar mixing due to Rayleigh–Taylor instability is summarized. A range of numerical approaches has been used: direct numerical simulation, implicit large eddy simulation and large eddy simulation with an explicit model for sub-grid-scale dissipation. However, few papers have made direct comparisons between the various approaches. The main purpose of the current paper is to give comparisons of direct numerical simulations and implicit large eddy simulations using the same computational framework. Results are shown for four test cases: (i) single-mode Rayleigh–Taylor instability, (ii) self-similar Rayleigh–Taylor mixing, (iii) three-layer mixing and (iv) a tilted-rig Rayleigh–Taylor experiment. It is found that both approaches give similar results for the high-Reynolds number behavior. Direct numerical simulation is needed to assess the influence of finite Reynolds number.

We report results obtained for two elementary unstable flow configurations relevant to high energy density physics: the ablation front instability and the Rayleigh–Taylor -instability induced mixing layer. These two flows are characterized by a transience of their perturbation dynamics. In the ablative flow case, this perturbation dynamics transience takes the form of finite-durations of successive linear-perturbation evolution phases until reaching regimes of decaying oscillations. This behaviour is observed in various regimes: weakly or strongly accelerated ablation fronts, irradiation asymmetries or initial external-surface defects, and is a result of the mean-flow unsteadiness and stretching. In the case of the Rayleigh–Taylor-instability induced mixing layer, perturbation dynamics transience manifests itself through the extinction of turbulence and mixing as the flow reaches a stable state made of two stably stratified layers of pure fluids separated by an unstratified mixing layer. A second feature, also due to compressibility, takes the form of an intense acoustic wave production, mainly localized in the heavy fluid. Finally, we point out that a systematic short-term linear-perturbation dynamics analysis should be undertaken within the framework of non-normal stability theory.

Rayleigh–Taylor (RT) mixing occurs in a variety of natural and man-made phenomena in fluids, plasmas and materials, from celestial event to atoms. In many circumstances, RT flows are driven by variable acceleration, whereas majority of existing studies have considered only sustained acceleration. In this work we perform detailed analytical and numerical study of RT mixing with a power-law time-dependent acceleration. A set of deterministic nonlinear non-homogeneous ordinary differential equations and nonlinear stochastic differential equations with multiplicative noise are derived on the basis of momentum model. For a broad range of parameters, self-similar asymptotic solutions are found analytically, and their statistical properties are studied numerically. We identify two sub-regimes of RT mixing dynamics depending on the acceleration exponent—the acceleration-driven mixing and dissipation-driven mixing. Transition between the sub-regimes is studied, and it is found that each sub-regime has its own characteristic dimensionless invariant quantity.

Along with Newtonian fluids (for example, water), fluids with non-Newtonian rheology are widespread in nature and industry. The characteristic feature of a non-Newtonian fluid is the non-linear dependence between the shear stress and shear rate tensors. The form of this relation defines the types of non-Newtonian behavior: viscoplastic, pseudoplastic, dilatant and viscoelastic. The present work is devoted to the study of the Rayleigh–Taylor instability in pseudoplastic fluids. The main aim of the work is to undertake a direct three-dimensional numerical simulation of the mixing of two media with various rheologies and obtain the width of the mixing layer and the kinetic energy spectra, depending on the basic properties of the shear thinning liquids and the Atwood number. A theoretical study is carried out on the basis of the Navier–Stokes equation system for weakly compressible media.

Stellar evolution models of massive stars are important for many areas of astrophysics, for example nucleosynthesis yields, supernova progenitor models and understanding physics under extreme conditions. Turbulence occurs in stars primarily due to nuclear burning at different mass coordinates within the star. The understanding and correct treatment of turbulence and turbulent mixing at convective boundaries in stellar models has been studied for decades but still lacks a definitive solution. This paper presents initial results of a study on convective boundary mixing (CBM) in massive stars. The 'stiffness' of a convective boundary can be quantified using the bulk Richardson number (${\mathrm{Ri}}_{{\rm{B}}}$), the ratio of the potential energy for restoration of the boundary to the kinetic energy of turbulent eddies. A 'stiff' boundary (${\mathrm{Ri}}_{{\rm{B}}}\sim {10}^{4}$) will suppress CBM, whereas in the opposite case a 'soft' boundary (${\mathrm{Ri}}_{{\rm{B}}}\sim 10$) will be more susceptible to CBM. One of the key results obtained so far is that lower convective boundaries (closer to the centre) of nuclear burning shells are 'stiffer' than the corresponding upper boundaries, implying limited CBM at lower shell boundaries. This is in agreement with 3D hydrodynamic simulations carried out by Meakin and Arnett (2007 Astrophys. J.  667 448–75). This result also has implications for new CBM prescriptions in massive stars as well as for nuclear burning flame front propagation in super-asymptotic giant branch stars and also the onset of novae.

We present initial results from three-dimensional simulations of parametrized core-collapse supernova (CCSN) explosions obtained with our astrophysical simulation code General Astrophysical Simulation System (GenASIS). We are interested in nonlinear flows resulting from neutrino-driven convection and the standing accretion shock instability (SASI) in the CCSN environment prior to and during the explosion. By varying parameters in our model that control neutrino heating and shock dissociation, our simulations result in convection-dominated and SASI-dominated evolution. We describe this initial set of simulation results in some detail. To characterize the turbulent flows in the simulations, we compute and compare velocity power spectra from convection-dominated and SASI-dominated (both non-exploding and exploding) models. When compared to SASI-dominated models, convection-dominated models exhibit significantly more power on small spatial scales.

We discuss results of the applicability of discrete filters for the large-eddy simulation (LES) method of forced compressible magnetohydrodynamic (MHD) turbulent flows with the scale-similarity model. New results are obtained for cross-helicity and residual energy. Cross-helicity and residual energy are important quantities in magnetohydrodynamic turbulence and have no hydrodynamic counterpart. The influences and effects of discrete filter shapes on the scale-similarity model are examined in physical space using finite-difference numerical schemes. We restrict ourselves to the Gaussian filter and the top-hat filter. Representations of this subgrid-scale model, which correspond to various 3- and 5-point approximations of both Gaussian and top-hat filters for different values of parameter $\epsilon$ (the ratio of the cut-off length-scale of the filter to the mesh size), are investigated. Discrete filters produce more discrepancies for the magnetic field. It is shown that the Gaussian filter is more sensitive to the parameter than the top-hat filter in compressible forced MHD turbulence. The 3-point filters at $\epsilon =2$ and $\epsilon =3$ give the least accurate results whereas the 5-point Gaussian filter shows the best results at $\epsilon =2$ and $\epsilon =3$. There are only very small differences deep into the dissipation region in favor of $\epsilon =2$. For cross-helicity, the 5-point discrete filters are in good agreement with the results of direct numerical simulation (DNS), while the 3-point filter produces the largest discrepancies with DNS results. There is no strong dependence on the choice of the parameter $\epsilon$ and order approximation is a much more important factor for the cross-helicity. The difference between the filters is less for the residual energy compared with total energy. Thus, the total energy is more sensitive to the choice of discrete filter in the modeling of compressible MHD turbulence using the LES method.

We study the evolution of primordial magnetic fields in an expanding cosmic plasma. For this purpose we present a comprehensive theoretical model to consider the evolution of MHD turbulence that can be used over a wide range of physical conditions, including cosmological and astrophysical applications. We model different types of decaying cosmic MHD turbulence in the expanding Universe and characterize the large-scale magnetic fields in such a medium. Direct numerical simulations of freely decaying MHD turbulence are performed for different magnetogenesis scenarios: magnetic fields generated during cosmic inflation as well as electroweak and QCD phase transitions in the early Universe. Magnetic fields and fluid motions are strongly coupled due to the high Reynolds number in the early Universe. Hence, we abandon the simple adiabatic dilution model to estimate magnetic field amplitudes in the expanding Universe and include turbulent mixing effects on the large-scale magnetic field evolution. Numerical simulations have been carried out for non-helical and helical magnetic field configurations. The numerical results show the possibility of inverse transfer of energy in magnetically dominated non-helical MHD turbulence. On the other hand, decay properties of helical turbulence depend on whether the turbulent magnetic field is in a weakly or a fully helical state. Our results show that primordial magnetic fields can be considered as a seed for the observed large-scale magnetic fields in galaxies and clusters. Bounds on the magnetic field strength are obtained and are consistent with the upper and lower limits set by observations of extragalactic magnetic fields.

Topological constraints play a key role in the self-organizing processes that create structures in macro systems. In fact, if all possible degrees of freedom are actualized on equal footing without constraint, the state of 'equipartition' may bear no specific structure. Fluid turbulence is a typical example—while turbulent mixing seems to increase entropy, a variety of sustained vortical structures can emerge. In Hamiltonian formalism, some topological constraints are represented by Casimir invariants (for example, helicities of a fluid or a plasma), and then, the effective phase space is reduced to the Casimir leaves. However, a general constraint is not necessarily integrable, which precludes the existence of an appropriate Casimir invariant; the circulation is an example of such an invariant. In this work, we formulate a systematic method to embed a Hamiltonian system in an extended phase space; we introduce phantom fields and extend the Poisson algebra. A phantom field defines a new Casimir invariant, a cross helicity, which represents a topological constraint that is not integrable in the original phase space. Changing the perspective, a singularity of the extended system may be viewed as a subsystem on which the phantom fields (though they are actual fields, when viewed from the extended system) vanish, i.e., the original system. This hierarchical relation of degenerate Poisson manifolds enables us to see the 'interior' of a singularity as a sub Poisson manifold. The theory can be applied to describe bifurcations and instabilities in a wide class of general Hamiltonian systems (Yoshida and Morrison 2014 Fluid Dyn. Res. 46 031412).

In this paper the problem of evolution of diffusion induced flow on a wedge-shaped obstacle is analyzed numerically. The governing set of fundamental equations is solved using original solvers from the open source OpenFOAM package on supercomputer facilities. Due to breaking of naturally existing diffusion flux of a stratifying agent by the impermeable surface of the wedge a complex multi-level vortex system of compensatory fluid motions is formed around the obstacle. Sharp edges of the obstacle generate extended high-gradient horizontal interfaces which are clearly observed in laboratory experiments by high-resolution Schlieren visualization. Formation of an intensive pressure depression zone in front of the leading vertex of the wedge is responsible for generation of propulsive force resulting in a self-displacement of the obstacle along the neutral buoyancy horizon in a stably stratified environment. The size of the pressure deficiency area near the sharp vertex of a concave wedge is about twice that for a convex one. This demonstrates a more intensive propulsion mechanism in case of the concave wedge and, accordingly, a higher velocity of its self-movement in a continuously stratified medium.

We present direct numerical simulations of two minimal flow units (MFUs) to investigate the differences between inviscid and viscous simulations, and the different behavior of the evolution for conducting fluids. In these circumstances the introduction of the Lorentz force in the momentum equation produces different scenarios. The Taylor–Green vortex, in the past, was an MFU widely considered for both conducting and non-conducting fluids. The simulations were performed by pseudo-spectral numerical methods; these are repeated here by using a finite difference second-order accurate, energy-conserving scheme for $\nu =0$. Having observed that this initial condition could be inefficient for capturing the eventual occurrence of a finite time singularity a potentially more efficient MFU consisting of two interacting Lamb dipoles was considered. It was found that the two flows have a different time evolution in the vortical dominated stage. In this stage, turbulent structures of different size are generated leading to spectra, in the inviscid conditions, with a ${k}^{-3}$ range. In real conditions the viscosity produces smaller scales characteristic of fully developed turbulence with energy spectra with well defined exponential and inertial ranges. In the presence of non-conducting conditions the passive vector behaves as the vorticity. The evolution is different in the presence of conducting conditions. Although the time evolution is different, both flows lead to spectra in Kolmogorov units with the same shape at high and intermediate wave numbers.

Flows of electrically conducting fluids under the action of external magnetic field present an example of strongly anisotropic turbulence. Such flows are not only important for different engineering applications, but also provide an interesting framework for studies of quasi-two-dimensional turbulence with strongly modified transport properties in easily controllable laboratory experiments. We present theoretical results that advance our understanding of magnetohydrodynamic (MHD) flows with low magnetic Reynolds number by treating this phenomenon within the quasi-normal scale elimination (QNSE) theory. Previous applications of the theory to turbulent flows with stable stratification and solid body rotation have demonstrated that QNSE is a powerful tool for studies of anisotropic turbulent flows. We derive expressions for scale-dependent eddy viscosities and eddy diffusivities in the directions parallel and normal to the external magnetic field and investigate progressive anisotropization of turbulent transport of momentum and passive scalar. The theory yields analytical expressions for anisotropic one-dimensional spectra of MHD turbulence. In particular, the theory sheds light upon the modification of the Kolmogorov k^−5/3 spectrum by anisotropic Ohmic (Joule) dissipation.

Propagation of a gel/glass transition boundary in a polymer is considered in the context of drug release. Drug molecules are assumed to undergo subdiffusive motion in the gel and be quiescent in the glass region. Exact self-similar solutions for the drug concentration are constructed, and the amount of released drug is determined as a function of time.

An overview of recent developments in a wide variety of enclosed rapidly rotating flows is presented. Highlighted is the interplay between inertial waves, which have been predicted from linear inviscid considerations, and the viscous boundary layer dynamics which result from instabilities as the nonlinearities in the systems are increased. Further, even in the absence of boundary layer instabilities, nonlinearity in the system often leads to complicated interior flows due to subcritical instabilities, Eckhaus bands and heteroclinic dynamics. The ensuing spatio-temporally complex dynamics is analysed in terms of equivariant dynamical systems, providing a general perspective for the wide range of dynamics involved.

We assess the performance of an ensemble Kalman filter for data assimilation and forecasting of ion density in a model of the ionosphere given noisy observations of varying sparsity. The domain of the numerical model is a mid-latitude ionosphere between 80 and 440 km. This domain includes the D–E layers and the peak in the F layer in the ionosphere. The model simulates the time evolution of an ion density field and the coupled electrostatic potential as charge-neutral winds from gravity waves propagate up from the stratosphere. Forecasts are generated for an ensemble of initial conditions, and synthetic observations, which are generated at random locations in the model domain, are assimilated into the ensemble at time intervals corresponding to about a half-period of the gravity wave. The data assimilation scheme, called the local ensemble transform Kalman filter (LETKF), incorporates observations within a fixed radius of each grid point to compute a unique linear combination of the forecast ensembles at each grid point. The collection of updated grid points forms the updated initial conditions (analysis ensemble) for the next forecast. Even when the observation density is spatially sparse, accurate analyses of the ion density still can be obtained, but the results depend on the size of the local region used. The LETKF is robust to large levels of Gaussian noise in the observations. Our results suggest that the LETKF merits consideration as a data assimilation scheme for space weather forecasting.

Anelastic Rayleigh–Taylor mixing layers for miscible fluids are investigated with a recently built model (Schneider and Gauthier 2015 J. Eng. Math. 92 55–71). Four Chebyshev–Fourier–Fourier direct numerical simulations are analyzed. They use different values for the compressibility parameters: Atwood number (the dimensionless difference of the heavy and light fluid densities) and stratification (accounts for the vertical variation of density due to gravity). For intermediate Atwood numbers and finite stratification, compressibility effects quickly occurs. As a result only nonlinear behaviours are reached. The influence of the compressibility parameters on the growth speed of the RTI is discussed. The 0.1—Atwood number/0.4—stratification configuration reaches a turbulent regime. This turbulent mixing layer is analyzed with statistical tools such as moments, PDFs, anisotropy indicators and spectra.

A scalar mixing layer in fractal grid turbulence is simulated by the implicit large eddy simulation (ILES) using low-pass filtering as an implicit subgrid-scale model. The square-type fractal grid with three fractal iterations is used for generating turbulence. The streamwise evolutions of the streamwise velocity statistics obtained in the ILES are in good agreement with the experimental results. The ILES results are used for investigating the development of the scalar mixing layer behind the fractal grid. The results show that the vertical development of the scalar mixing layer strongly depends on the spanwise location. Near the fractal grid, the scalar mixing layer rapidly develops just behind the largest grid bars owing to the vertical turbulent transport. The scalar mixing layer near the fractal grid also develops outside the largest grid bars because the scalar is transported between the outside and back of the largest grid bars by the spanwise turbulent transport. In the downstream region, the scalar mixing layer develops more rapidly near the grid centerline by the vertical turbulent transport and by the spanwise one which transports the scalar between the back of the largest grid bars and both the centerline and outer edge of the fractal grid. Then, the mean scalar profile becomes close to be homogeneous in the spanwise direction.

In this paper, we perform a numerical study on the heat transfer and pressure drop in hydraulically and thermally developing turbulent flow of nanofluid through an internally ribbed pipe. The effects of volume fraction of nanoparticles and the distance between the ribs are investigated on the heat transfer and skin friction coefficients at the entrance region of the pipe. The set of governing equations followed by a two-layer zonal turbulence model are solved numerically by a velocity-pressure coupling algorithm based on finite-volume method. Moreover, available empirical relations are used to calculate the nanofluid properties in terms of the nanoparticles and the base fluid. The obtained results illustrate that increasing the volume fraction of nanoparticles makes the thermal entrance length decrease and consequently, the heat transfer increases. It reveals that 10% increase in the volume fraction of nanoparticles causes about 15% rise in average Nusselt number. In addition, it is found that the friction factor rises by increasing the volume fraction of nanoparticles compared with turbulent flow of the base-fluid. Also, the average Nusselt number in nanofluid flow increases with the interval between the ribs compared with pure-fluid flow.

Many plasmas in natural settings or in laboratory experiments carry currents. In magnetized plasmas the currents can be narrow field-aligned filaments as small as the electron inertial length $\left(\tfrac{c}{{\omega }_{pe}}\right)$ in the transverse dimension or fill the entire plasma column. Currents can take the form of sheets, again with the transverse dimension the narrow one. Are laminar sheets of electric current in a magnetized plasma stable? This became an important issue in the 1960s when current-carrying plasmas became key in the quest for thermonuclear fusion. The subject is still under study today. The conditions necessary for the onset for tearing are known, the key issue is that of the final state. Is there a final state? One possibility is a collection of stable tubes of current. On the other hand, is the interaction between the current filaments which are the byproduct endless, or does it go on to become chaotic? The subject of three-dimensional current systems is intriguing, rich in a variety of phenomena on multiple scale sizes and frequencies, and relevant to fusion studies, solar physics, space plasmas and astrophysical phenomena. In this study a long (δz = 11 m) and narrow (δx = 1 cm, δy = 20 cm) current sheet is generated in a background magnetoplasma capable of supporting Alfvén waves. The current is observed to rapidly tear into a series of magnetic islands when viewed in a cross-sectional plane, but they are in essence three-dimensional flux ropes. At the onset of the current, magnetic field line reconnection is observed between the flux ropes. The sheet on the whole is kink-unstable, and after kinking exhibits large-scale, low-frequency (f ≪ f_ci) rotation about the background field with an amplitude that grows with distance from the source of the current. Three-dimensional data of the magnetic and electric fields is acquired throughout the duration of the experiment and the parallel resistivity is derived from it. The parallel resistivity, for the most part, is not largest in the reconnection regions, but peaks in the neighborhood of large current gradients. At early times a quasi-separatrix layer (QSL) is observed where the current sheet tears, but later on a QSL of larger value, not obviously associated with reconnection, is measured at the edge of the current sheet. This QSL enhancement is connected with the rapidly spatially diverging magnetic fields in the moving sheet (ropes).

The results of experiments researching the stability of the dome of a large water bubble rising in a salt solution are presented. The experiments demonstrate the suppression of the Rayleigh–Taylor instability on the dome of the rising bubble with the Atwood number being A ≪ 1. The intensive development of the Kelvin–Helmholtz instability on the lateral surface of the bubble is observed as it rises. The stability of the dome of the rising bubble is explained by the action of an accelerated shear flow of water over the bubble surface. The results of computational modeling of the problem by the STAR-CCM + program are presented.