We attempt to formulate the simplest possible model mimicking turbulent dynamics, such as quasi-cyclic behaviour (QCB), using only three variables. To this end, we first conduct direct numerical simulations of three-dimensional flow driven by the steady Taylor–Green forcing to find a similarity between a stable periodic orbit (SPO) at a small Reynolds number (Re) and turbulent QCB at higher Re. A close examination of the SPO allows the heuristic formulation of a three-equation model, representing the evolution of Fourier modes in three distinct scales. The model reproduces the continuous bifurcation from SPO to turbulence with QCB when Re is varied. We also demonstrate that, by changing model parameters, the proposed model exhibits a discontinuous transition from steady to chaotic solutions without going through an SPO.

The formation and evolution of helical vortices in various media is an important hydrodynamic problem. A separate problem is the study of the behavior of the initial vortex, which is elevated above the surface. The evolution of such vortices is a complex multiparameter phenomenon. Based on a simple hydrodynamic model (or minimal model) in Elikashvili et al (2017 Phys. Fluids 29 026602) have been studied the formation of vorticity near the surface as a function of the initial height of the vortex and the Reynolds number. However, the influence of the parameters of the initial vortex profile on its evolution was not considered. In this paper, based on a simple hydrodynamic model, we study the evolution and formation of vortices near a solid surface for various initial vorticity profiles. The most widespread vortex profiles of Rankine, Burgers, and Vatistas were chosen for research. The simulation shows that the evolution of the vortex depends on its initial profile.

The article presents a three-dimensional numerical study of the large-amplitude, acoustically driven streaming flow in rectangular resonator for different frequencies of the acoustic wave and different temperature regime, isothermal and 60 K temperature difference between the top and bottom walls. The utilized numerical model was based on the Navier–Stokes compressible equations, the ideal gas model, and finite volume discretization. The oscillating wall of the resonator was modeled as a dynamically moving boundary of the numerical domain. The size of the resonators was adjusted to fit one period of the acoustic wave. The research revealed a stationary pair of streaming vortices in the resonator with a characteristic three-dimensional structure. Their intensity was much greater in the case of nonisothermal flow. The study of the impact of side walls on the intensity of streaming revealed its gradual decrease with approaching the walls, creating a quasiparabolic profile in the resonator. Interestingly, the relationship between the intensity of streaming and the frequency of the acoustic wave turned out to be not trivial and two maxima for different frequencies could be observed.

The numerical modeling of an electroosmosis flow in a rectangular three-dimensional rotating microchannel has been studied. The study’s goal is to calculate the flow’s development length, and as a novelty, a correlation is proposed to estimate the development length. The flow was simulated for angular velocity (ω) ranges of 0–9 and electric potential (φ) ranges of 0.1–0.3. The results were imported into the curve fitting toolbox to determine a correlation for the development length. The correlation was obtained as a function of angular velocity, electric potential, and hydraulic diameter. The results show that increasing both ω and φ leads to an increase in flow development length, where for constant φ, increasing ω from 0 to 9 results in a 20%–30% increase in development length. Furthermore, increasing φ from 0.1 to 0.3 for a constant ω raises development length by 35%–50%. The velocity field and its parameters, such as ω and φ, were analyzed and discussed.

This article presents an extension of Liepmann’s characterization of an aeroacoustic source in terms of the motion of a bounding surface containing the source region. Rather than using an arbitrary surface, we express the problem in terms of bounding material surfaces, identified by Lagrangian coherent structures (LCSs), which demarcate flow into regions with distinct dynamics. The sound generation of the flow is written in terms of the motion of these material surfaces using the Kirchhoff integral equation, so that the flow noise problem now appears like that of a deforming body. This approach provides a natural connection between the flow topology, as revealed through LCS analysis, and sound generation mechanisms. As examples, we examine two-dimensional cases of co-rotating vortices and leap-frogging vortex pairs and compare estimated sound sources to vortex sound theory.

The paper concerns some aspects of the induction melting technology improvement. The generalized mathematical model is presented which contains governing equations for the alternating magnetic field (AMF) diffusion into the liquid metal, heat and mass transfer in the melt and elastic deformation of the dielectric film covering partially the melt surface. The integral strain criterion is suggested which describes the total stress excited in the film by the melt motion. The model validation results are described. The influence of the film size on its stress–strain state is studied numerically for different values of external AMF frequency and strength. We calculate and classify realizable surface flow regimes depending on the AMF frequency and model, how this near-surface flow deforms the film of different sizes. An integral strain criterion is introduced, which lets to estimate the film break condition. The map of regimes is drawn which demonstrates the possible film radii at which the film does not break and does not deform depending on the AMF frequency and strength. It is shown, that integral strain criterion predicts well the film stress–strain state and conforms to the map of regimes. The results of numerical modeling, technique of the integral strain criterion calculation and examples of its application are given.

Control of flow separation is a great issue to deal with a moving body to ensure its proper aerodynamic characteristics. To achieve this, various methods including active and passive control are suggested depends upon the flow characteristics and the surface in which control is necessary. To make the better use of both active and passive method of flow control this article proposed a new type of double sided plasma actuator (DSPVG) to overcome the drag penalty of conventional vortex generators (VGs) that commonly used in controlling flow and to use actively control. In this regard, the effectiveness of DSPVG has been numerically and experimentally investigated in a separated flow region of a 20° diffuser of an open type tunnel. DSPVG is placed at the upstream of separation location normal to the surface as like as conventional VG except zero angle with flow direction. Both numerical and experimental results of DSPVG are compared with that of VG and baseline flow and better agreements are found. Moreover, DSPVG has shown better separation suppression ability than conventional VGs due to its dual vortices. It is found that DSPVG significantly delay the separation. A freestream flow of 4 m s−1 is used for experiments and numerical computations.

Cellular secondary flows are inevitably present in turbulent flows through ducts, natural or artificial channels, and compound channels. Secondary currents significantly modify the characteristics of turbulent quantities, the pattern of primary flow velocity by causing dip-phenomenon. To understand the detailed mechanism and hidden cause, modelling of secondary flow velocities is crucial. In this study, proper mathematical models of secondary flow velocities along vertical and transverse directions are proposed for steady and uniform turbulent flow through wide open channels with equal smooth and rough bed strips. Starting from the continuity and the Reynolds averaged Navier–Stokes equations, governing equation for secondary velocity is derived first and then using appropriate boundary conditions (no-slip boundary conditions at channel bottom and free surface, and maximum vertical velocity in magnitude at the interface of two cellular secondary cells and at mid-depth of the channel. All these conditions are consistent with several experimental observations). A new model of the streamwise Reynolds shear stress is proposed for the entire cross-sectional plane and using it, the analytical solutions are obtained. Proposed models include the effects of viscosity of the fluid and the eddy viscosity model of turbulence. All suggested models are validated with existing experimental data in rectangular open-channel flows, compound open channel flows, and duct flows, and satisfactory results are obtained. Furthermore, models are also compared with existing empirical models from literature to show the effectiveness and superiority of proposed models. Apart from these, the obtained results from this study are used to investigate the effects of vertical and transverse secondary flow velocities on the settling velocity vector in a cross-sectional plane. Effective alternative models for the settling velocity vector are suggested. The model of settling velocity vector is also compared with the existing model. Finally, all results are justified from physical viewpoints.

The Okubo (1970 Deep Sea Res. 17 445)–Weiss (1991 Physica D 48 273) criterion, has been extensively used as a diagnostic tool to divide a two-dimensional (2D) hydrodynamical flow field into hyperbolic and elliptic regions and to serve as a useful qualitative guide to the complex quantitative criteria. The Okubo–Weiss criterion is frequently validated on empirical grounds by the results ensuing its application. So, we will explore topological implications into the Okubo–Weiss criterion and show the Okubo–Weiss parameter is, to within a positive multiplicative factor, the negative of the Gaussian curvature of the vorticity manifold. The Okubo–Weiss criterion is then reformulated in polar coordinates, and is validated for several examples including the Lamb–Oseen vortex, and the Burgers vortex. These developments are then extended to 2D quasi-geostrophic (QG) flows. The Okubo–Weiss parameter is shown to remain robust under the β-plane approximation to the Coriolis parameter. The Okubo–Weiss criterion is shown to be able to separate the 2D flow-field into coherent elliptic structures and hyperbolic flow configurations very well via numerical simulations of quasi-stationary vortices in QG flows. An Okubo–Weiss type criterion is formulate for 3D axisymmetric slows, and is validated via application to the round Landau–Squire Laminar jet flow.

We present a novel computationally efficient approach for investigating the effect of surface roughness on the fluid flow in small discrete fracture networks at low Reynolds number. The effect of parallel and series fracture arrangements on the flow rate and hydraulic resistance was studied numerically by patching Hele-Shaw (HS) cells to represent the network. In this analysis, the impact of surface roughness was studied in different arrangements of the network. For this aim, four models with different sequences of fracture connections were studied. The validity of the models was assessed by comparing the results with solutions of the full Navier–Stokes equations (NSE). The approximate hydraulic resistance and flow rate calculated by the HS method were found to be in good agreement with the NSE (less than 7% deviation). Results suggest a quadratic relationship between the network hydraulic resistance and the joint roughness coefficient (JRC). Notably, an increase in surface roughness caused a growth in hydraulic resistance and a fall in flow rate. Further insight was provided by drawing an analogy between resistors in electrical circuits and fractures in networks.