Layer Vortices Research Articles

Pressure gradient tailoring effects on vorticity dynamics in the near-wake of bluff-body premixed flames

We investigate the role of mean streamwise pressure gradients in the development of a bluff-body-stabilized premixed flame in the near-wake of the bluff body. To this end, a triangular prism flame holder is situated in three different channel geometries: a nominal case with straight walls, a nozzle with a stronger mean pressure gradient, and a diffuser with a comparatively weaker mean pressure gradient. All geometries are implemented using embedded boundaries, and adaptive mesh refinement is used to locally resolve all relevant thermal (i.e., flame) and fluid-mechanical (i.e., vorticity) scales. A premixed propane flame, modeled using a 66-step skeletal mechanism, interacts with vorticity in the boundary layer of the triangular bluff body in the presence of each mean pressure gradient. Analysis of flame-related enstrophy budget terms reveals key differences in the behavior of baroclinic torque between cases, the specifics of which are tied to larger variations in the mean flow structure, recirculation zone structure, and confinement effects. Our results show that the baroclinic torque changes significantly among the configurations, with the nozzle exhibiting the largest baroclinic torque production. However, these differences are shown to be only a secondary consequence of the background pressure gradient, with the primary consequence being the change in the recirculation zone length resulting from the different channel configurations. These results are relevant for flame stabilization with bluff bodies, where clear understanding of the sensitivities to global mean pressure gradient is important to engineering design.

Reacting and non-reacting, three-dimensional shear layers with spanwise stretching

A three-dimensional, steady, laminar shear-layer flow spatially developing under a boundary-layer approximation with mixing, chemical reaction, and imposed normal strain is analyzed. The purpose of this study is to determine conditions by which certain stretched vortex layers appearing in turbulent combustion are the asymptotic result of a spatially developing shear flow with imposed compressive strain. The imposed strain creates a counterflow that stretches the vorticity in the spanwise direction. Equations are reduced to a two-dimensional form for three velocity components. The non-reactive and reactive cases of the two-dimensional form of the governing equations are solved numerically, with consideration of several parameter inputs, such as the Damköhler number, the Prandtl number, chemical composition, and free-stream velocity ratios. The analysis of the non-reactive case focuses on the mixing between hotter gaseous oxygen and cooler gaseous propane. The free-stream strain rate κ* is predicted by ordinary differential equations based on the imposed spanwise pressure variation. One-step chemical kinetics are used to describe diffusion flames and multi-flame structures. The imposed normal strain rate has a significant effect on the width of downstream mixing layers as well as the burning rate. Asymptotically in the downstream direction, a constant width of the shear layer is obtained if the imposed normal strain rate is constant. The one-dimensional asymptotic result is an exact solution to the multicomponent Navier–Stokes equation for both reacting and non-reacting flows, although it was obtained using the boundary-layer approximation. A similar solution with the layer width growing with the square root of downstream distance is found when the imposed strain rate decreases as the reciprocal of downstream distance. The reduced-order asymptotic solutions can provide useful guidance in developing flamelet models for simulations of turbulent combustion.

Pretreatment in Vortex Layer Apparatus Boosts Dark Fermentative Hydrogen Production from Cheese Whey

Dark fermentation (DF) is a promising process for mitigating environmental pollution and producing “green” H2. However, wider implementation and scaling of this technology is hampered by insufficient process efficiency. In this work, for the first time, the effect of innovative pretreatment of cheese whey (CW) in a vortex layer apparatus (VLA) on characteristics and DF of CW was studied. Pretreatment in VLA resulted in a heating of the CW, slight increase in pH, volatile fatty acids, iron, and reduction in fat, sugar, and chemical oxygen demand (COD). The biochemical hydrogen potential test and analysis of H2 production kinetics confirmed the significant potential of using VLA in enhancement of dark fermentative H2 production. The maximum potential H2 yield (202.4 mL H2/g COD or 3.4 mol H2/mol hexose) was obtained after pretreatment in VLA for 45 s and was 45.8% higher than the control. The maximum H2 production rate after 5 and 45 s of pretreatment was 256.5 and 237.2 mL H2/g COD/d, respectively, which is 8.06 and 7.46 times higher than in the control. The lag phase was more than halved as a function of the pretreatment time. The pretreatment time positively correlated with the total final concentration of Fe2+ and Fe3+ and negatively with the lag phase, indicating a positive effect of pretreatment in VLA on the start of H2 production.

Submesoscale eddies in eastern Guangdong identified using high-frequency radar observations

The statistical characteristics and mechanism underlying the generation of submesoscale eddies in eastern Guangdong were examined using high-frequency radar (HFR) observations of surface currents during 2019_2021. By applying the vector geometry-based (VG) eddy detection algorithm to HFR datasets, 313 submesoscale eddies with 229 cyclonic and 84 anticyclonic eddies were identified. Cyclonic eddies were significantly more common than the anticyclonic eddies, but they had similar distributions in terms of eddy lifespan and radius. The trajectories showed that the submesoscale eddies within the study area tended to move northward and westward. Submesoscale eddies revealed annual variations with decreasing cyclonic eddies and increasing anticyclonic eddies during the observation period. Submesoscale eddies displayed a remarkable spatial distribution. Most of cyclonic (anticyclonic) eddies occurred at the eastern and southeastern regions of the Huilai Headland (south of the Nanao Island). Eddy evolution was linked to the production of vorticity in a narrow layer along the headland, the injection of vorticity into the interior at the point of flow separation, and vorticity damping by bottom friction.

Interaction of Rossby waves with the Gulf Stream and Kuroshio using altimetry in a framework of a vortex layer model

In this paper, we show the potential of satellite altimetry to study the interaction of Rossby waves with the shear flow. The Miles-Ribner approach, which was developed in gas dynamics in the 1960 s, is used to describe Rossby waves interacting with the Gulf Stream and Kuroshio areas. The region of interaction is approximated by a nonzonal vortex layer. We apply the main formulations of the problem of a nonzonal vortex layer on the β-plane in the formulation of Miles-Ribner to observations in the real ocean. Earlier, we showed that the interaction of waves with a nonzonal flow gives rise to a new class of solutions, which is absent in the case of a zonal flow. This new class of solutions can be interpreted as the pure emission of Rossby waves by the nonzonal flow. We apply this theoretical approach to the areas of the Gulf Stream and Kuroshio as well. We use for analysis altimetry data available at Copernicus Marine Environment Monitoring Service. The analysis of Hovmöller diagrams in the areas under consideration confirms the previously obtained theoretical conclusions of the problem of the interaction of planetary waves with a nonzonal flow on the β-plane in the formulation of Miles-Ribner. The incident waves, as well as refracted and reflected waves are distinguished. The speed of refracted and reflected waves exceeds the speed of incident waves, which confirms the conclusions about the existence of mechanisms for the amplification of planetary waves when they interact with a nonzonal flow.

Low Reynolds Number Flow Past Square Cylinder in the Vicinity of a Plane Wall

The characteristics of flow over a square cylinder in the vicinity of a plane stationary wall have been numerically investigated. 2D time-dependent incompressible flow at low-Reynolds numbers of 100 and 200 has been calculated using the finite volume method. CFRUNS scheme is used for pressure-velocity coupling in numerical calculation. The authors have tried to make an attempt to analyze the features of the complex flow field through flow streamlines and the vorticity contours. The impact of the gap between the cylinder and the plane wall upon flow pattern behavior is also studied. An intense interaction between vorticity in the boundary layer generated over the plane wall and the vorticity associated with the shear layer emanating from the separation points on the cylinder surface has been observed producing a very complex flow field in the cylinder wake and the gap between the cylinder and the wall.

Analysis of tip leakage flow unsteadiness in a transonic turbine cascade using data-driven modal decomposition methods

The evolution of tip leakage flow and subsequent vortical structures is accompanied by inherent unsteadiness. This paper presents a novel characterization for the unsteady dynamics of turbine tip flow using data-driven, i.e., equation-free modal decomposition methods, which are applied to the hybrid Reynolds-averaged Navier–Stokes/large eddy simulation data at a transonic condition. By combining these techniques, the identified eigen-tuples (eigenvalues, eigenvectors, and time evolution) are well determined, and the differences between the obtained patterns (modes) are also pronounced. The snapshot proper orthogonal decomposition (POD) analysis can isolate the large-scale fluctuating structures that populate the rear part of the suction-side, which is mainly attributed to the shock-induced vortex instability. Similar to the turbulence cascade, macro-scale coherent structures that correspond to the tip leakage vortex shedding phenomena and the subsequently transitional and noisy parts closely related to the dissipation can be well derived by a quadruple reconstruction. Three dynamic mode decomposition (DMD) variants including the amplitude selecting-DMD method, the DMD with criterion method, and the sparsity promoting (SP)-DMD method are also compared in extracting dominant modes from the periodic tip flow, and the SP-DMD method which can distill modes of broadband frequencies and low dissipation is proved to be more conducive to representing and reconstructing the complex tip flow. Additional spectral-kernel-based POD (SPOD) analysis that can identify the similar primary unsteadiness frequencies as the DMD method is also encompassed in this study. Specifically, although it manifests that a physical resemblance of the pattern of pressure fluctuations to tip eddy unsteadiness can be captured by all these approaches, the behavior of small-scale vortical interaction downstream of the trailing edge can be clearly isolated with the intrinsic Karman-type vortex layer shedding process via DMD and SPOD approaches, which also demonstrates that these two techniques are more favorable to decomposing the complex tip flows into uncoupled single-frequency coherent structures compared to the conventional POD method. On this basis, resulting modes of velocity components have been accounted for verifying their contributions to the turbulent kinetic energy fields. The ensuing observations can offer a glimpse of the complex dynamics in the tip region, which also sheds light on features previously masked by conventional analysis approaches.

Approbation of an innovative method of pretreatment of dark fermentation feedstocks

According to the International Energy Agency, only a small part of the full potential of biomass energy is currently used in the world. The annual amount of agricultural waste in the Russian Federation is estimated at about 152 million tons, and the energy potential of animal waste is 201 PJ/year. Anaerobic digestion is an efficient method of converting organic waste into renewable energy sources. Previously, the positive effect of pretreatment of various organic feedstocks in vortex layer apparatus (VLA) on the characteristics of anaerobic digestion and energy efficiency was shown. Currently, there is a significant interest in the world in obtaining biohydrogen from organic waste using the dark fermentation (DF) process. During pretreatment in the VLA, the iron working bodies are abraded and iron particles are introduced into the feedstock of the DF reactor. This may have a positive effect on the production rate and yield of hydrogen, which has not been previously studied. This work is aimed at evaluating the possibility of using the VLA as a method for pretreatment of a dark fermentation feedstock for the intensification of biohydrogen production. To achieve this goal, an experimental setup was constructed. It consisted of a 45 L DF reactor, a VLA and a process control system to collect data on the DF process parameters every 5 min. At a hydraulic retention time in the DF reactor of 24 h and in the VLA of 30 s, the hydrogen content in the biogas increased from 51.1% to 52.2%. At the same time, the pH increased from 3.85 to 4.8–4.9, and the hydrogen production rate increased by 16% to 1.941 L/(L day). The hydrogen yield was 80.9 ml/g VS. Thus, pretreatment of the feedstock in VLA can be an effective way to intensify the DF process; however, further study of the VLA operating modes is required in order to optimize the concentrations of iron particles introduced into the feedstock for the most efficient continuous production of dark fermentative biohydrogen.

NUMERICAL INVESTIGATION OF X-45A TYPE UNMANNED COMBAT AIR VEHICLE

In this paper, the low-speed aerodynamic performance of unmanned combat air vehicle (UCAV) X-45 delta wing was investigated by a numerical method using computational fluid dynamic approaches (CFD). The investigation was conducted with X-45 and the formation of leading-edge vortices (LEV) and vortex breakdown was studied by a varying angle of attack with the range of 5° to 30° at the Reynolds number of 10,000 using the SST turbulence model and are compared with experimental data to validate simulation accuracy of CFD. Stall conditions happened at around 30°, averaged vorticity layer demonstrates a prolonged form that goes along by narrow recirculation zones neighboring to the wing surface. Detail about flow field, including LEV formation, vortex breakdown, interaction, and nonlinear aerodynamic characteristics of X-45 was presented and discussed.

Stretched vortex layer flamelet

A new sub-grid flamelet model is developed based on a steady-state, viscous vortex layer with an imposed compressive strain orthogonal to both the vorticity and the shear force. The imposed normal strain results in the stretching of the vorticity in the direction orthogonal to the plane of the shear strain. The model has certain special features. (i) Non-premixed flames, premixed flames, or multi-branched flame structures are determined rather than prescribed. (ii) Three components of velocity exist although the flamelet model is two-dimensional. (iii) The effect of variable density is addressed in the flamelet model. The vortex-layer configuration distinguishes this model from recent models by this author that address flames in other practical and ubiquitous vortical structures: tube-like stretched vortices or vortices stretched in two directions. Thereby, the model collection available for application to vortical configurations found in turbulent combustion is increased. Solutions to the Navier-Stokes equations and the associated scalar equations governing the flamelet model are obtained without the boundary-layer approximation and demonstrate the impact of the new features of the model. The shear strain and vorticity are found not to affect the scalar profiles, mixing and burning rates, or the two velocity components orthogonal to the shear force; only the velocity parallel to the shear force is affected. The compressive strain rate is the influential constraint affecting the scalars and the other two velocity components. However, the vorticity is strongly affected by the scalar profiles. The relation to classical concepts for incompressible flow is discussed.

МАТЕМАТИЧЕСКОЕ ОПИСАНИЕ ПРОЦЕССА МЕХАНОАКТИВАЦИИ MoS2 и МУНТ ДЛЯ МОТОРНОГО ТОПЛИВА И МАСЛА

It is possible to improve the properties of motor fuel and oil by using a new generation of additives that can improve a number of functional indicators. Increasing the efficiency of additives can be achieved through both the use of combinations of different types of additives that provide different properties, and the use of new effects realized during the transition to a nanoscale form. Thus, one of the nanoscale materials that can be used in combination with molybdenum disulfide (MoS2) are multi-walled carbon nanotubes (MWCNTs). The introduction of MoS2 and MWCNTs into motor fuel and oil is advisable to organize using a combined method of dispersion and mechanical activation, which can be implemented in devices with a vortex electromagnetic field. Such devices allow mechanical action by moving the grinding bodies in an alternating electromagnetic field. This breaks up agglomerates into MWCNTs and reduces MoS2, which increases the effectiveness of these additives and reduces their concentration in motor fuel and oil. The paper presents a mathematical description of the process of mechanical activation. The grinding of a dispersed material is presented in the form of matrices and the equations of motion of a ferromagnetic particle in a vortex layer are given. The principle of operation of the vortex layer apparatus (VLA) is described and the electromagnetic processes in the stator windings of the VLA are considered. An analysis of the VLA thermal control device with an implicitly pole inductor was carried out. The developed mathematical description of the process of mechanical activation of motor fuel and oil makes it possible to take into account a number of factors that affect the operating modes of the installation for mechanical activation.

TO DETERMINATION OF SPEED AND TRACTION OF PARTICLE MOVEMENT IN THE HEAT FLOW

The article presents experimental data on the basis of which a mathematical model of particle motion in a vortex layer during heat treatment is created, taking into account changes in their sizes. The peculiarities of particle motion in the vortex apparatus are determined in the work. There is also a dependence that allows you to control the duration of heat treatment. Based on the results of research and modeling, you can design a device for drying dispersed particles.
 The current level of development of vortex devices stimulates the relevance of research aimed at a deeper study of heat treatment processes, improving the design of devices and manufacturing technology of individual components. The lack of a strict modern theory is particularly acute in the design of systems and devices in which the vortex apparatus is one of the important units. In this regard, the priority today is to develop a theory that will provide a fairly reliable mathematical description of the processes occurring in the vortex chamber of the device.
 In many fields of technology use different mass transfer devices for drying granular material for various purposes. In general, the methods of designing such devices are known, and if the technological process is implemented without any features, the calculation methods justify themselves. In cases where the properties of the material in the heat treatment process change, traditional calculation methods give significant errors. Then there is a need for mathematical modeling of basic technological processes.
 In the hydrodynamics of the apparatus presented in the work, and accordingly in the processing, it is necessary to distinguish two main stages: pre-drying of particles in a flat jet of coolant and the final heat treatment in the vortex layer. In this paper, we dwelled in more detail on the first stage of technology.
 The equations presented in this paper reflect the features of heat treatment of particles in the vortex apparatus taking into account their variable sizes and can complement the existing methods of designing such installations.
 The equations obtained in this way reflect the above-mentioned features of heat treatment of particles in a vortex apparatus taking into account their variable sizes and can supplement the existing methods of designing such installations.

Effects of pretreatment in a vortex layer apparatus on the properties of confectionery wastewater and its dark fermentation

Pretreatment prior to anaerobic digestion is an effective option for increasing the biodegradability of organic waste. Vortex layer apparatus (VLA) is considered one of the promising types of equipment for pretreatment. In this work, confectionery wastewater (CW) was pretreated in VLA for 1 and 3 min before dark fermentative hydrogen production in anaerobic upflow biofilters. The pretreatment resulted in a slight increase in soluble chemical oxygen demand (COD), soluble sugars and acetic acid, and a decrease in the concentration of propionic, butyric and caproic acids. Due to the abrasion of steel needles in VLA, the concentration of iron in the pretreated CW increased by 2.57 times. Hydraulic retention time in anaerobic upflow biofilters was gradually reduced from 5.6 to 1.8 and 1.3 days, which corresponded to organic loading rate of 2.0, 6.3 and 8.8 kg COD/(m3 day). Although the highest hydrogen yield (96.2 ± 8.1 ml/g COD) was obtained for non-pretreated CW, the pretreatment contributed to a significant increase in methane yield (39.2 ± 2.5 ml/g COD), possibly due to higher iron content (1.8 ± 0.3 mg/L). The highest energy production rate (4407 J/(L day)) was achieved after 3 min CW pretreatment. Thus, pretreatment in VLA can be a promising method for improving the biohythane production process.

The Influence of Physical Activation of Portland Cement in the Electromagnetic Vortex Layer on the Structure Formation of Cement Stone: The Effect of Extended Storage Period and Carbon Nanotubes Modification

The article presents research of the influence of the electromagnetic vortex layer on the structure formation of cement stone during the activation of portland cement, both without additives and with carbon nanotubes modification. It has been shown that the storage of portland cement powders in open air for 60 days after activation in the electromagnetic mill leads to partial carbonization, wherein the role in absorption reducing of the super plasticizer additive is increased since there is more uniformly localization of the additive on the surface of the portland cement particles. The processing of portland cement in the electromagnetic mill leads to the physical activation of portland cement, which is accompanied by an increase in the amount of heat generated by the hydration of portland cement and the rate of hydration. Thus, the rate of hydration of compositions activated in the electromagnetic mill isincreased 1.615 times at the temperature of the thermostat 22 °C; 1.85 times at 40 °C; 2.71 times at 60 °C; 2.3 times at 80 °C. The modification of cement stonewith carbon nanotubes, which was obtained from portland cement activated in an electromagnetic mill, leads to a higher quantity of silicate phase of portland cement (by 12–39%), as confirmed by a decrease in the number of portlandite in these compositions by 8% in comparison with control composition.

Long-wavelength equations of motion for thin double vorticity layers

We consider the time evolution in two spatial dimensions of a double vorticity layer consisting of two contiguous, infinite material fluid strips, each with uniform but generally differing vorticity, embedded in an otherwise infinite, irrotational, inviscid incompressible fluid. The potential application is to the wake dynamics formed by two boundary layers separating from a splitter plate. A thin-layer approximation is constructed where each layer thickness, measured normal to the common centre curve, is small in comparison with the local radius of curvature of the centre curve. The three-curve equations of contour dynamics that fully describe the double-layer dynamics are expanded in the small thickness parameter. At leading order, closed nonlinear initial-value evolution equations are obtained that describe the motion of the centre curve together with the time and spatial variation of each layer thickness. In the special case where the layer vorticities are equal, these equations reduce to the single-layer equation of Moore (Stud. Appl. Math., vol. 58, 1978, pp. 119–140). Analysis of the linear stability of the first-order equations to small-amplitude perturbations shows Kelvin–Helmholtz instability when the far-field fluid velocities on either side of the double layer are unequal. Equal velocities define a circulation-free double vorticity layer, for which solution of the initial-value problem using the Laplace transform reveals a double pole in transform space leading to linear algebraic growth in general, but there is a class of interesting initial conditions with no linear growth. This is shown to agree with the long-wavelength limit of the full linearized, three-curve stability equations.

Mechanical behavior and microstructural characteristics of additively manufactured AlSi10MgCu/Al2O3 composites fabricated using an electromagnetic vortex layer system

The process chain of AlSi10MgCu/Al2O3 from the characterization of feedstock materials to the final properties of samples after SLM was investigated. Initial AMC powder mixing was performed with a vortex layer system. A comprehensive characterization of the powders after mixing and microstructural features were performed. Selective laser melting regimes were optimized regarding the content of Al2O3 and the optimal processing window was investigated. Synthesized samples with 1,5% of Al2O3 content demonstrated increased hardness, yield, and tensile strength with about the same ductility compared with the initial AlSi10MgCu printed alloy. Obtained results demonstrated the feasibility of an electromagnetic vortex system for powders preparation and their application in selective laser melting.

Linear and weakly nonlinear dominant dynamics in a boundary layer flow

The aim of this paper is to investigate the linear and weakly nonlinear dynamics in flow over a flat-plate with leading edge. Linear optimal and suboptimal inflow perturbations are obtained using a Lagrangian multiplier technique. In particular, the suboptimal inflow conditions and the corresponding downstream responses are investigated in detail for the first time. Unlike the suboptimal dynamics reported in other canonical cases such as the backward-facing step flow, the growth rate of the suboptimal perturbation is in the same order as the optimal one, and both of them depend on the lift-up mechanism even though they are orthogonal. The suboptimal mode has an additional layer of vorticity that penetrates into the boundary layer farther downstream, generating a second patch of high- and low-speed streaks. The farther suboptimal ones spread to the free-stream without entering the boundary layer. The weakly nonlinear dynamics are examined by decomposing the flow field into multiple orders of perturbations using the Volterra series. Small structures in the higher order perturbations mainly concentrate in the region farther away from wall, suggesting a mechanism of outward perturbation developments, which is opposite with the well reported inward development of perturbations, i.e., from free-stream to boundary layer. The significance of these modes is then demonstrated through a prediction of flow field from the inflow condition by exploiting the orthogonality of the modes.

PERSPECTIVE TECHNOLOGIES AND TECHNICAL TOOLS FOR LIQUID MANURE TREATMENT ON PIG FARMS

The main requirements for manure transportation and treatment systems are the following: ensuring the isolation of manure flows from air, soil, water; ensuring the maximum possible disinfection; ensuring the conversion of chemical elements into a form suitable for consumption by plants. The aim of the research is to analyze the technical and technological equipment of liquid manure processing processes using the process activation unit (UAP) using vortex layer devices (VHF) of ferromagnetic elements. As a result of the analysis of liquid manure processing technology of pigs it is established that the most effective technology in the conditions of Ukrainian farms is liquid manure processing by means of process activation unit (UAP) using vortex layer devices (VHF) of ferromagnetic elements. The essence of the proposed technology is that the manure together with the appropriate reagent in the working area of UAP is activated, which significantly accelerates the chemical reactions associated with the hydrolysis of fatty substances contained in effluents (alkaline environment). At the same time suspended substances in the manure are mechanically treated with ferromagnetic elements. Disinfected liquid manure at the exit of UAP has no specific odor, can accumulate in open manure storages (lagoons) directly on the farm. As a result of the analysis of the principle of work of installation of activation of processes features of its use are established: reception of multicomponent suspensions and emulsions; acceleration of the processes of obtaining fine mixtures, activation of substances both in the dry state and in the form of aqueous dispersions; for purification of industrial wastewater from phenol, formaldehyde, heavy metals, arsenic, cyanide compounds, acceleration of heat treatment processes, obtaining protein substances from yeast cells; increasing the microbiological stability of food and yeast activation in the bakery industry; intensification of extraction processes, including during the preparation of broths, production of berry drinks (juices), pectin, etc .; to obtain suspensions and emulsions of increased microbiological safety in the food industry without the use of stabilizers, as well as increase the yield of finished products.

Multiscale analysis of some shear layers in a fully developed turbulent channel flow

Multiscale edge detection-wavelet analysis is applied to the velocity field emanating from direct numerical simulations of a fully developed turbulent channel flow. The direct numerical simulations are realized in large computational domains at four different Karman numbers up to 1100. The shear layers (SL) related to the streamwise and spanwise velocity fields involving streamwise and spanwise gradients are analyzed scale-by-scale, over the homogeneous planes. The SL involving the spanwise gradient, in particular the wall vorticity layers surrounding the quasi-streamwise vortices (QSV) are organized into long streamwise streaks, whose spanwise spacing and thickness are determined versus the wavelet-wavenumber. The shear layers related to the streamwise gradient are further analyzed by using the Rice decomposition of the wavelet coefficients into a local phase and a local amplitude. Large zones of constant phase with slowly varying local amplitude have been identified at different scales. It is found that the constant phase-locked regions coincide with the wakes of the buffer layer QSV. The arrival of the quasi-streamwise vortices cause phase jumps and large intermittency in the local amplitude. The analogy between these peculiarities and the imperfect chaos synchronization phenomena together with the consequences in term of wall turbulence control are discussed. These results confirm globally our previous investigation realized through a low Reynolds number channel flow DNS in a small computational box and clarify some points that could not then elucidated.

Nonlinear evolution and low-frequency acoustic radiation of ring-mode coherent structures on subsonic turbulent circular jets

By adapting the triple decomposition of an instantaneous turbulent flow into a time-averaged mean field, large-scale coherent motion and fine-scale random fluctuations, and treating the coherent motion as instability modes on the mean flow, a mathematical theory is developed to describe the nonlinear spatial–temporal modulation and acoustic radiation of a coherent structure (CS) on a circular jet in the form of a wavepacket consisting of an axisymmetric (ring) mode and its sideband components. The effect of fine-scale turbulence on the CS is characterised via a gradient closure model, and the non-parallelism due to the axial variation and radial velocity of the mean flow is taken into account. By employing the matched asymptotic expansion and multi-scale techniques, a strongly nonlinear system is derived, which governs the envelope of the CS and its vorticity and temperature in the critical layer. Numerical solutions to the evolution system show that the theory captures the nonlinear amplitude attenuation and vorticity roll-up as observed in experiments. The large-distance asymptotic properties of the CS allow us to describe and predict its acoustic radiation on the basis of first principles. The CS is trapped within the jet, but its self-interaction generates a temporally and axially modulated mean-flow distortion, which acts as the emitter to radiate low-frequency sound waves, with the Reynolds stresses driving this mean-flow distortion being identified unambiguously to be the physical source in the present context. An equivalent source in the Lighthill type of acoustic analogy is also identified. For the present ring-mode CS in the fully developed region of a circular jet, the equivalent source can be determined before the acoustic field is, and the intensity of the radiated sound waves is found to be $O(\epsilon ^3)$ , where $\epsilon$ measures the magnitude of the CS. The directivity and spectrum of the acoustic far field are calculated for representative parameters, and the predicted features resemble experimental measurements.