Turbulent Mixing Research Articles

ATOMIX benchmark datasets for dissipation rate measurements using shear probes

Turbulent mixing in the ocean, lakes and reservoirs facilitates the transport of momentum, heat, nutrients, and other passive tracers. Turbulent fluxes are proportional to the rate of turbulent kinetic energy dissipation per unit mass, ε. A common method for ε measurements is using microstructure profilers with shear probes. Such measurements are now widespread, and a non-expert practitioner will benefit from best practice guidelines and benchmark datasets. As a part of the Scientific Committee on Oceanographic Research (SCOR) working group on “Analysing ocean turbulence observations to quantify mixing” (ATOMIX), we compiled a collection of five benchmark data of ε from measurements of turbulence shear using shear probes. The datasets are processed using the ATOMIX recommendations for best practices documented separately. Here, we describe and validate the datasets. The benchmark collection is from different types of instruments and covers a wide range of environmental conditions. These datasets serve to guide the users to test their ε estimation methods and quality-assurance metrics, and to standardize their data for archiving.

Eduction of coherent structures from schlieren images of twin jets using SPOD informed with momentum potential theory in the spectral domain

Abstract This work presents a methodology to extract coherent structures from high-speed schlieren images of turbulent twin jets which are more physically interpretable than those obtained with currently existing techniques. Recently, Prasad and Gaitonde (J Fluid Mech 940:1–11, 2022) introduced an approach which employs the momentum potential theory of Doak (J Sound Vib 131(1):67–90, 1989) to compute potential (acoustic and thermal) energy fluctuations from the schlieren images by solving a Poisson equation, and combines it with spectral proper orthogonal decomposition (SPOD) to educe coherent structures from the momentum potential field instead of the original schlieren field. While the latter field is dominated by a broad range of vortical fluctuations in the turbulent mixing region of unheated high-speed jets, the momentum potential field is governed by fluctuations which are intimately related to acoustic emission, and its spatial structure in the frequency domain is very organized. The proposed methodology in this paper improves the technique of Prasad and Gaitonde (J Fluid Mech 940:1–11, 2022) in three new ways. First, the solution of the Poisson equation is carried out in the frequency-wavenumber domain instead of the time-space domain, which simplifies and integrates the solution of the Poisson equation within the SPOD framework based on momentum potential fluctuations. Second, the issue of solving the Poisson equation on a finite domain with ad hoc boundary conditions is explicitly addressed, identifying and removing those unphysical harmonic components introduced in the solution process. Third, the solution of the SPOD problem in terms of momentum potential fluctuations is used to reconstruct schlieren SPOD fields associated with each mode, allowing the visualization of the obtained coherent structures also in terms of the density gradient. The method is applied here to schlieren images of a twin-jet configuration with a small jet separation at two supersonic operation conditions: a perfectly-expanded and an overexpanded one. The SPOD modes based on momentum potential fluctuations retain the wavepacket structure including the direct Mach-wave radiation, together with upstream- and downstream-traveling acoustic waves, similar to SPOD modes based on the schlieren images. However, for the same dataset, they result in a lower-rank decomposition than schlieren-based SPOD and provide an effective separation of twin-jet fluctuations into independent toroidal and flapping oscillations that are recovered as different SPOD modes. These coherent structures are more consistent with twin-jet wavepacket models available in the literature than those originally obtained with direct schlieren-based SPOD, facilitating their interpretation and comparison against theoretical analyses. Graphical abstract

Life Cycle Evolution of Mixing in Shallow Cumulus Clouds

AbstractUnderstanding how entrainment and mixing shape the cloud droplet size distribution (DSD) is crucial for understanding the optical properties and precipitation efficiency of clouds. Different mixing scenarios, mainly homogeneous and inhomogeneous, shape the DSD in a distinct way and alter the cloud's impact on climate. However, the prevalence of these mixing scenarios and how they vary in space and time is still uncertain, as underlying processes are commonly unresolved by conventional numerical models. To overcome this challenge, we employ the L3 model, which considers supersaturation fluctuations and turbulent mixing down to the finest relevant lengthscales, making it possible to represent different mixing scenarios realistically. We investigate the spatial and temporal evolution of mixing scenarios over the life cycle of shallow cumulus clouds for varying boundary layer humidities and aerosol concentrations. Our findings suggest homogeneous mixing is generally predominant in cumulus clouds, while different mixing scenarios occur concurrently in the same cloud. Notably, inhomogeneous mixing increases over the cloud life cycle across all analyzed cases. The mean and standard deviation of supersaturation are found to be the most capable indicators of this evolution, providing a comprehensive insight into the characteristics of mixing scenarios. Finally, we show inhomogeneous mixing is more prevalent in drier boundary layers and for higher aerosol concentrations, underscoring the need for a more comprehensive investigation of how these mixing dynamics evolve in a changing climate.

Effects of surface moisture flux on the formation and evolution of cold fog over complex terrain with large‐eddy simulation

AbstractThis study examines the effect of surface moisture flux on fog formation, as it is an essential factor of water vapor distribution that supports fog formation. A one‐way nested large‐eddy simulation embedded in the mesoscale community Weather Research and Forecasting model is used to examine the effect of surface moisture flux on a cold fog event over the Heber Valley on January 16, 2015. Results indicate that large‐eddy simulation successfully reproduces the fog over the mountainous valley, with turbulent mixing of the fog aloft in the valley downward. However, the simulated fog is too dense and has higher humidity, a larger mean surface moisture flux, more extensive liquid water content, and longer duration relative to the observations. The sensitivity of fog simulations to surface moisture flux is then examined. Results indicate that reduction of surface moisture flux leads to fog with a shorter duration and a lower height extension than the original simulation, as the decrease in surface moisture flux impairs water vapor transport from the surface. Consequently, the lower humidity combined with the cold air helps the model reproduce a realistic thin fog close to the observations. The outcomes of this study illustrate that a minor change in moisture flux can have a significant impact on the formation and evolution of fog events over complex terrain, even during the winter when moisture flux is typically very weak.

Marine Stratus—A Boundary-Layer Model

A relatively simple 1D RANS model of the time evolution of the planetary boundary layer is extended to include water vapor and cloud droplets plus transfers between them. Radiative fluxes and flux divergence are also included. An underlying ocean surface is treated as a source of water vapor and as a sink for cloud or fog droplets. With a constant sea surface temperature and a steady wind, initially dry or relatively dry air will moisten, starting at the surface. Turbulent boundary layer mixing will then lead towards a layer with a well-mixed potential temperature (and so temperature decreasing with height) and well-mixed water vapor mixing ratio. As a result, the air will, sooner or later, become saturated at some level, and a stratus cloud will form.

Characteristics of jet noise: A synthesis

It is a distinct privilege to produce this article to honor Professor Tam, the foremost authority on jet aeroacoustics. The fundamental characteristics of jet noise have been studied for 70 years, since the pioneering work of Lighthill in the 1950s. The acoustic analogy, with many variants, has served as the leading theory for nearly 50 years. Many leading researchers in the 1970s formulated theories to interpret the measured trends from subsonic and supersonic jets, using acoustic analogy and flow features as the framework. Quadrupoles, dipoles and monopoles were believed to constitute the sources of noise. The discovery of large-scale organized structures in free shear layers and jets sparked a different avenue of thinking about their importance for noise generation. Tam was the first to clearly demonstrate that these structures are efficient generators of noise and constitute the dominant noise sources, especially in the downstream direction. Now, two schools of thought emerged on the sources of jet noise. Experimental measurements showed that the mean flow as well as the turbulence statistics exhibit a self-similarity in the mixing layer and another similarity in the fully developed jet. Based on these observations, Tam proposed that since noise is generated by the turbulence of the jet, the noise spectra generated by fine-scale and large-scale turbulence should also exhibit self-similarity. By examining a large set of supersonic jet noise data acquired at NASA Langley, Tam offered evidence that the turbulent mixing noise of high-speed jets does consist of two independent self-similar components. In this paper, experimental evidence is compiled from an extensive database that quantifies the effect of several parameters that affect jet spectra. A new scaling method is developed and extended to noise predictions for realistic dual-stream nozzle geometries. The objectives of this paper are to serve as a synthesis of noise characteristics and to focus on application to real-world problems. Results from five different experimental measurements are examined: (1) farfield spectral characteristics; (2) azimuthal and polar correlations in the farfield; (3) correlations of jet turbulence fluctuations and farfield sound; (4) measurement of source distributions with an elliptic mirror; and (5) space-time correlation measurements in the nearfield with a cage array, and nearfield-farfield correlations. Two distinctly different trends are observed in the angular ranges of 50° – ∼120° and ∼120° – 165° for all the parameters investigated with the above five approaches. The salient observations are mutually supporting, and the cumulative weight lends credence to the proposition that there are two distinct sources of turbulent mixing noise.

Large-eddy simulation investigation on the effects of inlet swirl/Reynolds number and fuel heating value on a turbulent kerosene spray flame

To progress toward the high efficiency and low emission aviation engine technology, it is mandatory to understand the complex phenomena including kerosene spray atomization, evaporation, turbulent mixing and combustion in the engine combustor. Nowadays with the rapid growth of computational capacity over the world, large-eddy simulation (LES) performs a more and more important role in understanding the complex multi-phase combustion process of kerosene fuels in aviation engine configuration. In the present work, LES is employed to investigate a swirling kerosene spray jet flame in a model combustor, which has been studied experimentally. The turbulent combustion is modeled by the flamelet generated manifold (FGM) approach with a 3-component surrogate kerosene skeletal mechanism. The averaged gas velocity and temperature predicted by LES generally agrees well with the experimental measurements. Local extinction is observed at the inner shear layer of the swirling spray flame, due to droplet-turbulence-flame interactions. A parametric study with 11 cases is then performed to investigate the effects of inlet swirl/Reynolds number and fuel heating value on the kerosene flame. As the swirl number increases, the enhanced turbulent mixing between kerosene fuel and air facilitates the combustion process, but combustion instabilities may occur if the swirl number is too high. A higher Reynolds number can promote the turbulent combustion via a stronger recirculation zone, but it also has strong dilution effects on the combustion field. Variations in the fuel heating value directly impact the temperature field, but the flow field, major species concentrations and droplet phase statistics are only slightly affected. These LES results give clues to achieve optimal combustion performance in realistic aviation engine configurations via better arrangements of fuel and air injections.

Transport and retention of sinking microplastics in a well-mixed estuary

Estuaries have been shown to be potential hotspots of microplastic accumulation, but the hydrodynamic conditions and particle properties that control this process need further investigation. We have designed a series of numerical particle-tracking experiments to examine the sensitivity of retention in estuaries to particle size, particle density and varying tides and freshwater flow. At the end of the simulation, over 90 % of sinking particles are retained in the estuary, and the retention rate is further increased by high river runoff. In contrast, increased river discharge increases the number of marginally-buoyant (i.e. density close to estuarine water) particles that escape the estuary. Larger particle size tends to limit the downstream transport of sinking particles but can facilitate the transport of marginally-buoyant particles. Tidal asymmetry, vertical turbulent mixing and the vertical structure of the subtidal circulation are proposed as the underlying mechanisms controlling the fate of particles.

On the power-law exponent of multimode Richtmyer–Meshkov turbulent mixing width

Turbulent mixing induced by the Richtmyer–Meshkov (RM) instability occurs extensively in natural phenomena and engineering applications. Among the physical quantities characterizing the RM turbulent mixing, the mixing width has prominent importance. The total mixing width h can be divided into the spike mixing zone width hs and the bubble mixing zone width hb. For multimode perturbed RM problems that commonly occur in engineering practice, early instability develops rapidly into the self-similar regime. In this regime, it is widely accepted that hs,bt∼tθs,b, where t is the time and θs,b is the power-law exponent. However, this scaling law is associated with two open questions. (1) How should a reasonable reference interface be selected to segment h into hs and hb? (2) Are the resulting θs and θb equal to each other or not? To answer these two questions, in this study, we propose a general definition of reference interface based on the position corresponding to any fixed value of either the mass fraction, volume fraction, or density. Under this definition, the invariance of fraction and density profiles by self-similar transformation leads to hs,bt∼tθs,b with θs=θb. The general definition covers those provided in linear electronic motor experiment [Dimonte and Schneider, “Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories,” Phys. Fluids 12, 304–312 (2000)] and shock tube experiment [Krivets et al., “Turbulent mixing induced by Richtmyer-Meshkov instability,” AIP Conf. Proc. 1793, 150003 (2017)]. Moreover, these two definitions are proved to be, respectively, special cases of newly proposed general definition. Finally, it is deduced that θs≠θb observed in high-density ratio experiments is possibly because the turbulent mixing has not entered a self-similar regime. Compared to the low-density ratio cases, mixing of high-density ratio is much more difficult to enter the self-similar regime.

Numerical Diffusion and Turbulent Mixing in Convective Self‐Aggregation

AbstractConvective Self‐Aggregation (CSA) is a common feature of idealized numerical simulations of the tropical atmosphere in Radiative‐Convective Equilibrium (RCE). However, at coarse grid resolution where deep convection is not fully resolved, the occurrence of this phenomenon is extremely sensitive to subgrid‐scale processes. This study examines the role of mixing and entrainment, provided by the turbulence model and the implicit numerical diffusion. The study compares the results of two models, WRF and SAM, by varying turbulence models, initial conditions, and horizontal spatial resolution. At a coarse grid resolution of 3 km, the removal of turbulent mixing prevents CSA in models with low numerical diffusivity but is preserved in models with high numerical diffusivity. When the horizontal grid resolution is refined to 1 km, CSA can only be achieved by increasing explicit turbulent mixing, even with a small amount of shallow clouds. Therefore, the sensitivity of CSA to horizontal grid resolution is not primarily caused by the decrease in shallow clouds. The analysis of the total water path spectrum suggests that the amplitude of initial humidity perturbations introduced by convection in the free troposphere is the key factor. This amplitude is regulated by turbulent mixing and diffusion at small scales. Prior to the onset of CSA, increased mixing makes updrafts more sensitive to the dryness of the free troposphere, which strengthens the moisture‐convection feedback. This leads to an increased distance between convective cores and a stronger humidity perturbation in the free troposphere, which can destabilize the RCE state.

Characterization of Mixing at the Edge of a Kuroshio Intrusion into the South China Sea: Analysis of Thermal Variance Diffusivity Measurements

Abstract The Kuroshio occasionally carries warm and salty North Pacific Water into fresher waters of the South China Sea, forming a front with a complex temperature–salinity (T–S) structure to the west of the Luzon Strait. In this study, we examine the T–S interleavings formed by alternating layers of North Pacific Water with South China Sea Water in a front formed during the winter monsoon season of 2014. Using observations from a glider array following a free-floating wave-powered vertical profiling float to calculate the fine-scale parameters Turner angle, Tu, and Richardson number, Ri, we identified areas favorable to double-diffusion convection and shear instability observed in a T–S interleaving. We evaluated the contribution of double-diffusion convection and shear instabilities to the thermal variance diffusivity, χ, using microstructure data and compared it with previous parameterization schemes based on fine-scale properties. We discover that turbulent mixing is not accurately parameterized when both Tu and Ri are within critical ranges (Tu > 60; Ri < ¼). In particular, χ associated with salt finger processes was an order of magnitude higher (6.7 × 10−7 K2 s−1) than in regions where only velocity shear was likely to drive mixing (8.7 × 10−8 K2 s−1).

Parameterization of Shear‐To‐Strain Ratio Used in Finescale Parameterization

AbstractThe Gregg‐Henyey‐Polzin (GHP) finescale parameterization is widely employed to infer turbulent mixing when microstructure measurements are unavailable. However, the strain‐only GHP scaling is the only option when shear information is lacking, in which case the shear‐to‐strain ratio (Rω) is commonly treated as a constant. Since Rω has been reported to vary spatiotemporally, using a fixed value of Rω might result in a significant bias in inferring turbulent mixing. In this study, we present a global map of Rω, based on the microstructure database contributed by the Climate Process Team on internal wave‐driven ocean mixing, which covers the Indian, Pacific, and Atlantic oceans across both high and low latitudes. Then, we propose a parameterization of Rω by considering buoyancy frequency, Coriolis frequency, and topographic features. Compared to the GHP scaling with constant Rω, the turbulent dissipation rate values inferred from the GHP scaling with parameterized Rω are more accurate. In this manner, this study provides a reference for choosing optimal Rω when using the strain‐only GHP scaling to explore turbulent mixing in the open ocean.

Effect of U-shaped notches on nozzle performance and jet flow structures

In nacelle design, optimization of nozzle shape is crucial for flow control. To understand the effect of nozzle shape on its aerodynamic performance and jet flow structures, the numerical experiment is performed using the dual separate flow reference (DSFR) nozzle released by the Aero Systems Engineering (ASE) FluidDyne Laboratory. A pair of U-shaped notches are made on the nozzle. The results show that the discharge coefficient and thrust angle increase with the size of the notches in all the simulated operating conditions. The notches induce a pair of streamwise vortices, which enhance turbulent mixing and decrease turbulent kinetic energy in the mixing layer.

Using NIW Observations to Assess Mixed Layer Parameterizations: A Case Study in the Tropical Atlantic

AbstractTropical sea surface temperature (SST) biases can cause atmospheric biases on global scales, hence SST needs to be represented well in climate models. A major source of uncertainties is the representation of turbulent mixing in the oceanic boundary layer, or mixed layer (ML). In the present study we focus on near‐inertial wave (NIW) induced mixing. The performance of two mixing schemes, Turbulent Kinetic Energy and K‐profile parameterization (KPP), is assessed at two sites (11.5°N, 23°W and 15°N, 38°W) in the tropical Atlantic. At 11.5°N, turbulence observations (eddy diffusivities, shear and stratification) are available for comparison. We find that the schemes differ in their representation of NIWs, but both under‐represent the observed enhanced diffusivities below the observed ML. However, we find that the models do mix below the ML at 15°N when a storm passes nearby. The near‐inertial oscillations remain below the ML for the following 10 days. Near‐inertial kinetic energy (NIKE) biases in the models are not directly correlated with the wind speed, the MLD biases, or the stratification at the ML base. Instead, NIKE biases are sensitive to the vertical mixing scheme parameterization. NIKE biases are lowest when the KPP scheme is used.

Exploring near-bottom turbulent mixing across the Challenger Deep based on temperature spectral analysis

The hadal Mariana Trench remains poorly understood. In December 2016, an array of high-resolution temperature loggers, attached to the ocean bottom seismometers (OBSs), was deployed from 1665 to 7520 m for two weeks across the Challenger Deep of the Southern Mariana Trench. The temperature variance spectrum reveals that the bottom water is mildly turbulent and it is mainly modulated by the semidiurnal internal tides. At the second deepest observation station (depth of 7015 m), the viscous subrange is resolved in the high-frequency spectrum. Applying the proposed method with Taylor’s frozen field hypothesis and Kraichnan theoretical spectrum analysis, it is revealed that turbulent dissipation rate ɛ is 7.8×10−10m2/s3 and flow speed U is 8.9 mm/s. Dissipation rates ɛ of all stations vary between 5.9×10−11 and 1.4×10−9m2/s3, with the northern region of Challenger Deep experiencing stronger energy dissipation than the southern one. The vertical distribution of dissipation rate ɛ shows that it decreases with increasing depth from 1000 to 6000 m, but then increases to around 8000 m, which is consistent with previous observations and numerical simulations. The available turbulent mixing data indicates that the energy dissipation is vertically distributed in a distinct multilayer structure in the deep ocean of Challenger Deep, which is proposed to link to the intrusion of water mass in the deep Mariana trench.

Numerical study on heat transfer deterioration of supercritical CO2 in lattice structure array channel

This study numerically explores the fluid flow and heat transfer features of supercritical carbon dioxide (CO2) in lattice structure array channel. The mitigation mechanism of the miniature cylindrical lattice structure array on heat transfer deterioration (HTD) of supercritical CO2 in vertically upward heated channel is studied. This paper evaluates the effect of several key influential parameters (length, diameter, pitch and number) of cylindrical lattice structure array on fluid flow field involving vortex structures, heat transfer coefficient, buoyancy effect and accelerated effect. The results indicate that the lattice structure can effectively suppress the HTD by generating the vortex structure which promoting the turbulent mixing effect and enhancing the turbulent kinetic energy (TKE) of the fluid. Compared with the smooth channel, the peak wall temperature of the lattice structure channel is reduced by about 50 °C, with a corresponding increase in the heat transfer coefficient of about 140 %. The average heat transfer coefficient of the channel is increased by more than 1/3. Furthermore, by increasing lattice length can reduce flow layer stratification and by increasing lattice diameter can creating a composite vortex, which enhance flow mixing strength. The larger the lattice pitch, the worse the overall suppression effect. A denser lattice arrangement produces more temperature valleys, thereby increasing the heat transfer coefficient. The conclusions in this study could provide the main theory support for security and stability of supercritical CO2 heat exchangers in power system.

Transformation of internal solitary waves at the edge of ice cover

Abstract. Internal wave-driven mixing is an important factor in the balance of heat and salt fluxes in the polar regions of the ocean. Transformation of internal waves at the edge of the ice cover can enhance the mixing and melting of ice in the Arctic Ocean and Antarctica. In the polar oceans, internal solitary waves (ISWs) are generated by various sources, including tidal currents over bottom topography, the interaction of ice keels with tides, time-varying winds, vortices, and lee waves. In this study, a numerical investigation of the transformation of ISWs propagating from open water in the stratified sea under the edge of the ice cover is carried out to compare the depression ISW transformation and loss of energy on smooth ice surfaces, including those on the ice shelf and glacier outlets, with the processes beneath the ridged underside of the ice. They were carried out using a non-hydrostatic model that is based on the Reynolds-averaged Navier–Stokes equations in the Boussinesq approximation for a continuously stratified fluid. The Smagorinsky turbulence model extended for stratified fluid was used to describe the small-scale turbulent mixing explicitly. Two series of numerical experiments were carried out in an idealized 2D setup. The first series aimed to study the processes of the ISWs of depression transformation under an ice cover of constant submerged ice thickness. Energy loss was estimated based on a budget of depth-integrated pseudoenergy before and after the wave transformation. The transformation of ISWs of depressions is controlled by the blocking parameter β, which is the ratio of the minimum thickness of the upper layer under the ice cover to the incident wave amplitude. The energy loss was relatively small for large positive and large negative values of β. The maximal value of energy loss was about 38 %, and it was reached at β≈0 for ISWs. In the second series of experiments, a number of keels were located on the underside of the constant-thickness ice layer. The ISW transformation under ridged ice also depends on the blocking parameter β. For large keels (β<0), more than 40 % of energy is lost on the first keel, while for relatively small keels (β>0.3), the losses on the first keel are less than 6 %. Energy losses due to all keels depend on the distance between them, which is characterized by the parameter μ, i.e. the ratio of keel depth to the distance between keels. In turn, for a finite length of the ice layer, the distance between keels depends on the keel quantity.

Investigating the Interaction Between Transboundary Haze and Planetary Boundary Layer in Singapore

AbstractTransboundary air pollution is one of the critical environmental problems in Southeast Asia; nevertheless the interaction between transboundary haze and local planetary boundary layer (PBL) remains unclear due to a lack of sufficient observations and sophisticated simulations. This study applied LiDAR observations and model simulations to comprehensively evaluate the interaction between transboundary haze and local PBL during a recent transboundary haze episode in Singapore in October 2023. Results show that upper‐level southeasterly wind, especially the nocturnal low‐level jet, created favorable conditions for aerosol transport when fire hotspot numbers increased in Indonesia. The rapid diurnal increase in PBL height facilitated the entrainment of upper‐level haze into the PBL, interacting with ground‐level aerosols through turbulent mixing. Model simulations further show the significant contributions of fire emissions to the transboundary haze episode in maritime Southeast Asia. The impacts extended toward the southern region of Peninsular Malaysia, driven by the persistent prevailing southeasterly wind.

LES of autoignition process in a turbulent droplet-laden mixing layer – impact of an evaporation model and discretisation method

This paper focuses on the numerical modelling of the autoignition process in an ethanol-air mixture within a turbulent droplet-laden temporally evolving mixing layer, utilising the Large Eddy Simulation (LES) method. We compare results obtained by implementing two notably distinct discretisation methods (second-order Total Variation Diminishing – TVD, and fifth-order Weighted Essentially Non-Oscillatory – WENO) in the species and energy transport equations. Additionally, we examine three widely recognised evaporation models (the ‘ D 2 ’ model, the Abramzon–Sirignano model, and a non-equilibrium model based on the Langmuir-Knudsen law). For modelling the combustion process, we employ the Eulerian Stochastic Field method and a laminar chemistry model. The simulations encompass two droplet diameter distributions, one with low and the other with significant diameter non-uniformity. Furthermore, nine distinct initial conditions are considered. Our findings indicate that adjusting the discretisation scheme or the evaporation model can yield simulation outcomes differing to a substantial degree, similar to the impact of modifying the actual properties of the spray droplets or their initial distribution. This is particularly pronounced in the case of sprays featuring a narrowed droplet diameter distribution. We found that the Abramzon–Sirignano model results in the most rapid autoignition. The TVD scheme contributes to a more even spatial distribution of the evaporated fuel, consequently facilitating quicker evaporation and faster autoignition. Using the WENO scheme generates higher fuel vapor gradients near the droplets, leading to less intense evaporation and slower fuel transport in space.

Development of a multi-layer network model for characterizing energy cascade behavior on turbulent mixing

Eddies of various sizes are visible to the naked eye in turbulent flow. Each eddy scale corresponds to a fraction of the total energy released by the turbulence cascade. Understanding the dynamic mechanism of the energy cascade is crucial to the study of turbulent mixing. In this paper, an energy cascade multi-layer network (ECMN) based on the complex network algorithm is proposed to investigate the spatio-temporal evolution of the energy cascade, covering both the inertial and dispersive ranges. The dynamic process of energy cascade is transformed into a topological structure based on the node definition and edge determination. The topological structure allows for the exploration of eddies interaction and chaotic energy transfer across scales. The model results show the intermittent and non-uniform nature of the energy cascade. Meanwhile, the scale gap found in the model verifies the fractal property of the energy evolution. We also found that scales of the generated eddies in energy cascade process are stochastic, and a synchronous energy cascade pattern is demonstrated according to the constructed framework. Furthermore, it provides a topological way to evaluate the contribution of large and small scale eddies. In addition, a network structure coefficient κ is proposed to evaluate the energy transfer strength. It agrees very well with the fluctuation of dissipation rates. All of this shows that the network model can effectively reveal the inhomogeneous properties of the energy cascade and quantify the turbulent mixing intensity based on the intermittent scale interaction. This also provides new insights into the study of fractal scales of nonlinear complex systems and the bridging of chaotic dynamics with topological frameworks.