EFFECT OF SUSPENDED SOLID PARTICLES ON UNSTABILITY OF TWO-DIMENSION MIXING LAYER

By considering the effect of suspended solid particles in the ordinary equations for two-dimension inviscid incompressible mixing layer, the Rayleigh equation and the modified Rayleigh equation are obtained. And then, by solving the corresponding eigen-value equations with numerical computational method, the relation curves between perturbation frequency and spacial growth rate of the mixing layer for the varying particle loading, ratio of particle velocity to fluid velocity and Stokes number are got. Sever al important conclusions on the effect of suspended solid particles on unstability of the mixing layer are presented in the end by analyzing all the relation curves.

Evaluation of Nonbreaking Wave-Induced Mixing Parameterization Schemes Based on a One-Dimensional Ocean Model

Surface waves have a considerable effect on vertical mixing in the upper ocean.In the past two decades,the vertical mixing induced through nonbreaking surface waves has been used in ocean and climate models to improve the simulation of the upper ocean.Thus far,several nonbreaking wave-induced mixing parameterization schemes have been proposed;however,no quantitative comparison has been performed among them.In this paper,a one-dimensional ocean model was used to compare the performances of five schemes,including those of Qiao et al.(Q),Hu and Wang(HW),Huang and Qiao(HQ),Pleskachevsky et al.(P),and Ghantous and Babanin(GB).Similar to previous studies,all of these schemes can decrease the simulated sea surface temperature(SST),increase the subsurface temperature,and deepen the mixed layer,thereby alleviating the common thermal deviation problem of the ocean model for upper ocean simulation.Among these schemes,the HQ scheme exhibited the weakest wave-induced mixing effect,and the HW scheme exhibited the strongest effect;the other three schemes exhibited roughly the same effect.In particular,the Q and P schemes exhibited nearly the same effect.In the simulation based on observations from the Ocean Weather Station Papa,the HQ scheme exhibited the best performance,followed by the Q scheme.In the experiment with the HQ scheme,the root-mean-square deviation of the simulated SST from the observations was 0.43℃,and the mixed layer depth(MLD)was 2.0 m.As a contrast,the deviations of the SST and MLD reached 1.25℃ and 8.4 m,respectively,in the experiment without wave-induced mixing.

Persistent mixing bursts in the equatorial Pacific thermocline induced by persistent equatorial waves

A recent study by Liu et al.(2020)suggested that due to the saturation of equatorially trapped planetary waves with different dynamical types,temporal periods,meridional and baroclinic modes,complex layer structures of vertical velocity shear and hence turbulent mixing could frequently occur in the thermocline of the eastern equatorial Pacific.We investigated the occurrence of the interior turbulent mixing as indicated by shear instabilities,above the Equatorial Undercurrent(EUC)core at three equatorial sites along 140°W,170°W,and 165°E,respectively,based mainly on data from the Tropical Atmosphere and Ocean(TAO)mooring array.We found that turbulent mixing bursts persisted in the thermocline of all three sites.Specifically,the interior turbulent mixing layers(ITMLs)could occur in probability of approximately 68%,53%,and 48%at the three sites,respectively.The overall occurrence probability shows obvious and similar biannual variations at 140°W and 170°W,which is higher in boreal from late summer to winter and lower in spring.Vertically,the ITMLs are primarily located above the EUC core and prevail in deeper(shallower)layers from late summer to winter(spring).Most ITMLs(70%)lasted for hours to 3 days,and a few of them(15%)for more than 7 days.The thicknesses of ITMLs were concentrated between 15 and 55 m.At 165°E,the vertical distribution of ITML occurrence probability was different from that at 140°W and 170°W,as it did not show a preference for depths;the durations of ITMLs are short(also from hours to several days)and their thicknesses were between 5 and 25 m.These properties,particularly the high occurrence probability,and short durations demonstrated the persistence of thermocline mixing in the western to eastern equatorial Pacific thermocline and confirmed the generation mechanism by persistent equatorial waves as well.

What induced the trend shift of mixed-layer depths in the Antarctic Circumpolar Current region in the mid-1980s?

An obvious trend shift in the annual mean and winter mixed layer depth(MLD)in the Antarctic Circumpolar Current(ACC)region was detected during the 1960–2021 period.Shallowing trends stopped in mid-1980s,followed by a period of weak trends.The MLD deepening trend difference between the two periods were mainly distributed in the western areas in the Drake Passage,the areas north to Victoria Land and Wilkes Land,and the central parts of the South Indian sector.The newly formed ocean current shear due to the meridional shift of the ACC flow axis between the two periods is the dominant driver for the MLD trends shift distributed in the western areas in the Drake Passage and the central parts of the South Indian sector.The saltier trends in the regions north to Victoria Land and Wilkes Land could be responsible for the strengthening mixing processes in this region.

Tide-Induced Mixing in the Bottom Boundary Layer in the Western East China Sea

The East China Sea(ECS)boasts a vast continental shelf,where strong tidal motions play an important role in the substance transport and energy budget.In this study,the tide-induced mixing in the bottom boundary layer in the western ECS is analyzed based on records measured by moored acoustic Doppler current profilers from June to October 2014.Results show that the M_(2) tide is strong and shows a barotropic feature,whereas the O_(1) tide is much weaker.Based on the M_(2) tidal currents,the eddy viscosity in the bottom Ekman boundary layer is estimated with three schemes.The estimated eddy viscosity values vary within 10^(-4)–10^(-2)m^(2) s^(−1),reaching a maximum at approximately 5 m height from the bottom and decreasing exponentially with the height at all three stations.Moreover,the shear production of turbulent kinetic energy is calculated to quantify the mixing induced by different tidal constituents.The results show that the shear production of the M_(2) tide is much stronger than that of the O_(1) tide and shows a bottom intensified feature.

Addressing cation mixing in layered structured cathodes for lithium-ion batteries:A critical review

High-performance lithium-ion batteries(LIB)are important in powering emerging technologies.Cathodes are regarded as the bottleneck of increasing battery energy density,among which layered oxides are the most promising candidates for LIB.However,a limitation with layered oxides cathodes is the transition metal and Li site mixing,which significantly impacts battery capacity and cycling stability.Despite recent research on Li/Ni mixing,there is a lack of comprehensive understanding of the origin of cation mixing between the transition metal and Li;therefore,practical means to address it.Here,a critical review of cation mixing in layered cathodes has been provided,emphasising the understanding of cation mixing mechanisms and their impact on cathode material design.We list and compare advanced characterisation techniques to detect cation mixing in the material structure;examine methods to regulate the degree of cation mixing in layered oxides to boost battery capacity and cycling performance,and critically assess how these can be applied practically.An appraisal of future research directions,including superexchange interaction to stabilise structures and boost capacity retention has also been concluded.Findings will be of immediate benefit in the design of layered cathodes for high-performance rechargeable LIB and,therefore,of interest to researchers and manufacturers.

Influence of the upper mixed layer depth on Langmuir turbulence characteristics

The upper mixed layer depth(h)has a significant seasonal variation in the real ocean and the low-order statistics of Langmuir turbulence are dramatically influenced by the upper mixed layer depth.To explore the influence of the upper mixed layer depth on Langmuir turbulence under the condition of the wind and wave equilibrium,the changes of Langmuir turbulence characteristics with the idealized variation of the upper mixed layer depth from very shallow(h=5 m)to deep enough(h=40 m)are studied using a non-hydrostatic large eddy simulation model.The simulation results show that there is a direct entrainment depth induced by Langmuir turbulence(h_(LT))within the thermocline.The normalized depthaveraged vertical velocity variance is smaller and larger than the downwind velocity variance for the ratio of the upper mixed layer to a direct entrainment depth induced by Langmuir turbulence h/h_(LT)<1 and h/h_(LT)>1,respectively,indicating that turbulence characteristics have the essential change(i.e.,depth-averaged vertical velocity variance(DAVV)DADV for Langmuir turbulence)between h/h_(LT)<1 and h/h_(LT)>1.The rate of change of the normalized depth-averaged low-order statistics for h/h_(LT)<1 is much larger than that for h/h_(LT)>1.The reason is that the downward pressure perturbation induced by Langmuir cells is strongly inhibited by the upward reactive force of the strong stratified thermocline for h/h_(LT)<1 and the eff ect of upward reactive force on the downward pressure perturbation becomes weak for h/h_(LT)>1.Hence,the upper mixed layer depth has significant influences on Langmuir turbulence characteristics.

The Effect of Boreal Summer Intraseasonal Oscillation on Mixed Layer and Upper Ocean Temperature over the South China Sea

Intraseasonal oscillation of the mixed layer and upper ocean temperature has been found to occur over the South China Sea(SCS)in the summer monsoon season based on the multiple reanalysis and observational data in this study.The method of composite analysis and an upper ocean temperature equation assisted the analysis of physical mechanisms.The results show that the mixed layer depth(MLD)in the SCS has a significant oscillation with a 30-60 d period over the SCS region,which is closely related to boreal summer intraseasonal oscillation(BSISO)activities.The MLD can increase(decrease)during the positive(negative)phase of the BSISO and usually lags behind by approximately one-eighth of the lifecycle(5 days)of the BSISO-related convection.The BSISO may cause periodic anomalies at the air-sea boundary,such as wind stress and heat flux,so it can play a dominant role in modulating the variation in MLD.There also are significant intraseasonal seawater temperature anomalies in both the surface and subsurface layers of the SCS.In addition,during the initial phase of the BSISO,the temperature anomaly signals of the thermocline are obviously opposite to the sea surface temperature(SST),especially in the southern SCS.According to the results from the analysis of the temperature equation,the vertical entrainment term caused by BSISO-related wind stress is stronger than the thermal forcing during the initial stage of convection,and it is more significant in the southern SCS.

Groundwater monitoring of an open-pit limestone quarry:Water-rock interaction and mixing estimation within the rock layers by geochemical and statistical analyses

Water-rock interaction and groundwater mixing are important phenomena in understanding hydrogeological systems and the stability of rock slopes especially those consisting largely of moderately watersoluble minerals like calcite. In this study, the hydrogeological and geochemical evolutions of groundwater in a limestone quarry composed of three strata: limestone layer(covering), interbedded layer under the covering layer, and slaty greenstone layer(basement) were investigated. Water-rock interaction in the open-pit limestone quarry was evaluated using PHREEQC, while hierarchical cluster analysis(HCA)and principal component analysis(PCA) were used to classify and identify water sources responsible for possible groundwater mixing within rock layers. In addition, Geochemist's Workbench was applied to estimate the mixing fractions to clarify sensitive zones that may affect rock slope stability. The results showed that the changes in Ca2+and HCO3àconcentrations of several groundwater samples along the interbedded layer could be attributed to mixing groundwater from the limestone layer and that from slaty greenstone layer. Based on the HCA and PCA results, groundwaters were classified into several types depending on their origin:(1) groundwater from the limestone layer(LO),(2) mixed groundwater flowing along the interbedded layer(e.g., groundwater samples L-7, L-11, S-3 and S-4), and(3) groundwater originating from the slaty greenstone layer(SO). The mixing fractions of 41% LO: 59% SO, 64% LO: 36% SO, 43%LO: 57% SOand 25% LO: 75% SOon the normal days corresponded to groundwaters L-7, L-11, S-3 and S-4,respectively, while the mixing fractions of groundwaters L-7 and L-11(61% LO: 39% SOand 93% LO: 7% SO,respectively) on rainy days became the majority of groundwater originating from the limestone layer.These indicate that groundwater along the interbedded layer significantly affected the stability of rock slopes by enlarging multi-breaking zones in the layer through calcite dissolution and inducing high water pressure, tension cracks and potential sliding plane along this layer particularly during intense rainfall episodes.

WAVELET ANALYSIS OF COHERENT STRUCTURES IN A THREE-DIMENSIONAL MIXING LAYER

Wavelet analysis is applied to the results obtained by the direct numerical simulation of a three-dimensional (3D) mixing layer in order to investigate coherent structures in dimension of scale. First, 3D orthonormal wavelet bases are constructed, and the corresponding decomposition algorithm is developed. Then the Navier-Stokes equations are transformed into the wavelet space and the architecture for multi-scale analysis is established. From this architecture, the coarse field images in different scales are obtained and some local statistical quantities are calculated. The results show that, with the development of a mixing layer, the energy spectrum densities for different wavenumbers increase and the energy is transferred from the average flow to vortex structures in different scales. Due to the non-linear interactions between different scales, cascade processes of energy are very complex. Because vortices always roll and pair at special areas, for a definite scale, the energy is obtained from other scales at some areas while it is transferred to other scales at other areas. In addition, energy dissipation and transfer always occur where an intense interaction between vortices exists.

Impacts of a wind stress and a buoyancy flux on the seasonal variation of mixing layer depth in the South China Sea

The seasonal variation of mixing layer depth （MLD） in the ocean is determined by a wind stress and a buoy- ance flux. A South China Sea （SCS） ocean data assimilation system is used to analyze the seasonal cycle of its MLD. It is found that the variability of MLD in the SCS is shallow in summer and deep in winter, as is the case in general. Owing to local atmosphere forcing and ocean dynamics, the seasonal variability shows a regional characteristic in the SCS. In the northern SCS, the MLD is shallow in summer and deep in winter, affected coherently by the wind stress and the buoyance flux. The variation of MLD in the west is close to that in the central SCS, influenced by the advection of strong western boundary currents. The eastern SCS presents an annual cycle, which is deep in summer and shallow in winter, primarily impacted by a heat flux on the air-sea interface. So regional characteristic needs to be cared in the analysis about the MLD of SCS.

The stress-microstructure relationship in an evolving mixing layer of fiber suspensions

The equations for fiber suspensions in an evolving mixing layer were solved by the spectral method, and the trajectory and orientation of fibers were calculated based on the slender body theory. The calculated spatial and orientation distributions of fibers are consistent with the experimental ones that were performed in this paper. The relationship between the microstructure of fibers and additional stress was examined. The results show that the spatial and orientation distributions of fibers are heterogeneous because of the influence of coherent vortices in the flow, which leads to the heterogeneity of the additional stress. The degree of heterogeneity increases with the increasing of St number and fiber aspect ratio. The fibers in the flow make the momentum loss thickness of the mixing layer thicker and accelerate the vorticity dispersion.

Mixed layer warming by the barrier layer in the southeastern Indian Ocean

The southeastern Indian Ocean is characterized by the warm barrier layer(BL)underlying the cool mixed layer water in austral winter.This phenomenon lasts almost half a year and thus provides a unique positive effect on the upper mixed layer heat content through the entrainment processes at the base of the mixed layer,which has not been well evaluated due to the lack of proper method and dataset.Among various traditional threshold methods,here it is shown that the 5 m fixed depth difference can produce a reliable and accurate estimate of the entrainment heat flux(EHF)in this BL region.The comparison between the daily and monthly EHF warming indicates that the account for high-frequency EHF variability almost doubles the warming effect in the BL period,which can compensate for or even surpass the surface heat loss.This increased warming is a result of stronger relative rate of the mixed layer deepening and larger temperature differences between the mixed layer and its immediate below in the daily-resolving data.The interannual EHF shows a moderately increasing trend and similar variabilities to the Southern Annular Mode(SAM),likely because the mixed layer deepening under the positive SAM trend is accompanied by enhanced turbulent entrainment and thus increases the BL warming.

Numerical simulations of compressible mixing layers with a discontinuous Galerkin method

Discontinuous Galerkin（DG） method is known to have several advantages for flow simulations,in particular,in fiexible accuracy management and adaptability to mesh refinement. In the present work,the DG method is developed for numerical simulations of both temporally and spatially developing mixing layers. For the temporally developing mixing layer,both the instantaneous fiow field and time evolution of momentum thickness agree very well with the previous results. Shocklets are observed at higher convective Mach numbers and the vortex paring manner is changed for high compressibility. For the spatially developing mixing layer,large-scale coherent structures and self-similar behavior for mean profiles are investigated. The instantaneous fiow field for a three-dimensional compressible mixing layer is also reported,which shows the development of largescale coherent structures in the streamwise direction. All numerical results suggest that the DG method is effective in performing accurate numerical simulations for compressible shear fiows.

FORMATION AND EVOLUTION OF THE STREAMWISE VORTICES IN MIXING LAYERS

The evolution of the three-dimensional time-developing mixing layer was simulated numerically using the pseudo-spectral method. The initial perturbations consisted of the two-dimensional fundamental wave and the streamwise-invariant three-dimensional disturbance. A comparison of the formations of the streamwise vortices with different amplitude functions for three-dimensional disturbances was made. In one case the results are similar to that of Rogers and Moser (1992), whereas a different way in which the quadrupole forms and sudden expansion of the rib were observed in another case. The simulation also confirms that stretching by the forming roller rather than Rayleigh centrifugal instability is responsible for the formation of the rib. Finally, numerical flow visualization results were presented. (Edited author abstract) 9 Refs.

Nanoparticle nucleation and coagulation in a mixing layer

Numerical simulation of nanoparticle nucleation and coagulation in a mixing layer with sulfuric acid vapor binary system is performed using the large eddy simulation and the direct quadrature method of moment. The distributions of number concentration, volume concentration, and average diameter of nanoparticles are obtained. The results show that the coherent structures have an important effect on the distributions of number concentration, volume concentration and average diameter of nanoparticles via continuously transporting and diffusing the nanoparticles to the area of low particle concentration. In the streamwise direction, the number concentration of nanoparticles decreases, while the volume concentration and the average diameter increase. The distributions of number concentration, volume concentration and average diameter of nanoparticles are spatially inhomogeneous. The characteristic time of nucleation is shorter than that of coagulation. The nucleation takes place more easily in the area of low temperature because where the number concentration of nanoparticles is high, while the intensity of coagulation is mainly affected by the number concentration. Both nucleation and coagulation result in the variation of average diameter of nanoparticles.

NUMERICAL SIMULATION OF SUPERSONIC REACTING MIXING LAYER

In this paper, the supersonic chemically reacting mixing layer is simulated with the third order ENN scheme, based on the Navier-Stokes equations, containing transport equations of all species. The numerical results show that the thickness of mixing layer increases gradually along the flow direction, and that the Kelvin-Helmholtz, instabilities may not exist in mixing layer flows.

Analysing the structure of the optical path length of a supersonic mixing layer by using wavelet methods

The nano-particle-based planar laser scattering （NPLS） technique is used to measure the density distribution in the supersonic mixing layer of the convective Mach number 0.12, and the optical path difference （OPL）, which is quite crucial for the study of aero-optics, is obtained by post processing. Based on the high spatiotemporal resolutions of the NPLS, the structure of the OPL is ana]ysed using wavelet methods. The coherent structures of the OPL are extracted using three methods, including the methods of thresholding the coefficients of the orthogonal wavelet transform and the wavelet packet transform, and preserving a number of wavelet packet coefficients with the largest amplitudes determined by the entropy dimension. Their performances are compared, and the method using the wavelet packet is the best. Based on the viewpoint of multifractals, we study the OPL by the wavelet transform maxima method （WTMM）, and the result indicates that its scaling behaviour is evident.

Seasonal variability of the mixed layer depth determined using an improved maximum angle method in the Arctic basins

To investigate the spatiotemporal variations in the mixed layer depth(MLD)in the Arctic basins,a new criterion to determine the MLD,called the improved maximum angle method(IMAM),was developed.A total of 45123 potential density profiles collected using Ice-Tethered Profilers(ITPs)in the Arctic basins during 2005-2021 were used to demonstrate the method’s effectiveness.By comparing the results obtained by the fixed threshold method(FTM),percentage threshold method(PTM),and maximum gradient method(MGM)for profiles in the Canada Basin,Makarov Basin,and Eurasian Basin,we determined that the quality index(1.0 for perfect identification of the MLD)of the IMAM regarding the assessment of the MLD determination method reached 0.94,which is much greater than those of other criteria.Moreover,two types of the density profiles were identified based on the mixed layer development stage.The MLDs of the typical profiles determined using the IMAM were found to have better consistency with the original definition.By utilizing the new mixed layer criterion,the seasonal variations and regional differences in the MLD in the Arctic basins were analyzed.Spatially,the summer and winter MLDs in the Canada Basin were the shallowest(13.55 m in summer,26.76 m in winter)than those in the Makarov(29.51 m in summer,49.08 m in winter)and Eurasian(20.36 m in summer,46.81 m in winter)basins due to the stable stratification in the upper ocean and the subsequent small effects of dynamic and thermodynamic processes(wind-driven stirring and brine rejection)in the Canada Basin.Seasonally,in the three Arctic basins,the average MLD was shallowest(22.77 m)in summer;it deepened through autumn and reached a winter maximum(41.12 m).

Mode decomposition of a noise suppressed mixing layer

Noise is generated in a two-dimensional mixing layer due to the growing of instability waves and vortex pairings. The adjoint-based control methodology has shown to be a robust tool to suppress noise radiation. The mode decomposition algorithms such as the compressible version of proper orthogonal decomposition （POD） and dynamic mode decomposition （DMD） are employed to analyze the spatial/spatial-temporal coherent structures for a consecutive data sets of the controlled mixing layer and its uncontrolled counterpart. The analyses of POD indicate that the y-direction body force control mainly modify the most energetic spatial structures, and increase the uniformity of the flow. The analyses of DMD show us prevalent frequencies and corresponding mode structures, and the stability characteristics of each mode can be obtained from DMD-spectrum. The spectral signatures illustrate that a lot of neutral/slightly damping modes emerging in uncontrolled flow within the frequency range （w 〈 0.4） are suppressed due to control, relevant spatial-temporal structures are also varied, which is coincident with the change of far-field noise spectra. From the view of mode decomposition, the action of control redistribute the energy for frequency components of ~ 〈 0.4 by weakening nonlinearities and regularizing corresponding dynamic structures in streamwise direction, and thus suppress the noise radiation. Moreover, the POD- and DMD-analysis in this study demon- strate that DMD can serve as an important supplement for POD in analyzing a time-resolved physical process.