Strong Mixing Research Articles

Flow control of blade-end oscillating jets on corner separation in a high-load compressor cascade

Based on unsteady numerical simulation, the feasibility of utilizing a fluid oscillator to generate oscillating jets for relieving the compressor cascade's corner separation was investigated. First, at design incidence angle, the optimal jet position is located where corner separation is not fully developed (74% axial chord length). Jets at more upstream and downstream positions are less effective due to premature dissipation of jet effects and the occurrence of high corner losses, respectively. The effectiveness of separation control through jet injection increases with higher jet mass flow rates, and the scheme with 0.66% relative jet flow rate exhibits a wide effective jet position range. However, excessively low jet flow rates are sensitive to jet position selection, while excessively high jet flow rates lead to significant mixing losses, resulting in high overall field losses and reduced engineering applicability. Second, the optimal jet scheme remains consistent at both design and high incidence angles and exhibits effective control at other off-design incidence angles. Finally, the oscillating jet suppresses the spanwise development of wall vortex and passage vortex within the blade passage by injecting high-momentum flow. Moreover, proper orthogonal decomposition analysis indicates that the oscillating jet redistributes the modal energy of the original flow field, exciting the vortex structures into high-frequency, small-scale oscillations at the jet frequency. Meanwhile, the oscillating jet primarily facilitates momentum exchange through strong mixing with passage vortex, wall vortex, and concentrated separation vortex, ultimately mitigating corner separation and reducing corner loss.

Rank-one systems, flexible classes and Shannon orbit equivalence

Abstract We build a Shannon orbit equivalence between the universal odometer and a variety of rank-one systems. This is done in a unified manner using what we call flexible classes of rank-one transformations. Our main result is that every flexible class contains an element which is Shannon orbit equivalent to the universal odometer. Since a typical example of flexible class is $\{T\}$ when T is an odometer, our work generalizes a recent result by Kerr and Li, stating that every odometer is Shannon orbit equivalent to the universal odometer. When the flexible class is a singleton, the rank-one transformation given by the main result is explicit. This applies to odometers and Chacon’s map. We also prove that strongly mixing systems, systems with a given eigenvalue, or irrational rotations whose angle belongs to any fixed non-empty open subset of the real line form flexible classes. In particular, strong mixing, rationality or irrationality of the eigenvalues are not preserved under Shannon orbit equivalence.

Irradiated Atmospheres. I. Heating by Vertical-mixing-induced Energy Transport

Observations have revealed unique temperature profiles in hot Jupiter atmospheres. We propose that the energy transport by vertical mixing could lead to such thermal features. In our new scenario, strong absorbers, TiO, and VO are not necessary. Vertical mixing could be naturally excited by atmospheric circulation or internal gravity wave breaking. We perform radiative transfer calculations by taking into account the vertical-mixing-driven energy transport. The radiative equilibrium is replaced by the radiative-mixing equilibrium. We investigate how the mixing strength, K zz, affects the atmospheric temperature–pressure profile. Strong mixing can heat the lower atmosphere and cool the upper atmosphere. This effect has important effects on the atmosphere's thermal features that would form without mixing. In certain circumstances, it can induce temperature inversions in scenarios where the temperature monotonically increases with increasing pressure under conditions of lower thermal band opacity. Temperature inversions show up as K zz increases with altitude due to shear interaction with the convection layer. The atmospheric thermal structure of HD 209458b can be well fitted with K zz ∝ (P/1 bar)−1/2 cm2 s−1. Our findings suggest vertical mixing promotes temperature inversions and lowers K zz estimates compared to prior studies. Incorporating chemical species into vertical mixing will significantly affect the thermal profile due to their temperature sensitivity.

Nutrient Vertical Flux in the Indonesian Seas as Constrained by Non‐Atmospheric Helium‐3

AbstractThe Indonesian seas are a renowned global biodiversity hotspot, yet nutrient sources and fluxes (especially the vertical flux) sustaining this richness remain unclear. Here, we used non‐atmospheric helium‐3 (3He) to constrain the vertical diffusion coefficient (Kd) in the Indonesian seas, which ranges from 5.2 × 10−5 to 2.3 × 10−3 m2 s−1 and averages 6.6 × 10−4 m2 s−1, a value notably higher than those found in the open ocean and in most marginal seas. We estimated that 6.9 ± 7.9 mmol m−2 d−1 of nitrate (NO3−) is vertically transported into the surface mixed layer, that is, >90% of the total NO3− required to support a net community production (NCP) of 470 ± 467 mg‐C m−2 d−1. Regions with narrow straits, steep topography and dynamic circulation with strong vertical mixing display high NCP and chlorophyll‐a, suggesting that vertical nutrient transport dominates biological productivity. Findings highlight the importance of vertical mixing in supplying nutrients and maintaining the extraordinary biological productivity and diversity in the Indonesian seas.

Contribution of High-mode Near-inertial Waves to Enhanced Typhoon-induced Sea Surface Temperature Cooling in the South China Sea

Sea surface temperature cooling (SSTC) is an important indicator of the ocean response to typhoons and is a factor in the evolution of typhoons. Understanding the intricate mechanisms underlying the SSTC induced by different typhoons is important. Based on the numerical simulation, we investigated the SSTC induced by typhoons Megi (2010), Linfa (2015), and Sarika (2011), which had relatively similar tracks in the South China Sea. As the strongest (weakest) typhoon, Megi (Sarika) induced the largest (smallest) SSTC, which is consistent with the traditional understanding that stronger typhoons usually induce larger SSTC than weaker typhoons. However, the SSTC induced by the moderate typhoon Linfa was nearly comparable to that induced by Megi, while Linfa had a wind power input an order of magnitude smaller. A comparison of near-inertial waves (NIWs) induced by Linfa and Megi showed that the former contained a larger proportion of high modes, substantially contributing to vertical shear. Consequently, the vertical mixing coefficient during Linfa reached one third of that during Megi. Because the SSTC is primarily influenced by vertical mixing, which is dominated by vertical diffusion at the mixed layer depth, the relatively strong vertical mixing coefficient and large temperature gradient during Linfa ultimately resulted in the SSTC nearly comparable to that induced by Megi. The results of this study enhance the understanding of typhoon-induced SSTC.

Symmetrical Convergence Rates and Asymptotic Properties of Estimators in a Semi-Parametric Errors-in-Variables Model with Strong Mixing Errors and Missing Responses

This paper considers a semi-parametric errors-in-variables (EV) model, ηi=xiβ+g(τi)+ϵi, ξi=xi+δi, 1⩽i⩽n. The properties of estimators are investigated under conditions of missing data and strong mixing errors. Three approaches are used to handle missing data: direct deletion, imputation, and the regression surrogate. Furthermore, estimators for the coefficient β and the nonparametric function g(·) are obtained. Notably, both estimators achieve strong consistency at a rate of o(n−1/4), exhibiting a symmetry in their convergence rates, and they also demonstrate asymptotic normality. Additionally, the validity of our theoretical results is supported by simulations demonstrating the finite sample behaviour of these estimators.

Influence of clouds on planetary boundary layer height: A comparative study and factors analysis

Clouds are one of the key factors influencing the evolution of the planetary boundary layer (PBL). Understanding the complex interactions between clouds and PBL height (PBLH) is essential for accurately simulating and predicting PBL processes. This study investigates the impact of clouds on PBLH evolution based on the lidar, radiosonde, ceilometer, and meteorological parameters observations at the Southern Great Plains site during the period January 2013 to December 2020. The findings indicates that the presence of clouds has an impact on the evolution of the PBLH. During the daytime, PBLH is lower under cloudy conditions than clear conditions, whereas during nighttime, PBLH is higher under cloudy conditions. This phenomenon arises because the intense solar radiation on clear days and strong turbulent mixing on cloudy nights contribute to the formation and maintenance of PBLH. Furthermore, during the daytime, clouds scatter and absorb solar radiation, leading to lower net radiation (NetR), sensible heat flux (SHF), surface temperature (TEM), and soil temperature (SoilT). These conditions, coupled with weaker turbulence intensity and high relative humidity (RH), leading to lower PBLH under cloudy conditions. Although TEM and SoilT are relatively high during clear nights, rapid surface radiative cooling and strong atmospheric stability inhibit the development of the PBLH. Consequently, during cloudy nights, clouds absorb and reflect longwave radiation from the surface, reducing surface radiative cooling rates, enhancing atmospheric instability and turbulence intensity. Furthermore, higher NetR and SHF, along with decreased RH, result in slightly deeper PBLH compared to clear conditions. Overall, this study systematically elucidates the influence of clouds on PBLH evolution and contributes to the understanding of the modulation of cloud on PBL structure.

New a Priori estimate for stochastic 2D Navier–Stokes equations with applications to invariant measure

AbstractThe paper deals with the stochastic two-dimensional Navier–Stokes equations for homogeneous and incompressible fluids, set in a bounded domain with Dirichlet boundary conditions. We consider additive noise in the form $$G\,\textrm{d}W$$ G d W , where W is a cylindrical Wiener process and G a bounded linear operator with range dense in the domain of $$A^\gamma $$ A γ , A being the Stokes operator. While it is known that existence of invariant measure holds for $$\gamma >1/4$$ γ > 1 / 4 , previous results show its uniqueness only for $$\gamma > 3/8$$ γ > 3 / 8 . We fill this gap and prove uniqueness and strong mixing property in the range $$\gamma \in (1/4, 3/8]$$ γ ∈ ( 1 / 4 , 3 / 8 ] by adapting the so-called Sobolevskiĭ-Kato-Fujita approach to the stochastic N–S equations. This method provides new a priori estimates, which entail both better regularity in space for the solution and strong Feller and irreducibility properties for the associated Markov semigroup.

On the convergence of phase space distributions to microcanonical equilibrium: dynamical isometry and generalized coarse-graining

Abstract This work explores the manner in which classical phase space distribution functions converge to the microcanonical distribution. We first prove a theorem about the lack of convergence, then define a generalization of the coarse-graining procedure that leads to convergence. We prove that the time evolution of phase space distributions is an isometry for a broad class of statistical distance metrics, implying that ensembles do not get any closer to (or farther from) equilibrium, according to these metrics. This extends the known result that strong convergence of phase space distributions to the microcanonical distribution does not occur. However, it has long been known that weak convergence can occur, such that coarse-grained distributions---defined by partitioning phase space into a finite number of cells---converge pointwise to the microcanonical distribution. We define a generalization of coarse-graining that removes the need for partitioning phase space into cells. We prove that our generalized coarse-grained distribution converges pointwise to the microcanonical distribution if the dynamics are strong mixing. As an example, we study an ensemble of triangular billiard systems.

Analisis Pengaruh Penerapan Strategi Bauran Pemasaran terhadap Keputusan Pembelian pada UMKM Serba Nanas Alam Sari Subang Jawa Barat

UMKM One of the producers in Subang offering processed pineapples is Serba Nanas Alam Sari. Processed pineapple sales are erratic. Businesses must create a strong marketing mix strategy in order to overcome consumer preferences and market rivalry. The purpose of this study is to examine how purchase decisions at Serba Nanas Alam Sari UMKM in Subang, West Java, are affected by the application of a marketing mix approach. In order to collect data for this study, 100 UMKM customers were given questionnaires. Mixed methods were used in this research. The techniques employed for gathering data included surveys, interviews, documentation, and observation. A Likert scale is used for variable measurement, and MSI is used to alter it. Multiple linear regression data analysis was used to ascertain the impact of place, promotion, price, and product variables on consumer purchase decisions. The study's findings indicate that the significant value is less than 0.05, indicating that purchase decisions are influenced by product, price, place, and promotion all at the same time. With a result of 1,042, the product variable has the biggest impact. This is due to the product's variety, good taste, and guaranteed product quality. The variables that affect promotion, pricing, and location are next in line. Based on the study's findings, Serba Nanas Alam Sari UMKM can benefit from an efficient marketing plan that combines quality products, competitive pricing, effective distribution, and eye-catching promotions to influence more customers' purchases.

Effects of the internal temperature on vertical mixing and on cloud structures in ultra-hot Jupiters

Context. The vertical mixing in hot-Jupiter atmospheres plays a critical role in the formation and spacial distribution of cloud particles in their atmospheres. This affects the observed spectra of a planet through cloud opacity, which can be influenced by the degree of cold trapping of refractory species in the deep atmosphere. Aims. We aim to isolate the effects of the internal temperature on the mixing efficiency in the atmospheres of ultra-hot Jupiters (UHJs) and the spacial distribution of cloud particles across the planet. Methods. We combined a simplified tracer-based cloud model, a picket fence radiative-transfer scheme, and a mixing length theory to the Exo-FMS general circulation model. We ran the model for five different internal temperatures at typical UHJ atmosphere system parameters. Results. Our results show the convective eddy diffusion coefficient remains low throughout the vast majority of the atmosphere, with mixing dominated by advective flows. However, some regions can show convective mixing in the upper atmosphere for colder interior temperatures. The vertical extent of the clouds is reduced as the internal temperature is increased. Additionally, a global cloud layer gets formed below the radiative-convective boundary (RCB) in the cooler cases. Conclusions. Convection is generally strongly inhibited in UHJ atmospheres above the RCB due to their strong irradiation. Convective mixing plays a minor role compared to advective mixing in keeping cloud particles aloft in UHJs with warm interiors. Higher vertical turbulent heat fluxes and the advection of potential temperature inhibit convection in warmer interiors. Our results suggest that isolated upper atmosphere regions above cold interiors may exhibit strong convective mixing in isolated regions around Rossby gyres, allowing aerosols to be better retained in these areas.

Particle-Hole Asymmetric Ferromagnetism and Spin Textures in the Triangular Hubbard-Hofstadter Model

In a lattice model subject to a perpendicular magnetic field, when the lattice constant is comparable to the magnetic length, one enters the “Hofstadter regime,” where continuum Landau levels become fractal magnetic Bloch bands. Strong mixing between bands alters the nature of the resulting quantum phases compared to the continuum limit; lattice potential, magnetic field, and Coulomb interaction must be treated on equal footing. Using determinant quantum Monte Carlo and density matrix renormalization group techniques, we study this regime numerically in the context of the Hubbard-Hofstadter model on a triangular lattice. In the field-filling phase diagram, we find a broad wedge-shaped region of ferromagnetic ground states for filling factor ν≤1, bounded below by filling factor ν=1 and bounded above by half filling the lowest Hofstadter subband. We observe signatures of SU(2) quantum Hall ferromagnetism at filling factors ν=1 and ν=3. The phases near ν=1 are particle-hole asymmetric, and we observe a rapid decrease in ground-state spin polarization consistent with the formation of skyrmions only on the electron doped side. At large fields, above the ferromagnetic wedge, we observe a low-spin metallic region with spin correlations peaked at small momenta. We argue that the phenomenology of this region likely results from exchange interaction mixing fractal Hofstadter subbands. The phase diagram derived beyond the continuum limit points to a rich landscape to explore interaction effects in magnetic Bloch bands. Published by the American Physical Society 2024

Design, experimental optimization, and flow analysis of a novel bioreactor for dynamic mammalian cell culture at laboratory scale using Box-Behnken design

Improving the quality of dynamic cell culture in laboratories is an important field in bioengineering. In this study, a novel lab-scale bioreactor using a vibrating agitator and a modified flask has been introduced to create a strong mixing at low shear stress. This bioreactor has been optimized using Box-Behnken design based on three dimensionless important structural factors including disc diameter, vibration amplitude, and the height of the disc placement. Three growth indicators including the specific growth rate, the natural logarithm of the maximum cell density, and productivity have been considered as biological responses. The results show that the disc diameter has the most important role in these indicators. If the disc diameter, vibration amplitude, and the height of disc placement are set to 0.24, 0.02, and 0.4 of the flask diameter, respectively, the values of the specific growth rate, the maximum cell density, and productivity at this optimum settings are 0.033 (h−1), 13.11, and 5133 (cells/(mL.h)), respectively. These values of the indicators are high and indicate the better performance of this bioreactor than other lab-scale bioreactors. In addition, investigating Reynolds number in the fluid flow indicates that in the range of 780 up to 1150, growth indices are high.

Cosmological Flow of Primordial Correlators.

Correlation functions of primordial density fluctuations provide an exciting probe of the physics governing the earliest moments of our Universe. However, the standard approach to compute them is technically challenging. Theoretical predictions are therefore available only in restricted classes of theories. In this Letter, we present a complete method to systematically compute tree-level inflationary correlators. This method is based on following the time evolution of equal-time correlators and it accurately captures all physical effects in any theory. These theories are conveniently formulated at the level of inflationary fluctuations, and can feature any number of degrees of freedom with arbitrary dispersion relations and masses, coupled through any type of time-dependent interactions. We demonstrate the power of this approach by exploring the properties of the cosmological collider signal, a discovery channel for new high-energy physics, in theories with strong mixing and in the presence of features. This work lays the foundation for a universal program to assist our theoretical understanding of inflationary physics and generate theoretical data for an unbiased interpretation of upcoming cosmological observations.

Thermal mixing and structure of the jet in swirling crossflow

The dilution zone in modern aero-engine combustors is characterized by a strong swirling mainstream with weak transverse jets. This characteristic brings new challenges in homogenizing the temperature distribution at the combustor exit. Therefore, it is imperative to understand the temperature penetration and mixing process of the jet in swirling crossflow (JISCF). This investigation provides new insight in the temperature mixing process for a JISCF in nozzle exit diameter (D) at 7.4, 10.7, and 14 mm and jet to mainstream velocity ratio (VR) from 2.0 to 6.6. The temperature mixing process was measured in a specially designed optical assessable three-dome model gas turbine combustor by planar 1-methylnaphthalene (1-MN) tracer laser-induced fluorescence thermometry. A detailed quantitative measurement of temperature distribution is achieved through the spectral red shift in the fluorescence of 1-MN as the temperature increase. This diagnostic was employed to provide the first two-dimensional temperature distribution for the JISCF. The results showed that the swirling crossflows induce strong spanwise thermal advection, forming secondary low-temperature regions downstream. Generally, the flow structure and mixing process are governed by the interaction of jet and swirling flow. The jet flow parameters, including velocity ratio and diameter, changed the flow structures by changing the interaction between jet and swirling flow. Statistical results and proper orthogonal decomposition (POD) analyses showed a strong anisotropic mixing process in the downstream of the jet.

A comparative study on aquatic environment of two mega reservoirs in the mainstream of Yangtze River

With the mega dams being built in large rivers around the world for water resources utilization and flood prevention, their environmental impacts such as algae bloom are increasingly concerned by the professionals and the publics, but the mechanism controlling the occurrence of algae are still unclear. Along the mainstream of the Yangtze River, world-class reservoirs have been put into operation successively. Among these reservoirs, the Three Gorges Reservoir (TGR) and the cascade reservoirs (CRs) are adjacent but the conditions of algae bloom in the tributary bays of them are totally different. To explore the reasons of the distinguished situations and factors relating to the high frequent algae bloom in the tributary bays of the TGR, a comparative study was carried out between the TGR and its neighbored reservoir out of the CRs based on field survey investigation, water quality records and literature review. The result reveals the considerable influences of geological and climatic factors on the hydrodynamic processes and environmental problems happening in the tributary bays of mega reservoirs. The two reservoirs exhibit significant differences in physical properties such as the hydrodynamic condition, terrain characteristics and climate. The field-investigation suggests that the water columns in the tributary bays of the CRs tend to experience weak vertical stratification. The analysis shows that this is the result of the combining result of the local terrain characteristics and the cooler, rainier and cloudier climate in the CRs region which significantly affect the hydro-thermal dynamic processes in the tributary bays. With the low level of nutrient and strong vertical mixing, the growth of the algae is constrained and these should be the significant reasons of the low frequency of algae bloom in the tributary bays of the CRs.

Hybrid spin-orbit exciton-magnon excitations in FePS3

FePS3 is a layered van der Waals (vdW) Ising antiferromagnet that has recently been studied in the context of true 2D magnetism and emerged as an ideal material platform for investigating strong spin-phonon coupling, and non-linear magneto-optical phenomena. In this work, we demonstrate an important unresolved role of spin-orbit coupling (SOC) in the ground state and excitations of this compound. Combining first-principles calculations with linear flavor wave theory (LFWT), we find strong mixing and spectral overlap of different spin-orbital single-ion states. Low-lying excitations form hybrid spin-orbit exciton/magnon modes. Complete parameterization of the low-energy model requires nearly half a million coupling constants. Despite this complexity, such a model can be inexpensively derived using local many-body-based approaches, which yield quantitative agreement with recent experiments. The results highlight the importance of SOC even in first-row transition metals and provide essential insight into the properties of 2D magnets with unquenched orbital moments.

Simulation of a cold spell in Guangdong-Hong Kong-Macao Greater Bay Area with WRF: Sensitivity to PBL schemes

The selection of the planetary boundary layer (PBL) parameterisation schemes is crucial for the simulation of local meteorology, especially under extreme weather events. A suitable PBL scheme is one of the key conditions to accurately reproduce the real weather conditions. In this study, the performance of all the three available PBL schemes that can be coupled with the multi-layer urban canopy model in the Weather Research and Forecasting (WRF) model: Yonsei University (YSU), Mellor-Yamada-Janjic (MYJ), and Bougeault-Lacarrere (BL), is evaluated for a cold spell event with Guangdong-Hong Kong-Macao Greater Bay Area (GBA) as the study region. It is found that accurate prediction of the strength of the vertical mixing and the change in wind speeds over the upper atmosphere is critical for reproducing the nighttime temperatures during the cold spell. The simulations of the BL scheme are consistent with observations that wind speeds do not vary much during daytime and nighttime, thus exhibiting strong vertical mixing and slowing down the near-surface temperature decrease during nighttime. The MYJ and YSU schemes cause significant underestimation of the nighttime 2-m temperature due to significant overestimation of the nighttime upper-air wind speeds, which leads to more heat transport through horizontal advection and hinders vertical mixing and convective activities. The results confirm that selection of a suitable PBL scheme can effectively reduce the uncertainty of the simulation results, and the coupling of the BL scheme with the multi-layer urban canopy model can better simulate the cold spell events occurring in the GBA, which also provides valuable references for the simulation of other similar coastal cities.

Characteristics and Mechanisms of Spring Tidal Mixing and Sediment Transport in a Microtidal Funnel-Shaped Estuary

Information about estuarine mixing and its control of sediment transport is crucial to elucidating the dynamics and evolution of estuaries. Here, the microtidal and funnel-shaped Zhenhai Estuary, located in the southwestern Pearl River Delta of China, is used to investigate the characteristics and mechanisms of water mixing and sediment transport based on observations from three spring tides. The results reveal that the studied estuary remains well mixed during spring tides from 2013–2022 despite its microtidal regime. Tidal stirring, which is enhanced by tidal energy convergence and benefits from the funnel-shaped geometry and shallow bathymetry, favors vertical mixing, contributing to the formation of strong mixing in the estuary. Due to the well-mixed regime, sediment transport in the estuary is dominated by the advective term, followed by a moderate tidal pumping term and minor estuarine circulation term. Accordingly, sediments within the estuary tend to be transported landward owing to the regulation of the funnel-shaped geometry, and a gradual but slow infilling trend is predictable. This paper deepens our understanding of hydrodynamics and sediment transport in microtidal estuaries.

Dispersion of particles in a sessile droplet evaporating on a heated substrate

A coupled volume-of-fluid (VOF) and discrete element model (DEM) is developed and used to study the dispersion of particles in an evaporating pinned sessile droplet on a heated substrate. Fully resolved simulations of evaporating droplets are performed to study the effects of substrate temperature and the Marangoni stresses to study the fluid flow and temperature distribution within the droplet. The fluid flow inside the evaporating droplets is used to predict the behavior of particles, studying the effect of relative particle density and the aforementioned effects on the particle dispersion within the droplet. This study shows that the presence of Marangoni stresses significantly affects the flow and temperature distribution inside the droplet, which, in turn, influences the dispersion of particles in the droplet. The fluid velocity induced by the Marangoni stresses is nearly two orders of magnitude larger than the velocity generated by capillary flow as a result of evaporation, promoting a strong convective mixing within the droplet, while working to equilibrate the temperature distribution at the interface. In the absence of Marangoni stresses, the dispersion of particles is governed by the competing effects of adsorption by the downward-moving interface as a result of evaporation, and particle sedimentation under the influence of gravity. However, both these effects become less dominant in the presence of a flow induced by the Marangoni stresses, causing the particles to initially move toward the apex of the droplet along the interface and, subsequently, toward a stagnation point on the interface.