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The magnetohydrodynamic (MHD) control has great potential in the applications of hypersonic vehicles. Typically, the MHD flowfield in these applications is low magnetic Reynolds (Rem) compressible turbulent flow, which is different from that without magnetic field and within the high Rem range. This paper investigated the low Rem compressible MHD isotropic turbulence in different Taylor-scale Reynolds numbers and interaction parameters via the Direct Numerical Simulation (DNS), and the influence of the magnetic field on the turbulence is researched. Results indicate that the normal Reynolds stress decreases in the direction perpendicular to the magnetic field. Moreover, the eddies are stretched in the direction parallel to the magnetic field. Besides, the Joule dissipation quicken the decay of the turbulent kinetic energy, and occurs mainly in large scale vortex. Based on the DNS data, the correlation between fluctuating electric intensity and velocity is studied. Results indicate that the electric intensity agrees well with the first-order approximate solution of the electric potential equation. Accordingly, an improved closure model of the correlation terms is established, where a coefficient related to the local turbulent Mach number is proposed. Comparisons with the DNS results reveal that the proposed model could correctly predict the correlation terms. [ABSTRACT FROM AUTHOR]

In this paper, we consider modeling missing dynamics with a nonparametric non-Markovian model, constructed using the theory of kernel embedding of conditional distributions on appropriate reproducing kernel Hilbert spaces (RKHS), equipped with orthonormal basis functions. Depending on the choice of the basis functions, the resulting closure model from this nonparametric modeling formulation is in the form of parametric model. This suggests that the success of various parametric modeling approaches that were proposed in various domains of applications can be understood through the RKHS representations. When the missing dynamical terms evolve faster than the relevant observable of interest, the proposed approach is consistent with the effective dynamics derived from the classical averaging theory. In the linear Gaussian case without the time-scale gap, we will show that the proposed non-Markovian model with a very long memory yields an accurate estimation of the nontrivial autocovariance function for the relevant variable of the full dynamics. The supporting numerical results on instructive nonlinear dynamics show that the proposed approach is able to replicate high-dimensional missing dynamical terms on problems with and without the separation of temporal scales. [ABSTRACT FROM AUTHOR]

Carboniferous volcanic rocks are widely distributed in the Junggar Basin and may provide a unique insight into the tectonic history of this basin. In this paper, we focus on the tectonic evolution of the northern Junggar Basin (NJB) using geochronological and geochemical data to establish the diachronous closure model for the Keramaili oceanic basin. The Lower Carboniferous strata in the eastern part (well WC‐1) and the Upper Carboniferous strata in the western part (well Y‐2) of the NJB are composed of a mix of compositional and rock‐type forms. These volcanic rocks are mostly high‐K assemblages characterized by high K (1.73–6.48%), high alkali (Na2O + K2O = 5.04–7.45%), and low TiO2 (0.57–1.06%). They also exhibit various REE concentrations (68.44–168.19 ppm), an enrichment of LREE (LaN/YbN = 4.54–8.09), and small negative Eu anomalies (δEu = 0.74–0.90). The depletion of HFSE and relevant tectonic setting discrimination diagrams demonstrate that these two volcanic associations were formed in a subduction‐related environment. The data also indicate that the high‐K volcanic rocks are derived from a mix of melted subducted sediments and mantle metasomatized by silica‐rich fluids. Although these two sets of volcanic rocks formed in Early and Late Carboniferous, the similar petrographic and geochemical natures suggest similar magma source and tectonic setting. Along with different regional tectonic settings in the NJB during the Carboniferous, we propose an asynchronous subduction of Keramaili oceanic basin, resulting in the inconsistent temporal and spatial distribution of Upper Carboniferous volcanic rocks in the NJB. [ABSTRACT FROM AUTHOR]

The transition-sensitive, three-equation k - kL - ω eddy-viscosity closure model was used for simulations of three-dimensional, single-element and multi-element wing configurations operating in close proximity to the ground. The aim of the study was to understand whether the model correctly simulated the transitional phenomena that occurred in the low Reynolds number operating conditions and whether it offered an improvement over the classical fully turbulent k-ω shear stress transport model. This was accomplished by comparing the simulation results to experiments conducted in a 2.7 m × 1.7 m closed-return, three-quarter-open-jet wind tunnel. The model was capable of capturing the presence of a laminar separation bubble on the wing and predicted sectional forces and surface-flow structures generated by the wings in wind tunnel testing to within 2.5% in downforce and 4.1% in drag for a multi-element wing. It was found, however, that the model produced insufficient turbulent kinetic energy during shear-layer reattachment, predicted turbulent trailing-edge separation prematurely in areas of large adverse pressure gradients, and was found to be very sensitive to inlet turbulence quantities. Despite these deficiencies, the model gave results that were much closer to wind-tunnel tests than those given by the fully turbulent k-ω shear stress transport model, which tended to underestimate downforce. Significant differences between the transitional and fully turbulent models in terms of pressure field, wake thickness and turbulent kinetic energy production were found and highlighted the importance of using transitional models for wings operating at low Reynolds numbers in ground effect. The k - kL - ω model has been shown to be appropriate for the simulation of separation-induced transition on a three-dimensional wing operating in ground effect at low Reynolds number. [ABSTRACT FROM AUTHOR]

Closure models started from Chou's work have been developed for more than 70 years, aiming at providing analytical tools to describe turbulent flows in the spectral space. In this study, a preliminary attempt is presented to introduce a closure model in the physical space, using the velocity structure functions as key parameters. The present closure model appears to qualitatively reproduce the asymptotic scaling behav-iors at small and large scales, despite some inappropriate behaviors such as oscillations. Therefore, further improvements of the present model are expected to provide appropriate descriptions of turbulent flows in the physical space. [ABSTRACT FROM AUTHOR]

A proper orthogonal decomposition (POD) technique has been successfully employed to develop reduced-order models for flow control purposes. For complex flows, higher POD modes also play a significant role in the stability and accuracy of the reduced-order model, thus require a closure, as in turbulent flows. In the presence of nonhomogeneous boundary conditions, developing a closure model becomes a challenging task. This paper discusses nonlinear closure modeling approaches for homogeneous and nonhomogeneous boundary conditions. Burgers’ equations, both one-dimensional and two-dimensional, are considered as the governing equations to develop reduced-order models with different boundary conditions. Homogeneous and nonhomogeneous boundary conditions are considered to demonstrate the effectiveness of the proposed closure modeling technique in boundary control applications. Numerical results show that the proposed closure model improves the accuracy of the reduced-order model. [ABSTRACT FROM AUTHOR]

In the numerical simulation of multi-material large deformation flow problems, the most important thing is tracking the material interfaces accurately while dealing with the large deformation of fluid simultaneously. The multi-material arbitrary Lagrangian Eulerian (MMALE) method coupled with the moment-of-fluid (MOF) interface reconstruction, was named a MOF-MMALE method and applied to multi-material large deformation flow problems. For the MOF-MMALE method, the mesh lines were allowed to cross the material interfaces and the mixed cells were introduced. In the mixed cells, the MOF interface reconstruction was used to determine the position and direction of the material interface. The numerical results of several typical examples, including the 2-material shock tube problem, the triple point problem, the Rayleigh-Taylor instability problem and the shock wave-Helium bubble interaction problem, show high accuracy and good resolution of the MOF-MMALE method, which is validated to be an effective way to simulate multi-material fluid flow problems with large deformation. [ABSTRACT FROM AUTHOR]

A closure model for flow-induced fiber orientation is proposed that is based on a reconstruction of the orientation distribution function (ODF). An a priori analysis by using Monte-Carlo simulation was performed. The main results are as follows. For strong rotary Brownian motion (low Péclet numbers), the model performs well even by using only the second moment to reconstruct the ODF. By considering the fourth moment in the reconstruction procedure, the accuracy of the model is improved and the model is applicable to higher Péclet numbers. At very high Péclet numbers and for non-Brownian fibers, the solution predicted by the proposed model deviates from the reference solution. [ABSTRACT FROM AUTHOR]

We investigate the scaling behaviour of a turbulent kinetic energy (TKE) closure model for stably stratified conditions. The mixing length scale for stable stratification is proportional to the ratio of the square root of the TKE and the local Brunt–Väisälä frequency, which is a commonly applied formulation. We analyze the scaling behaviour of our model in terms of traditional Monin–Obukov Similarity Theory and local scaling. From the model equations, we derive expressions for the stable limit behaviour of the flux–gradient relations and other scaling quantities. It turns out that the scaling behaviour depends on only a few model parameters and that the results obey local scaling theory. The analytical findings are illustrated with model simulations for the second GABLS intercomparison study. We also investigate solutions for the case in which an empirical correction function is used to express the eddy diffusivity for momentum as a function of the Richardson number (i.e. an increasing turbulent Prandtl number with stability). In this case, it seems that for certain parameter combinations the model cannot generate a steady-state solution. At the same time, its scaling behaviour becomes unrealistic. This shows that the inclusion of empirical correction functions may have large and undesired consequences for the model behaviour. [ABSTRACT FROM AUTHOR]

Three different kinds of closure model of fiber orientation tensors were applied to simulate numerically the hydrodynamic stability of fiber suspensions in a channel flow. The effects of closure models and three-dimensional ( 3-D) orientation distribution of fibers on the results of stability analysis were examined. It is found that the relationship of the behavior in hydrodynamic stability and the parameter of the fiber given by all the three models are the same. However, the attenuation of flow instability is most distinct using 3-D hybrid model because the orientation of the fiber departures from the flow direction, and least apparent using its 2-D counterpart for the the fibers show a tendency towards alignment with the flow direction in this case. [ABSTRACT FROM AUTHOR]

Given that land surface processes most often depend nonlinearly on soil moisture and that coarse-grained soil moisture fields are often used in modern large-scale applications, it becomes necessary to account in some way for the subgrid variability of physiographic properties and their interactions with subgrid soil moisture dynamics in order to derive robust estimates of grid-scale land surface fluxes. Albertson and Montaldo [2003] present a conservation equation for subgrid soil moisture spatial variability, which includes production and destruction terms related to the various interactions between moisture fields and flux fields (i.e., infiltration, drainage, evapotranspiration, and horizontal redistribution). Here we present a rigorous closure of the conservation equations of the first and second moments of the soil moisture field (omitting topographic redistribution in this effort). Closed terms include correlation coefficients between soil moisture and physiographic properties. The approach presented here provides accounting for the effects of dynamic interaction between soil moisture spatial variability and the underlying soil texture and vegetation density fields. Closure is achieved in terms of the spatial mean soil moisture evolution, with closure coefficients being functions of the correlation coefficient between the underlying soil texture and vegetation density patterns (i.e., the physiographic setting). Making use of these relationships, the proposed approach uses known subgrid soil texture and vegetation density fields to accurately simulate the temporal trajectory of subgrid variance of soil moisture, which supports improved estimates of grid-scale land surface fluxes. The approach is tested synthetically (closure model versus distributed model) over a wide range of physiographic characteristics and meteorological conditions, with results demonstrating that the closure model based approach reproduces the temporal dynamics of the soil moisture variability and provides improved grid-scale land surface flux estimates. In fact, the second-order closure was shown to reduce the errors in integrated land surface flux estimates, as compared to those derived from zero-order approximation estimates, by an order of magnitude in certain conditions. [ABSTRACT FROM AUTHOR]

Infiltration of foreign materials into a fatigue crack has previously been shown to be able to retard the crack and extend fatigue life. Most of the related studies were empirical and phenomenological in nature. To aid engineering decisions, it would be advantageous if the possible outcome of a repair can be evaluated beforehand. To this end, a crack closure model taking into account the additional closure effect of the infiltrant has been developed and verified against experimental results. With this model, the sensitivity of the repair effect to various parameters such as mechanical properties of the infiltrant, depth of penetration and infiltration load level can be assessed. [ABSTRACT FROM AUTHOR]

We present a class of efficient parametric closure models for 1D stochastic Burgers equations. Casting it as statistical learning of the flow map, we derive the parametric form by representing the unresolved high wavenumber Fourier modes as functionals of the resolved variable's trajectory. The reduced models are nonlinear autoregression (NAR) time series models, with coefficients estimated from data by least squares. The NAR models can accurately reproduce the energy spectrum, the invariant densities, and the autocorrelations. Taking advantage of the simplicity of the NAR models, we investigate maximal space-time reduction. Reduction in space dimension is unlimited, and NAR models with two Fourier modes can perform well. The NAR model's stability limits time reduction, with a maximal time step smaller than that of the K-mode Galerkin system. We report a potential criterion for optimal space-time reduction: the NAR models achieve minimal relative error in the energy spectrum at the time step, where the K-mode Galerkin system's mean Courant–Friedrichs–Lewy (CFL) number agrees with that of the full model. [ABSTRACT FROM AUTHOR]