Academic literature on the topic 'Moment tensor, anisotropy'

Abstract Full moment tensor inversion has become a standard method for understanding the mechanisms of earthquakes as the resolution of the inversion process increases. Thus, it is important to know the possible forms of non–double‐couple (non‐DC) moment tensors, which can be obtained because of either the different source mechanisms or the anisotropy of the focal regions. In this study, the form of the moment tensors of seismic sources occurring in transversely isotropic (TI) focal regions is obtained using the eigendecomposition of the elasticity tensor. More precisely, a moment tensor is obtained as a linear combination of the eigenspaces of TI elasticity tensor in which the coefficients of the terms are the corresponding eigenvalues multiplied with the projection of the potency tensor onto the corresponding eigenspaces. Moreover, the eigendecomposition method is also applied to obtain the three different forms of moment tensors in isotropic focal regions, in particular, for the shear source, tensile source, and for any type of potency tensor whose rank is three. This linear algebra point of view makes the structure of the moment tensors more apparent; for example, a shear source tensor is an eigenvector of isotropic elasticity tensor, and hence the resulting moment tensor is proportional to its shear source tensor. Moreover, a geometric interpretation for the scalar seismic moment, which is the norm of the moment tensor, for anisotropic focal regions is achieved through the eigendecomposition method. This method also gives a simple way to quantify the percentage of the isotropic component of the moment tensor of shear sources in TI focal regions. Hence, the complexities in the moment tensor introduced by the anisotropy of the focal region and by the source mechanism can be differentiated.

Radiation patterns of earthquakes contain important information on tectonic strain responsible for seismic events. However, elastic anisotropy may significantly impact these patterns. We systematically investigate and visualize the effect of anisotropy on the radiation patterns of microseismic events. For visualization, we use a vertical-transverse-isotropic (VTI) medium. We distinguish between two different effects: the anisotropy in the source and the anisotropy on the propagation path. Source anisotropy mathematically comes from the matrix multiplication of the anisotropic stiffness tensor with the source strain expressed by the potency tensor. We analyze this effect using the corresponding radiation pattern and the moment tensor decomposition. Propagation anisotropy mathematically comes from the deviation between the polarization and the propagation direction of a quasi P-wave in an anisotropic medium. We investigate both effects separately by either assuming the source to be anisotropic and the propagation to be isotropic or vice versa. We find that both effects have a significant impact on the radiation pattern of a pure-slip source. Finally, we develop an alternative visualization of source mechanisms by plotting beach balls proportional to their potency tensors. For this, we multiply the potency tensor with an isotropic elasticity tensor having the equivalent shear modulus [Formula: see text] and [Formula: see text]. In this way, we visualize the tectonic deformation in the source, independently of the rock anisotropy.

Abstract Anisotropy affects the focal mechanism and makes it complicated. A shear motion generates a pure double-couple (DC) source in isotropic media. While in anisotropic media, it will produce non-DC components, which contain isotropic (ISO) and compensated linear vector dipole (CLVD) components. Besides, coupled with the diversity of fault motion, the source may become extremely complicated. In this paper, the seismic moment tensor is obtained based on the dislocation model, and then a variety of analyses are performed with the moment tensor, including moment tensor decomposition, radiation pattern, radiated energy ratio and seismic propagation characteristics. Since the anisotropy of the medium also influences seismic wave propagation, a hypothesis is made that the source region is minimal and anisotropic, but the propagation path is isotropic. The research gives some interesting conclusions. It is found that the anisotropy mainly affects the focal mechanism under low slope angle while high slope angle has little effect on the polarity. In terms of the moment tensor decomposition, if only one of ISO or CLVD exists, it can be asserted that the source region is anisotropic because ISO components are accompanied by CLVD components in isotropy media. As for the DC component, the results indicate it is one of the most important factors for determining the ratio of radiant energy. This paper presents some valuable findings of the focal mechanism of the general dislocation source under anisotropy, which helps to recognise the source characteristics of the earthquake and build solid foundations for the subsequent inversion of the focal mechanism.

ABSTRACT The non-double-couple (non-DC) components of the moment tensor provide insight into the earthquake processes and anisotropy of the near-source region. We investigate the behavior of the isotropic (ISO) and compensated linear vector dipole (CLVD) components of the moment tensor for shear faulting in a transversely ISO medium with an arbitrarily oriented symmetry axis. Analytic formulas for ISO and CLVD depend on the orientation of the fault relative to the anisotropy symmetry axis as well as three anisotropic parameters, which describe deviations of the medium from isotropy. Numerical experiments are presented for the preliminary reference Earth model. Both ISO and CLVD components are zero when the axis of symmetry is within the fault plane or the auxiliary plane. For any orientation in which the ISO component is zero, the CLVD component is also zero, but the opposite is not always true (e.g., for strong anisotropy). The relative signs of the non-DC components of neighboring earthquakes may help distinguish source processes from source-region anisotropy. We prove that an inversion of ISO and CLVD components of a set of earthquakes with different focal mechanisms can uniquely determine the orientation and strength of anisotropy. This study highlights the importance of the ISO component for constraining deep slab anisotropy and demonstrates that it cannot be neglected.

Lattice Boltzmann (LB) methods are usually developed on cubic lattices that discretize the configuration space using uniform grids. For efficient computations of anisotropic and inhomogeneous flows, it would be beneficial to develop LB algorithms involving the collision-and-stream steps based on orthorhombic cuboid lattices. We present a new 3D central moment LB scheme based on a cuboid D3Q27 lattice. This scheme involves two free parameters representing the ratios of the characteristic particle speeds along the two directions with respect to those in the remaining direction, and these parameters are referred to as the grid aspect ratios. Unlike the existing LB schemes for cuboid lattices, which are based on orthogonalized raw moments, we construct the collision step based on the relaxation of central moments and avoid the orthogonalization of moment basis, which leads to a more robust formulation. Moreover, prior cuboid LB algorithms prescribe the mappings between the distribution functions and raw moments before and after collision by using a moment basis designed to separate the trace of the second order moments (related to bulk viscosity) from its other components (related to shear viscosity), which lead to cumbersome relations for the transformations. By contrast, in our approach, the bulk and shear viscosity effects associated with the viscous stress tensor are naturally segregated only within the collision step and not for such mappings, while the grid aspect ratios are introduced via simpler pre- and post-collision diagonal scaling matrices in the above mappings. These lead to a compact approach, which can be interpreted based on special matrices. It also results in a modular 3D LB scheme on the cuboid lattice, which allows the existing cubic lattice implementations to be readily extended to those based on the more general cuboid lattices. To maintain the isotropy of the viscous stress tensor of the 3D Navier–Stokes equations using the cuboid lattice, corrections for eliminating the truncation errors resulting from the grid anisotropy as well as those from the aliasing effects are derived using a Chapman–Enskog analysis. Such local corrections, which involve the diagonal components of the velocity gradient tensor and are parameterized by two grid aspect ratios, augment the second order moment equilibria in the collision step. We present a numerical study validating the accuracy of our approach for various benchmark problems at different grid aspect ratios. In addition, we show that our 3D cuboid central moment LB method is numerically more robust than its corresponding raw moment formulation. Finally, we demonstrate the effectiveness of the 3D cuboid central moment LB scheme for the simulations of anisotropic and inhomogeneous flows and show significant savings in memory storage and computational cost when used in lieu of that based on the cubic lattice.

AbstractThe equation of the dynamics of the magnetic moment motion that has been averaged over the ensemble of nonequilibrium spin-injected electrons in a ferromagnetic transition in the presence of exchange interaction, interaction with an external electromagnetic field, and a thermostat has been obtained taking into account the spatial inhomogeneity of the charge carrier distribution. It has been shown that taking into account the spatial inhomogeneity of the charge carrier distribution in the equation of the dynamics of the magnetic moment motion allows for describing the various processes of electron transfer in the magnetic transition. The probability of quantum transitions of electrons with opposite spin directions, which determine spin relaxation in interaction with a thermostat, has been estimated. It has been shown that the anisotropy of the radiation medium is determined not only by the anisotropy of the sd -exchange tensor, but also by the additional anisotropy that is caused by the electron impulse derivatives of this tensor. The considered phenomena have a great potential for the detection of new effects and development of new devices based on them, including compact tunable radiation sources in the terahertz frequency range, which is obviously difficult to generate.

AbstractThe non-Newtonian stress tensor, collisional dissipation rate and heat flux in the plane shear flow of smooth inelastic disks are analysed from the Grad-level moment equations using the anisotropic Gaussian as a reference. For steady uniform shear flow, the balance equation for the second moment of velocity fluctuations is solved semi-analytically, yielding closed-form expressions for the shear viscosity $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mu $, pressure $p$, first normal stress difference ${\mathcal{N}}_1$ and dissipation rate ${\mathcal{D}}$ as functions of (i) density or area fraction $\nu $, (ii) restitution coefficient $e$, (iii) dimensionless shear rate $R$, (iv) temperature anisotropy $\eta $ (the difference between the principal eigenvalues of the second-moment tensor) and (v) angle $\phi $ between the principal directions of the shear tensor and the second-moment tensor. The last two parameters are zero at the Navier–Stokes order, recovering the known exact transport coefficients from the present analysis in the limit $\eta ,\phi \to 0$, and are therefore measures of the non-Newtonian rheology of the medium. An exact analytical solution for leading-order moment equations is given, which helped to determine the scaling relations of $R$, $\eta $ and $\phi $ with inelasticity. We show that the terms at super-Burnett order must be retained for a quantitative prediction of transport coefficients, especially at moderate to large densities for small values of the restitution coefficient ($e \ll 1$). Particle simulation data for a sheared inelastic hard-disk system are compared with theoretical results, with good agreement for $p$, $\mu $ and ${\mathcal{N}}_1$ over a range of densities spanning from the dilute to close to the freezing point. In contrast, the predictions from a constitutive model at Navier–Stokes order are found to deviate significantly from both the simulation and the moment theory even at moderate values of the restitution coefficient ($e\sim 0.9$). Lastly, a generalized Fourier law for the granular heat flux, which vanishes identically in the uniform shear state, is derived for a dilute granular gas by analysing the non-uniform shear flow via an expansion around the anisotropic Gaussian state. We show that the gradient of the deviatoric part of the kinetic stress drives a heat current and the thermal conductivity is characterized by an anisotropic second-rank tensor, for which explicit analytical expressions are given.

Abstract It is shown that, due to the hyperfine interaction between the electron and the positron, positronium atoms in a crystal can acquire an effective quadrupole moment and a tensor polarizability. In such a case the effective quadrupolar interaction with intracrystalline fields leads to a quadrupolar splitting of the triplet level of positronium and also to an anisotropy of its magnetic quenching in the presence of an external magnetic field. The possibilities of observating this anisotropy experimentally are discussed.

NMR line splitting under a strong static electric field (EF-NMR) allows one to measure the average alignment (second spherical harmonic) of the molecule studied under the influence of the field. This average alignment (per unit squared field) can be formulated theoretically by an expression involving the permanent dipole moment, the anisotropy of the static polarizability, etc. and possibly orientational intercorrelations within the liquid. On the other hand the Kerr constant per molecule can be represented by the same expression, multiplified by a factor that is independent of any static electrical property of the molecule (for a gas this factor would be simply proportional to the anisotropy of the optical polarizability). Consequently the ratio of the above experimental results contains information bearing only on the optical properties. The formalism of the "tensor of polarizability increment" developed by the author for liquids made up of ellipsoidal molecules is employed. It is shown that by combining the above ratio with the constitutive equation for the refractivity of the liquid, the two distinct principal elements of the tensor of polarizability increment of the symmetric top molecules constituting the liquid are immediately obtained. Using then the molecular volume, a van der Waals estimate for the elongation of the molecule, and the index of refraction of the liquid, one can calculate the elements of the optical polarizability tensor invacuo. The method is illustrated by neat acetonitrile for which the necessary experimental data exist in the literature. One finds, in units 1040 C2 m2 J−1 5.06 for the mean polarizability and 2.52 for its anisotropy. A published experimental study using depolarized light scattering in the gas phase indicates that the corresponding figures are 4.96 and 2.49 respectively at λ = 633 nm. Finally and accessorily, it is suggested that dipolar intercorrelations are weak in acetonitrile. Indeed, using an analogous formalism for the static permittivity of the liquid, a value for the permanent moment of the molecule is deduced. This value is within 1% of the experimental gas value. Keywords: polarizability tensors, liquids, Kerr constant, NMR.

Earthquake swarms occur frequently in West Bohemia, Central Europe. Their occurrence is correlated with and propably triggered by fluids that escape on the earth's surface near the epicentres. These fluids raise up periodically from a seemingbly deep-seated source in the upper mantle. Moment tensors for swarm events in 1997 indicate tensile faulting. However, they were determined under assumption of seismic isotropy although anisotropy can be observed. Anisotropy may obscure moment tensors and their interpretation. In 2000, more than 10,000 swarm earthquakes occurred near Novy Kostel, West Bohemia. Event triggering by fluid injection is likely. Activity lasted from 28/08 until 31/12/00 (9 phases) with maximum ML=3.2. High quality P-wave seismograms were used to retrieve the source mechanisms for 112 events between 28/08/00 and 30/10/00 using > 20 stations. We determine the source geometry using a new algorithm and different velocity models including anisotropy. From inversions of P waves we observe ML<3.2, strike-slip events on steep N-S oriented faults with additional normal or reverse components. Tensile components seem to be evident for more than 60% of the processed swarm events in West Bohemia during the phases 1-7. Being most significant at great depths and at phases 1-4 during the swarm they are time and location dependent. Although tensile components are reduced when anisotropy is assumed they persist and seem to be important. They can be explained by pore-pressure changes due to the injection of fluids that raise up. Our findings agree with other observations e.g. correlation of fluid transport and seismicity, variations in b-value, forcing rate, and in pore pressure diffusion. Tests of our results show their significance.

Earthquakes form by sudden brittle failure of rock mostly as shear ruptures along a rupture plane. Beside this, mechanisms other than pure shearing have been observed for some earthquakes mainly in volcanic areas. Possible explanations include complex rupture geometries and tensile earthquakes. Tensile earthquakes occur by opening or closure of cracks during rupturing. They are likely to be often connected with fluids that cause pressure changes in the pore space of rocks leading to earthquake triggering. Tensile components have been reported for swarm earthquakes in West Bohemia in 2000. The aim and subject of this work is an assessment and the accurate determination of such tensile components for earthquakes in anisotropic media. Currently used standard techniques for the retrieval of earthquake source mechanisms assume isotropic rock properties. By means of moment tensors, equivalent forces acting at the source are used to explain the radiated wavefield. Conversely, seismic anisotropy, i.e. directional dependence of elastic properties, has been observed in the earth's crust and mantle such as in West Bohemia. In comparison to isotropy, anisotropy causes modifications in wave amplitudes and shear-wave splitting. In this work, effects of seismic anisotropy on true or apparent tensile source components of earthquakes are investigated. In addition, earthquake source parameters are determined considering anisotropy. It is shown that moment tensors and radiation patterns due to shear sources in anisotropic media may be similar to those of tensile sources in isotropic media. In contrast, similarities between tensile earthquakes in anisotropic rocks and shear sources in isotropic media may exist. As a consequence, the interpretation of tensile source components is ambiguous. The effects that are due to anisotropy depend on the orientation of the earthquake source and the degree of anisotropy. The moment of an earthquake is also influenced by anisotropy. The orientation of fault planes can be reliably determined even if isotropy instead of anisotropy is assumed and if the spectra of the compressional waves are used. Greater difficulties may arise when the spectra of split shear waves are additionally included. Retrieved moment tensors show systematic artefacts. Observed tensile source components determined for events in West Bohemia in 1997 can only partly be attributed to the effects of moderate anisotropy. Furthermore, moment tensors determined earlier for earthquakes induced at the German Continental Deep Drilling Program (KTB), Bavaria, were reinterpreted under assumptions of anisotropic rock properties near the borehole. The events can be consistently identified as shear sources, although their moment tensors comprise tensile components that are considered to be apparent. These results emphasise the necessity to consider anisotropy to uniquely determine tensile source parameters. Therefore, a new inversion algorithm has been developed, tested, and successfully applied to 112 earthquakes that occurred during the most recent intense swarm episode in West Bohemia in 2000 at the German-Czech border. Their source mechanisms have been retrieved using isotropic and anisotropic velocity models. Determined local magnitudes are in the range between 1.6 and 3.2. Fault-plane solutions are similar to each other and characterised by left-lateral faulting on steeply dipping, roughly North-South oriented rupture planes. Their dip angles decrease above a depth of about 8.4km. Tensile source components indicating positive volume changes are found for more than 60% of the considered earthquakes. Their size depends on source time and location. They are significant at the beginning of the swarm and at depths below 8.4km but they decrease in importance later in the course of the swarm. Determined principle stress axes include P axes striking Northeast and Taxes striking Southeast. They resemble those found earlier in Central Europe. However, depth-dependence in plunge is observed. Plunge angles of the P axes decrease gradually from 50° towards shallow angles with increasing depth. In contrast, the plunge angles of the T axes change rapidly from about 8° above a depth of 8.4km to 21° below this depth. By this thesis, spatial and temporal variations in tensile source components and stress conditions have been reported for the first time for swarm earthquakes in West Bohemia in 2000. They also persist, when anisotropy is assumed and can be explained by intrusion of fluids into the opened cracks during tensile faulting.
Erdbeben entstehen durch plötzlichen Sprödbruch des Gesteins, meist als Scherbruch entlang einer Bruchfläche. Daneben werden für einige Beben v.a. in vulkanischen Gebieten auch Mechanismen beobachtet, die scheinbar vom Modell des Scherbruches abweichen. Ursachen dafür beinhalten komplexe Bruchgeometrien und tensile Erdbeben. Bei tensilen Erdbeben kommt es während des Bruchs zum Öffnen oder Schließen der Bruchfläche und damit zu Volumenänderungen. Erdbeben mit tensilen Anteilen stehen wahrscheinlich oft im Zusammenhang mit Fluiden, welche zur Durckänderung im Porenraum von Gesteinen und damit zum Auslösen des Bebens führen. Sie wurden auch im Vogtland während eines Erdbebenschwarms im Jahr 1997 beobachtet. Die Beurteilung und sichere Bestimmung tensiler Anteile von Erdbeben sind Ziel und Gegenstand dieser Arbeit. Bei Standardverfahren zur Bestimmung von Erdbebenmechanismen werden isotrope Gesteinseigenschaften angenommen. Momententensoren beschreiben dabei Kräfte, die das abgestrahlte Wellenfeld erklären. Allerdings wird seismische Anisotropie, d.h. Richtungsabhängigkeit elastischer Eigenschaften, in der Erdkruste und im Mantel wie z.B. im Vogtland beobachtet. Anisotropie bewirkt im Vergleich zu isotropen Medien Veränderungen der Wellenamplituden und -polariserungen sowie das Aufspalten von Scherwellen. In der vorliegenden Arbeit werden daher der Einfluss seismischer Anisotropie auf wahre oder scheinbar auftretende tensile Quellanteile untersucht und Erdbebenmechanismen unter Berücksichtigung seismischer Anisotropie bestimmt. Es wird gezeigt, dass Momententensoren und Abstrahlmuster von Scherbrüchen in anisotropen Medien denen von tensilen Brüchen in isotropen Medien ähneln können. Umgekehrt treten Ähnlichkeiten tensiler Beben in anisotropen Gesteinen mit Scherbrüchen in isotropen Medien auf. Damit existieren Mehrdeutigkeiten beobachteter tensiler Quellanteile. Die Effekte von Anisotropie hängen von der Orientierung des Bruches und vom Grad der Anisotropie ab. Außerdem beeinflusst Anisotropie das Moment eines Bebens. Herdflächenorientierungen können auch dann verlässlich bestimmt werden, wenn man Isotropie statt Anisotropie annimmt und die Spektren von Kompressionswellen verwendet. Bei Hinzunahme der Spektren von Scherwellen können Uneindeutigkeiten auftreten. Abgeleitete Momententensoren zeigen systematische Artefakte. Beobachtungen tensiler Quellanteile von Beben im Vogtland im Jahr 1997 können nicht allein durch moderate Anisotropie erklärt werden. Weiterhin wurden früher bestimmte Momententensoren induzierter Beben nahe der Kontinentalen Tiefbohrung, Bayern, unter Annahme anisotroper Parameter reinterpretiert. Die Beben werden einheitlich als Scherbrüche charakterisiert, obwohl deren Momententensoren tensile Bestandteile enthalten, die als scheinbar angesehen werden. Die Resultate unterstreichen die Notwendigkeit, seismische Anisotropie zu berücksichtigen, um tensile Komponenten von Erdbeben eindeutig zu bestimmen. Ein daher neu entwickelter Inversionsalgorithmus wurde getestet und erfolgreich auf 112 Erdbeben der letzten intensiven Schwarmepisode im Jahr 2000 im Vogtland an der deutsch-tschechischen Grenze angewandt. Die Herdparameter wurden unter Verwendung isotroper und anisotroper Geschwindigkeitsmodelle ermittelt. Die Beben zeigen Lokalmagnituden zwischen 1,6 und 3,2. Sie weisen zueinander ähnliche Herdflächenlösungen mit linkslateralem Versatz auf steil einfallenden, etwa Nord-Süd orientierten Bruchflächen auf. Die Fallwinkel nehmen oberhalb 8,4km Tiefe ab. Für über 60% der betrachteten Erdbeben werden tensile Quellanteile mit Volumenvergrößerung beobachtet. Die tensilen Komponenten zeigen Abhängigkeiten von Herdzeit und -ort. Sie sind zu Beginn des Schwarms sowie in Tiefen unterhalb 8,4km besonders signifikant und nehmen später an Bedeutung ab. Abgeleitete Hauptspannungsachsen enthalten P Achsen mit nordwestlicher und T Achsen mit südwestlicher Streichrichtung. Sie ähneln denen in Mitteleuropa. Es werden tiefenabhängige Fallwinkel beobachtet. Die Änderungen erfolgen für die P Achsen graduell von 50° hin zu flacheren Fallwinkeln bei tieferen Beben. Sie erfolgen jedoch abrupt für die T Achsen von etwa 8° oberhalb einer Tiefe von etwa 8,4km zu 21° einfallend unterhalb dessen. Mit dieser Arbeit werden erstmals zeitliche und räumliche Veränderungen tensiler Quellanteile und Spannungszustände im Vogtland für Erdbeben im Jahr 2000 beobachtet. Diese haben auch dann Bestand, wenn seismische Anisotropie berücksichtigt wird. Sie können durch Fluide erklärt werden, die in die Bruchflächen eindringen.

This chapter deals with small-volume expansions of the displacement fields. It first introduces the notion of elastic moment tensor, a geometric quantity associated with a small-volume inclusion, before discussing some of its important properties such as symmetry and positive-definiteness. The asymptotic expansion of the displacement in the presence of a small-volume inclusion is expressed in terms of the elastic moment tensor. The chapter proceeds by deriving formulas for the elastic moment tensors under linear transformations and computes those associated with ellipses and balls. It also considers both the static and time-harmonic regimes and extends the small-volume asymptotic framework to anisotropic elasticity. Finally, it provides the leading-order terms in the asymptotic expansions of the solutions to the static and time-harmonic elasticity equations with respect to the size of a small inclusion.

An experimental investigation is performed on a fully developed turbulent channel flow with local injection through a porous strip. The Reynolds number based on the channel half-width was set to 5000. In addition to the no blowing data, measurements are made for three different blowing rates σ = 0.22, 0.36 and 0.58 (where σ is the ratio of momentum flux gain due to the blowing and momentum flux of the incoming channel flow). Measurements carried out with hot-wire anemometry reveal that injection strongly affects both the velocity profiles and the turbulence characteristics. The injection decreases the skin friction coefficient and increases all the Reynolds stresses downstream the blowing strip. Moreover, the anisotropic invariant map (A.I.M.) for the Reynolds stress tensor revealed that blowing decreased the anisotropy of the turbulent structure in the near wall region and a decrease in the longitudinal integral length scale was observed when the blowing rate increased. The space time correlation measurements show that injection increases the inclination of the coherent structures in both (x,y) and (x,z) plan.

The comparison of the structures of the boundary layer with and without suction of the same momentum thickness Reynolds number Rθ have been made in a turbulent boundary subjected to concentrated suction, applied through a short porous wall strip. The results indicate that, relative to σ = 0, the mean velocity collapses reasonably well but there are some discrepancies in the Reynolds stresses distributions. These discrepancies are also noted in the distributions of the anisotropy invariant tensor, skewness and flatness factors. The result would suggest that the differences are a result of the difference in the initial boundary condition, which influences the flow structures to a significant streamwise location.

Abstract Computational fluid dynamics (CFD) results are presented for synthetic turbulence generation by a proposed statistically targeted forcing (STF) method. The new method seeks to introduce a fluctuating velocity field with a distribution of first and second moments that match a user-specified target mean velocity and Reynolds stress tensor, by incorporating deterministic time-dependent forcing terms into the momentum equation for the resolved flow. The STF method is formulated to extend the applicability of previously documented methods and provide flexibility in regions where synthetic turbulence needs to be generated or damped, for use in engineering level large-eddy and hybrid large-eddy/Reynolds-averaged Navier-Stokes CFD simulations. The objective of this study is to evaluate the performance of the proposed STF method in LES simulations of isotropic and anisotropic homogeneous turbulent flow test cases. Results are interrogated and compared to target statistical velocity and turbulent stress distributions and evaluated in terms of energy spectra. Analysis of the influence of STF model parameters, mesh resolution, and LES subgrid stress model on the results is investigated. Results show that the new method can successfully reproduce desired statistical distributions in a homogeneous turbulent flow.

Flow-alignment of sheared nematic polymers occurs in various flow-concentration regimes. Analytical descriptions of shear-aligned nematic monodomains have a long history across continuum, mesoscopic and mean-field kinetic models, sacrificing precision at each finer scale. Continuum Leslie-Ericksen theory applies to highly concentrated, weak flows of small molecular weight polymers, giving an explicit macroscopic alignment angle formula dependent only on Miesowicz viscosities. Mesoscopic tensor models apply at all concentrations and shear rates, but explicit “Leslie angle” formulas exist only in the weak shear limit (Cocchini et. al, 90; Bhave et. al, 93; Wang, 97; Rienacker and Hess, 99; Maffettone et. al, 00; Forest and Wang, 02; Forest et. al, 02c; Grecov and Rey, 02), with distinct behavior in dilute versus concentrated regimes. Exact probability distribution functions (pdf’s) of kinetic theory do not exist for highly concentrated nematic states, even without flow, although appealing flow-aligned approximations have been derived (Kuzuu and Doi, 83; Kuzuu and Doi, 84; Semenov, 83; Semenov, 86; Archer and Larson, 95; Kroger and Seller, 95), which offer a molecular theory basis for the Leslie alignment angle. A simpler problem concerns the dilute concentration regime where the unique quiescent equilibrium is isotropic, corresponding to a constant pdf, and whose weak shear deformation is robust to mesoscopic closure approximation (Forest and Wang, 02; Forest et. al, 02c): steady, flow-aligning, weakly anisotropic, and biaxial. The purpose of this paper is to explicitly construct the weakly anisotropic branch of stationary pdf’s by a weak-shear asymptotic expansion of kinetic theory. A second-moment pdf projection confirms mesoscopic model predictions, and further yields explicit Leslie angle and degree of alignment formulas in terms of molecular parameters and normalized shear rate.

This paper is concerned with the prediction of heat transfer rates in fully-developed turbulent flows in straight channels with mass transfer by suction and blowing through opposite walls, and with rotation about the spanwise axis. The predictions are based on the solution of the Reynolds-averaged forms of the governing equations using a second-order accurate finite-volume formulation. The effects of turbulence on momentum transport were accounted for by using turbulence closures based on the solution of modeled differential transport equations for the Reynolds stresses. A number of alternative models were assessed. These included a high turbulence Reynolds-number model in which the computationally-efficient ‘wall-function’ approach was used to bridge the near-wall region. As the effects of stabilizing system rotation can cause flow relaminarization, the wall-function approach becomes unreliable and integration must be carried out through the viscous sub-layer, directly to the walls. The suitability of three alternative low Reynolds-number models was assessed in these flows. Experimental data from flows in stationary channels with Reynolds numbers spanning the range of laminar, transitional and turbulent regimes were also used in this assessment. Excellent predictions of the wall skin-friction coefficient across the entire range were obtained with a low Reynolds-number model in which the effects of a rigid wall on the fluctuating pressure field in its vicinity were accounted for by a method which incorporates the gradients of the turbulence length scale and the invariants of turbulence anisotropy. For the cases of heated flows, two very different models for the turbulent heat fluxes were examined: one involved the solution of a differential transport equation for each component of the heat-flux tensor and another in which the heat fluxes were obtained from an explicit algebraic model derived from tensor representation theory. It was found that the two models yielded results that were essentially similar and in close agreement with results from recent Direct Numerical Simulations.