Isotropic Turbulence

The development of precipitating warm clouds is affected by several effects of small-scale air turbulence including enhancement of droplet-droplet collision rate by turbulence, entrainment and mixing at the cloud edges, and coupling of mechanical and thermal energies at various scales. Large-scale computation is a viable research tool for quantifying these multiscale processes. Specifically, top-down large-eddy simulations (LES) of shallow convective clouds typically resolve scales of turbulent energy-containing eddies while the effects of turbulent cascade toward viscous dissipation are parameterized. Bottom-up hybrid direct numerical simulations (HDNS) of cloud microphysical processes resolve fully the dissipation-range flow scales but only partially the inertial subrange scales. it is desirable to systematically decrease the grid length in LES and increase the domain size in HDNS so that they can be better integrated to address the full range of scales and their coupling. In this paper, we discuss computational issues and physical modeling questions in expanding the ranges of scales realizable in LES and HDNS, and in bridging LES and HDNS. We review our on-going efforts in transforming our simulation codes towards PetaScale computing, in improving physical representations in LES and HDNS, and in developing better methods to analyze and interpret the simulation results.

In recent years, there has been a renewed interest in the impact of turbulence on aquatic organisms. In response to this interest, a novel instrument has been constructed, TURBOGEN, that generates turbulence in water volumes up to 13 l. TURBOGEN is fully computer controlled, thus, allowing for a high level of reproducibility and for variations of the intensity and characteristics of turbulence during the experiment. The calibration tests, carried out by particle image velocimetry, showed TURBOGEN to be successful in generating isotropic turbulence at the typical relatively low levels of the marine environment. TURBOGEN and its sizing have been devised with the long-term scope of analyzing in detail the molecular responses of plankton to different mixing regimes, which is of great importance in both environmental and biotechnological processes.

The energy cascade in magnetohydrodynamics is studied using high resolution direct numerical simulations of forced isotropic turbulence. The magnetic Prandtl number is unity and the large scale forcing is a function of the velocity that injects a constant rate of energy without generating a mean flow. A shell decomposition of the velocity and magnetic fields is proposed and is extended to the Elsässer variables. The analysis of energy exchanges between these shell variables shows that the velocity and magnetic energy cascades are mainly local and forward, though non-local energy transfer does exist between the large, forced, velocity scales and the small magnetic structures. The possibility of splitting the shell-to-shell energy transfer into forward and backward contributions is also discussed.

An analysis that includes the effects of Basset and gravitational forces is presented for the dispersion of particles experiencing Stokes drag in isotropic turbulence. The fluid velocity correlation function evaluated on the particle trajectory is obtained by using the independence approximation and the assumption of Gaussian velocity distributions for both the fluid and the particle, formulated by Pismen & Nir (1978). The dynamic equation for particle motion with the Basset force is Fourier transformed to the frequency domain where it can be solved exactly. It is found that the Basset force has virtually no influence on the structure of the fluid velocity fluctuations seen by the particles or on particle diffusivities. It does, however, affect the motion of the particle by increasing (reducing) the intensities of particle turbulence for particles with larger (smaller) inertia. The crossing of trajectories associated with the gravitational force tends to enhance the effect of the'Basset force on the particle turbulence. An ordering of the terms in the particle equation of motion shows that the solution is valid for high particle/fluid density ratios and to O(1) in the Stokes number.

We study the degree to which Kraichnan–Leith–Batchelor (KLB) phenomenology describes two-dimensional energy cascades in$\alpha $turbulence, governed by$\partial \theta / \partial t+ J(\psi , \theta )= \nu {\nabla }^{2} \theta + f$, where$\theta = {(- \Delta )}^{\alpha / 2} \psi $is generalized vorticity, and$\hat {\psi } (\boldsymbol{k})= {k}^{- \alpha } \hat {\theta } (\boldsymbol{k})$in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow ($\alpha = 1$), regular two-dimensional flow ($\alpha = 2$) and rotating shallow flow ($\alpha = 3$), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general$\alpha $, and point out their limitations. Using an$\alpha $-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our p...

In this paper a multilayer feed-forward neural network (NN) is used as subgrid scale (SGS) model in a large eddy simulation (LES). The NN was previously off-line trained using numerical data generated by a LES of a channel flow at Re s ¼ 180 with Bardina's scale similar (BFR) SGS model. Results show the ability of NNs to identify and reproduce the highly nonlinear behavior of the turbulent flows, and therefore the possibility of using NN techniques in numerical simulations of turbulent flows.

The coefficient C 0 , which determines the effective turbulent diffusion in velocity space, is fundamental in Lagrangian modeling. Others, for example, Yeung and Pope ͓J. Fluid Mech. 207, 531 ͑1989͔͒ have investigated this coefficient numerically with direct numerical simulation ͑DNS͒ by analyzing the dispersion of discrete particles. In our paper we estimate the coefficient C 0 by using DNS to study the initial evolution of continuous passive scalar fields. Using an equivalent probability density function ͑pdf͒ and conditional moment analyses we examine the initial transient behavior for passive scalar mixing, with both linear and Gaussian-type initial distributions in the velocity space. Our estimates of C 0 are found to be consistent with the data found in the literature.

The energy transfer process and the interaction of different scales in a flow induced by the variable-density Rayleigh-Taylor instability in miscible fluids is investigated using a three-dimensional direct numerical simulation database with a spatial resolution of N x ϫN y ϫN z ϭ512ϫ512ϫ2040. The method used to study the transfer of energy between the supergrid and subgrid scales in the homogeneous planes, determined by partitioning the modes into resolved and unresolved scales defined by a two-dimensional cutoff wave number k c in Fourier space, is applied to the kinetic energy evolution equation. The treatment of the flow inhomogeneity in the direction z parallel to the acceleration is analogous to that used in the analysis of incompressible wall-bounded flows, including channel flow and Rayleigh-Bénard convection ͓J. A. Domaradzki et al., Phys. Fluids 6, 1583 ͑1994͒; J. A. Domaradzki and W. Liu, ibid. 7, 2025 ͑1995͔͒. Using a sharp Fourier cutoff filter, the kinetic energy transfer is decomposed into ͑1͒ the resolved part; ͑2͒ a part corresponding to the interaction between resolved and unresolved scales; and ͑3͒ a part corresponding to the interaction between unresolved scales. The sum of these last two contributions is the subgrid-scale kinetic energy transfer, which is studied in the present work. These z-dependent spectra are computed for three different cutoff wave numbers to investigate the dependence of the transfer process on the scales contributing to the subgrid interactions. The kinetic energy transfer is further decomposed into its positive and negative components corresponding to the forward and backward cascades of energy, respectively, that arise from the nonlinear modal interactions. The decomposition into resolved and unresolved scales is used to define an effective eddy viscosity and backscatter viscosity. The principal conclusions of the analysis are ͑1͒ the transfer spectra and eddy viscosities exhibit a strong dependence on the wave number cutoff; ͑2͒ the contributions from the interaction between resolved and unresolved scales dominate the contribution to the total subgrid eddy viscosities and are responsible for the cusp at large k/k c ; ͑3͒ the contributions from the interaction between unresolved scales dominate the contribution to the total subgrid eddy viscosities at small k/k c and are responsible for the small, negative contribution ͑associated with an inverse energy transfer͒, and ͑4͒ backscatter is strongest in the regions near the boundaries of the mixing layer. The physical implications of these results for subgrid-scale modeling in a large-eddy simulation of Rayleigh-Taylor instability-induced turbulence are discussed.

The passive scalar dynamics in a freely decaying turbulent flow is studied. The classical framework of homogeneous isotropic turbulence without forcing is considered. Both low and high Reynolds number regimes are investigated for very small and very large Prandtl numbers. The long time behaviours of integrated quantities such as the scalar variance or the scalar dissipation rate are analysed by considering that the decay follows power laws. This study addresses three major topics. First, the Comte-Bellot and Corrsin (CBC) dimensional analysis for the temporal decay exponents is extended to the case of a passive scalar when the permanence of large eddies is broken. Secondly, using numerical simulations based on an eddy-damped quasi-normal Markovian (EDQNM) model, the time evolution of integrated quantities is accurately determined for a wide range of Reynolds and Prandtl numbers. These simulations show that, whatever the values of the Reynolds and the Prandtl numbers are, the decay f...

The paper presents large-eddy simulation (LES) formalism, along with the various subgrid-scale models developed since Smagorinsky's model. We show how Kraichnan's spectral eddy viscosity may be implemented in physical space, yielding the structure-function model. Recent developments of this model that allow the eddy viscosity to be inhibited in transitional regions are discussed. We present a dynamic procedure, where a double filtering allows one to dynamically determine the subgrid-scale model constants. The importance of backscatter effects is discussed. Alternatives to the eddy-viscosity assumption, such as scalesimilarity models, are considered. Pseudo-direct simulations in which numerical diffusion replaces subgrid transfers are mentioned. Various applications of LES to incompressible and compressible turbulent flows are given, with an emphasis on the generation of coherent vortices.

In this work, we present a localized form of the dynamic eddy viscosity model for computationally efficient and accurate simulation of the turbulent flows governed by Euler equations. In our framework, we determine the dynamic model coefficient locally using the information from neighboring grid points through a test filtering process. We then develop an optimized Gaussian filtering kernel, using a consistent definition with respect to the test filtering ratio, which gives full attenuation at the grid cutoff wave number. A systematic a-posteriori analysis of our model is performed by solving two 3D test problems: (i) incompressible Taylor-Green vortex flow and (ii) compressible shear layer turbulence induced by Kelvin-Helmholtz instability to show the wide range of applicability of the proposed localized dynamic model. We demonstrate that the proposed dynamic model is robust and provides a better estimation of the inertial range turbulence dynamics than other numerical models tested in this study.

The coherent vorticity extraction method (CVE) is based on the nonlinear filtering of the vorticity field projected onto an orthonormal wavelet basis made of compactly supported functions. CVE decomposes each turbulent flow realization into two orthogonal components: a coherent and an incoherent random flow. They both contribute to all scales in the inertial range, but exhibit different statistical behavior. We apply CVE to 256 3 subcubes extracted from 3D homogeneous isotropic turbulent flows at different Taylor microscale Reynolds numbers (R λ = 140, 240 and 680), computed by a direct numerical simulation (DNS) at different resolutions (N = 256 3 , 512 3 and 2048 3), respectively. We compare the total, coherent and incoherent vorticity fields obtained by using CVE and show that few wavelets coefficients are sufficient to represent the coherent vortices of the flows. Geometrical statistics in term of helicity are also analyzed and the λ 2 criterion is applied to the filtered flow fields.

The coefficient C 0 , which determines the effective turbulent diffusion in velocity space, is fundamental in Lagrangian modeling. Others, for example, Yeung and Pope ͓J. Fluid Mech. 207, 531 ͑1989͔͒ have investigated this coefficient numerically with direct numerical simulation ͑DNS͒ by analyzing the dispersion of discrete particles. In our paper we estimate the coefficient C 0 by using DNS to study the initial evolution of continuous passive scalar fields. Using an equivalent probability density function ͑pdf͒ and conditional moment analyses we examine the initial transient behavior for passive scalar mixing, with both linear and Gaussian-type initial distributions in the velocity space. Our estimates of C 0 are found to be consistent with the data found in the literature.

The energy cascade in magnetohydrodynamics is studied using high resolution direct numerical simulations of forced isotropic turbulence. The magnetic Prandtl number is unity and the large scale forcing is a function of the velocity that injects a constant rate of energy without generating a mean flow. A shell decomposition of the velocity and magnetic fields is proposed and is extended to the Elsässer variables. The analysis of energy exchanges between these shell variables shows that the velocity and magnetic energy cascades are mainly local and forward, though non-local energy transfer does exist between the large, forced, velocity scales and the small magnetic structures. The possibility of splitting the shell-to-shell energy transfer into forward and backward contributions is also discussed.

Laboratory experiments on components of complex systems such as gas turbines require many conditions to be met. Requirements to be met in order to simulate real world conditions include inlet flow conditions such as velocity profile, Reynold's number, and temperature. The methodology to be introduced designs a velocity profile generating screen to match real world conditions through the use of perforated plates. The velocity profile generating screen is an array of jets arranged in a manner to produce sections of different solidities, a ratio of area that obstructs fluid flow compared to that of the total area. In an effort to better understand the interaction between perforated plate sections of different solidities, a collection of experimental data sets is presented to characterize the plates. This includes identification of fluid flow regions with characterization of the flow dynamics, though the analysis of velocity and turbulence decay. The aim of this characterization is to determine how the perforated plate's solidity affects the velocity development downstream and the location at which the velocity profile being produced can be considered complete.

Thermal plumes are the energy containing eddy motions that carry heat and momentum in a convective boundary layer. The detailed understanding of their structure is of fundamental interest for a range of applications, from wall-bounded engineering flows to quantifying surface-atmosphere flux exchanges. We address the aspect of Reynolds stress anisotropy associated with the intermittent nature of heat transport in thermal plumes by performing an invariant analysis of the Reynolds stress tensor in an unstable atmospheric surface layer flow, using a field-experimental dataset. Given the intermittent and asymmetric nature of the turbulent heat flux, we formulate this problem in an eventbased framework. In this approach, we provide structural descriptions of warm-updraft and cold-downdraft events and investigate the degree of isotropy of the Reynolds stress tensor within these events of different sizes. We discover that only a subset of these events are associated with the least anisotropic turbulence in highly-convective conditions. Additionally, intermittent large heat flux events are found to contribute substantially to turbulence anisotropy under unstable stratification. Moreover, we find that the sizes related to the maximum value of the degree of isotropy do not correspond to the peak positions of the heat flux distributions. This is because, the vertical velocity fluctuations pertaining to the sizes associated with the maximum heat flux, transport significant amount of streamwise momentum. A preliminary investigation shows that the sizes of the least anisotropic events probably scale with a mixed-length scale (z 0.5 λ 0.5 , where z is the measurement height and λ is the large-eddy length scale).

Helicity in vortex structures and spectra is studied in the developmental stages of a numerical simulation of the Navier-Stokes equations using 3D visualisations and spectra. First, time scales are set using the growth and decay of energy dissipation, the peak value of vorticity and the helicity. Then two stages between the early time, nearly inviscid Euler dynamics with vortex sheets and a final state of fully-developed turbulence with vortex tubes are described. In the first stage, helicity fluctuations develop in Fourier space during a period still dominated by vortex sheets and rapidly growing peak vorticity. At the end of this period the strongest structure consists of transverse vortex sheets with mixed signs of helicity. During the second stage, a dissipative interaction propagates along one of these vortices as the sheets roll each other into vortex tubes.

X-ray observations of galaxy cluster merger shocks can be used to constrain nonthermal processes in the intracluster medium (ICM). The presence of nonthermal pressure components in the ICM, as well as the shock acceleration of particles and their escape, all affect shock jump conditions in distinct ways. Therefore, these processes can be constrained using X-ray surface brightness and temperature maps of merger shock fronts. Here we use these observations to place constraints on particle acceleration efficiency in intermediate Mach number (M ≈ 2 − 3) shocks and explore the potential to constrain the contribution of nonthermal components (e.g., cosmic rays, magnetic field, and turbulence) to ICM pressure in cluster outskirts. We model the hydrodynamic jump conditions in merger shocks discovered in the galaxy clusters A520 (M ≈ 2) and 1E 0657−56 (M ≈ 3) using a multifluid model comprised of a thermal plasma, a nonthermal plasma, and a magnetic field. Based on the published X-ray spectroscopic data alone, we find that the fractional contribution of cosmic rays accelerated in these shocks is 10% of the shock downstream pressure. Current observations do not constrain the fractional contribution of nonthermal components to the pressure of the undisturbed shock upstream. Future X-ray observations, however, have the potential to either detect particle acceleration in these shocks through its effect on the shock dynamics, or to place a lower limit on the nonthermal pressure contributions in the undisturbed ICM. We briefly discuss implications for models of particle acceleration in collisionless shocks and the estimates of galaxy cluster masses derived from X-ray and Sunyaev-Zel'dovich effect observations.

Direct numerical simulation of turbulent channel flows between isothermal walls have been carried out using discontinuous Galerkin method. Three Mach numbers are considered (0.2, 0.7, and 1.5) at a fixed Reynolds number %2800, based on the bulk velocity, bulk density, half channel width, and dynamic viscosity at the wall. Power law and log-law with the scaling of the mean streamwise velocity are considered to study their performance on compressible flows and their dependence on Mach numbers. It indicates that power law seems slightly better and less dependent on Mach number than the log-law in the overlap region. Mach number effects on the second-order (velocity, pressure, density, temperature, shear stress, and vorticity fluctuations) and higher-order (skewness and flatness of velocity, pressure, density, and temperature fluctuations) statistics are explored and discussed. Both inner (that is wall variables) and outer (that is global) scalings (with Mach number) are considered. It is found that for some second-order statistics (i.e. velocity, density, and temperature), the outer scaling collapses better than the inner scaling. It is also found that near-wall large-scale motions are affected by Mach number. The near-wall spanwise streak spacing increases with increasing Mach number. Iso-surfaces of the second invariant of the velocity gradient tensor are more sparsely distributed and elongated as Mach number increases, which is similar to the distribution of near-wall low speed streaks.

The behavior of the second-order Lagrangian structure functions on state-of-the-art numerical data both in two and three dimensions is studied. On the basis of a phenomenological connection between Eulerian space-fluctuations and the Lagrangian time-fluctuations, it is possible to rephrase the Kolmogorov 4/5-law into a relation predicting the linear (in time) scaling for the second order Lagrangian structure function. When such a function is directly observed on current experimental or numerical data, it does not clearly display a scaling regime. A parameterization of the Lagrangian structure functions based on Batchelor model is introduced and tested on data for 3d turbulence, and for 2d turbulence in the inverse cascade regime. Such parameterization supports the idea, previously suggested, that both Eulerian and Lagrangian data are consistent with a linear scaling plus finite-Reynolds number effects affecting the small-and large-time scales. When largetime saturation effects are properly accounted for, compensated plots show a detectable plateau already at the available Reynolds number. Furthermore, this parameterization allows us to make quantitative predictions on the Reynolds number value for which Lagrangian structure functions are expected to display a scaling region. Finally, we show that this is also sufficient to predict the anomalous dependency of the normalized root mean squared acceleration as a function of the Reynolds number, without fitting parameters.

Direct numerical simulations are used to investigate the individual dynamics of large spherical particles suspended in a developed homogeneous turbulent flow. A definition of the direction of the particle motion relative to the surrounding flow is introduced and used to construct the mean fluid velocity profile around the particle. This leads to an estimate of the particle slipping velocity and its associated Reynolds number. The flow modifications due to the particle are then studied. The particle is responsible for a shadowing effect that occurs in the wake up to distances of the order of its diameter: the particle calms turbulent fluctuations and reduces the energy dissipation rate compared to its average value in the bulk. Dimensional arguments are presented to draw an analogy between particle effects on turbulence and wall flows. Evidence is obtained for the presence of a logarithmic sublayer at distances between the thickness of the viscous boundary layer and the particle diam...

The energy cascade in magnetohydrodynamics is studied using high resolution direct numerical simulations of forced isotropic turbulence. The magnetic Prandtl number is unity and the large scale forcing is a function of the velocity that injects a constant rate of energy without generating a mean flow. A shell decomposition of the velocity and magnetic fields is proposed and is extended to the Elsässer variables. The analysis of energy exchanges between these shell variables shows that the velocity and magnetic energy cascades are mainly local and forward, though non-local energy transfer does exist between the large, forced, velocity scales and the small magnetic structures. The possibility of splitting the shell-to-shell energy transfer into forward and backward contributions is also discussed.

The coherent vorticity extraction method (CVE) is based on the nonlinear filtering of the vorticity field projected onto an orthonormal wavelet basis made of compactly supported functions. CVE decomposes each turbulent flow realization into two orthogonal components: a coherent and an incoherent random flow. They both contribute to all scales in the inertial range, but exhibit different statistical behavior. We apply CVE to 256 3 subcubes extracted from 3D homogeneous isotropic turbulent flows at different Taylor microscale Reynolds numbers (R λ = 140, 240 and 680), computed by a direct numerical simulation (DNS) at different resolutions (N = 256 3 , 512 3 and 2048 3), respectively. We compare the total, coherent and incoherent vorticity fields obtained by using CVE and show that few wavelets coefficients are sufficient to represent the coherent vortices of the flows. Geometrical statistics in term of helicity are also analyzed and the λ 2 criterion is applied to the filtered flow fields.

In this paper, we study the capability of implicit large eddy simulation (ILES) to capture transition. In particular, we study a planar temporal mixing layer subjected to low free stream perturbations. We simulated this problem by ILES and other approaches like Reynolds averaged Navier Stokes, conventional (LES) and direct numerical simulation. Qualitative and quantitative assessment of their relative performance reveals the advantage of ILES over other methods. We propose that any scheme, upwinding in this case, will be successful in simulating such flows if the discrete dispersion relationship of the linearized equation is similar to the theoretical dispersion relation. To verify our conjecture, we derived discretized dispersion relationship with upwinding and central difference scheme for a simple prototype of Navier Stokes equation namely Ginzburg Landau equation. We found that the two relations and thus perturbation growth are significantly different from each other for, at least, convection dominated flows.

In recent years, there has been a renewed interest in the impact of turbulence on aquatic organisms. In response to this interest, a novel instrument has been constructed, TURBOGEN, that generates turbulence in water volumes up to 13 l. TURBOGEN is fully computer controlled, thus, allowing for a high level of reproducibility and for variations of the intensity and characteristics of turbulence during the experiment. The calibration tests, carried out by particle image velocimetry, showed TURBOGEN to be successful in generating isotropic turbulence at the typical relatively low levels of the marine environment. TURBOGEN and its sizing have been devised with the long-term scope of analyzing in detail the molecular responses of plankton to different mixing regimes, which is of great importance in both environmental and biotechnological processes.

This paper extends the gas-kinetic BGK-NS scheme to an adaptive grid for the viscous flow simulations. The grid movement and adaptation is controlled by a monitor function which may depend on velocity gradient or other flow variables, such as density or pressure. For the viscous flow computation, the use of adaptive mesh much improves the efficiency and accuracy of the method in comparison with the methods with static mesh points. The current method is an accurate and efficient method for the viscous flow computation, where the grid points can be easily moved and concentrated on the regions with large velocity and density gradients, such as the boundary layer and multi-material interface. Many numerical examples validate the current approach for the viscous flow simulations.

Summary We give a summary of the derivation of an implicit subgrid-scale model for LES which is obtained from a new approach for the approximation of hyperbolic conservation laws. Adaptive local deconvolution is performed using a quasi-linear solution-adaptive combination of local interpolation polynomials. The physical flux function is substituted by a suitable numerical flux function. The truncation error has physical significance and effectively acts as subgrid-scale model. It can be determined by a modified- ...

We present an experimental study on the statistical properties of the injected power needed to maintain an inelastic ball bouncing constantly on a randomly accelerating piston in the presence of gravity. We compute the injected power at each collision of the ball with the moving piston by measuring the velocity of the piston and the force exerted on the piston by the ball. The probability density function of the injected power has its most probable value close to zero and displays two asymmetric exponential tails, depending on the restitution coefficient, the piston acceleration, and its frequency content. This distribution can be deduced from a simple model assuming quasi-Gaussian statistics for the force and velocity of the piston.

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Subgrid-scale models for large eddy simulation (LES) in both the velocity-pressure and the vorticity-velocity f o r m ulations were evaluated and compared in a priori tests using spectral Direct Numerical Simulation (DNS) databases of isotropic turbulence: 128 3 DNS of forced turbulence (Re = 9 5 :8) ltered, using the sharp cuto lter, to both 32 3 and 16 3 synthetic LES elds 512 3 DNS of decaying turbulence (Re = 6 3 :5) ltered to both 64 3 and 32 3 LES elds. Gaussian and top-hat lters were also used with the 128 3 database. Di erent LES models were evaluated for each formulation: eddy-viscosity models, hyper eddy-viscosity models, mixed models, and scale-similarity m o d e l s. Correlations between exact versus modeled subgrid-scale quantities were measured at three levels: tensor (traceless), vector (solenoidal`force'), and scalar (dissipation) levels, and for both cases of uniform and variable coe cient(s). Di erent c hoices for the 1=T scaling appearing in the eddy-viscosity w ere also evaluated. It was found that the models for the vorticityvelocity formulation produce higher correlations with the ltered DNS data than their counterpart in the velocity-pressure formulation. It was also found that the hyper eddy-viscosity model performs better than the eddy viscosity model, in both formulations.

We present a numerical method for Large Eddy Simulations (LES) of compressible two-phase flows. The method is validated for the flow in a micro channel with a step-like restriction. This setup is representative for typical cavitating multi-phase flows in fuel injectors and follows an experimental study of Iben et al. [1]. While a diesel-like test fuel was used in the experiment, we solve the compressible Navier-Stokes equations with a barotropic equation of state for water and vapor and a simple phase-change model based on equilibrium assumptions. Our LES resolve all wave dynamics in the compressible fluid and the turbulence production in shear layers.

Further development of Large Eddy Simulation faces as major obstacle the strong coupling between subgrid-scale model and the truncation error of the numerical discretization. Recent analyzes indicate that for certain discretizations and certain flow configurations the truncation error itself can act as implicit SGS model. Relevant discretizations are e.g. finite-volume schemes with a nonlinear regularization to maintain nonlinear stability. Whereas previous approaches in implicit subgrid-scale (SGS) modeling employed available discretization schemes without analyzing the effective SGS model, and not incorporating physical modeling approaches into the implicit model, we have developed an approach where a full coupling of SGS model and discretization scheme is accomplished. The ALDM (Adaptive Local Deconvolution Method) approach is introduced as an implicit subgrid-scale modeling environment and discussed with respect to its numerical and turbulence-theoretical background. We summarize recent accomplishments in terms of complex flows computed successfully with ALDM and provide a brief outlook on future work.

In recent years, there has been a renewed interest in the impact of turbulence on aquatic organisms. In response to this interest, a novel instrument has been constructed, TURBOGEN, that generates turbulence in water volumes up to 13 l. TURBOGEN is fully computer controlled, thus, allowing for a high level of reproducibility and for variations of the intensity and characteristics of turbulence during the experiment. The calibration tests, carried out by particle image velocimetry, showed TURBOGEN to be successful in generating isotropic turbulence at the typical relatively low levels of the marine environment. TURBOGEN and its sizing have been devised with the long-term scope of analyzing in detail the molecular responses of plankton to different mixing regimes, which is of great importance in both environmental and biotechnological processes.

The time evolution of the pressure spectrum E_p in freely decaying homogeneous isotropic turbulence (HIT) is investigated via Eddy-Damped Quasi-Normal Markovian(EDQNM) computations. It is well known that physical quantities associated to the energy spectrum evolve through power laws in HIT decay. For both low and high values of Reλ , the associated power law exponents of these laws are known to depend on the initial conditions, such as the slope of the energy spectrum at the large scales σ , with E(k → 0, 0) ∝ k^σ . Batchelor (1951) and Lesieur et al. (1999) proposed theoretical frameworks to evaluate the power law exponents associated to the pressure decay statistics. These formulae, which relate pressure and energy decay, have been recovered by the use of several underlying hypothesis, such as Reλ → +∞ and the Joint Gaussian Assumption (JGA). Such hypothesis are not completely satisfied in experiments and numerical simulations, the departure from the theoretical background being c...

In this research a direct numerical simulation (DNS) of turbulent flow is performed in a geometrically standard case like plane channel flow. Pseudo spectral (PS) method is used due to geometry specifications and very high accuracy achieved despite relatively few grid points. A variable time-stepping algorithm is proposed which may reduce requirement of computational cost in simulation of such wall-bounded flow. Channel flow analysis is performed with both constant and varied time-step for 128 × 65×128 grid points. The time advancement is carried out by implicit third-order backward differentiation scheme for linear terms and explicit forward Euler for nonlinear convection term. PS method is used in Cartesian coordinates with Chebychev polynomial expansion in normal direction for one non-periodic boundary condition. Also Fourier series is employed in stream-wise and span-wise directions for two periodic boundary conditions. The friction Reynolds number is about Re τ =175 based on a friction velocity and channel half width. Standard common rotational form was chosen for discritization of nonlinear convective term of Navier-Stocks equation. The comparison is made between turbulent quantities such as the turbulent statistics, Reynolds stress, wall shear velocity, standard deviation of (u) and total normalized energy of instantaneous velocities in both time-discretization methods. The results show that if final decision rests on economics, the proposed variable time-stepping algorithm will be proper choice which satisfies the accuracy and reduces the computational cost.

We conduct a detailed comparison of the lattice Boltzmann equation (LBE) and the pseudo-spectral (PS) methods for direct numerical simulations (DNS) of the decaying homogeneous isotropic turbulence in a three-dimensional periodic cube. We use a mesh size of N 1⁄4 128 and the Taylor micro-scale Reynolds number 24:35 6 Rek 6 72:37, and carry out all simulations to t 30s0, where s0 is the turbulence turnover time. In the PS method, the second-order Adam–Bashforth scheme is used to numerically integrate the nonlinear term while the viscous term is treated exactly. We compare the following quantities computed by the LBE and PS methods: instantaneous velocity u and vorticity x fields, and statistical quantities such as, the total energy KðtÞ and the energy spectrum Eðk; tÞ, the dissipation rate eðtÞ, the root-meansquared (rms) pressure fluctuation dpðtÞ and the pressure spectrum Pðk; tÞ, and the skewness and flatness of the velocity derivative. Our results show that the LBE method perform...

Recently, the implicit SGS modeling environment provided by the Adaptive Local Deconvolution Method (ALDM) has been extended to Large-Eddy Simulations (LES) of passive-scalar transport. The resulting adaptive advection algorithm has been described and discussed with respect to its numerical and turbulencetheoretical background by Hickel et al., 2007. Results demonstrate that this method allows for reliable predictions of the turbulent transport of passive-scalars in isotropic turbulence and in turbulent channel flow for a wide range of Schmidt numbers. We now intend to use this new method to perform LES of a confined rectangular-jet reactor and compare obtained results to experimental data available in the literature.

Turbulence modeling and the numerical discretization of the Navier-Stokes equations are strongly coupled in large-eddy simulations. The truncation error of common approximations for the convective terms can outweigh the effect of a physically sound subgrid-scale model. The subject of this thesis is the analysis and the control of local truncation errors in large-eddy simulations. We show that physical reasoning can be incorporated into the design of discretization schemes. Using systematic procedures, a nonlinear discretization method has been developed where numerical and turbulence-theoretical modeling are fully merged. The truncation error itself functions as an implicit turbulence model accurately representing the effects of unresolved scales. Various applications demonstrate the efficiency and reliability of the new method as well as the superiority of an holistic approach.

The adaptive local deconvolution method (ALDM) [9] provides a systematic framework for the implicit large-eddy simulation (ILES) of turbulent flows. Exploiting numerical truncation errors, the subgrid scale (SGS) model of ALDM is implicitly contained within the discretization. An explicit computation of model terms therefore becomes unnecessary. Subject of the present paper is a modification of the numerical algorithm that allows for reducing the amount of computational operations without affecting the quality of the results. Computational results for isotropic turbulence and plane channel flow show that the simplified adaptive local deconvolution (SALD) method performs similarly to the original method ALDM and at least as well as established explicit models.

Further development of Large Eddy Simulation faces as major obstacle the strong coupling between subgrid-scale model and the truncation error of the numerical discretization. Recent analyzes indicate that for certain discretizations and certain ∞ow conflgurations the truncation error itself can act as implicit SGS model. Relevant dis- cretizations are e.g. flnite-volume schemes with a nonlinear regularization to maintain nonlinear stability.

The numerical truncation error of vortex-in-cell methods is analyzed a-posteriori through the effective spectral numerical viscosity for simulations of three-dimensional isotropic turbulence. The interpolation kernels used for velocity-smoothing and re-meshing are identified as the most relevant components affecting the shape of the spectral numerical viscosity as a function of wave number. A linear combination of well-known standard kernels leads to new kernels assigned to the specific use for implicit large-eddy simulation of turbulent flows, i.e. their truncation errors acts as subgrid-scale model. Numerical results are provided to show the potential and drawbacks of the approach.

We present a numerical method for Large Eddy Simulations (LES) of compressible two-phase flows. The method is validated for the flow in a micro channel with a step-like restriction. This setup is representative for typical cavitating multi-phase flows in fuel injectors and follows an experimental study of Iben et al. [1]. While a diesel-like test fuel was used in the experiment, we solve the compressible Navier-Stokes equations with a barotropic equation of state for water and vapor and a simple phase-change model based on equilibrium assumptions. Our LES resolve all wave dynamics in the compressible fluid and the turbulence production in shear layers.

The adaptive local deconvolution method (ALDM) provides a systematic framework for the implicit large-eddy simulation (ILES) of turbulent flows. Exploiting numerical truncation errors, the subgrid scale model of ALDM is implicitly contained within the discretization. An explicit computation of model terms therefore becomes unnecessary. Subject of the present paper is the efficient implementation and the application to large-scale computations of this method. We propose a modification of the numerical algorithm that allows for reducing the amount of computational operations without affecting the quality of the LES results. Computational results for isotropic turbulence and plane channel flow show that the proposed simplified adaptive local deconvolution (SALD) method performs similarly to the original ALDM and at least as well as established explicit models.