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Verification of Nek4nuc (Nek5000 Integrated in NEAMS Workbench) via Turbulent Pipe Flow Simulation
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A SHORT-TIMESCALE CHANNEL OF DISSIPATION OF THE STRONG SOLAR WIND TURBULENCE
Hybrid numerical simulations of a turbulent cascade nearly perpendicular to the background magnetic field are carried out at the proton kinetic scales. It is shown that the cascade produces exponentially growing current sheets previously observed in fluid simulations. In the kinetic limit, the sheets are developing on a timescale as fast as the proton gyration. The rapid variations of the electric field associated with the sheets can demagnetize the protons and increase their thermal energy preferentially across the mean magnetic field. The relevance of this mechanism to the solar wind heating is discussed.
A stochastic perturbation method to generate inflow turbulence in large-eddy simulation models: Application to neutrally stratified atmospheric boundary layers
Despite the variety of existing methods, efficient generation of turbulent inflow conditions for large-eddy simulation (LES) models remains a challenging and active research area. Herein, we extend our previous research on the cell perturbation method, which uses a novel stochastic approach based upon finite amplitude perturbations of the potential temperature field applied within a region near the inflow boundaries of the LES domain [Muñoz-Esparza et al., “Bridging the transition from mesoscale to microscale turbulence in numerical weather prediction models,” Boundary-Layer Meteorol., 153, 409–440 (2014)]. The objective was twofold: (i) to identify the governing parameters of the method and their optimum values and (ii) to generalize the results over a broad range of atmospheric large-scale forcing conditions, U{sub g} = 5 − 25 m s{sup −1}, where U{sub g} is the geostrophic wind. We identified the perturbation Eckert number, Ec=U{sub g}{sup 2}/ρc{sub p}θ{sup ~}{sub pm}, to be the parameter governing the flow transition to turbulence in neutrally stratified boundary layers. Here, θ{sup ~}{sub pm} is the maximum perturbation amplitude applied, c{sub p} is the specific heat capacity at constant pressure, and ρ is the density. The optimal Eckert number was found for nonlinear perturbations allowed by Ec ≈ 0.16, which instigate formation of hairpin-like vortices that most rapidly transition to a developed turbulent state. Larger Ec numbers (linear small-amplitude perturbations) result in streaky structures requiring larger fetches to reach the quasi-equilibrium solution, while smaller Ec numbers lead to buoyancy dominated perturbations exhibiting difficulties for hairpin-like vortices to emerge. Cell perturbations with wavelengths within the inertial range of three-dimensional turbulence achieved identical quasi-equilibrium values of resolved turbulent kinetic energy, q, and Reynolds-shear stress, . In contrast, large-scale perturbations acting at the production range exhibited reduced levels of , due to the formation of coherent streamwise structures, while q was maintained, requiring larger fetches for the turbulent solution to stabilize. Additionally, the cell perturbation method was compared to a synthetic turbulence generator. The proposed stochastic approach provided at least the same efficiency in developing realistic turbulence, while accelerating the formation of large-scales associated with production of turbulent kinetic energy. Also, it is computationally inexpensive and does not require any turbulent information.
An ILLIAC program for the numerical simulation of homogeneous incompressible turbulence
An algorithm and ILLIAC computer program, developed for the simulation of homogeneous incompressible turbulence in the presence of an applied mean strain, are described. The turbulence field is represented spatially by a truncated triple Fourier series (spectral method) and followed in time using a fourth-order Runge-Kutta algorithm. These include: (1) transformation of variables suggested by Taylor's sudden-distortion theory; (2) implicit viscous diffusion by use of an integrating factor; (3) implicit pressure calculation suggested by Taylor's sudden-distortion theory, and (4) inexpensive control of aliasing by random and phased coordinate shifts.
Numerical simulation of transition to turbulence
The purpose of the present study is the numerical simulation of transition to turbulence in a boundary layer. Starting from a three-dimensional disturbance, the evolution of the Navier-Stokes solution until breakdown is followed. Qualitative comparison with available experimental observations is carried out.
Direct simulations of compressible wall-bounded turbulence
Several direct numerical simulations of high-speed turbulent Couette flow were performed with a new spectral code. Mach numbers up to three and a Reynolds number of 3000 were used. A new time-integration scheme was developed to handle Mach numbers above 1.5, which require greater accuracy and stability than lower Mach numbers. At low Mach number, the large streamwise eddies found by M. J. Lee in high incompressible Couette flow simulations were reproduced. At higher Mach numbers these structures still exist, but they become considerably less organized (although the disorganization may be a function of the spanwise box size). While the same types of vortical structures seen in the incompressible flow are observed at higher Mach numbers, a new structure involving the divergence of the velocity is also observed. This structure is generally associated with low shear areas next to the walls, but it has not been determined whether it is a cause or an effect of the low shear. A 'nonphysical' simulation was performed to determine by what mechanism the Mach number affects the flow. It appears that pressure gradient (acoustic) effects are more important than variable viscosity effects in determining the wall shear, but the size of vortical structures is determined more by the local kinematic viscosity. Low-order mean statistics are provided to help quantify these effects.
Initial conditions and modeling for simulations of shock driven turbulent material mixing
Here, we focus on the simulation of shock-driven material mixing driven by flow instabilities and initial conditions (IC). Beyond complex multi-scale resolution issues of shocks and variable density turbulence, me must address the equally difficult problem of predicting flow transition promoted by energy deposited at the material interfacial layer during the shock interface interactions. Transition involves unsteady large-scale coherent-structure dynamics capturable by a large eddy simulation (LES) strategy, but not by an unsteady Reynolds-Averaged Navier–Stokes (URANS) approach based on developed equilibrium turbulence assumptions and single-point-closure modeling. On the engineering end of computations, such URANS with reduced 1D/2D dimensionality and coarser grids, tend to be preferred for faster turnaround in full-scale configurations.
Wavelet methods for studying the onset of strong plasma turbulence
Recent simulations have demonstrated that coherent current sheets dominate the kinetic-scale energy dissipation in strong turbulence of magnetized plasma. Wavelet basis functions are a natural tool for analyzing turbulent flows containing localized coherent structures of different spatial scales. Here, wavelets are used to study the onset and subsequent transition to fully developed turbulence from a laminar state. Originally applied to neutral fluid turbulence, an iterative wavelet technique decomposes the field into coherent and incoherent contributions. In contrast to Fourier power spectra, finite time Lyapunov exponents, and simple measures of intermittency such as non-Gaussian statistics of field increments, the wavelet technique is found to provide a quantitative measure for the onset of turbulence and to track the transition to fully developed turbulence. The wavelet method makes no assumptions about the structure of the coherent current sheets or the underlying plasma model. Temporal evolution of the coherent and incoherent wavelet fluctuations is found to be highly correlated (a Pearson correlation coefficient of >0.9) with the magnetic field energy and plasma thermal energy, respectively. The onset of turbulence is identified with the rapid growth of a background of incoherent fluctuations spreading across a range of scales and a corresponding drop in the coherent components. This is suggestive of the interpretation of the coherent and incoherent wavelet fluctuations as measures of coherent structures (e.g., current sheets) and dissipation, respectively. The ratio of the incoherent to coherent fluctuations Ric is found to be fairly uniform in the turbulent state across different plasma models and provides an empirical threshold of ~0.1 for turbulence onset. The utility of this technique is illustrated through examples. First, it is applied to the Kelvin–Helmholtz instability from different simulation models including fully kinetic, hybrid (kinetic ion/fluid electron), and Hall MHD simulations. Second, the wavelet diagnostic is applied to the development of turbulence downstream of the bowshock in a global magnetosphere simulation. Finally, the wavelet technique is also shown to be useful as a de-noising method for particle simulations.
Direct Simulation of a Self-Similar Turbulent Mixing Layer
Three direct numerical simulations of incompressible turbulent plane mixing layers have been performed. All the simulations were initialized with the same two velocity fields obtained from a direct numerical simulation of a turbulent boundary layer with a momentum thickness Reynolds number of 300 computed by Spalart (J. Fluid Mech. 187, 61, 1988). In addition to a baseline case with no additional disturbances, two simulations were begun with two-dimensional disturbances of varying strength in addition to the boundary layer turbulence. After a development stage, the baseline case and the case with weaker additional two-dimensional disturbances evolve self-similarly, reaching visual thickness Reynolds numbers of up to 20 000. This self-similar period is characterized by a lack of large-scale organized pairings, a lack of streamwise vortices in the 'braid' regions, and scalar mixing that is characterized by 'marching' Probability Density Functions (PDFs). The case begun with strong additional two-dimensional disturbances only becomes approximately self-similar, but exhibits sustained organized large-scale pairings, clearly defined braid regions with streamwise vortices that span them, and scalar PDFs that are 'nonmarching.' It is also characterized by much more intense vertical velocity fluctuations than the other two cases. The statistics and structures in several experiments involving turbulent mixing layers are in better agreement with those of the simulations that do not exhibit organized pairings.
Helicopter response to atmospheric turbulence
A new time-domain method for simulating cyclostationary turbulence as seen by a translating and rotating blade element has recently been developed for the case of one-dimensional spectral distribution. This paper extends the simulation method to the cases of two- and three-dimensional spectral distributions and presents validation results for the two-dimensional case. The statistics of an isolated rigid blade flapping response to turbulence are computed using a two-dimensional spectral representation of the von Karman turbulence model, and the results are compared with those obtained using the conventional space-fixed turbulence analysis. The new turbulence simulation method is used for predicting the Black Hawk helicopter response to atmospheric turbulence.
Fantastic Striations and Where to Find Them: The Origin of Magnetically Aligned Striations in Interstellar Clouds
Thin, magnetically aligned striations of relatively moderate contrast with the background are commonly observed in both atomic and molecular clouds. They are also prominent in MHD simulations with turbulent converging shocks. The simulated striations develop within a dense, stagnated sheet in the midplane of the post-shock region where magnetically induced converging flows collide. We show analytically that the secondary flows are an inevitable consequence of the jump conditions of oblique MHD shocks. They produce the stagnated, sheet-like sub-layer through a secondary shock when, roughly speaking, the Alfvénic speed in the primary converging flows is supersonic, a condition that is relatively easy to satisfy in interstellar clouds. The dense sub-layer is naturally threaded by a strong magnetic field that lies close to the plane of the sub-layer. The substantial magnetic field makes the sheet highly anisotropic, which is the key to the striation formation. Specifically, perturbations of the primary inflow that vary spatially perpendicular to the magnetic field can easily roll up the sheet around the field lines without bending them, creating corrugations that appear as magnetically aligned striations in column density maps. On the other hand, perturbations that vary spatially along the field lines curve the sub-layer and alter its orientation relative to the magnetic field locally, seeding special locations that become slanted overdense filaments and prestellar cores through enhanced mass accumulation along field lines. In our scenario, the dense sub-layer, which is unique to magnetized oblique shocks, is the birthplace for both magnetically aligned diffuse striations and massive star-forming structures.
Intermittency and Dissipative Structures Arising from Relativistic Magnetized Turbulence
Abstract Kinetic simulations of relativistic turbulence have significantly advanced our understanding of turbulent particle acceleration. Recent progress has highlighted the need for an updated acceleration theory that can account for particle acceleration within the plasma’s coherent structures. Here, we investigate how intermittency modeling connects statistical fluctuations in turbulence to regions of high-energy dissipation. This connection is established by employing a generalized She–Leveque model to characterize the exponents ζ p for the structure functions S p ∝ l ζ p . The fitting of the scaling exponents provides us with a measure of the codimension of the dissipative structures, for which we subsequently determine the filling fraction. We perform our analysis for a range of magnetizations σ and relative fluctuation amplitudes δ B 0 / B 0 . We find that increasing values of σ and δ B 0 / B 0 allow the turbulent cascade to break sheetlike structures into smaller regions of dissipation that resemble chains of flux ropes. However, as their dissipation measure increases, the dissipative regions become less volume filling. With this work, we aim to inform future turbulent acceleration theories that incorporate particle energization from interactions with coherent structures within relativistic turbulence.
Quantitative Approach for the Accurate CFD Simulation of Hover in Turbulent Flow
Time-dependent Navier-Stokes simulations have been carried out for a V22 rotor in hover using an improved, low-diffusion, HLLE++ upwind algorithm in the OVERFLOW code. Emphasis is placed on lessons learned over the past decade regarding the effects of high-order spatial accuracy, grid resolution, and the use of detached eddy simulation in predicting the rotor performance, i.e., figure-of-merit (FM). A quick-start procedure is described together with a statistical measure of FM convergence that reduces hover computations by 5 times, similar in computational work for forward flight. Furthermore, Cartesian adaptive mesh refinement in the rotor wake revealed a complex turbulent flow with worm-like structures of various scales. These turbulent worms, found computationally more than a decade ago, have recently been observed in a separate German Aerospace Center (DLR) experiment. Moreover, adaptive mesh refinement has been used to resolve the tip-vortex to its correct physical size.
Coarse grained simulation of convectively driven turbulent mixing, transition, and turbulence decay
Accurate predictions with quantifiable uncertainties are essential to many practical turbulent flow applications exhibiting extreme geometrical complexity and broad ranges of length and time scales. Under-resolved computer simulations are typically unavoidable in such applications, and implicit large-eddy simulation (ILES) often becomes the effective strategy. In this work, we focus on assessing ILES initialized with well-characterized 25 6 3 homogeneous isotropic turbulence datasets generated with direct numerical simulation (DNS). ILES solutions based on the LANL xRAGE code are studied as function of resolution for 6 4 3 , 12 8 3 , 25 6 3 , and 51 2 3 grids. ILES performance of new directionally-unsplit high-order numerical hydrodynamics algorithms in xRAGE is examined in this context. Compared to the initial 25 6 3 DNS, we find longer inertial subranges and higher turbulence Reynolds number (Re) for 25 6 3 and 51 2 3 xRAGE — attributed to having linked DNS (Navier–Stokes based) solutions to nominally inviscid (higher Re) Euler based ILES solutions. For fixed 25 6 3 resolution, we find that significantly larger simulated turbulence Re can be achieved with the higher-order unsplit (vs. split) discretizations.
Large eddy simulation of homogeneous isotropic turbulence
This paper presents results from a comprehensive investigation of large-eddy simulations of homogeneous isotropic turbulence. Calculations have been made using grid meshes, a number of flowfield filters, and two simple subgrid scale turbulence models. Particular attention has been paid to the degree of isotropy and the ability of the approach to predict higher-order statistical quantities (skewness and flatness). Directions for needed improvement in the simulation approach are indicated, and a plea is made to experimenters to process their data in a way which will facilitate comparison with large eddy simulations.