Multiscale Turbulence Research Articles

Reconnecting flux-rope dynamo

We develop a model of the fluctuation dynamo in which the magnetic field is confined to thin flux ropes advected by a multiscale model of turbulence. Magnetic dissipation occurs only via reconnection of the flux ropes. This model can be viewed as an implementation of the asymptotic limit R_{m}-->infinity for a continuous magnetic field, where magnetic dissipation is strongly localized to small regions of strong-field gradients. We investigate the kinetic-energy release into heat mediated by the dynamo action, both in our model and by solving the induction equation with the same flow. We find that a flux-rope dynamo is an order of magnitude more efficient at converting mechanical energy into heat. The probability density of the magnetic energy release in reconnections has a power-law form with the slope -3 , consistent with the solar corona heating by nanoflares.

The Law of Multi-Scale Turbulence

This is a study of the classical physical and mathematical principles that govern turbulent fluid dynamics. Contrary to the general conception that views turbulent flows as incomprehensible; it can, in fact, be cast as a deterministic phenomenon that obeys a universal law. This universal law was introduced by A. N. Kolmogorov in the work that has now been immortalized as K41, widely accepted as among the most significant contributions to fluid dynamics research. A presentation of the universal law of multiscale turbulence is given here with the objective of assuaging apprehensions in regard to turbulent fluid dynamics and to garner interest in this very fascinating concept.

Finite frequency zonal flows in multi-scale plasma turbulence including resistive MHD and drift wave instabilities

The evolution of multi-scale plasma turbulence including resistive MHD and micro-instabilities is studied based on a 5-field slab gyrofluid simulation aiming to understand complex nonlinear interactions and turbulent transport. It is observed that the spatial structure of the mixed-scale electromagnetic turbulence is characterized by a power-law scaling spectrum typical of MHD perturbations, but the spectral amplitude is enhanced by the micro-instability at all scales. A robust oscillatory zonal flow (ZF) with finite frequency is created in slab geometry for the first time due to the multi-scale interaction so that the ion heat transport is not efficiently suppressed. It is identified that the finite frequency ZF results from a net oscillatory electromagnetic torque, which is sustained by micro-instability through multi-scale nonlinear interaction.

Laboratory modelling of atmospheric dynamical processes

We discuss how atmospheric or oceanic flow processes can be repro- duced at laboratory scale. The similarity conditions for the effects of density stratification and Earth rotation are first presented. It is argued that a large size is required to reproduce multi-scale turbulence with minimal viscous effects. Examples of results obtained on the large 'Coriolis' platform in Grenoble, 13 m in diameter, are described. The development of the baroclinic instability, the main source of perturbations in the mid-latitude atmosphere, is first presented. The second example is the driving of alternating azimuthal jets by small scale convective eddies, relevant for the zonal bands in the Giant planet atmosphere. Finally examples of topographic wakes in a stratified fluid and gravity currents are presented. It is argued that physical modelling must be used in close relationship with theory and numerical modelling, using advanced measurement and data assimilation techniques.

Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes

In this work, we combine (i) NURBS-based isogeometric analysis, (ii) residual-driven turbulence modeling and iii) weak imposition of no-slip and no-penetration Dirichlet boundary conditions on unstretched meshes to compute wall-bounded turbulent flows. While the first two ingredients were shown to be successful for turbulence computations at medium-to-high Reynolds number [I. Akkerman, Y. Bazilevs, V. M. Calo, T. J. R. Hughes, S. Hulshoff, The role of continuity in residual-based variational multiscale modeling of turbulence, Comput. Mech. 41 (2008) 371–378; Y. Bazilevs, V.M. Calo, J.A. Cottrell, T.J.R. Hughes, A. Reali, G. Scovazzi, Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows, Comput. Methods Appl. Mech. Engrg., 197 (2007) 173–201], it is the weak imposition of no-slip boundary conditions on coarse uniform meshes that maintains the good performance of the proposed methodology at higher Reynolds number [Y. Bazilevs, T.J.R. Hughes. Weak imposition of Dirichlet boundary conditions in fluid mechanics, Comput. Fluids 36 (2007) 12–26; Y. Bazilevs, C. Michler, V.M. Calo, T.J.R. Hughes, Weak Dirichlet boundary conditions for wall-bounded turbulent flows. Comput. Methods Appl. Mech. Engrg. 196 (2007) 4853–4862]. These three ingredients form a basis of a possible practical strategy for computing engineering flows, somewhere between RANS and LES in complexity. We demonstrate this by solving two challenging incompressible turbulent benchmark problems: channel flow at friction-velocity Reynolds number 2003 and flow in a planar asymmetric diffuser. We observe good agreement between our calculations of mean flow quantities and both reference computations and experimental data. This lends some credence to the proposed approach, which we believe may become a viable engineering tool.

Intermittent turbulence, noisy fluctuations, and wavy structures in the Venusian magnetosheath and wake

Recent research has shown that distinct physical regions in the Venusian induced magnetosphere are recognizable from the variations of strength of the magnetic field and its wave/fluctuation activity. In this paper the statistical properties of magnetic fluctuations are investigated in the Venusian magnetosheath and wake regions. The main goal is to identify the characteristic scaling features of fluctuations along Venus Express (VEX) trajectory and to understand the specific circumstances of the occurrence of different types of scalings. For the latter task we also use the results of measurements from the previous missions to Venus. Our main result is that the changing character of physical interactions between the solar wind and the planetary obstacle is leading to different types of spectral scaling in the near‐Venusian space. Noisy fluctuations are observed in the magnetosheath, wavy structures near the terminator, and in the nightside near‐planet wake. Multiscale turbulence is observed at the magnetosheath boundary layer and near the quasi‐parallel bow shock. Magnetosheath boundary layer turbulence is associated with an average magnetic field which is nearly aligned with the Sun‐Venus line. Noisy magnetic fluctuations are well described with the Gaussian statistics. Both magnetosheath boundary layer and near‐shock turbulence statistics exhibit non‐Gaussian features and intermittency over small spatiotemporal scales. The occurrence of turbulence near magnetosheath boundaries can be responsible for the local heating of plasma observed by previous missions.

Scale‐free and scale‐dependent modes of energy release dynamics in the nighttime magnetosphere

Based on a spatiotemporal analysis of POLAR UVI images, we show for the first time that energy, power, area and lifetime probability distributions of electron precipitation events in the nighttime auroral oval have a significant latitudinal dependence. The low‐latitude group of the events contains a distinct subpopulation of strong auroral disturbances violating the uniform power‐law behavior reported in previous publications, while the high latitude group is described by nearly perfect power‐law statistics over the entire range of scales studied, in agreement with earlier findings. The results obtained indicate that the inner and outer portions of the plasma sheet may be characterized by substantially different scaling regimes of bursty energy dissipation suggestive of different universality classes and/or driving conditions associated with multiscale turbulence in these regions.

Role of secondary long wavelength structures in the saturation of electron temperature gradient driven turbulence

The dynamics of secondary long wavelength structures (LWSs) in electron temperature gradient (ETG) driven turbulence are investigated by performing gyrofluid simulations and modeling analyses in a slab geometry with an emphasis of the underlying nonlinear interaction processes. It is shown that the back-reaction of the secondary LWS on the ambient fluctuations essentially contributes to saturating ETG instability and limiting the electron transport. The LWS is nonlinearly generated mainly through the beating of the most unstable ETG modes, even a weak modulation instability. The back-reaction is identified as the enhanced stabilization of the ETG modes due to the streamer-type feature of the LWS, which dominantly produces a local poloidal mode coupling among unstable and highly damped spectral components to form a global mode, besides the suppression effect of the LWS due to the radial shearing decorrelation and/or the radial mode coupling. Finally, the correspondence between the LWS in the slab model and the quasimode observed in toroidal ETG simulation [Z. Lin et al., Phys. Plasmas 12, 056125 (2005)] and the importance of the nonlinear mode coupling in the multiscale turbulence interaction are discussed.

Development of a Variational Multiscale Large-Eddy Simulation Code ‘MISTRAL’ Using Double-Scale Finite Elements

A variational multiscale large-eddy simulation (VMS-LES) code, named MISTRAL, has been developed based upon the finite element method (FEM) for accurate and practical computation of geometrically complicated turbulent flow problems. The numerical strategy of the FEM-based VMS-LES is explained, especially focusing on the double-scale approximation for velocity and pressure in the incompressible Navier-Stokes equations, a pressure stabilization technique and a multiscale turbulence modeling. A unique technique is also employed in the time integration to realize an efficient inversion of the multiscale mass matrix and to form the multiscale pressure Poisson equation used in the approximate projection method for divergence-free constraint of velocity. As a numerical demonstration, a 2D driven cavity flow problem has been solved with the MISTRAL code in a wide range of Reynolds number (Re=1000 to 50000). The results are compared with reference data to quantitatively estimate the accuracy (magnitude of errors in terms of L2 norms) of the proposed VMS-LES method.

Setup of Turbulence Mechanics Accounting for a Preffered Orientation of Eddy Rotation

Some principal aspects of a modified setup of turbulence mechanics accounting for a preferred orientation of eddy rotation by distinguishing the velocity fluctuations at each flow field point (in addition to their magnitude and direction) by the curvature of their streamlines are discussed. The approach is formalized by including the velocity fluctuation streamline curvature radius into the set of arguments of the probability distribution specifying the applied statistical averaging procedure. It is shown that the decomposed presentation of the suggested turbulence mechanics, resulting from the simultaneous application of a sequence of averaging operations of the same type, enriches the setup by reflecting several aspects of the multi-scale turbulence structure (like cascading processes) immediately in terms of average fields.

Spectral scaling in the turbulent Earth's plasma sheet revisited

Abstract. Bursty bulk flow associated magnetic fluctuations exhibit at least three spectral scaling ranges in the Earth's plasma sheet. Two of the three scaling ranges can be associated with multi-scale magnetohydrodynamic turbulence between the spatial scales from ~100 km to several RE (RE is the Earth's radius). These scales include the inertial range and below ~0.5 RE a steepened scaling range, theoretically not fully understood yet. It is shown that, in the near-Earth plasma sheet, the inertial range can be robustly identified only if multi-scale quasi stationary (MSQS) data intervals are selected. Multiple bursty flow associated magnetic fluctuations, however, exhibit 1/f type scaling indicating that large-scale fluctuations are controlled by multiple uncorrelated driving sources of the bulk flows (e.g. magnetic reconnection, instabilities).

Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows

We present an LES-type variational multiscale theory of turbulence. Our approach derives completely from the incompressible Navier–Stokes equations and does not employ any ad hoc devices, such as eddy viscosities. We tested the formulation on forced homogeneous isotropic turbulence and turbulent channel flows. In the calculations, we employed linear, quadratic and cubic NURBS. A dispersion analysis of simple model problems revealed NURBS elements to be superior to classical finite elements in approximating advective and diffusive processes, which play a significant role in turbulence computations. The numerical results are very good and confirm the viability of the theoretical framework.

Spontaneous generation of vortex crystals from forced two-dimensional homogeneous turbulence

The long-term limit of statistically stationary two-dimensional turbulence is shown to depend on the form of the large-scale forcing, in agreement with previous results. That effect is studied systematically by continuously varying the forcing from deterministic to Brownian in direct numerical simulations in doubly periodic boxes. As expected, this switches on or off the enstrophy cascade and the presence of strong coherent structures, but the transition is not monotonic. Under intermediate forcing conditions, the flow evolves to a stationary vortex crystal with triangular lattice, which appears to be stable and to last indefinitely. Deterministic forcings frustrate crystallization through the formation of fast-moving dipoles, and very random ones melt the crystal. The dispersion properties of the different regimes are studied, and it is shown that efficient particle dispersion depends on the presence of multiscale turbulence. The relation with other two-dimensional systems is discussed.

The role of continuity in residual-based variational multiscale modeling of turbulence

This paper examines the role of continuity of the basis in the computation of turbulent flows. We compare standard finite elements and non-uniform rational B-splines (NURBS) discretizations that are employed in Isogeometric Analysis (Hughes et al. in Comput Methods Appl Mech Eng, 194:4135–4195, 2005). We make use of quadratic discretizations that are C 0-continuous across element boundaries in standard finite elements, and C 1-continuous in the case of NURBS. The variational multiscale residual-based method (Bazilevs in Isogeometric analysis of turbulence and fluid-structure interaction, PhD thesis, ICES, UT Austin, 2006; Bazilevs et al. in Comput Methods Appl Mech Eng, submitted, 2007; Calo in Residual-based multiscale turbulence modeling: finite volume simulation of bypass transition. PhD thesis, Department of Civil and Environmental Engineering, Stanford University, 2004; Hughes et al. in proceedings of the XXI international congress of theoretical and applied mechanics (IUTAM), Kluwer, 2004; Scovazzi in Multiscale methods in science and engineering, PhD thesis, Department of Mechanical Engineering, Stanford Universty, 2004) is employed as a turbulence modeling technique. We find that C 1-continuous discretizations outperform their C 0-continuous counterparts on a per-degree-of-freedom basis. We also find that the effect of continuity is greater for higher Reynolds number flows.

Response of multiscale turbulence to electron cyclotron heating in the DIII-D tokamak

Small-scale density turbulence (k⊥ρi∼4–10) and electron thermal flux are both observed to increase during electron cyclotron heating (ECH) of a high-temperature tokamak plasma (k⊥ is the turbulent wavenumber and ρi the ion gyroradius). In contrast, large- (k⊥ρi≤1) and intermediate-scale (k⊥ρi∼1–3) turbulence ñ∕n levels and ion thermal transport remain effectively constant. This implies that the small-scale turbulence is not a remnant or tail of the ubiquitous, large-scale or intermediate-scale turbulence, and also indicates a potentially important role in determining anomalous electron thermal transport. Radial scans of small-scale turbulence during ECH indicate decreased fluctuations in the deep core compared with increased levels towards the edge. This trend is consistent with linear gyrokinetic growth rate predictions for electron temperature gradient driven instabilities.

On a mechanism of stabilizing turbulent free shear layers in cavity flows

Turbulent free shear flows are subject to the well-known Kelvin–Helmholtz type [Panton RL. Incompressible flow. John Wiley and Sons; 1984. p. 675] instability, and it is well-known that any free shear flow which approximates a thin vorticity layer will be unstable to a wide range of amplitudes and frequencies of disturbance. In fact, much of what constitutes flow control in turbulent free shear layers consists of feeding a prescribed destabilizing disturbance to these layers. The question in the control of free shear flows is not whether the shear layer will be stable, but whether you can influence how the layer becomes unstable. In most cases, since these flows are so receptive to forcing input, and naturally tend toward instability, large changes in flow conditions can be achieved with very small amplitude periodic inputs. Recently, it has been discovered that turbulent free shear flows can also be stabilized using periodic forcing. This is, at first glance, counter-intuitive, considering our long history of considering these flows to be very unstable to forcing input. It is a phenomenon not described in modern fluid dynamic text books. The forcing required to achieve this effect (which we will call turbulent shear layer stabilization) is of a much higher amplitude and frequency than the more traditional type of shear layer flow control effect seen in the literature (which we will call turbulent shear layer destabilization). A numerical study is undertaken to investigate the effect of frequency of pulsed mass injection on the nature of stabilization, destabilization and acoustic suppression in high speed cavity flows. An implicit, 2nd-order in space and time flow solver, coupled with a recently developed hybrid RANS-LES (Reynolds Averaged Navier Stokes-Large Eddy Simulation) turbulence model by Nichols and Nelson [Nichols RH, Nelson CC. Weapons bay acoustic predictions using a multi-scale turbulence model. In: Proceedings of the ITEA 2001 aircraft-stores compatibility symposium, March 2001], is utilized in a Chimera-based parallel format. This tool is used to numerically simulate both an unsuppressed cavity in resonance, as well as the effect of mass-addition pulsed jet flow control on cavity flow physics and ultimately, cavity acoustic levels. Frequency (and in a limited number of cases, amplitude) of pulse is varied, from 0 Hz (steady) up to 5000 Hz. The change in the character of the flow control effect as pulsing frequency is changed is described, and linked to changes in acoustic levels. Limited comparison to 1/10th scale experiments is presented. The observed local stabilization of the cavity turbulent shear layer, when subjected to high frequency pulsed blowing, is shown in simulation to be the result of a violent instability and breakdown of a pair of opposite sign vortical structures created with each high frequency “pulse”. This unique shear layer stabilization behavior is only observed in simulation above a certain critical pulsing frequency. Below this critical frequency, pulsing is shown in simulation to provide little benefit with respect to suppression of high cavity acoustic levels.

A multi-scale formulation for compressible turbulent flows suitable for general variational discretization techniques

Based on the recently introduced variational multi-scale (VMS) approach to large-eddy simulation (LES) as introduced in [T.J.R. Hughes, L. Mazzei, K.E. Jansen, Large eddy simulation and the variational multiscale method, Comput. Visual. Sci. 3 (2001) 47–59; S.S. Collis, Monitoring unresolved scales in multiscale turbulence modeling, Phys. Fluids 13 (6) (2001) 1800–1806], we present a VMS formulation which can be used in the simulation of compressible flows. Special attention is given to obtain a VMS formulation which is suitable for complex flow domains and general variational discretization techniques. A generalization of the Favre-averaging procedure is introduced such that the formulation resembles the Favre-filtered Navier–Stokes equations traditionally used in LES of compressible flow, and no explicit subgrid terms arise in the continuity equation. Also, we show that with the use of discretization methods other than Fourier-spectral methods the VMS-projection no longer commutes with differentiation. This results in additional subgrid scale terms which resemble the commutator error as encountered in the traditional filtering approach to LES.

マルチスケールＬＥＳ解析コードＭＩＳＴＲＡＬによる旋回渦解析

For numerical prediction of gas entrainment from a free surface in an upper plenum of a sodium-cooled fast breeder reactor (FBR), accurate computation of a swirling flow or vortices is one of the crucial ingredients. In this study, a multiscale large-eddy simulation (LES) code, MISTRAL, is applied to a swirl flow in a cylindrical vessel to examine the effects of the multiscale turbulence models on the accuracy of vortex prediction. The numerical results are compared with experimental results and another numerical results computed with a conventional LES code (SMART-fem). The comparison indicates that the multiscale LES code is able to resolve the fine vortex core structure more accurately than the conventional LES code. Especially, elimination of eddy viscosity in the large-scale equations (or introduction of eddy viscosity only in the small-scale equations) can improve the accuracy in computing a circumferential velocity around the vortex core. It has also turned out that a use of coarse mesh suppresses the peak value of circumferential velocity, which suggests us to employ an extrapolation method such as a vortex model in practice for quantitative estimate of unresolved vortex features.

Multi-scale Turbulence in the Inner Solar Wind

Spacecraft measurements made in the solar wind show velocity and magnetic fluctuations over a broad range of frequencies. These fluctuations possess many properties expected of fully developed turbulence. In this paper, a brief overview is given on turbulence in the inner ( 1Hz) frequencies for which non linear dispersive effects dominate. Then, a discussion is given about recent theoretical results on anisotropy in magnetohydrodynamic (MHD) turbulence and their relevance for understanding the data at low frequency. Finally, I show that incompressible Hall MHD may give a multi-scale description of inner solar wind turbulence; in particular, the non-linear dispersive effects lead to a steepening of the magnetic fluctuation power law spectrum similar to what is observed at high frequency.

Partition selection in multiscale turbulence modeling

The variational multiscale (VMS) method for large-eddy simulation (LES) is a promising new approach that employs variational projection to achieve a priori scale separation in lieu of traditional spatial filtering. However, depending on the numerical method used, VMS may not be convenient in all spatial directions. We apply the VMS methodology to a numerical method that does not support explicit scale separation in the wall-normal direction for turbulent channel flow. Similar to the common LES practice of filtering only in the planes, variational projection is performed only in the planes and this strategy is found to be as successful as the full VMS method. However, in all VMS approaches, the partition between the large and small scales and the overall resolution are crucial parameters for obtaining quality solutions. By applying scale separation in just one of the coordinate directions, we have developed a consistent method for partition and resolution selection in channel flow that is related to the physical structures in the near-wall region. The idea behind this approach can, potentially, be extended for informed VMS parameter selection in other flows.