Dissipation Tensor Research Articles

Geometry of stratified turbulent mixing: local alignment of the density gradient with rotation, shear and viscous dissipation

We introduce a geometric analysis of turbulent mixing in density-stratified flows based on the alignment of the density gradient in two orthogonal bases that are locally constructed from the velocity gradient tensor. The first basis connects diapycnal mixing to rotation and shearing motions, building on the recent ‘rortex–shear decomposition’ in stratified shear layers (Jiang et al., J. Fluid Mech., vol. 947, 2022, A30), while the second basis connects mixing to the principal axes of the viscous dissipation tensor. Applying this framework to datasets taken in the stratified inclined duct laboratory experiment reveals that density gradients in locations of high shear tend to align preferentially (i) along the direction of minimum dissipation and (ii) normal to the plane spanned by the rortex and shear vectors. The analysis of the local alignment across increasingly turbulent flows offers new insights into the intricate relationship between the density gradient and dissipation, and thus diapycnal mixing.

Turbulence anisotropy in a wall-wake flow downstream of two horizontal cylinders

In this study, experimental results of flow past two horizontal cylinders — one above the other are discussed. The research was conducted using experimental data collected on a rough-bed with double cylinders of three different sizes. First, fundamental features such as streamwise velocity, Reynolds shear stress (RSS), and turbulence intensity profiles have been explained at various downstream positions with respect to the cylinders; next, some advanced analysis such as correlation coefficient, stress anisotropy, and dissipation anisotropy have been presented and compared location-wise. To demonstrate anisotropy, stress, dissipation tensors along with anisotropic invariant map and function are plotted and thoroughly analyzed. Lastly, A different diagrammatic representation of the level of anisotropy of turbulence is obtained by incorporating the eigenvalues of the Reynolds stress tensor, namely barycentric coordinates.© 2017 ElsevierInc.Allrightsreserved.

Some remarks on relativistic fluids of divergence type

Relativistic fluids of divergence type constitute a special class of fluids whose states are determined from the knowledge of a scalar generating function χ and a dissipation tensor i.e. a second rank, symmetric and traceless tensor. Both depend upon fourteen variables, known in the literature as Lagrange multipliers, and these multipliers satisfy a symmetric, quasilinear, first order system determined by . For particular choices of the generating function χ, this system can be symmetric-hyperbolic and causal. We show in this work that this characteristic property of fluids of divergence type originates in the overdetermined nature of their dynamical equations. Combining their overdetermined nature with the work of Friedrichs on overdetermined system of conservation laws with more recent work by Boillat, Ruggeri and coworkers, we prove that fluids of divergence type are locally determined by a vector potential depending upon the Lagrange multipliers. For the case where the dynamical variables describing fluid states contain a symmetric energy momentum tensor, this vector potential is the gradient of a scalar field and this field is precisely the generating function χ introduced by Pennisi and independently by Geroch and Lindblom. Examples of scalar generating functions χ are discussed where this system is a symmetric hyperbolic and causal system in an open vicinity of equilibrium states.

Multiscale analysis of the Reynolds stress, dissipation, and subgrid-scale tensor in turbulent bubbly channel flows: Characterization of anisotropy and modeling implications

A direct numerical simulation database of bubbly channel flows at friction Reynolds number 180 and with three different global void fractions has been used to perform a multiscale analysis of the anisotropy of the Reynolds stress tensor, the dissipation tensor, and the subgrid-scale (SGS) tensor in order to characterize the turbulence for a wide range of scales down to the smallest structures occurring in the flow. Based on the hypothesis of Kolmogorov, the non-linear turbulent energy transfer is expected to result in a loss of directional information such that, for a sufficiently high Reynolds number, the small-scale turbulence is expected to be isotropic and universal. The present analysis reveals that the presence of the bubbles increases the anisotropy of the flow which persists down to the smallest scales of motion, even for the dissipation and SGS tensor. This has implications for the complete landscape of turbulence modeling approaches ranging from large eddy simulation, over hybrid approaches to Reynolds averaged Navier–Stokes based modeling.

Asymmetric Motion of Magnetic Skyrmions in Ferromagnetic Nanotubes Induced by a Magnetic Field

Magnetic skyrmions, featuring topological stability and low driving current density, are believed to be a promising candidate of information carriers. One of the obstacles to application is the skyrmion Hall effect, which can lead to the annihilation of moving skyrmions at the lateral boundary of thin-film tracks. In order to resolve this issue, it was recently proposed to exploit ferromagnetic nanotubes as alternative skyrmion guides. In this work, we investigate the field-effect of current-driven skyrmion motion in nanotubes using micromagnetic simulations. It is found that, in the presence of an axial field, the skyrmion motion becomes asymmetric in tubes. This is fundamentally different from the flat strip, in which a field has little influence on the skyrmion dynamics. Based on the dissipation tensor determined by the spin texture of the skyrmions, the solution of the Thiele equation is obtained, yielding a perfect match with simulations. We argue that the asymmetry of the skyrmion dynamics originates from the curvature of the nanotube.

Multiscale Analysis of Anisotropy of Reynolds Stresses, Subgrid Stresses and Dissipation in Statistically Planar Turbulent Premixed Flames

The characterisation of small-scale turbulence has been an active area of research for decades and this includes, particularly, the analysis of small-scale isotropy, as postulated by Kolmogorov. In particular, the question if the dissipation tensor is isotropic or not, and how it is related to the anisotropy of the Reynolds stresses is of particular interest for modelling purposes. While this subject has been extensively studied in the context of isothermal flows, the situation is more complicated in turbulent reacting flows because of heat release. Furthermore, the landscape of Computational Fluid Dynamics is characterised by a multitude of methods ranging from Reynolds-averaged to Large Eddy Simulation techniques, and they address different ranges of scales of the turbulence kinetic energy spectrum. Therefore, a multiscale analysis of the anisotropies of Reynolds stress, dissipation and sub-grid scale tensor has been performed by using a DNS database of statistically planar turbulent premixed flames. Results show that the coupling between dissipation tensor and Reynolds stress tensor is weaker compared to isothermal turbulent boundary layer flows. In particular, for low and moderate turbulence intensities, heat release induces pronounced anisotropies which affect not only fluctuation strengths but also the characteristic size of structures associated with different velocity components.

Transport coefficients for modeling fission dynamics

Transport coefficients are important ingredients in dynamical investigations of a nuclear fission process, which determine the dynamical evolution of the fissioning system. The inertia (mass) and friction (dissipation) tensors influence substantially on different observables. The proper calculation of these tensors is a necessary condition for correct modeling of the fission process. The calculation of the inertia and friction tensors is presented for a large variety of nuclear shapes generated by a {c,h,α} parametrization. The inertia tensor is calculated within the Werner-Wheeler approximation for incompressible irrotational flow. The friction tensor is calculated within the one-body and two-body mechanisms of nuclear dissipation. A numerical code is made available, which calculates all these quantities. Program summaryProgram Title: Mass_DissCPC Library link to program files:https://doi.org/10.17632/rcndf6sbns.1Licensing provisions: CC BY NC 3.0Programming language: C++Nature of problem: The modeling of the nuclear fission within dynamical consideration requires calculation of the inertia and friction coefficients. This calculation should be performed for a large variety of the nuclear shapes, which describe the evolution of the shape of compound nucleus from the ground state till the separated fission fragments.Solution method: The inertia tensor is calculated within the Werner-Wheeler approximation for incompressible irrotational flow. The friction tensor is calculated within the one-body and two-body mechanisms of the nuclear dissipation. The shape of the fissioning nucleus is described by the {c,h,α} parametrization. This parametrization determines the axially symmetric shapes in cylindrical coordinates. The inertia and friction tensors are calculated using numerical integration procedure as a function of the three shape parameters. All subroutines, which define the nuclear shape, are separated from the code, which calculates the inertia and friction tensors. Thus, the program could be adopted for any other shape parameterization in case if it is given in cylindrical coordinates.

Inflationary anisotropic phases with bianchi-I cosmic model

This paper is devoted to studying warm anisotropic inflation using modified Chaplygin gas in the context of the Bianchi-I comic model. We investigate the dynamics of the warm intermediate universe model in two distinct regimes, i.e., weak and strong regimes in the context of generalized dissipative coefficient. We formulate solutions of dissipation coefficient, inflaton field, scalar & tensor (S/T) power spectra, spectral index in an environment of slow-roll approximation to discuss the existence of warm weak and strong inflation and checked their viability in view of 2018 Planck data. It is seen through graphical representation that the condition for the existence of warm weak inflation is preserved only for z=0 and z=1 whereas in the case of the strong dissipative regime, the compatibility is achieved for z=3. The corresponding decay rates and the S/T are found to be consistent with the current observations.

Conditional and unconditional second-order structure functions in bubbly channel flows of power-law fluids

The influence of non-Newtonian fluid behavior and the Eötvös number on conditional and unconditional second-order structure functions of bubbly channel flows has been investigated by conducting a series of direct numerical simulations at a friction Reynolds number of 127.3. Two Eötvös numbers have been considered (Eo = 0.3125 and Eo = 3.75) together with three different power-law indexes representing shear-thinning (n = 0.7), Newtonian (n = 1.0), and shear-thickening (n = 1.3) fluid behavior. The scaling of the second-order structure functions (SFs) can be translated into an inertial range scaling of the turbulent kinetic energy spectrum. However, because of the discontinuous character of the fluid properties in bubbly flows, SFs are more easily accessible than turbulence spectra, which are based on Fourier transform. It has been found that the different parameters (i.e., Eo, n) have an influence on the energy content as well as the peak location of the compensated second-order SFs (i.e., the dimensions of the large scales). However, after appropriate scaling, the curves nearly collapse. To confirm and further explain the above findings, directional length scales have been evaluated and discussed in detail. Finally, the anisotropy of the Reynolds stress tensor and dissipation tensor has been analyzed in terms of the Lumley triangle, showing that bubbly channel flows are less isotropic than their single-phase counterpart, although they are more homogeneous in the channel center. While the dissipation tensor is slightly more isotropic than the Reynolds stress tensor in the bulk region of the channel flow, overall, a very similar behavior is observed.

Inertia–Gravity Waves Breaking in the Middle Atmosphere at High Latitudes: Energy Transfer and Dissipation Tensor Anisotropy

Abstract We present direct numerical simulations of inertia–gravity waves breaking in the middle–upper mesosphere. We consider two different altitudes, which correspond to the Reynolds number of 28 647 and 114 591 based on wavelength and buoyancy period. While the former was studied by Remmler et al., it is here repeated at a higher resolution and serves as a baseline for comparison with the high-Reynolds-number case. The simulations are designed based on the study of Fruman et al., and are initialized by superimposing primary and secondary perturbations to the convectively unstable base wave. Transient growth leads to an almost instantaneous wave breaking and secondary bursts of turbulence. We show that this process is characterized by the formation of fine flow structures that are predominantly located in the vicinity of the wave’s least stable point. During the wave breakdown, the energy dissipation rate tends to be an isotropic tensor, whereas it is strongly anisotropic in between the breaking events. We find that the vertical kinetic energy spectra exhibit a clear 5/3 scaling law at instants of intense energy dissipation rate and a cubic power law at calmer periods. The term-by-term energy budget reveals that the pressure term is the most important contributor to the global energy budget, as it couples the vertical and the horizontal kinetic energy. During the breaking events, the local energy transfer is predominantly from the mean to the fluctuating field and the kinetic energy production is in balance with the pseudo kinetic energy dissipation rate.

Destruction-of-dissipation and time-scales in wall turbulence

This paper studies the dynamics and scalings of dissipation processes in wall turbulence, focussing on the destruction-of-dissipation tensor εεij (and its halftrace εε), which acts as destruction-by-molecular-viscosity mechanism in the transport equations for the dissipation tensor εij (or its halftrace ε). Budgets of εεij-transport (and εε-transport) are studied for low-Reynolds turbulent plane channel flow. These transport equations also include a destruction-by-molecular-viscosity mechanism, the destruction-of-destruction tensor εεεij (or its halftrace εεε), and indeed, recursively, we identify terms εij[n+1] defined by correlations of [n + 1]-derivatives which correspond to the destruction mechanism of εij[n]. Using halftraces ε[n], we may define time-scales, whose study reveals that εεε−1εε is approximately equal to the Kolmogorov time-scale. The dependence of the time-scales on the Reynolds number is discussed.

Causal dissipation in the relativistic dynamics of barotropic fluids

This paper develops two causal four-field theories of relativistic fluid dynamics, one for viscous fluids that are barotropic and the other for viscous heat-conductive fluids that are “thermo-barotropic,” a property that is newly defined here. While similar to the deduction of a five-field theory in the authors’ article Causal dissipation for the relativistic dynamics of ideal gases [Freistühler, H. and Temple, B., Proc. R. Soc. A 473, 20160729 (2017)], the argumentation is consistently carried out in a way that stays closer to Eckart’s flow frame (than to Landau’s), and the result is directly compared with the four-field theories resulting from early proposals made by Eckart, Lichnerowicz, and Choquet-Bruhat. The key idea is to impose second-order symmetric hyperbolicity in the sense of Hughes, Kato, and Marsden [Arch. Rational Mech. Anal. 63, 273–294 (1976)], in the natural Godunov variables that make the corresponding system of perfect-fluid conservation laws symmetric hyperbolic in the first order sense. The new theory for viscous heat-conductive thermo-barotropic fluids belongs to the Hughes-Kato-Marsden class; the new theory for viscous general barotropic fluids lies on the boundary of that class. As in the five-field theory, the coefficients of bulk viscosity ζ, shear viscosity η, and, in the case of thermo-barotropic fluids, that of heat conductivity χ are free parameters, and in terms of these, the relativistic dissipation tensor is uniquely determined under three conditions which the authors propose as definitive: symmetric hyperbolicity, sharp causality, and first-order equivalence with Eckart—the requirement that the resulting equations be equivalent to the Eckart equations to leading order in ζ, η, and χ. The new theory for general viscous barotropic fluids complements the one given in the abovementioned paper for massive ideal gases. The new theory for viscous heat-conductive thermo-barotropic fluids notably includes the case of pure radiation, providing as one application a quantitative correction to the authors’ previous proposal in Causal dissipation and shock profiles in the relativistic fluid dynamics of pure radiation [Freistühler, H. and Temple, B., Proc. R. Soc. A 470, 20140055 (2014)].

Dissipation of Turbulent Kinetic Energy in a Cylinder Wall Junction Flow

The subject of this study is the discussion of the dissipation of turbulent kinetic energy and its Reynolds number scaling in front of a wall-mounted cylinder. We employed highly resolved Large-Eddy Simulation and ensured that the computational grid was fine enough to resolve most of the scales. A perceptible fraction of the total dissipation is modeled. However, this fraction - about one third - is small enough so that the total dissipation suffers only marginally from some potential shortcomings of the turbulence model. Individual terms of the pseudo dissipation tensor and their Reynolds number scaling are discussed and compared. This tensor and thus the turbulent small scale structures are not isotropic at the Reynolds numbers investigated. Furthermore, the near-wall anisotropy under the horseshoe vortex is likely to persist to larger Reynolds numbers as it can be linked to a flapping of the near-wall layer. The turbulent length scale shows a strong spatial variability. In the region of the vortex system in the cylinder front, the distribution reveals a similar shape as the one of the turbulent kinetic energy and its amplitude is in the order of magnitude of the cylinder diameter. In contrast to the region dominated by the approach flow, the turbulent length scale is independent of the Reynolds number in the region dominated by the vortex system. Even though the flow investigated is in non-equilibrium, common a priori estimations and scalings of the Kolmogorov length scale based on macro scales give satisfying results.

Energy stable numerical methods for porous media flow type problems

Many problems arising in the context of multiphase porous media flows that take the form of degenerate parabolic equations have a dissipative structure, so that the energy of an isolated system is decreasing along time. In this paper, we discuss two approaches to tune a rather large family of numerical method in order to ensure a control on the energy at the discrete level as well. The first methodology is based on upwinding of the mobilities and leads to schemes that are unconditionally positivity preserving but only first order accurate in space. We present a second methodology which is based on the construction of local positive dissipation tensors. This allows to recover a second order accuracy w.r.t. space, but the preservation of the positivity is conditioned to some additional assumption on the nonlinearities. Both methods are based on an underlying numerical method for a linear anisotropic diffusion equation. We do not suppose that this building block is monotone.

Invariants of Turbulence Reynolds Stress and of Dissipation Tensors in Regular Breaking Waves

A series of measurements in a flume with a particle-tracking system in three dimensions applied to breaking waves is used to analyse the structure of turbulence with a full set of variables that usually are available only in numerical simulations. After extracting turbulence, in addition to the standard analysis aiming to quantify the fluxes, i.e., the time-average and the phase-average levels of turbulence and vorticity (details are given in two former papers), a more in-depth description of the structure of turbulence Reynolds stress tensor is given, focussing on the invariants evolution in time and in the vertical. A relation between the components of the Reynolds stress tensor and of the dissipation tensor is depicted. This relation is finalised to possible models of turbulence in breaking waves.

Langevin model of low-energy fission

Background: Since the earliest days of fission, stochastic models have been used to describe and model the process. For a quarter century, numerical solutions of Langevin equations have been used to model fission of highly excited nuclei, where microscopic potential-energy effects have been neglected.Purpose: In this paper I present a Langevin model for the fission of nuclei with low to medium excitation energies, for which microscopic effects in the potential energy cannot be ignored.Method: I solve Langevin equations in a five-dimensional space of nuclear deformations. The macroscopic-microscopic potential energy from a global nuclear structure model well benchmarked to nuclear masses is tabulated on a mesh of approximately ${10}^{7}$ points in this deformation space. The potential is defined continuously inside the mesh boundaries by use of a moving five-dimensional cubic spline approximation. Because of reflection symmetry, the effective mesh is nearly twice this size. For the inertia, I use a (possibly scaled) approximation to the inertia tensor defined by irrotational flow. A phenomenological dissipation tensor related to one-body dissipation is used. A normal-mode analysis of the dynamical system at the saddle point and the assumption of quasiequilibrium provide distributions of initial conditions appropriate to low excitation energies, and are extended to model spontaneous fission. A dynamical model of postscission fragment motion including dynamical deformations and separation allows the calculation of final mass and kinetic-energy distributions, along with other interesting quantities.Results: The model makes quantitative predictions for fragment mass and kinetic-energy yields, some of which are very close to measured ones. Varying the energy of the incident neutron for induced fission allows the prediction of energy dependencies of fragment yields and average kinetic energies. With a simple approximation for spontaneous fission starting conditions, quantitative predictions are made for some observables which are close to measurements.Conclusions: This model is able to reproduce several mass and energy yield observables with a small number of physical parameters, some of which do not need to be varied after benchmarking to $^{235}\mathrm{U}(n,f)$ to predict results for other fissioning isotopes.

Further analysis of the budgets of the dissipation tensor in turbulent plane channel flow

Recent results (Gerolymos and Vallet 2016 J. Fluid Mech. 807 386–418) have provided data for the terms in the transport equations for the components of the dissipation tensor in low-Reynolds turbulent plane channel flow. The present paper extends the previous results by a detailed analysis of the behaviour of various mechanisms in the -transport equations (production, diffusion, redistribution, destruction), with particular emphasis on the component-by-component comparison with the corresponding mechanisms in the transport equations for the Reynolds-stresses rij. The splitting of the pressure terms for the wall-normal components into redistribution and pressure-diffusion reveals substantially different behaviour near the wall. The wall-asymptotics of different terms in the transport equations are studied in detail, and examined using the data. Both data and wall-asympotic analysis show that the anisotropy of the destruction-of-dissipation tensor is fundamentally different from that of rij or , never approaching the two-component state at the solid wall.

Low Mach number preconditioning techniques for Roe-type and HLLC-type methods for a two-phase compressible flow model

We describe two-phase flows by a six-equation single-velocity two-phase compressible flow model with stiff mechanical relaxation. In particular, we are interested in the simulation of liquid–gas mixtures such as cavitating flows. For the numerical approximation of the homogeneous hyperbolic portion of the model equations we have previously developed two-dimensional wave propagation finite volume schemes that use Roe-type and HLLC-type Riemann solvers. These schemes are very suited to simulate the dynamics of transonic and supersonic flows. However, these methods suffer from the well known difficulties of loss of accuracy and efficiency encountered by classical upwind finite volume discretizations at low Mach number regimes. This issue is particularly critical for liquid–gas flows, where the Mach number may range from very low to very high values, due to the large and rapid variation of the acoustic impedance. In this work we focus on the problem of loss of accuracy of standard schemes related to the spatial discretization of the convective terms of the model equations. To address this difficulty, we consider the class of preconditioning strategies that correct at low Mach number the numerical dissipation tensor. First we extend the approach of the preconditioned Roe–Turkel scheme of Guillard–Viozat for the Euler equations [Computers & Fluids, 28, 1999] to our Roe-type method for the two-phase flow model, by defining a suitable Turkel-type preconditioning matrix. A similar low Mach number correction is then devised for the HLLC-type method, thanks to a novel reformulation of the HLLC solver. We present numerical results for two-dimensional liquid–gas channel flow tests that show the effectiveness of the proposed preconditioning techniques. In particular, we observe that the order of pressure fluctuations generated at low Mach number regimes by the preconditioned methods agrees with the theoretical results inferred for the continuous relaxed two-phase flow model by an asymptotic analysis.

Causal dissipation for the relativistic dynamics of ideal gases.

We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.

An Improved Model Including Length Scale Anisotropy for the Pressure Strain Correlation of Turbulence

In this paper, we consider the evolution of decaying homogeneous anisotropic turbulence without mean velocity gradients, where only the slow pressure rate of strain is nonzero. A higher degree nonlinear return-to-isotropy model has been developed for the slow pressure–strain correlation, considering anisotropies in Reynolds stress, dissipation rate, and length scale tensor. Assumption of single length scale across the flow is not sufficient, from which stems the introduction of length scale anisotropy tensor, which has been assumed to be a linear function of Reynolds stress and dissipation tensor. The present model with anisotropy in length scale shows better agreement with well-accepted experimental results and an improvement over the Sarkar and Speziale (SS) quadratic model.