Special Issue "Multiscale Turbulent Transport"

A special issue of Fluids (ISSN 2311-5521).

Deadline for manuscript submissions: closed (30 June 2019).

Special Issue Editors

Guest Editor
Dr. Marco Martins Afonso

Centro de Matemática da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
Website | E-Mail
Interests: fluid dynamics; turbulence; theoretical, non-linear and statistical physics; transport properties of inertial particles; multiple-scale formalism
Guest Editor
Prof. Sílvio Gama

Centro de Matemática da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
Website | E-Mail
Interests: fluid mechanics; magnetohydrodynamics; multiscale analysis; spectral methods; amplitude equations; econophysics; control theory

Special Issue Information

Dear Colleagues,

Turbulent transport is currently a great subject of ongoing investigation at the interface of methodologies running from theory to numerical simulations and experiments, and covering several spatio-temporal scales. Mathematical analysis, physical modelling and engineering applications represent different facets of a classical, long-standing problem still far from achieving a thorough comprehension. The goal of this Special Issue is to offer recent advances covering subjects identified in the keywords (and not only). Authors are welcome to submit regular articles, review papers focused on the state-of-the-art and the progress made over the last few years, as well as new research trends.

Dr. Marco Martins Afonso
Prof. Sílvio Gama
Guest Editors

Manuscript Submission Information

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Keywords

  • Multiscale analysis in turbulent transport processes
  • Lagrangian and Eulerian descriptions of turbulence
  • Advection of particles and fields in turbulent flows
  • Ideal or non-ideal turbulence (unstationary\inhomogeneous\anisotropic\compressible)
  • Turbulent flows in bio-fluid mechanics and magnetohydrodynamics
  • Control and optimization of turbulent transport

Published Papers (8 papers)

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Research

Open AccessArticle
Direct Numerical Simulation of a Warm Cloud Top Model Interface: Impact of the Transient Mixing on Different Droplet Population
Received: 27 May 2019 / Revised: 21 June 2019 / Accepted: 25 June 2019 / Published: 1 August 2019
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Abstract
Turbulent mixing through atmospheric cloud and clear air interface plays an important role in the life of a cloud. Entrainment and detrainment of clear air and cloudy volume result in mixing across the interface, which broadens the cloud droplet spectrum. In this study, [...] Read more.
Turbulent mixing through atmospheric cloud and clear air interface plays an important role in the life of a cloud. Entrainment and detrainment of clear air and cloudy volume result in mixing across the interface, which broadens the cloud droplet spectrum. In this study, we simulate the transient evolution of a turbulent cloud top interface with three initial mono-disperse cloud droplet population, using a pseudo-spectral Direct Numerical Simulation (DNS) along with Lagrangian droplet equations, including collision and coalescence. Transient evolution of in-cloud turbulent kinetic energy (TKE), density of water vapour and temperature is carried out as an initial value problem exhibiting transient decay. Mixing in between the clear air and cloudy volume produced turbulent fluctuations in the density of water vapour and temperature, resulting in supersaturation fluctuations. Small scale turbulence, local supersaturation conditions and gravitational forces have different weights on the droplet population depending on their sizes. Larger droplet populations, with initial 25 and 18 μ m radii, show significant growth by droplet-droplet collision and a higher rate of gravitational sedimentation. However, the smaller droplets, with an initial 6 μ m radius, did not show any collision but a large size distribution broadening due to differential condensation/evaporation induced by the mixing, without being influenced by gravity significantly. Full article
(This article belongs to the Special Issue Multiscale Turbulent Transport)
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Open AccessFeature PaperArticle
Computation of Kinematic and Magnetic α-Effect and Eddy Diffusivity Tensors by Padé Approximation
Received: 13 May 2019 / Revised: 5 June 2019 / Accepted: 7 June 2019 / Published: 14 June 2019
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Abstract
We present examples of Padé approximations of the α-effect and eddy viscosity/diffusivity tensors in various flows. Expressions for the tensors derived in the framework of the standard multiscale formalism are employed. Algebraically, the simplest case is that of a two-dimensional parity-invariant six-fold [...] Read more.
We present examples of Padé approximations of the α -effect and eddy viscosity/diffusivity tensors in various flows. Expressions for the tensors derived in the framework of the standard multiscale formalism are employed. Algebraically, the simplest case is that of a two-dimensional parity-invariant six-fold rotation-symmetric flow where eddy viscosity is negative, indicating intervals of large-scale instability of the flow. Turning to the kinematic dynamo problem for three-dimensional flows of an incompressible fluid, we explore the application of Padé approximants for the computation of tensors of magnetic α -effect and, for parity-invariant flows, of magnetic eddy diffusivity. We construct Padé approximants of the tensors expanded in power series in the inverse molecular diffusivity 1 / η around 1 / η = 0 . This yields the values of the dominant growth rate to satisfactory accuracy for η , several dozen times smaller than the threshold, above which the power series is convergent. We do computations in Fortran in the standard “double” (real*8) and extended “quadruple” (real*16) precision, and perform symbolic calculations in Mathematica. Full article
(This article belongs to the Special Issue Multiscale Turbulent Transport)
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Open AccessArticle
Baropycnal Work: A Mechanism for Energy Transfer across Scales
Received: 5 April 2019 / Revised: 9 May 2019 / Accepted: 13 May 2019 / Published: 18 May 2019
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Abstract
The role of baroclinicity, which arises from the misalignment of pressure and density gradients, is well-known in the vorticity equation, yet its role in the kinetic energy budget has never been obvious. Here, we show that baroclinicity appears naturally in the kinetic energy [...] Read more.
The role of baroclinicity, which arises from the misalignment of pressure and density gradients, is well-known in the vorticity equation, yet its role in the kinetic energy budget has never been obvious. Here, we show that baroclinicity appears naturally in the kinetic energy budget after carrying out the appropriate scale decomposition. Strain generation by pressure and density gradients, both barotropic and baroclinic, also results from our analysis. These two processes underlie the recently identified mechanism of “baropycnal work”, which can transfer energy across scales in variable density flows. As such, baropycnal work is markedly distinct from pressure-dilatation into which the former is implicitly lumped in Large Eddy Simulations. We provide numerical evidence from 1024 3 direct numerical simulations of compressible turbulence. The data shows excellent pointwise agreement between baropycnal work and the nonlinear model we derive, supporting our interpretation of how it operates. Full article
(This article belongs to the Special Issue Multiscale Turbulent Transport)
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Graphical abstract

Open AccessArticle
Turbulence Model Assessment in Compressible Flows around Complex Geometries with Unstructured Grids
Received: 23 February 2019 / Revised: 7 April 2019 / Accepted: 15 April 2019 / Published: 28 April 2019
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Abstract
One of the key factors in simulating realistic wall-bounded flows at high Reynolds numbers is the selection of an appropriate turbulence model for the steady Reynolds Averaged Navier–Stokes equations (RANS) equations. In this investigation, the performance of several turbulence models was explored for [...] Read more.
One of the key factors in simulating realistic wall-bounded flows at high Reynolds numbers is the selection of an appropriate turbulence model for the steady Reynolds Averaged Navier–Stokes equations (RANS) equations. In this investigation, the performance of several turbulence models was explored for the simulation of steady, compressible, turbulent flow on complex geometries (concave and convex surface curvatures) and unstructured grids. The turbulence models considered were the Spalart–Allmaras model, the Wilcox k- ω model and the Menter shear stress transport (SST) model. The FLITE3D flow solver was employed, which utilizes a stabilized finite volume method with discontinuity capturing. A numerical benchmarking of the different models was performed for classical Computational Fluid Dynamic (CFD) cases, such as supersonic flow over an isothermal flat plate, transonic flow over the RAE2822 airfoil, the ONERA M6 wing and a generic F15 aircraft configuration. Validation was performed by means of available experimental data from the literature as well as high spatial/temporal resolution Direct Numerical Simulation (DNS). For attached or mildly separated flows, the performance of all turbulence models was consistent. However, the contrary was observed in separated flows with recirculation zones. Particularly, the Menter SST model showed the best compromise between accurately describing the physics of the flow and numerical stability. Full article
(This article belongs to the Special Issue Multiscale Turbulent Transport)
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Open AccessArticle
A Relaxation Filtering Approach for Two-Dimensional Rayleigh–Taylor Instability-Induced Flows
Received: 12 February 2019 / Revised: 10 April 2019 / Accepted: 16 April 2019 / Published: 21 April 2019
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Abstract
In this paper, we investigate the performance of a relaxation filtering approach for the Euler turbulence using a central seven-point stencil reconstruction scheme. High-resolution numerical experiments are performed for both multi-mode and single-mode inviscid Rayleigh–Taylor instability (RTI) problems in two-dimensional canonical settings. In [...] Read more.
In this paper, we investigate the performance of a relaxation filtering approach for the Euler turbulence using a central seven-point stencil reconstruction scheme. High-resolution numerical experiments are performed for both multi-mode and single-mode inviscid Rayleigh–Taylor instability (RTI) problems in two-dimensional canonical settings. In our numerical assessments, we focus on the computational performance considering both time evolution of the flow field and its spectral resolution up to three decades of inertial range. Our assessments also include an implicit large eddy simulation (ILES) approach that is based on a fifth-order weighted essential non-oscillatory (WENO) with built-in numerical dissipation due to its upwind-based reconstruction architecture. We show that the relaxation filtering approach equipped with a central seven-point stencil, sixth-order accurate discrete filter yields accurate results efficiently, since there is no additional cost associated with the computation of the smoothness indicators and interface Riemann solvers. Our a-posteriori spectral analysis also demonstrates that its resolution capacity is sufficiently high to capture the details of the flow behavior induced by the instability. Furthermore, its resolution capability can be effectively controlled by the filter shape and strength. Full article
(This article belongs to the Special Issue Multiscale Turbulent Transport)
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Open AccessFeature PaperArticle
A Correction and Discussion on Log-Normal Intermittency B-Model
Received: 2 December 2018 / Revised: 28 January 2019 / Accepted: 13 February 2019 / Published: 21 February 2019
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Abstract
This paper discusses a turbulent intermittency model introduced in 1990, the B-model. It was found that the original manuscript which introduced the B-model contained a couple arithmetic errors in the equations. This work goes over corrections to the original equations, and [...] Read more.
This paper discusses a turbulent intermittency model introduced in 1990, the B-model. It was found that the original manuscript which introduced the B-model contained a couple arithmetic errors in the equations. This work goes over corrections to the original equations, and explains where problems arose in the derivations. These corrections cause the results to differ from those in the original manuscript, and these differences are discussed. A generalization of this B-model is then introduced to explore the range of behaviors this style of model provides. To distinguish between the different intermittency models discussed in this paper requires structure function power exponents of order greater than 12. As a source of comparison, data from a flume experiment is introduced, and, with the corrections introduced, this data seems to imply that an intermittency coefficient between 0.17 and 0.2 gives good agreement. Higher quality future measurements of high order moments could help with distinguishing the different intermittency models. Full article
(This article belongs to the Special Issue Multiscale Turbulent Transport)
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Open AccessFeature PaperArticle
Optimal Transient Growth in an Incompressible Flow past a Backward-Slanted Step
Received: 6 February 2019 / Revised: 12 February 2019 / Accepted: 14 February 2019 / Published: 20 February 2019
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Abstract
With the aim of providing a first step in the quest for a reduction of the aerodynamic drag on the rear-end of a car, we study the phenomena of separation and reattachment of an incompressible flow by focusing on a specific aerodynamic geometry, [...] Read more.
With the aim of providing a first step in the quest for a reduction of the aerodynamic drag on the rear-end of a car, we study the phenomena of separation and reattachment of an incompressible flow by focusing on a specific aerodynamic geometry, namely a backward-slanted step at 25 of inclination. The ensuing recirculation bubble provides the basis for an analytical and numerical investigation of streamwise-streak generation, lift-up effect, and turbulent-wake and Kelvin–Helmholtz instabilities. A linear stability analysis is performed, and an optimal control problem with a steady volumic forcing is tackled by means of a variational formulation, adjoint methods, penalization schemes, and an orthogonalization algorithm. Dealing with the transient growth of spanwise-periodic perturbations, and inspired by the need of physically-realizable disturbances, we finally provide a procedure attaining a kinetic-energy maximal gain on the order of 10 6 , with respect to the power introduced by the external forcing. Full article
(This article belongs to the Special Issue Multiscale Turbulent Transport)
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Open AccessFeature PaperArticle
Time-Dependent Diffusion Coefficients for Chaotic Advection due to Fluctuations of Convective Rolls
Received: 16 October 2018 / Revised: 19 November 2018 / Accepted: 22 November 2018 / Published: 27 November 2018
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Abstract
The properties of chaotic advection arising from defect turbulence, that is, weak turbulence in the electroconvection of nematic liquid crystals, were experimentally investigated. Defect turbulence is a phenomenon in which fluctuations of convective rolls arise and are globally disturbed while maintaining convective rolls [...] Read more.
The properties of chaotic advection arising from defect turbulence, that is, weak turbulence in the electroconvection of nematic liquid crystals, were experimentally investigated. Defect turbulence is a phenomenon in which fluctuations of convective rolls arise and are globally disturbed while maintaining convective rolls locally. The time-dependent diffusion coefficient, as measured from the motion of a tagged particle driven by the turbulence, was used to clarify the dependence of the type of diffusion on coarse-graining time. The results showed that, as coarse-graining time increases, the type of diffusion changes from superdiffusion → subdiffusion → normal diffusion. The change in diffusive properties over the observed timescale reflects the coexistence of local order and global disorder in the defect turbulence. Full article
(This article belongs to the Special Issue Multiscale Turbulent Transport)
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