The connection between the spectrum of turbulent scales and the skin-friction statistics in channel flow at

2019 ◽  
Vol 871 ◽  
pp. 22-51 ◽  
Author(s):  
Lionel Agostini ◽  
Michael Leschziner
Keyword(s):  
Skin Friction ◽  
Channel Flow ◽  
Large Scale ◽  
Direct Interaction ◽  
Conditional Probability Density ◽  
Small Scale ◽  
Shear Stresses ◽  
Mode Decomposition ◽  
Small Scales ◽  
Scale Turbulence

Data from a direct numerical simulation for channel flow at a friction Reynolds number of 1000 are analysed to derive statistical properties that offer insight into the mechanisms by which large-scale structures in the log-law region affect the small-scale turbulence field close to the wall and the statistical skin-friction properties. The data comprise full-volume velocity fields at 150 time levels separated by 50 wall-scaled viscous time units. The scales are separated into wavelength bands by means of the ‘empirical mode decomposition’, of which the two lowest modes are considered to represent the small scales and three upper modes to represent the large scales. Joint and conditional probability density functions are then derived for various scale-specific statistics, with particular emphasis placed on the streamwise and shear stresses conditional on the large-scale fluctuations of the skin friction, generally referred to as ‘footprinting’. Statistics for the small-scale stresses, conditional on the footprints, allow the amplification and attenuation of the small-scale skin friction, generally referred to as ‘modulation’, to be quantified in dependence on the footprints. The analysis leads to the conclusion that modulation does not reflect a direct interaction between small scales and large scales, but arises from variations in shear-induced production that arise from corresponding changes in the conditional velocity profile. This causal relationship also explains the wall-normal change in sign in the correlation between large scales and small scales at a wall-scaled wall distance of approximately 100. The effects of different scales on the skin friction are investigated by means of two identities that describe the relationship between the shear-stress components and the skin friction, one identity based on integral momentum and the other on energy production/dissipation. The two identities yield significant differences in the balance of scale-specific contributions, and the origins of these differences are discussed.

Triadic scale interactions in a turbulent boundary layer

2015 ◽  
Vol 767 ◽  
Author(s):  
Subrahmanyam Duvvuri ◽  
Beverley J. McKeon
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Small Scale ◽  
Velocity Signal ◽  
Small Scales ◽  
Amplitude Modulation Coefficient ◽  
Scale Turbulence ◽  
Scale Motion ◽  
Phase Relationships

AbstractA formal relationship between the skewness and the correlation coefficient of large and small scales, termed the amplitude modulation coefficient, is established for a general statistically stationary signal and is analysed in the context of a turbulent velocity signal. Both the quantities are seen to be measures of phase in triadically consistent interactions between scales of turbulence. The naturally existing phase relationships between large and small scales in a turbulent boundary layer are then manipulated by exciting a synthetic large-scale motion in the flow using a spatially impulsive dynamic wall roughness perturbation. The synthetic scale is seen to alter the phase relationships, or the degree of modulation, in a quasi-deterministic manner by exhibiting a phase-organizing influence on the small scales. The results presented provide encouragement for the development of a practical framework for favourable manipulation of energetic small-scale turbulence through large-scale inputs in a wall-bounded turbulent flow.

Kolmogorov’s contributions to the physical and geometrical understanding of small-scale turbulence and recent developments

1991 ◽  
Vol 434 (1890) ◽  
pp. 183-210 ◽  
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Inertial Range ◽  
Small Scale ◽  
Small Scales ◽  
Recent Developments ◽  
Self Similar ◽  
Scale Turbulence ◽  
High Reynolds ◽  
Non Gaussian

This paper reviews how Kolmogorov postulated for the first time the existence of a steady statistical state for small-scale turbulence, and its defining parameters of dissipation rate and kinematic viscosity. Thence he made quantitative predictions of the statistics by extending previous methods of dimensional scaling to multiscale random processes. We present theoretical arguments and experimental evidence to indicate when the small-scale motions might tend to a universal form (paradoxically not necessarily in uniform flows when the large scales are gaussian and isotropic), and discuss the implications for the kinematics and dynamics of the fact that there must be singularities in the velocity field associated with the - 5/3 inertial range spectrum. These may be particular forms of eddy or ‘eigenstructure’ such as spiral vortices, which may not be unique to turbulent flows. Also, they tend to lead to the notable spiral contours of scalars in turbulence, whose self-similar structure enables the ‘box-counting’ technique to be used to measure the ‘capacity’ D K of the contours themselves or of their intersections with lines, D' K . Although the capacity, a term invented by Kolmogorov (and studied thoroughly by Kolmogorov & Tikhomirov), is like the exponent 2 p of a spectrum in being a measure of the distribution of length scales ( D' K being related to 2 p in the limit of very high Reynolds numbers), the capacity is also different in that experimentally it can be evaluated at local regions within a flow and at lower values of the Reynolds number. Thus Kolmogorov & Tikhomirov provide the basis for a more widely applicable measure of the self-similar structure of turbulence. Finally, we also review how Kolmogorov’s concept of the universal spatial structure of the small scales, together with appropriate additional physical hypotheses, enables other aspects of turbulence to be understood at these scales; in particular the general forms of the temporal statistics such as the high-frequency (inertial range) spectra in eulerian and lagrangian frames of reference, and the perturbations to the small scales caused by non-isotropic, non-gaussian and inhomogeneous large-scale motions.

scholarly journals Role of large-scale advection and small-scale turbulence on vertical migration of gyrotactic swimmers

2019 ◽  
Vol 4 (12) ◽  
Author(s):  
C. Marchioli ◽  
H. Bhatia ◽  
G. Sardina ◽  
L. Brandt ◽  
A. Soldati
Keyword(s):  
Vertical Migration ◽  
Large Scale ◽  
Small Scale ◽  
Scale Turbulence

Modeling an Enclosed, Turbulent Reacting Methane Jet With the Premixed Conditional Moment Closure Method

2013 ◽  
Author(s):  
Scott Martin ◽  
Aleksandar Jemcov ◽  
Björn de Ruijter
Keyword(s):  
Turbulent Combustion ◽  
Large Scale ◽  
Reaction Rates ◽  
Moment Closure ◽  
Scalar Dissipation ◽  
Small Scale ◽  
Conditional Moment ◽  
Progress Variable ◽  
Conditional Moment Closure ◽  
Scale Turbulence

Here the premixed Conditional Moment Closure (CMC) method is used to model the recent PIV and Raman turbulent, enclosed reacting methane jet data from DLR Stuttgart [1]. The experimental data has a rectangular test section at atmospheric pressure and temperature with a single inlet jet. A jet velocity of 90 m/s is used with an adiabatic flame temperature of 2,064 K. Contours of major species, temperature and velocities along with velocity rms values are provided. The conditional moment closure model has been shown to provide the capability to model turbulent, premixed methane flames with detailed chemistry and reasonable runtimes [2]. The simplified CMC model used here falls into the class of table lookup turbulent combustion models where the chemical kinetics are solved offline over a range of conditions and stored in a table that is accessed by the CFD code. Most table lookup models are based on the laminar 1-D flamelet equations, which assume the small scale turbulence does not affect the reaction rates, only the large scale turbulence has an effect on the reaction rates. The CMC model is derived from first principles to account for the effects of small scale turbulence on the reaction rates, as well as the effects of the large scale mixing, making it more versatile than other models. This is accomplished by conditioning the scalars with the reaction progress variable. By conditioning the scalars and accounting for the small scale mixing, the effects of turbulent fluctuations of the temperature on the reaction rates are more accurately modeled. The scalar dissipation is used to account for the effects of the small scale mixing on the reaction rates. The original premixed CMC model used a constant value of scalar dissipation, here the scalar dissipation is conditioned by the reaction progress variable. The steady RANS 3-D version of the open source CFD code OpenFOAM is used. Velocity, temperature and species are compared to the experimental data. Once validated, this CFD turbulent combustion model will have great utility for designing lean premixed gas turbine combustors.

A Novel Turbulent Aggregation Device for Flue Gas

2014 ◽  
Vol 955-959 ◽  
pp. 2425-2429 ◽  
Author(s):  
Yun Fei Li ◽  
Jian Guo Yang ◽  
Yan Yan Wang ◽  
Xiao Guo Wang
Keyword(s):  
Size Distribution ◽  
Flue Gas ◽  
Large Scale ◽  
Balance Model ◽  
Small Scale ◽  
Multiphase Model ◽  
Specific Performance ◽  
Particles Size Distribution ◽  
Scale Turbulence ◽  
Eulerian Multiphase Model

The purpose of this study is to construct a turbulent aggregation device which has specific performance for fine particle aggregation in flue gas. The device consists of two cylindrical pipes and an array of vanes. The pipes extending fully and normal to the gas stream induce large scale turbulence in the form of vortices, while the vanes downstream a certain distance from the pipes induce small one. The process of turbulent aggregation was numerically simulated by coupling the Eulerian multiphase model and population balance model together with a proposed aggregation kernel function taking the size and inertia of particles into account, and based on data of particles’ size distribution measured from the flue of one power plant. The results show that the large scale turbulence generated by pipes favours the aggregation of smaller particles (smaller than 1μm) notably, while the small scale turbulence benefits the aggregation of bigger particles (larger than 1μm) notably and enhances the uniformity of particle size distribution among different particle groups.

scholarly journals An overview of the effect of large-scale inhomogeneities on small-scale turbulence

2002 ◽  
Vol 14 (7) ◽  
pp. 2475 ◽  
Author(s):  
L. Danaila ◽  
F. Anselmet ◽  
R. A. Antonia
Keyword(s):  
Large Scale ◽  
Small Scale ◽  
Scale Turbulence

scholarly journals Effect of Turbulence on Emerging Magnetic Flux Tubes in the Convection Zone

1990 ◽  
Vol 142 ◽  
pp. 60-61
Author(s):  
Sydney D'Silva ◽  
Arnab Rai Choudhuri
Keyword(s):  
Magnetic Flux ◽  
Coriolis Force ◽  
Large Scale ◽  
Convection Zone ◽  
Rotation Axis ◽  
Giant Cells ◽  
Magnetic Flux Tube ◽  
Small Scale ◽  
Flux Tubes ◽  
Scale Turbulence

Working under the hypothesis that magnetic flux in the sun is generated at the bottom of the convection zone, Choudhuri and Gilman (1987; Astrophys. J. 316, 788) found that a magnetic flux tube symmetric around the rotation axis, when released at the bottom of the convection zone, gets deflected by the Coriolis force and tends to move parallel to the rotation axis as it rises in the convection zone. As a result, all the flux emerges at rather high latitudes and the flux observed at the typical sunspot latitudes remains unexplained. Choudhuri(1989; Solar Physics, in press) finds that non-axisymmetric perturbations too cannot subdue the Coriolis force. In this paper, we no longer treat the convection zone to be passive as in the previous papers, but we consider the role of turbulence in the convection zone in inhibiting the Coriolis force. The interaction of the flux tubes with the turbulence is treated in a phenomenological way as follows: (1) Large scale turbulence on the scale of giant cells can physically drag the tubes outwards, thus pulling the flux towards lower latitudes by dominating over the Coriolis force. (2) Small scale turbulence of the size of the tubes can exchange angular momentum with the tube, thus suppressing the growth of the Coriolis force and making the tubes emerge at lower latitudes. Numerical simulations show that the giant cells can drag the tubes and make them emerge at lower latitudes only if the velocities within the giant cells are unrealistically large or if the radii of the flux tubes are as small as 10 km. However, small scale turbulence can successfully suppress the growth of the Coriolis force if the tubes have radii smaller than about 300 km which may not be unreasonable. Such flux tubes can then emerge at low latitudes where sunspots are seen.

A new model of shoaling and breaking waves. Part 2. Run-up and two-dimensional waves

2019 ◽  
Vol 867 ◽  
pp. 146-194 ◽  
Author(s):  
G. L. Richard ◽  
A. Duran ◽  
B. Fabrèges
Keyword(s):  
Large Scale ◽  
Turbulent Viscosity ◽  
Breaking Waves ◽  
Small Scale ◽  
Two Dimensional ◽  
Numerical Resolution ◽  
Wide Range ◽  
Scale Turbulence ◽  
Run Up ◽  
Averaged Model

We derive a two-dimensional depth-averaged model for coastal waves with both dispersive and dissipative effects. A tensor quantity called enstrophy models the subdepth large-scale turbulence, including its anisotropic character, and is a source of vorticity of the average flow. The small-scale turbulence is modelled through a turbulent-viscosity hypothesis. This fully nonlinear model has equivalent dispersive properties to the Green–Naghdi equations and is treated, both for the optimization of these properties and for the numerical resolution, with the same techniques which are used for the Green–Naghdi system. The model equations are solved with a discontinuous Galerkin discretization based on a decoupling between the hyperbolic and non-hydrostatic parts of the system. The predictions of the model are compared to experimental data in a wide range of physical conditions. Simulations were run in one-dimensional and two-dimensional cases, including run-up and run-down on beaches, non-trivial topographies, wave trains over a bar or propagation around an island or a reef. A very good agreement is reached in every cases, validating the predictive empirical laws for the parameters of the model. These comparisons confirm the efficiency of the present strategy, highlighting the enstrophy as a robust and reliable tool to describe wave breaking even in a two-dimensional context. Compared with existing depth-averaged models, this approach is numerically robust and adds more physical effects without significant increase in numerical complexity.

scholarly journals Magnetospheric Processes Possibly Related to the Origin of Cosmic Rays

1981 ◽  
Vol 94 ◽  
pp. 373-391
Author(s):  
Gerhard Haerendel
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Small Scale ◽  
Shear Stresses ◽  
Acceleration Process ◽  
Dayside Magnetopause ◽  
Field Lines ◽  
The Magnetic Field ◽  
Auroral Particles

Two processes are discussed which violate the frozen-in condition in a highly conducting plasma, reconnection and the auroral acceleration process. The first applies to situations in which . It plays an important role in the interaction of the solar wind with the Earth's magnetic field and controls energy input into as well as energetic particle release from the magnetosphere. Detailed in situ studies of the process on the dayside magnetopause reveal its transient and small-scale nature. The auroral acceleration process occurs in the low magnetosphere (β « 1) and accompanies sudden releases of magnetic shear stresses which exist in large-scale magnetospheric-ionospheric current circuits. The process is interpreted as a kind of breaking. The movements of the magnetospheric plasma which lead to a relief of the magnetic tensions occur in thin sheets and are decoupled along the magnetic field lines by parallel electric potential drops. It is this voltage that accelerates the primary auroral particles. The visible arcs are then traces of the magnetic breaking process at several 1000 km altitude.

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