scholarly journals Entropy and Turbulence Structure

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 11
Author(s):  
T.-W. Lee ◽  
J. E. Park
Keyword(s):  
Turbulent Flows ◽  
Maximum Entropy Principle ◽  
Reynolds Numbers ◽  
Turbulence Energy ◽  
Turbulence Structure ◽  
Reynolds Stresses ◽  
Dissipation Structure ◽  
Stress Components ◽  
Entropy Principle ◽  
Good Agreement

Some new perspectives are offered on the spectral and spatial structure of turbulent flows, in the context of conservation principles and entropy. In recent works, we have shown that the turbulence energy spectra are derivable from the maximum entropy principle, with good agreement with experimental data across the entire wavenumber range. Dissipation can also be attributed to the Reynolds number effect in wall-bounded turbulent flows. Within the global energy and dissipation constraints, the gradients (d/dy+ or d2/dy+2) of the Reynolds stress components neatly fold onto respective curves, so that function prescriptions (dissipation structure functions) can serve as a template to expand to other Reynolds numbers. The Reynolds stresses are fairly well prescribed by the current scaling and dynamical formalism so that the origins of the turbulence structure can be understood and quantified from the entropy perspective.

scholarly journals Asymmetrical Order in Wall-Bounded Turbulent Flows

Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 329
Author(s):  
T.-W. Lee
Keyword(s):  
Turbulent Flows ◽  
Outer Boundary ◽  
Plate Boundary ◽  
Turbulence Structure ◽  
Boundary Layer Flows ◽  
Self Similarity ◽  
Transport Dynamics ◽  
Dissipation Structure ◽  
Stress Components ◽  
Turbulent Wall

Scaling of turbulent wall-bounded flows is revealed in the gradient structures, for each of the Reynolds stress components. Within the “dissipation” structure, an asymmetrical order exists, which we can deploy to unify the scaling and transport dynamics within and across these flows. There are subtle differences in the outer boundary conditions between channel and flat-plate boundary-layer flows, which modify the turbulence structure far from the wall. The self-similarity exhibited in the gradient space and corresponding transport dynamics establish capabilities and encompassing knowledge of wall-bounded turbulent flows.

A Continuous Prediction Method for Fully Developed Laminar, Transitional, and Turbulent Flows in Pipes

1975 ◽  
Vol 42 (1) ◽  
pp. 51-54 ◽  
Author(s):  
N. W. Wilson ◽  
R. S. Azad
Keyword(s):  
Turbulent Flows ◽  
Flow Characteristics ◽  
Prediction Method ◽  
Reynolds Numbers ◽  
Mean Flow ◽  
Number Range ◽  
Circular Pipes ◽  
The Mean ◽  
Single Set ◽  
Good Agreement

A single set of equations is developed to predict the mean flow characteristics in long circular pipes operating at laminar, transitional, and turbulent Reynolds numbers. Generally good agreement is obtained with available data in the Reynolds number range 100 < Re < 500,000.

scholarly journals Energy and Enstrophy Spectra of Geostrophic Turbulent Flows Derived from a Maximum Entropy Principle

2009 ◽  
Vol 66 (8) ◽  
pp. 2216-2236 ◽  
Author(s):  
W. T. M. Verkley ◽  
Peter Lynch
Keyword(s):  
Maximum Entropy ◽  
Turbulent Flows ◽  
Good Description ◽  
Maximum Entropy Principle ◽  
Relative Vorticity ◽  
Decay Rates ◽  
Entropy Principle ◽  
Geostrophic Turbulence ◽  
Reasonable Description ◽  
Inviscid Case

Abstract The principle of maximum entropy is used to obtain energy and enstrophy spectra as well as average relative vorticity fields in the context of geostrophic turbulence on a rotating sphere. In the unforced-undamped (inviscid) case, the maximization of entropy is constrained by the constant energy and enstrophy of the system, leading to the familiar results of absolute statistical equilibrium. In the damped (freely decaying) and forced-damped case, the maximization of entropy is constrained by either the decay rates of energy and enstrophy or by the energy and enstrophy in combination with their decay rates. Integrations with a numerical spectral model are used to check the theoretical results for the different cases. Maximizing the entropy, constrained by the energy and enstrophy, gives a good description of the energy and enstrophy spectra in the inviscid case, in accordance with known results. In the freely decaying case, not too long after the damping has set in, good descriptions of the energy and enstrophy spectra are obtained if the entropy is maximized, constrained by the energy and enstrophy in combination with their decay rates. Maximizing the entropy, constrained by the energy and enstrophy in combination with their (zero) decay rates, gives a reasonable description of the spectra in the forced-damped case, although discrepancies remain here.

Heat Transfer in Two-Dimensional Turbulent Confined Flows

1972 ◽  
Vol 186 (1) ◽  
pp. 625-633
Author(s):  
A. P. Hatton ◽  
N. H. Woolley
Keyword(s):  
Prediction Method ◽  
Eddy Diffusivity ◽  
Reynolds Numbers ◽  
Turbulence Energy ◽  
Two Dimensional ◽  
Narrow Angle ◽  
Before And After ◽  
Dimensional Equation ◽  
Confined Flows ◽  
Good Agreement

Measurements of displacement and momentum thickness, friction factor and Stanton number were made in a narrow angle diverging duct consisting of two plane walls, width 0·82 m. The height of the duct varied from 0·051 to 0·152 m over a length of 3·94 m. Reynolds numbers ranged from 8·7 × 104 to 20·7 × 104. The results are compared with a prediction method using a numerical solution of the two-dimensional equation of motion and energy. An eddy diffusivity hypothesis was used, based on the turbulence energy equation and an empirical length scale distribution. Good agreement was obtained between the theoretical and experimental results, both before and after the boundary layers interfered, and with previously reported experiments in a parallel duct. It was necessary to change the value of one of the constants in the analysis for each geometry.

scholarly journals Kazantsev model in non-helical 2.5-dimensional flows

2016 ◽  
Vol 806 ◽  
pp. 627-648 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Three Dimensional ◽  
Analytical Calculation ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Control Parameters ◽  
Governing Equations ◽  
Field Correlation ◽  
Good Agreement

We study the dynamo instability for a Kazantsev–Kraichnan flow with three velocity components that depend only on two dimensions $\boldsymbol{u}=(u(x,y,t),v(x,y,t),w(x,y,t))$ often referred to as 2.5-dimensional (2.5-D) flow. Within the Kazantsev–Kraichnan framework we derive the governing equations for the second-order magnetic field correlation function and examine the growth rate of the dynamo instability as a function of the control parameters of the system. In particular we investigate the dynamo behaviour for large magnetic Reynolds numbers $Rm$ and flows close to being two-dimensional and show that these two limiting procedures do not commute. The energy spectra of the unstable modes are derived analytically and lead to power-law behaviour that differs from the three-dimensional and two-dimensional cases. The results of our analytical calculation are compared with the results of numerical simulations of dynamos driven by prescribed fluctuating flows as well as freely evolving turbulent flows, showing good agreement.

Computation of Three-Dimensional Turbulent Flows in a Pipe Junction with Reference to Engine Inlet Manifolds

1992 ◽  
Vol 206 (4) ◽  
pp. 285-296 ◽  
Author(s):  
H Fu ◽  
M J Tindal ◽  
A P Watkins ◽  
M Yianneskis
Keyword(s):  
Turbulent Flows ◽  
Combustion Engine ◽  
Laser Doppler Anemometry ◽  
Numerical Study ◽  
Three Dimensional ◽  
Turbulence Energy ◽  
Numerical Predictions ◽  
Split Ratio ◽  
Inlet Manifold ◽  
Good Agreement

This paper presents a numerical study of the flows in an internal combustion engine inlet manifold. The three-dimensional turbulent flows through a single branched manifold were simulated using the κ-ɛ model of turbulence. The flow structure was characterized in detail and the effects of the flow split ratio and inlet flowrate were investigated. Detailed measurements were performed to validate the numerical predictions, using laser Doppler anemometry. Good agreement was obtained between the predicted and the measured mean velocities. The predicted levels of turbulence energy are in qualitative agreement with the measurements.

An Experimental and Theoretical Study of Heat Transfer in Vertical Tube Flows

1978 ◽  
Vol 100 (1) ◽  
pp. 86-91 ◽  
Author(s):  
R. Greif
Keyword(s):  
Heat Transfer ◽  
Turbulent Flows ◽  
Theoretical Study ◽  
Numerical Solutions ◽  
Reynolds Numbers ◽  
Vertical Tube ◽  
Laminar Flows ◽  
Radial Temperature ◽  
Rayleigh Numbers ◽  
Good Agreement

An experimental and theoretical study was carried out for the heat transfer in laminar and turbulent tube flows with air and argon. Radial temperature profiles were measured at a location 108 tube diameters from the inlet of the vertical, electrically heated test section. The temperature of the tube wall was also measured. The experimental data were in good agreement with the results obtained from numerical solutions of the conservation equations and from simplified, fully developed solutions. For turbulent flows the Reynolds numbers varied from 10,000 to 19,500; for laminar flows the Reynolds numbers varied from 1850 to 2100 while the Rayleigh numbers varied from 70 to 80.

Maximum-entropy closure for a Galerkin model of an incompressible periodic wake

2012 ◽  
Vol 700 ◽  
pp. 187-213 ◽  
Author(s):  
Bernd R. Noack ◽  
Robert K. Niven
Keyword(s):  
Maximum Entropy ◽  
Energy Levels ◽  
Maximum Entropy Principle ◽  
Mean Amplitude ◽  
Navier Stokes ◽  
Cylinder Wake ◽  
Balance Equations ◽  
Side Constraints ◽  
Entropy Principle ◽  
Good Agreement

AbstractA statistical closure is proposed for a Galerkin model of an incompressible periodic cylinder wake. This closure employs Jaynes’ maximum entropy principle to infer the probability distribution for mode amplitudes using exact statistical balance equations as side constraints. The analysis predicts mean amplitude values and modal energy levels in good agreement with direct Navier–Stokes simulation. In addition, it provides an analytical equation for the modal energy distribution.

scholarly journals Experimental investigation of turbulent flows through a boulder array placed on a permeable bed

2020 ◽  
Vol 20 (4) ◽  
pp. 1281-1293
Author(s):  
Hui Cao ◽  
Chen Ye ◽  
Xu-Feng Yan ◽  
Xing-Nian Liu ◽  
Xie-Kang Wang
Keyword(s):  
Turbulent Flows ◽  
Turbulence Intensity ◽  
Diffusion Processes ◽  
Quadrant Analysis ◽  
Turbulence Structure ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Flume Experiments ◽  
Budget Analysis ◽  
Boulder Array

Abstract Glass beads were used to model permeable beds and boulders (simulated by plastic spherical balls) placed on the centre section of the bed. Flume experiments were conducted to investigate the hydrodynamics through a boulder array over impermeable and permeable beds (i.e. IMPB and PB). For background reference, hydrodynamics investigation was made over smooth beds (SB) with the boulder array. Through measuring the instantaneous velocity field, the major flow characteristics such as mean flow velocity, turbulence intensity, turbulent kinetic energy (TKE) and instantaneous Reynolds stresses (through quadrant analysis) were presented. The results show that the increase in bed permeability through decreasing the exposure height of boulders has little impact on the magnitude of streamwise velocity, but tends to decrease the near-bed velocity gradient, thus affecting the bed shear-stress. For turbulence, similar to the previous studies, the bed permeability is identified to enable a downward shift of the peak of turbulence intensity. The TKE budget analysis shows that bed permeability tends to inhibit the transport and diffusion processes of TKE generation. Finally, the quadrant analysis of turbulence structure clearly shows that the ejections (Q2) and sweeps (Q4) with and without the boulder array are dominated by turbulence structure of different scales.

The structure of a turbulent shear layer bounding a separation region

1987 ◽  
Vol 179 ◽  
pp. 439-468 ◽  
Author(s):  
I. P. Castro ◽  
A. Haque
Keyword(s):  
Shear Layer ◽  
Turbulent Flows ◽  
Large Scale ◽  
Turbulent Shear ◽  
Turbulence Structure ◽  
Similar Data ◽  
Reynolds Stresses ◽  
Plate Height ◽  
Separated Shear Layer ◽  
Wide Range

Detailed measurements within the separated shear layer behind a flat plate normal to an airflow are reported. A long, central splitter plate in the wake prevented vortex shedding and led to an extensive region of separated flow with mean reattachment some ten plate heights downstream. The Reynolds number based on plate height was in excess of 2 × 1044.Extensive use of pulsed-wire anemometry allowed measurements of all the Reynolds stresses throughout the flow, along with some velocity autocorrelations and integral timescale data. The latter help to substantiate the results of other workers obtained in separated flows of related geometry, particularly in the identification of a very low-frequency motion with a timescale much longer than that associated with the large eddies in the shear layer. Wall-skin-friction measurements are consistent with the few similar data previously published and indicate that the thin boundary layer developing beneath the separated region has some ‘laminar-like’ features.The Reynolds-stress measurements demonstrate that the turbulence structure of the separated shear layer differs from that of a plane mixing layer between two streams in a number of ways. In particular, the normal stresses all rise monotonically as reattachment is approached, are always considerably higher than the plane layer values and develop in quite different ways. Flow similarity is not a useful concept. A major conclusion is that any effects of stabilizing streamline curvature are weak compared with the effects of the re-entrainment at the low-velocity edge of the shear layer of turbulent fluid returned around reattachment. It is argued that the general features of the flow are likely to be similar to those that occur in a wide range of complex turbulent flows dominated by a shear layer bounding a large-scale recirculating region.

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