Nonlinear interactions in turbulence with strong irrotational straining

1997 ◽  
Vol 337 ◽  
pp. 333-364 ◽  
Author(s):  
N.K.-R. KEVLAHAN ◽  
J.C.R. HUNT
Keyword(s):  
Large Scale ◽  
Order Term ◽  
Initial Energy ◽  
Perturbation Series ◽  
Small Scale ◽  
Bluff Bodies ◽  
Leading Order ◽  
Viscous Effects ◽  
First Case ◽  
Maximum Amplification

The rate of growth of the nonlinear terms in the vorticity equation are analysed for a turbulent flow with r.m.s. velocity u0 and integral length scale L subjected to a strong uniform irrotational plane strain S, where (u0/L)/S=ε[Lt ]1. The rapid distortion theory (RDT) solution is the zeroth-order term of the perturbation series solution in terms of ε. We use the asymptotic form of the convolution integrals for the leading-order nonlinear terms when β= exp(−St)[Lt ]1 to determine at what time t and beyond what wavenumber k (normalized on L) the perturbation series in ε fails, and hence derive the following conditions for the validity of RDT in these flows. (a) The magnitude of the nonlinear terms of order ε depends sensitively on the amplitude of eddies with large length scales in the direction x2 of negative strain. (b) If the integral of the velocity component u2 is zero the leading-order nonlinear terms increase and decrease in the same way as the linear terms, even those that decrease exponentially. In this case RDT calculations of vorticity spectra become invalid at a time tNL∼L/u0k−3 independent of ε and the power law of the initial energy spectrum, but the calculation of the r.m.s. velocity components by RDT remains accurate until t= TNL∼L/u0, when the maximum amplification of r.m.s. vorticity is ω/S∼εexp(ε−1)[Gt ]1. (c) If this special condition does not apply, the leading-order nonlinear terms increase faster than the linear terms by a factor O(β−1). RDT calculations of the vorticity spectrum then fail at a shorter time tNL∼(1/S) ln(ε−1k−3); in this case TNL∼(1/S) ln(ε−1) and the maximum amplification of r.m.s. vorticity is ω/S∼1. (d) Viscous effects dominate when t[Gt ](1/S) ln(k−1(Re/ε)1/2). In the first case RDT fails immediately in this range, while in the second case RDT usually fails before viscosity becomes important. The general analytical result (a) is confirmed by numerical evaluation of the integrals for a particular form of eddy, while (a), (b), (c) are explained physically by considering the deformation of differently oriented vortex rings. The results are compared with small-scale turbulence approaching bluff bodies where ε[Lt ]1 and β[Lt ] 1.These results also explain dynamically why the intermediate eigenvector of the strain S aligns with the vorticity vector, why the greatest increase in enstrophy production occurs in regions where S has a positive intermediate eigenvalue; and why large-scale strain S of a small-scale vorticity can amplify the small-scale strain rates to a level greater than S – one of the essential characteristics of high-Reynolds-number turbulence.

scholarly journals Kicked Burgers turbulence

2000 ◽  
Vol 416 ◽  
pp. 239-267 ◽  
Author(s):  
J. BEC ◽  
U. FRISCH ◽  
K. KHANIN
Keyword(s):  
Numerical Simulations ◽  
Power Law ◽  
Large Scale ◽  
Order Term ◽  
Inviscid Limit ◽  
Order Structure ◽  
Legendre Transform ◽  
Leading Order ◽  
Space And Time ◽  
Burgers Turbulence

Burgers turbulence subject to a force f(x, t) = [sum ]jfj(x)δ(t − tj), where tj are 'kicking times' and the 'impulses' fj(x) have arbitrary space dependence, combines features of the purely decaying and the continuously forced cases. With large-scale forcing this ‘kicked’ Burgers turbulence presents many of the regimes proposed by E et al. (1997) for the case of random white-noise-in-time forcing. It is also amenable to efficient numerical simulations in the inviscid limit, using a modification of the fast Legendre transform method developed for decaying Burgers turbulence by Noullez & Vergassola (1994). For the kicked case, concepts such as ‘minimizers’ and ‘main shock’, which play crucial roles in recent developments for forced Burgers turbulence, become elementary since everything can be constructed from simple two-dimensional area-preserving Euler–Lagrange maps.The main results are for the case of identical deterministic kicks which are periodic and analytic in space and are applied periodically in time. When the space integrals of the initial velocity and of the impulses vanish, it is proved and illustrated numerically that a space- and time-periodic solution is achieved exponentially fast. In this regime, probabilities can be defined by averaging over space and time periods. The probability densities of large negative velocity gradients and of (not-too-large) negative velocity increments follow the power law with −7/2 exponent proposed by E et al. (1997) in the inviscid limit, whose existence is still controversial in the case of white-in-time forcing. This power law, which is seen very clearly in the numerical simulations, is the signature of nascent shocks (preshocks) and holds only when at least one new shock is born between successive kicks.It is shown that the third-order structure function over a spatial separation Δx is analytic in Δx although the velocity field is generally only piecewise analytic (i.e. between shocks). Structure functions of order p ≠ 3 are non-analytic at Δx = 0. For even p there is a leading-order term proportional to [mid ]Δx[mid ] and for odd p > 3 the leading-order term ∝Δx has a non-analytic correction ∝Δx[mid ]Δx[mid ] stemming from shock mergers.

Enabling Multi-Robot Cooperative Additive Manufacturing: Centralized vs. Decentralized Approaches

2021 ◽  
Author(s):  
Saivipulteja Elagandula ◽  
Laxmi Poudel ◽  
Wenchao Zhou ◽  
Zhenghui Sha
Keyword(s):  
3D Printing ◽  
Large Scale ◽  
Small Scale ◽  
Scale Problem ◽  
Problem Case ◽  
Large Scale Problem ◽  
First Case ◽  
Novel Approach ◽  
Multi Robot

Abstract This paper presents a decentralized approach based on a simple set of rules to carry out multi-robot cooperative 3D printing. Cooperative 3D printing is a novel approach to 3D printing that uses multiple mobile 3D printing robots to print a large part by dividing and assigning the part to multiple robots in parallel using the concept of chunk-based printing. The results obtained using the decentralized approach are then compared with those obtained from the centralized approach. Two case studies were performed to evaluate the performance of both approaches using makespan as the evaluation criterion. The first case is a small-scale problem with four printing robots and 20 chunks, whereas the second case study is a large-scale problem with ten printing robots and 200 chunks. The result shows that the centralized approach provides a better solution compared to the decentralized approach in both cases in terms of makespan. However, the gap between the solutions seems to shrink with the scale of the problem. While further study is required to verify this conclusion, the decrease in this gap indicates that the decentralized approach might compare favorably over the centralized approach for a large-scale problem in manufacturing using multiple mobile 3D printing robots. Additionally, the runtime for the large-scale problem (Case II) increases by 27-fold compared to the small-scale problem (Case I) for the centralized approach, whereas it only increased by less than 2-fold for the decentralized approach.

Control of Large-Scale Heat Transport by Small-Scale Mixing

2006 ◽  
Vol 36 (10) ◽  
pp. 1877-1894 ◽  
Author(s):  
Paola Cessi ◽  
W. R. Young ◽  
Jeff A. Polton
Keyword(s):  
Heat Transport ◽  
Mixed Layer ◽  
Large Scale ◽  
Scaling Laws ◽  
Mechanical Energy ◽  
Small Scale ◽  
Thermocline Depth ◽  
Leading Order ◽  
Diapycnal Diffusivity ◽  
The Mean

Abstract The equilibrium of an idealized flow driven at the surface by wind stress and rapid relaxation to nonuniform buoyancy is analyzed in terms of entropy production, mechanical energy balance, and heat transport. The flow is rapidly rotating, and dissipation is provided by bottom drag. Diabatic forcing is transmitted from the surface by isotropic diffusion of buoyancy. The domain is periodic so that zonal averaging provides a useful decomposition of the flow into mean and eddy components. The statistical equilibrium is characterized by quantities such as the lateral buoyancy flux and the thermocline depth; here, scaling laws are proposed for these quantities in terms of the external parameters. The scaling theory predicts relations between heat transport, thermocline depth, bottom drag, and diapycnal diffusivity, which are confirmed by numerical simulations. The authors find that the depth of the thermocline is independent of the diapycnal mixing to leading order, but depends on the bottom drag. This dependence arises because the mean stratification is due to a balance between the large-scale wind-driven heat transport and the heat transport due to baroclinic eddies. The eddies equilibrate at an amplitude that depends to leading order on the bottom drag. The net poleward heat transport is a residual between the mean and eddy heat transports. The size of this residual is determined by the details of the diapycnal diffusivity. If the diffusivity is uniform (as in laboratory experiments) then the heat transport is linearly proportional to the diffusivity. If a mixed layer is incorporated by greatly increasing the diffusivity in a thin surface layer then the net heat transport is dominated by the model mixed layer.

scholarly journals Small-scale turbulence characteristics of two-dimensional bluff body wakes

2002 ◽  
Vol 459 ◽  
pp. 67-92 ◽  
Author(s):  
R. A. ANTONIA ◽  
T. ZHOU ◽  
G. P. ROMANO
Keyword(s):  
Porous Body ◽  
Large Scale ◽  
Bluff Body ◽  
Inertial Range ◽  
Small Scale ◽  
Bluff Bodies ◽  
Two Dimensional ◽  
The Difference ◽  
Scale Turbulence ◽  
Made In

Measurements have been made in nominally two-dimensional turbulent wakes generated by five different bluff bodies. Each wake has a different level of large-scale organization which is reflected in different amounts of large-scale anisotropy. Structure functions of streamwise (u) and lateral (v) velocity fluctuations at approximately the same value of Rλ, the Taylor microscale Reynolds number, indicate that inertial-range scales are significantly affected by the large-scale anisotropy. The effect is greater on v than u and more pronounced for the porous-body wakes than the solid-body wakes. In particular, ‘relative’ values of the scaling (or power-law) exponents indicate that the magnitude of the transverse exponents can exceed that of the longitudinal ones in the porous-body wakes. This is supported by the inertial-range behaviour of the spectra of u and v. The difference between the transverse and longitudinal exponents appears to depend on the large-scale anisotropy of the flow, as measured by the ratio of the variances of v and u and ratio of the integral length scales of v and u. The spanwise vorticity spectra are much less affected by the anisotropy than the spectra of u and v.

scholarly journals An Investigation of Aerodynamic Effects of Body Morphing for Passenger Cars in Close-Proximity

Fluids ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 64
Author(s):  
Geoffrey Le Good ◽  
Max Resnick ◽  
Peter Boardman ◽  
Brian Clough
Keyword(s):  
Large Scale ◽  
Aerodynamic Drag ◽  
Autonomous Vehicle ◽  
Small Scale ◽  
Bluff Bodies ◽  
Passenger Cars ◽  
Current Trends ◽  
Close Proximity ◽  
Potential Energy Saving ◽  
The Individual

The potential energy-saving benefit for vehicles when travelling in a ‘platoon’ formation results from the reduction in total aerodynamic drag which may result from the interaction of bluff bodies in close-proximity. Early investigations of platooning, prompted by problems of congestion, had shown the potential for drag reduction but was not pursued. More recently, technologies developed for connected-autonomous vehicle control have provided a renewed interest in platooning particularly within the commercial vehicle industry. To date, most aerodynamics-based considerations of platooning have been conducted to assess the sensitivity of drag-saving to vehicle spacing and were based on formations of identically shaped constituents. In this study, the interest was the sensitivity of drag-saving to the shape of the individual platoon constituents. A new reference car, the Resnick model, was specially designed to include front and rear-end add-on sections to make distinct changes in profile form and simulate large-scale body morphing. The results of wind tunnel tests on small-scale models suggested that current trends in low-drag styling may not provide the ideal shape for platoon constituent members and that optimised forms are likely to be dependent upon position in the platoon.

scholarly journals Opportunities from low-resolution modelling of river morphology in remote parts of the world

2013 ◽  
Vol 1 (1) ◽  
pp. 407-435
Author(s):  
M. Nones ◽  
M. Guerrero
Keyword(s):  
Cross Sections ◽  
Large Scale ◽  
Initial Conditions ◽  
Large Rivers ◽  
Small Scale ◽  
First Case ◽  
The World ◽  
High Level ◽  
D Model

Abstract. The study of rivers morphodynamics requires modelling of a variety of processes ranging from the typical small scale of fluid mechanics (e.g. flow turbulence dissipation) to the large scale of landscape evolution (e.g. fan deposition). However, simplifications inherent in the long-term modelling of large rivers derive from limited computational resource and the high level of processes detail (i.e. spatial and temporal resolution). These modelling results depend on processes parameterization and calibration over detailed field data (e.g. initial morphology). Thus, in these cases, simplified tools are attractive. Here, a simplified 1-D code is used for the modelling of very large rivers. A synthetic description of the variation of cross-sections shape is implemented on the basis of satellite images, typically available also in remote parts of the world. The model's flexibility is highlighted here, by presenting two applications. In the first case the model is used for analysing the long-term evolution of the Lower Zambezi (Africa) related to the construction of two reservoirs for hydropower exploitation; while, in the second case, the same code is applied for studying the evolution of the Middle and Lower Parana (Argentina) in light of climate variability. In both cases, having only basic data for boundary and initial conditions, the 1-D model provides results that are in agreement with past studies and that may be used to assist sediment management at watershed scale or at boundaries of more detailed modelling.

scholarly journals Opportunities from low-resolution modelling of river morphology in remote parts of the world

2014 ◽  
Vol 2 (1) ◽  
pp. 9-19 ◽  
Author(s):  
M. Nones ◽  
M. Guerrero ◽  
P. Ronco
Keyword(s):  
Cross Sections ◽  
Large Scale ◽  
Initial Conditions ◽  
Large Rivers ◽  
Small Scale ◽  
First Case ◽  
The World ◽  
High Level ◽  
Computational Resources

Abstract. River morphodynamics are the result of a variety of processes, ranging from the typical small-scale of fluid mechanics (e.g. flow turbulence dissipation) to the large-scale of landscape evolution (e.g. fan deposition). However, problems inherent in the long-term modelling of large rivers derive from limited computational resources and the high level of process detail (i.e. spatial and temporal resolution). These modelling results depend on processes parameterization and calibrations based on detailed field data (e.g. initial morphology). Thus, for these cases, simplified tools are attractive. In this paper, a simplified 1-D approach is presented that is suited for modelling very large rivers. A synthetic description of the variations of cross-sections shapes is implemented on the basis of satellite images, typically also available for remote parts of the world. The model's flexibility is highlighted here by presenting two applications. In the first case, the model is used for analysing the long-term evolution of the lower Zambezi River (Africa) as it relates to the construction of two reservoirs for hydropower exploitation. In the second case, the same model is applied to study the evolution of the middle and lower Paraná River (Argentina), particularly in the context of climate variability. In both cases, having only basic data for boundary and initial conditions, the 1-D model provides results that are in agreement with past studies and therefore shows potential to be used to assist sediment management at the watershed scale or at boundaries of more detailed models.

Small-Scale Science to Large-Scale Profession

2000 ◽  
Vol 45 (4) ◽  
pp. 396-398
Author(s):  
Roger Smith
Keyword(s):  
Large Scale ◽  
Small Scale

Development of Physics Learning Module Based on Guided Inquiry with Light Wave Material in Class XI of Senior High School

2020 ◽  
Vol 1 (1) ◽  
pp. 1-10
Author(s):  
Evi Rahmawati ◽  
Irnin Agustina Dwi Astuti ◽  
N Nurhayati
Keyword(s):  
Large Scale ◽  
Learning Strategy ◽  
Student Response ◽  
Average Score ◽  
Small Scale ◽  
Design Development ◽  
Teacher Response ◽  
Student Responses ◽  
Analysis Design ◽  
Scientific Skills

IPA Integrated is a place for students to study themselves and the surrounding environment applied in daily life. Integrated IPA Learning provides a direct experience to students through the use and development of scientific skills and attitudes. The importance of integrated IPA requires to pack learning well, integrated IPA integration with the preparation of modules combined with learning strategy can maximize the learning process in school. In SMP 209 Jakarta, the value of the integrated IPA is obtained from 34 students there are 10 students completed and 24 students are not complete because they get the value below the KKM of 68. This research is a development study with the development model of ADDIE (Analysis, Design, Development, Implementation, and Evaluation). The use of KPS-based integrated IPA modules (Science Process sSkills) on the theme of rainbow phenomenon obtained by media expert validation results with an average score of 84.38%, average material expert 82.18%, average linguist 75.37%. So the average of all aspects obtained by 80.55% is worth using and tested to students. The results of the teacher response obtained 88.69% value with excellent criteria. Student responses on a small scale acquired an average score of 85.19% with highly agreed criteria and on the large-scale student response gained a yield of 86.44% with very agreed criteria. So the module can be concluded receiving a good response by the teacher and students.

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