Effects of Aspect Ratio on Higher-Order Moments, Conditional Statistics, TKE Budget and Anisotropy in Narrow Open Channel Flow

2020 ◽  
Author(s):  
Minakshee Mahananda ◽  
Prashanth Reddy Hanmaiahgari ◽  
Ram Balachandar ◽  
Vesselina Roussinova
Keyword(s):  
Aspect Ratio ◽  
Open Channel ◽  
Outer Region ◽  
Higher Order ◽  
Third Order ◽  
Velocity Fluctuations ◽  
The Third ◽  
Aspect Ratios ◽  
Ejections And Sweeps ◽  
Conditional Statistics

The paper investigates the influence of aspect ratio on the higher-order statistics of velocity fluctuations in hydraulically rough narrow OCF. In the experiments, the aspect ratios were varied between 2.5 and 4. Velocities were measured with ADV. The third-order moments were found to be sensitive to the aspect ratio in the outer region. The contributions of all quadrant events are approximately equal in lower aspect ratio flows, whereas ejections and sweeps are the dominant as the aspect ratio increases. The upward transfer of TKE flux increases in the outer layer with increase in aspect ratio. The TKE production and dissipation are found to be dependent on the aspect ratio. The analysis of Reynolds stress AIM reveals that for low aspect ratio flows turbulence tends to attain rod like axisymmetric turbulence only in the intermediate layer whereas for higher aspect ratio, turbulence attains rod like axisymmetric turbulence throughout the depth.

scholarly journals Effect of aspect ratio on higher order moments of velocity fluctuations in hydraulically rough open channel flow

2018 ◽  
Vol 40 ◽  
pp. 05045
Author(s):  
Minakshee Mahananda ◽  
Prashanth Reddy Hanmaiahgari
Keyword(s):  
Aspect Ratio ◽  
Order Statistics ◽  
Channel Flow ◽  
Open Channel ◽  
Outer Region ◽  
Open Channel Flow ◽  
Higher Order ◽  
Higher Order Statistics ◽  
Velocity Fluctuations ◽  
Bed Roughness

The effect of aspect ratio on the higher order statistics of velocity fluctuations in a hydraulically rough turbulent open channel flow is investigated. In this regard, an experiment was conducted in a rough bed narrow open channel flow of aspect ratio equal to three and the instantaneous flow velocities were measured using a Nortek Vectrino+ Acoustic Doppler Velocimeter. To understand the effect of aspect ratio, the results obtained from the present study are compared with the literature data of approximately same Reynolds number and bed roughness in a wide open channel flow for turbulence intensities and higher order statistics of velocity fluctuations. Comparison of turbulence intensities between Narrow OCF and Wide OCF shows occurrence of higher streamwise and vertical turbulence intensities in the outer region of Narrow OCF. The results of third order moments of velocity fluctuations are sensitive to aspect ratio in the outer region.

A SPECTRAL/hp NONLINEAR FINITE ELEMENT ANALYSIS OF HIGHER-ORDER BEAM THEORY WITH VISCOELASTICITY

2012 ◽  
Vol 04 (01) ◽  
pp. 1250010 ◽  
Author(s):  
V. P. VALLALA ◽  
G. S. PAYETTE ◽  
J. N. REDDY
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Virtual Work ◽  
Constitutive Relations ◽  
Beam Theory ◽  
Element Model ◽  
Higher Order ◽  
Time Step ◽  
Third Order ◽  
The Third

In this paper, a finite element model for efficient nonlinear analysis of the mechanical response of viscoelastic beams is presented. The principle of virtual work is utilized in conjunction with the third-order beam theory to develop displacement-based, weak-form Galerkin finite element model for both quasi-static and fully-transient analysis. The displacement field is assumed such that the third-order beam theory admits C0 Lagrange interpolation of all dependent variables and the constitutive equation can be that of an isotropic material. Also, higher-order interpolation functions of spectral/hp type are employed to efficiently eliminate numerical locking. The mechanical properties are considered to be linear viscoelastic while the beam may undergo von Kármán nonlinear geometric deformations. The constitutive equations are modeled using Prony exponential series with general n-parameter Kelvin chain as its mechanical analogy for quasi-static cases and a simple two-element Maxwell model for dynamic cases. The fully discretized finite element equations are obtained by approximating the convolution integrals from the viscous part of the constitutive relations using a trapezoidal rule. A two-point recurrence scheme is developed that uses the approximation of relaxation moduli with Prony series. This necessitates the data storage for only the last time step and not for the entire deformation history.

Propagation of the higher-order Landau modes of electron plasma wave

1977 ◽  
Vol 17 (2) ◽  
pp. 251-257 ◽  
Author(s):  
S. Ikezawa ◽  
Y. Kawai ◽  
T. Hara ◽  
Y. Nakamura ◽  
T. Itoh ◽  
...  
Keyword(s):  
Numerical Calculation ◽  
Reasonable Agreement ◽  
Plasma Frequency ◽  
Electron Plasma ◽  
Higher Order ◽  
Third Order ◽  
Electron Plasma Wave ◽  
The Third ◽  
Dipole Excitation ◽  
Unmagnetized Plasma

Propagation of electrostatic electron waves whose frequency is smaller than the electron plasma frequency in a large unmagnetized plasma is investigated both experimentally and theoretically. When a receiver is close to a transmitter, free-streaming electrons are detected owing to their large capacity for excitation. When the distance between the receiver and the transmitter becomes large, the third-order Landau mode is observed due to its smaller damping than that of free-streaming electrons. Finally, a dip in amplitude of the wave, caused by interference by the higher-order Landau modes, is seen. The results are in reasonable agreement with numerical calculation assuming a dipole excitation for the wave.

scholarly journals Higher order derivatives of bulk modulus of materials at infinite pressure

2016 ◽  
Vol 94 (8) ◽  
pp. 748-750 ◽  
Author(s):  
A. Dwivedi
Keyword(s):  
Bulk Modulus ◽  
Higher Order ◽  
Grüneisen Parameter ◽  
Third Order ◽  
Pressure Derivative ◽  
Basic Principles ◽  
Gruneisen Parameter ◽  
The Third ◽  
The Status ◽  
Derivatives Of

Pressure derivatives of bulk modulus of materials at infinite pressure or extreme compression have been studied using some basic principles of calculus. Expressions for higher order pressure derivatives at infinite pressure are obtained that are found to have the status of identities. A generalized formula is derived for the nth-order pressure derivative of bulk modulus in terms of the third-order Grüneisen parameter at infinite pressure.

scholarly journals CALCULATION OF THE HIGHER-ORDER AXIAL SPHERICAL ABERRATIONS OF A HIGH-APERTURE FOCUSING HOLOGRAPHIC OPTICAL ELEMENT WITH THE CORRECTED THIRD-ORDER SPHERICAL ABERRATION

2018 ◽  
Vol 42 (1) ◽  
pp. 44-53
Author(s):  
Yu. Ts. Batomunkuev ◽  
A. A. Dianova
Keyword(s):  
Spherical Aberration ◽  
Visible Spectrum ◽  
Optical Element ◽  
Higher Order ◽  
Point Sources ◽  
Third Order ◽  
The Third ◽  
Holographic Optical Element ◽  
Seventh Order ◽  
Spectral Ranges

Results of calculating the radius of higher-order spherical aberrations (fifth, seventh and ninth orders) of a high-aperture focusing holographic optical element (HOE) with corrected third-order spherical aberration in the operating spectral range are discussed. As examples, high-aperture axial HOEs with relative apertures close to 1:1 in specified spectral ranges are considered. Coordinates of the point sources of a divergent reference wave and a convergent object wave of the HOE are given. It is shown that when imaging a point source emitting in the 0.250-0.281-µm and 0.500- 0.563-µm spectral ranges, the use of an HOE in the first and second diffraction orders makes it is possible to correct the third-order spherical aberration on two wavelengths and the fifth- and seventh-order spherical aberrations on one wavelength. Note that these visible-spectrum wavelengths are different from the HOE's recording wavelength of 0.532 µm.

scholarly journals Multi-robot formation control based on high-order bilateral consensus

2020 ◽  
Vol 53 (5-6) ◽  
pp. 983-993
Author(s):  
Dejian Liu ◽  
Chengguo Zong ◽  
Detang Wang ◽  
Wenbin Zhao ◽  
Yuehua Wang ◽  
...  
Keyword(s):  
Information Exchange ◽  
Formation Control ◽  
Sufficient Conditions ◽  
Higher Order ◽  
High Order ◽  
Third Order ◽  
Control Protocol ◽  
The Third ◽  
Multi Agent ◽  
Multi Robot

A high-order bilateral consensus robot formation control protocol for multi-agent systems is proposed in this paper. Considering the relationship between the state of the information exchange topology and derivatives, a third-order bilateral consistency protocol is presented and is extended it to a higher order bilateral consensus protocol. First, sufficient conditions for the third-order multi-agent system are given to achieve the bilateral consensus control protocol, and the system’s asymptotical stability is also achieved by adjusting the feedback system gain parameters. Then, by further studying the cohesive relationship between each state variable of the third-order protocol and the gauge transformation, the sufficient conditions of the higher order system are also provided. Finally, by applying the third-order control protocol to the control of multi-robot formation, the general control scheme of robot formation is given and the control of robot formation is successfully achieved.

scholarly journals Smooth Open Channel with Increasing Aspect Ratio: Influence on Secondary Flow

Water ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1872
Author(s):  
Siyu Jing ◽  
Wenjun Yang ◽  
Yue Chen
Keyword(s):  
Aspect Ratio ◽  
Velocity Distribution ◽  
Secondary Flow ◽  
Open Channel ◽  
Maximum Velocity ◽  
Secondary Flows ◽  
Measuring Instruments ◽  
Contour Maps ◽  
Aspect Ratios ◽  
Logarithmic Distribution

A high-resolution particle image velocitmetry system is used to investigate the relationship between secondary flow and aspect ratio in a straight channel. Considering the symmetry of open channel flow, the flow parameters in half of the flume are measured. Since the variation of the aspect ratio has a direct impact on the intensity and structure of secondary flows, this study was conducted in a smooth open channel to study the influence of aspect ratio on the structure and strength of secondary flows with aspect ratio change from 3 to 7.5 under supercritical flow condition. Profiles and contour-maps of time-averaged stream-wise and vertical velocities were acquired using precise measuring instruments. The results show that there are several secondary flow cells in the cross section, and their structure affects the velocity distribution and energy distribution, which makes the velocity distribution deviate from the traditional logarithmic distribution, and the maximum velocity occur below the surface. The flow intensity of secondary flows is different under different aspect ratios. Results show great agreement with classical theory.

Submerged wall jets subjected to injection and suction from the wall

2010 ◽  
Vol 653 ◽  
pp. 57-97 ◽  
Author(s):  
SUBHASISH DEY ◽  
TUSHAR K. NATH ◽  
SUJIT K. BOSE
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Flow ◽  
Normal Stress ◽  
Reynolds Shear Stress ◽  
Flow Characteristics ◽  
Turbulent Energy ◽  
Third Order ◽  
Velocity Fluctuations ◽  
The Third

This paper presents an experimental study on turbulent flow characteristics in submerged plane wall jets subjected to injection (upward seepage) and suction (downward seepage) from the wall. The vertical distributions of time-averaged velocity components, turbulence intensity components and Reynolds shear stress at different horizontal distances are presented. The horizontal distributions of wall shear stress determined from the Reynolds shear stress profiles are also furnished. The flow field exhibits a decay of the jet velocity over a horizontal distance. The wall shear stress and the rate of decay of the jet velocity increase in the presence of injection and decrease with suction. Based on the two-dimensional Reynolds-averaged Navier–Stokes equations of a steady turbulent flow, the velocity and Reynolds shear stress distributions in the fully developed zone subjected to no seepage, injection and suction are theoretically computed. The response of the turbulent flow characteristics to injection and suction is analysed from the point of view of similarity characteristics, growth of the length scale and decay of the velocity and turbulence characteristics scales. The significant observation is that the velocity, Reynolds shear stress and turbulence intensities in the fully developed zone are reasonably similar under both injection and suction on applying the appropriate scaling laws. An analysis of the third-order moments of velocity fluctuations reveals that the inner layer of the jet is associated with the arrival of low-speed fluid streaks causing an effect of retardation. On the other hand, the upper layer of the jet is associated with the arrival of high-speed fluid streaks causing an effect of acceleration. Injection influences the near-wall distributions of the third-order moments by increasing the upward turbulent advection of the streamwise Reynolds normal stress. In contrast, suction influences the near-wall distributions of the third-order moments by increasing the downward turbulent advection of the streamwise Reynolds normal stress. Also, injection and suction change the vertical turbulent flux of the vertical Reynolds normal stress in a similar way. The streamwise turbulent energy flux travels towards the jet origin within the jet layer, while it travels away from the origin within the inner layer of the circulatory flow. The turbulent energy budget suggests that the turbulent and pressure energy diffusions oppose each other, and the turbulent dissipation lags the turbulent production. The quadrant analysis of velocity fluctuations reveals that the inward and outward interactions are the primary contributions to the Reynolds shear stress production in the inner and outer layers of the jet, respectively. However, injection induces feeble ejections in the vicinity of the wall.

scholarly journals 02. Social Pathologies, Reflexive Pathologies, and the Idea of Higher-Order Disorders

2015 ◽  
Author(s):  
Arto Laitinen
Keyword(s):  
Social Reality ◽  
Social Criticism ◽  
Higher Order ◽  
Second Order ◽  
Third Order ◽  
First Order ◽  
The Third ◽  
The Social ◽  
Order Reflection

This paper critically examines Christopher Zurn’s suggestion mentioned above that various social pathologies (pathologies of ideological recognition, maldistribution, invisibilization, rationality distortions, reification and institutionally forced self-realization) share the structure of being ‘second-order disorders’: that is, that they each entail ‘constitutive disconnects between first-order contents and secondorder reflexive comprehension of those contents, where those disconnects are pervasive and socially caused’ (Zurn, 2011, 345-346). The paper argues that the cases even as discussed by Zurn do not actually match that characterization, but that it would be premature to conclude that they are not thereby social pathologies, or that they do not have a structure in common. It is just that the structure is more complex than originally described, covering pervasive socially caused evils (i) in the social reality, (ii) in the first order experiences and understandings, (iii) in the second order reflection as discussed by Zurn, and also (iv) in the ‘third order’ phenomenon concerning the pre-emptive silencing or nullification of social criticism even before it takes place 

scholarly journals Rolling Bearing Diagnosis Based on the Higher Order Spectra

2020 ◽  
Vol 4 (2) ◽  
Author(s):  
Len Gelman ◽  
Tejas H. Patel ◽  
Brian Murray ◽  
Allan Thomson
Keyword(s):  
Ball Bearing ◽  
Rolling Bearing ◽  
Higher Order ◽  
Third Order ◽  
Spectral Kurtosis ◽  
The Third ◽  
Bearing Defects ◽  
Bearing Defect ◽  
Envelope Signal ◽  
Higher Order Spectra

Bearing defect diagnosis is traditionally done using the demodulation/enveloping technology. Diagnosis is mostly based on the spectrum of the squared envelope signal. In literature, the use of the higher order spectra (HOS) has shown to have a tremendous potential for vibration based diagnostics. In this paper we implemented and experimentally validated the higher order spectra based on the envelope analysis for the diagnosis of ball bearing defects. The implemented technology employs the spectral kurtosis to obtain a frequency band for the demodulation and the third order normalized spectra, i.e. the bicoherence for diagnosis of bearing fault. The high effectiveness of the diagnostics of the implemented technology has been experimentally revealed and compared with that of well-known demodulation/enveloping technology.

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