scholarly journals Small-Scale Spectrum of a Scalar Field in Water: The Batchelor and Kraichnan Models

2011 ◽  
Vol 41 (11) ◽  
pp. 2155-2167 ◽  
Author(s):  
Xavier Sanchez ◽  
Elena Roget ◽  
Jesus Planella ◽  
Francesc Forcat
Keyword(s):  
Scalar Field ◽  
Thermal Gradient ◽  
Theoretical Models ◽  
Measured Data ◽  
Small Scale ◽  
Temperature Profiles ◽  
One Dimensional ◽  
Kraichnan Model ◽  
The One ◽  
Rate Of Dissipation

Abstract The theoretical models of Batchelor and Kraichnan, which account for the smallest scales of a scalar field passively advected by a turbulent fluid (Prandtl > 1), have been validated using shear and temperature profiles measured with a microstructure profiler in a lake. The value of the rate of dissipation of turbulent kinetic energy ɛ has been computed by fitting the shear spectra to the Panchev and Kesich theoretical model and the one-dimensional spectra of the temperature gradient, once ɛ is known, to the Batchelor and Kraichnan models and from it determining the value of the turbulent parameter q. The goodness of the fit between the spectra corresponding to these models and the measured data shows a very clear dependence on the degree of isotropy, which is estimated by the Cox number. The Kraichnan model adjusts better to the measured data than the Batchelor model, and the values of the turbulent parameter that better fit the experimental data are qB = 4.4 ± 0.8 and qK = 7.9 ± 2.5 for Batchelor and Kraichnan, respectively, when Cox ≥ 50. Once the turbulent parameter is fixed, a comparison of the value of ɛ determined from fitting the thermal gradient spectra to the value obtained after fitting the shear spectra shows that the Kraichnan model gives a very good estimate of the dissipation, which the Batchelor model underestimates.

THE ESTIMATION OF MAGNETOTELLURIC IMPEDANCE TENSOR ELEMENTS FROM MEASURED DATA

Geophysics ◽  
1971 ◽  
Vol 36 (5) ◽  
pp. 938-942 ◽  
Author(s):  
W. E. Sims ◽  
F. X. Bostick ◽  
H. W. Smith
Keyword(s):  
Mean Square Error ◽  
Random Noise ◽  
Measured Data ◽  
Impedance Tensor ◽  
Mean Square ◽  
Signal To Noise ◽  
One Dimensional ◽  
Additional Information ◽  
The One ◽  
Mean Square Error Criterion

Six different estimates of the magnetotelluric impedance tensor elements may be computed from measured data by use of auto‐power and cross‐power density spectra. We show that each of the estimates satisfies a mean‐square error criterion. Two of the six estimates are relatively unstable in the one‐dimensional case when the incident fields are unpolarized. For the remaining four estimates, it is shown that two are unaffected by random noise on the H signal, but are biased upward by random noise on the E signal. The remaining two estimates are unaffected by random noise on the E signal, but are biased downward by random noise on the H signal. Computation of all of the estimates provides a measure of the total amount of noise present, as indicated by a stability coefficient for the estimates. In the absence of additional information as to the relative signal‐to‐noise ratios of the E and H signals, we suggest that a mean estimate be used. A numerical example is included.

Effects of Nanoparticle Clustering on the Heat Transport in Nanofluids Through Fractal Theories

2008 ◽  
Vol 59 (2) ◽  
pp. 195-198
Author(s):  
Manuela Girtu ◽  
Agop Maricel ◽  
Constantin Bejinariu ◽  
Anca Harabagiu ◽  
Camelia Popa
Keyword(s):  
Heat Transfer ◽  
Coherent Structures ◽  
Thermal Gradient ◽  
Relativity Theory ◽  
Growth Speed ◽  
Topological Dimension ◽  
One Dimensional ◽  
Oscillation Modes ◽  
Scale Relativity ◽  
The One

Considering that the motion of microphysical object takes place on continuous but non-differentiable curves, i.e. on fractals, effects of nanoparticle clustering on the heat transfer in nanofluids using the scale relativity theory in the topological dimension are analyzed. In the one-dimensional differentiable case, the clustering morphogenesis process is achieved by cnoidal oscillation modes of the speed field and a relation between the radius and growth speed of the cluster is obtained. In the non-differentiable case, the fractal kink spontaneously breaks the vacuum symmetry by tunneling and generates coherent structures. Since all the properties of the speed field are transferred to the thermal one and the fractal potential (fractal soliton) acts as an energy accumulator, for a certain condition of an external load (e.g. for a certain value of thermal gradient) the fractal soliton breaks down (blows up) and releases energy. As result, the thermal conductibility in nanofluids unexpectedly increases.

scholarly journals Electromechanical Impedance Model for Free 1D Thin-Walled Piezoelectric Ceramics with a Novel Derivation

Materials ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 4735
Author(s):  
Xiangxing Kong ◽  
Chunyang Chen ◽  
Xiao Liu ◽  
Jianjian Zhu ◽  
Xinlin Qing
Keyword(s):  
Pearson Correlation ◽  
Piezoelectric Ceramics ◽  
Measured Data ◽  
Theoretical Derivation ◽  
One Dimensional ◽  
Impedance Model ◽  
Electromechanical Impedance ◽  
Signal Processing Method ◽  
Thin Walled ◽  
The One

The electromechanical impedance model of the piezoelectric ceramics in a free state can be used for screening and quality control in the structural health monitoring community, but the derivation process of the existing model is usually complicated. This paper describes a novel theoretical derivation methodology based on the assumption of zero-stress on the free boundary of the one-dimensional transducer, which can simplify the derivation of the model to a large extent. To assess the accuracy of the model, a signal processing method based on frequency shifting transformation and the Pearson correlation coefficient is also proposed to calculate the similarity between theoretically predicted and experimentally measured data. Two different piezoelectric ceramics were used in experiments to verify the effectiveness of the model. Experimental results convincingly demonstrate that the assumption proposed in this paper possesses good feasibility for one-dimensional thin-walled piezoelectric ceramics and the model has excellent precision.

A power series formulation for two-dimensional wildfire shapes

2016 ◽  
Vol 25 (9) ◽  
pp. 970 ◽  
Author(s):  
J. E. Hilton ◽  
C. Miller ◽  
A. L. Sullivan
Keyword(s):  
Power Series ◽  
Small Scale ◽  
Two Dimensional ◽  
One Dimensional ◽  
Rate Of Spread ◽  
Mathematical Expressions ◽  
Fire Front ◽  
Small Set ◽  
Prediction Systems ◽  
The One

Computational simulations of wildfires require a model for the two-dimensional expansion of a fire perimeter. Although many expressions exist for the one-dimensional rate of spread of a fire front, there are currently no agreed mathematical expressions for the two-dimensional outward speed of a fire perimeter. Multiple two-dimensional shapes such as elliptical and oval-shaped perimeters have been observed and reported in the literature, and several studies have attempted to classify these shapes using geometric approximations. Here we show that a two-dimensional outward speed based on a power series results in a perimeter that can match many of these observed shapes. The power series is based on the dot product between the vector normal to the perimeter and a fixed wind vector. The formulation allows the evolution and shape of a fire perimeter to be expressed using a small set of scalar coefficients. The formulation is implemented using the level set method, and computed perimeters are shown to provide a good match to perimeters of small-scale experimental fires. The method could provide a framework for statistical matching of wildfire shapes or be used to improve current wildfire prediction systems.

The spectrum of temperature fluctuations in turbulent flow

1968 ◽  
Vol 34 (3) ◽  
pp. 423-442 ◽  
Author(s):  
H. L. Grant ◽  
B. A. Hughes ◽  
W. M. Vogel ◽  
A. Moilliet
Keyword(s):  
Power Spectra ◽  
Temperature Fluctuations ◽  
Inertial Subrange ◽  
Velocity Fluctuations ◽  
One Dimensional ◽  
Open Sea ◽  
Spectrum Function ◽  
Velocity Spectra ◽  
The One ◽  
Rate Of Dissipation

Temperature and velocity fluctuations have been recorded in the open sea and in a tidal channel, and power spectra have been determined from the records. The one-dimensional spectra of temperature fluctuations are found to have an inertial subrange. At larger wave-numbers the data can be fitted by Batchelor's spectrum function for the viscous-convective range. The spectra are inconsistent with the form proposed by Pao for the viscous-convective range.Estimates are given for the constants in Batchelor's spectrum function, but these depend upon knowledge of the rate of dissipation of kinetic energy, which is determined from the velocity spectra. There is doubt about the validity of some of the velocity spectra, and in other cases there is reason to suspect that the turbulence is not locally isotropic.

Evaluation and Enhancement of a One-Dimensional Performance Analysis Method for Centrifugal Compressors

2014 ◽  
Author(s):  
Enrico Klausner ◽  
Uwe Gampe
Keyword(s):  
Performance Analysis ◽  
Performance Prediction ◽  
Standard Procedure ◽  
Flow Analysis ◽  
Measurement Data ◽  
Theoretical Models ◽  
Analysis Method ◽  
Centrifugal Compressors ◽  
One Dimensional ◽  
The One

The one-dimensional flow analysis along a mean streamline is an appropriate and established procedure for initial design and performance analysis of turbomachinery. One such method for performance analysis of centrifugal compressors was published by Aungier in the 1990s. The latest description of Aungier’s performance prediction model was applied to a set of centrifugal compressor stages published in literature. For each test case the whole performance map was calculated and compared with measurement data. The calculation results correspond well with measured data over a wide operating range. However, near choke or stall the mean streamline performance prediction deviates from measurements. After evaluation of this “standard” mean streamline model specific loss correlations, e.g. for choking, incidence and shock losses were replaced by theoretical models. The aim was to implement a more physical based loss model which is able to predict the performance of compressor stages outside the limits of the standard procedure. The modified procedure was again validated against measurements of the above mentioned compressor stages. The modified procedure gives a better prediction of operating performance and behavior. Shortcomings of the procedure are still the overestimation of vaneless diffuser losses at low mass flow rates and the uncertainty in prediction of choke limit. In conclusion recommendations for advancement of the one-dimensional performance analysis method are given.

The Mexico Earthquake of September 19, 1985—A Theoretical Investigation of Large- and Small-scale Amplification Effects in the Mexico City Valley

1988 ◽  
Vol 4 (3) ◽  
pp. 609-633 ◽  
Author(s):  
P-Y. Bard ◽  
M. Campillo ◽  
F. J. Chávez-Garcia ◽  
F. Sánchez-Sesma
Keyword(s):  
Mexico City ◽  
Large Scale ◽  
Small Scale ◽  
Clay Layer ◽  
Local Surface ◽  
One Dimensional ◽  
Mexico Earthquake ◽  
The One ◽  
Deep Sediments ◽  
Lateral Heterogeneities

The linear, large-scale and small-scale amplification effects in the Mexico City valley, related to both the surficial clay layer and the underlying thick sediments, are investigated with two-dimensional (2D) models and compared with the results of simple one-dimensional (1D) models. The deep sediments are shown to be responsible, on their own, for an amplification ranging between 3 and 7, a part of which is due to the 2D effects in case of low damping and velocity gradient. This result is consistent with the observed relative amplification around 0.5 Hz at CU stations with respect to TACY station. The amplification due to the clay layer is much larger (above 10), and the corresponding 2D effects have very peculiar characteristics. On the one hand, the local surface waves generated on any lateral heterogeneity exhibit a strong spatial decay, even in case of low damping (2%), and the motion at a given site is therefore affected only by lateral heterogeneities lying within a radius smaller than 1 km. On the other hand, these local 2D effects may be extremely large, either on the very edges of the lake-bed zone, or over localized thicker areas, where they induce a duration increase and an overamplification. The main engineering consequences of these results are twofold: i) microzoning studies in Mexico City should take into account the effects of deep sediments, and ii) as the surface motion in the lake-bed zone is extremely sensitive to local heterogeneities, 1D models are probably inappropriate in many parts of Mexico City.

scholarly journals The response of rigid plates to blast in deep water: fluid–structure interaction experiments

2012 ◽  
Vol 468 (2145) ◽  
pp. 2807-2828 ◽  
Author(s):  
Andreas Schiffer ◽  
Vito L. Tagarielli
Keyword(s):  
Hydrostatic Pressure ◽  
Deep Water ◽  
Theoretical Models ◽  
Plate Motion ◽  
One Dimensional ◽  
Structure Interaction ◽  
Planar Shock ◽  
Dynamic Experiments ◽  
The One ◽  
Structural Mass

Laboratory-scale dynamic experiments are performed in order to explore the one-dimensional response of unsupported rigid plates to loading by exponentially decaying planar shock waves in deep water. Experiments are conducted in a transparent shock tube allowing measurements of plate motion and imparted impulse, as well as observation of cavitation in water, including motion of breaking fronts and closing fronts. Loading of both air-backed and water-backed rigid plates is examined, and the sensitivity of plate motion and imparted impulse to the structural mass and to the initial hydrostatic pressure in the water is measured. Experiments also serve to validate recently developed theoretical models, whose predictions are found to be in agreement with measurements.

Performance Evaluation of a Regenerative Blower for Hydrogen Recirculation Application in Fuel Cell Vehicles

2006 ◽  
Author(s):  
Young-Hoon Kim ◽  
Shin-Hyoung Kang
Keyword(s):  
Fuel Cell ◽  
Performance Prediction ◽  
Three Dimensional ◽  
Prediction Method ◽  
Theoretical Models ◽  
Hydrogen Gas ◽  
Fuel Cell Vehicles ◽  
One Dimensional ◽  
Loss Models ◽  
The One

Regenerative blowers are used for hydrogen gas recirculation application in fuel cell vehicles. In this paper we discuss the performance of theoretical models that describe the complex three dimensional flows in regenerative blowers. A one-dimensional performance prediction code is developed based on theoretical models and loss models. Numerical calculation is also performed using a commercial CFD code to analyze the three dimensional flows in a regenerative blower. The results of numerical analysis are used to evaluate the performance of the designed blower and improve the accuracy of performance prediction by correcting the loss models. The results of performance predictions are compared with measured data of a prototype regenerative blower to validate the one-dimensional performance prediction method.

Rational Homogeneous Algebras

2012 ◽  
Vol 55 (2) ◽  
pp. 351-354
Author(s):  
J. A. MacDougall ◽  
L. G. Sweet
Keyword(s):  
Scalar Field ◽  
Automorphism Group ◽  
One Dimensional ◽  
Homogeneous Algebras ◽  
The One ◽  
Homogeneous Algebra

AbstractAn algebra A is homogeneous if the automorphism group of A acts transitively on the one-dimensional subspaces of A. The existence of homogeneous algebras depends critically on the choice of the scalar field. We examine the case where the scalar field is the rationals. We prove that if A is a rational homogeneous algebra with dimA > 1, then A2 = 0.

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