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Joshua W Hollett - One of the best experts on this subject based on the ideXlab platform.
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measuring correlated electron motion in atoms with the Momentum Balance density
Journal of Chemical Physics, 2021Co-Authors: Lucy G Todd, Joshua W HollettAbstract:Three new measures of relative electron motion are introduced: equiMomentum, antiMomentum, and Momentum-Balance. The equiMomentum is the probability that two electrons have the exact same Momentum, whereas the antiMomentum is the probability that their momenta are the exact opposite. Momentum-Balance (MB) is the difference between the equiMomentum and antiMomentum and, therefore, indicates if equal or opposite Momentum is more probable in a system of electrons. The equiMomentum, antiMomentum, and MB densities are also introduced, which are the local contribution to each quantity. The MB and MB density of the extrapolated-full configuration interaction wave functions of atoms of the first three rows of the periodic table are analyzed, with a particular focus on contrasting the correlated motion of electrons with opposite-spin and parallel-spin. Coulomb correlation between opposite-spin electrons leads to a higher probability of equiMomentum, whereas Fermi correlation between parallel-spin electrons leads to a higher probability of antiMomentum. The local contribution to MB, given an electron is present, is a minimum at the nucleus and generally increases as the distance from the nucleus increases. There are also interesting similarities between the effects of Fermi correlation and Coulomb correlation (of opposite-spin electrons) on MB.
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measuring correlated electron motion in atoms with the Momentum Balance density
arXiv: Chemical Physics, 2020Co-Authors: Lucy G Todd, Joshua W HollettAbstract:Three new measures of relative electron motion are introduced: equiMomentum, antiMomentum, and Momentum-Balance. The equiMomentum is the probability that two electrons have the exact same Momentum, whereas the antiMomentum is the probability their momenta are the exact opposite. Momentum-Balance (MB) is the difference between the equiMomentum and antiMomentum, and therefore indicates if equal or opposite Momentum is more probably in a system of electrons. The equiMomentum, antiMomentum and MB densities are also introduced, which are the local contribution to each quantity. The MB and MB density of the extrapolated-Full Configuration Interaction wave functions of atoms of the first three rows of the periodic table are analyzed, with a particular focus on contrasting the correlated motion of electrons with opposite and parallel spin. Coulomb correlation between opposite-spin electrons leads to a higher probability of equiMomentum, whereas Fermi correlation between parallel-spin electrons leads to a higher probability of antiMomentum. The local contribution to MB, given an electron is present, is a minimum at the nucleus and generally increases as the distance from the nucleus increases. There are also interesting similarities between the effects of Fermi correlation and Coulomb correlation (of opposite-spin electrons) on MB.
Tie Wei - One of the best experts on this subject based on the ideXlab platform.
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properties of the mean Momentum Balance in turbulent taylor couette flow
Journal of Fluid Mechanics, 2020Co-Authors: Tie WeiAbstract:This paper investigates the properties of the mean Momentum Balance (MMB) equation in the azimuthal direction of a turbulent Taylor–Couette flow (TCF). The MMB- equation is integrated to determine the properties of the Reynolds shear stress. An approximation is developed for the Reynolds shear stress in the core region of a turbulent TCF, and the dependence of the peak Reynolds shear stress location on the Reynolds number and the gap geometry is revealed. The properties of the global integral of the turbulent Coriolis force are also revealed. For a turbulent TCF with a small gap or at high Reynolds numbers, the global integral of the turbulent Coriolis force is found to be only weakly influenced by the rotation ratio of the cylinders. Two controlling non-dimensional numbers are derived directly from the scaling analysis of the MMB- equation. The first is a geometry Atwood number to characterize the gap geometry, where is the gap half-width, and is the mid-gap radial location. The second is the friction Reynolds number defined as , where is the kinematic viscosity and is the friction velocity at the inner cylinder. A new three-layer structure is proposed for the inner half of a turbulent TCF at sufficiently high Reynolds number, based on the force Balance in the MMB- equation. Layer I is an inner layer, where the force Balance is between the viscous force and the Reynolds shear force: . Layer III occupies the core of the gap, where the force Balance is between the turbulent Coriolis force and the Reynolds shear force: . In Layer II, all three forces contribute to the Balance. An inner scaling is developed for Layer I, and an outer scaling is developed for Layer III. The inner and outer scalings are verified against direct numerical simulation data. Similarities and differences between the turbulent TCF and a pressure-driven turbulent channel flow are elucidated.
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multiscaling analysis of the mean thermal energy Balance equation in fully developed turbulent channel flow
Physical Review Fluids, 2018Co-Authors: Tie WeiAbstract:Properly accounting for the intricate Prandtl number dependence in different layers of turbulent channel flows, a multiscaling analysis is developed for the mean thermal energy Balance (MHB) equations. A formal analogy is established between the MHB equation and the mean Momentum Balance equation.
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a physical model of the turbulent boundary layer consonant with mean Momentum Balance structure
Philosophical Transactions of the Royal Society A, 2007Co-Authors: Joseph Klewicki, Tie Wei, Paul C Fife, Patrick McmurtryAbstract:Recent studies by the present authors have empirically and analytically explored the properties and scaling behaviours of the Reynolds averaged Momentum equation as applied to wall-bounded flows. The results from these efforts have yielded new perspectives regarding mean flow structure and dynamics, and thus provide a context for describing flow physics. A physical model of the turbulent boundary layer is constructed such that it is consonant with the dynamical structure of the mean Momentum Balance, while embracing independent experimental results relating, for example, to the statistical properties of the vorticity field and the coherent motions known to exist. For comparison, the prevalent, well-established, physical model of the boundary layer is briefly reviewed. The differences and similarities between the present and the established models are clarified and their implications discussed.
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properties of the mean Momentum Balance in turbulent boundary layer pipe and channel flows
Journal of Fluid Mechanics, 2005Co-Authors: Tie Wei, Paul C Fife, Joseph Klewicki, Patrick McmurtryAbstract:The properties of the mean Momentum Balance in turbulent boundary layer, pipe and channel flows are explored both experimentally and theoretically. Available highquality data reveal a dynamically relevant four-layer description that is a departure from the mean profile four-layer description traditionally and nearly universally ascribed to turbulent wall flows. Each of the four layers is characterized by a pre dominance of two of the three terms in the governing equations, and thus the mean dynamics of these four layers are unambiguously defined. The inner normalized physical extent of three of the layers exhibits significant Reynolds-number dependence. The scaling properties of these layer thicknesses are determined. Particular signi ficance is attached to the viscous/Reynolds-stress-gradient Balance layer since its thickness defines a required length scale. Multiscale analysis (necessarily incomplete) substantiates the four-layer structure in developed turbulent channel flow. In parti cular, the analysis verifies the existence of at least one intermediate layer, with its own characteristic scaling, between the traditional inner and outer layers. Other information is obtained, such as (i) the widths (in order of magnitude) of the four layers, (ii) a flattening of the Reynolds stress profile near its maximum, and (iii) the asymptotic increase rate of the peak value of the Reynolds stress as the Reynolds num ber approaches infinity. Finally, on the basis of the experimental observation that the velocity increments over two of the four layers are unbounded with increasing Reynolds num ber and have the same order of magnitude, there is additional theore tical evidence (outside traditional arguments) for the asymptotically logarithmic character of the mean velocity profile in two of the layers; and (in order of magnitude) the mean velocity increments across each of the four layers are determined. All of these results follow from a systematic train of reasoning, using the averaged Momentum Balance equation together with other minimal assumptions, such as that the mean velocity increases monotonically from the wall.
Paul C Fife - One of the best experts on this subject based on the ideXlab platform.
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mean Momentum Balance in moderately favourable pressure gradient turbulent boundary layers
Journal of Fluid Mechanics, 2008Co-Authors: Meredith Metzger, A Lyons, Paul C FifeAbstract:Moderately favourable pressure gradient turbulent boundary layers are investigated within a theoretical framework based on the unintegrated two-dimensional mean Momentum equation. The present theory stems from an observed exchange of Balance between terms in the mean Momentum equation across different regions of the boundary layer. This exchange of Balance leads to the identification of distinct physical layers, unambiguously defined by the predominant mean dynamics active in each layer. Scaling domains congruent with the physical layers are obtained from a multi-scale analysis of the mean Momentum equation. Scaling behaviours predicted by the present theory are evaluated using direct measurements of all of the terms in the mean Momentum Balance for the case of a sink-flow pressure gradient generated in a wind tunnel with a long development length. Measurements also captured the evolution of the turbulent boundary layers from a non-equilibrium state near the wind tunnel entrance towards an equilibrium state further downstream. Salient features of the present multi-scale theory were reproduced in all the experimental data. Under equilibrium conditions, a universal function was found to describe the decay of the Reynolds stress profile in the outer region of the boundary layer. Non-equilibrium effects appeared to be manifest primarily in the outer region, whereas differences in the inner region were attributed solely to Reynolds number effects.
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a physical model of the turbulent boundary layer consonant with mean Momentum Balance structure
Philosophical Transactions of the Royal Society A, 2007Co-Authors: Joseph Klewicki, Tie Wei, Paul C Fife, Patrick McmurtryAbstract:Recent studies by the present authors have empirically and analytically explored the properties and scaling behaviours of the Reynolds averaged Momentum equation as applied to wall-bounded flows. The results from these efforts have yielded new perspectives regarding mean flow structure and dynamics, and thus provide a context for describing flow physics. A physical model of the turbulent boundary layer is constructed such that it is consonant with the dynamical structure of the mean Momentum Balance, while embracing independent experimental results relating, for example, to the statistical properties of the vorticity field and the coherent motions known to exist. For comparison, the prevalent, well-established, physical model of the boundary layer is briefly reviewed. The differences and similarities between the present and the established models are clarified and their implications discussed.
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properties of the mean Momentum Balance in turbulent boundary layer pipe and channel flows
Journal of Fluid Mechanics, 2005Co-Authors: Tie Wei, Paul C Fife, Joseph Klewicki, Patrick McmurtryAbstract:The properties of the mean Momentum Balance in turbulent boundary layer, pipe and channel flows are explored both experimentally and theoretically. Available highquality data reveal a dynamically relevant four-layer description that is a departure from the mean profile four-layer description traditionally and nearly universally ascribed to turbulent wall flows. Each of the four layers is characterized by a pre dominance of two of the three terms in the governing equations, and thus the mean dynamics of these four layers are unambiguously defined. The inner normalized physical extent of three of the layers exhibits significant Reynolds-number dependence. The scaling properties of these layer thicknesses are determined. Particular signi ficance is attached to the viscous/Reynolds-stress-gradient Balance layer since its thickness defines a required length scale. Multiscale analysis (necessarily incomplete) substantiates the four-layer structure in developed turbulent channel flow. In parti cular, the analysis verifies the existence of at least one intermediate layer, with its own characteristic scaling, between the traditional inner and outer layers. Other information is obtained, such as (i) the widths (in order of magnitude) of the four layers, (ii) a flattening of the Reynolds stress profile near its maximum, and (iii) the asymptotic increase rate of the peak value of the Reynolds stress as the Reynolds num ber approaches infinity. Finally, on the basis of the experimental observation that the velocity increments over two of the four layers are unbounded with increasing Reynolds num ber and have the same order of magnitude, there is additional theore tical evidence (outside traditional arguments) for the asymptotically logarithmic character of the mean velocity profile in two of the layers; and (in order of magnitude) the mean velocity increments across each of the four layers are determined. All of these results follow from a systematic train of reasoning, using the averaged Momentum Balance equation together with other minimal assumptions, such as that the mean velocity increases monotonically from the wall.
Patrick Mcmurtry - One of the best experts on this subject based on the ideXlab platform.
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a physical model of the turbulent boundary layer consonant with mean Momentum Balance structure
Philosophical Transactions of the Royal Society A, 2007Co-Authors: Joseph Klewicki, Tie Wei, Paul C Fife, Patrick McmurtryAbstract:Recent studies by the present authors have empirically and analytically explored the properties and scaling behaviours of the Reynolds averaged Momentum equation as applied to wall-bounded flows. The results from these efforts have yielded new perspectives regarding mean flow structure and dynamics, and thus provide a context for describing flow physics. A physical model of the turbulent boundary layer is constructed such that it is consonant with the dynamical structure of the mean Momentum Balance, while embracing independent experimental results relating, for example, to the statistical properties of the vorticity field and the coherent motions known to exist. For comparison, the prevalent, well-established, physical model of the boundary layer is briefly reviewed. The differences and similarities between the present and the established models are clarified and their implications discussed.
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properties of the mean Momentum Balance in turbulent boundary layer pipe and channel flows
Journal of Fluid Mechanics, 2005Co-Authors: Tie Wei, Paul C Fife, Joseph Klewicki, Patrick McmurtryAbstract:The properties of the mean Momentum Balance in turbulent boundary layer, pipe and channel flows are explored both experimentally and theoretically. Available highquality data reveal a dynamically relevant four-layer description that is a departure from the mean profile four-layer description traditionally and nearly universally ascribed to turbulent wall flows. Each of the four layers is characterized by a pre dominance of two of the three terms in the governing equations, and thus the mean dynamics of these four layers are unambiguously defined. The inner normalized physical extent of three of the layers exhibits significant Reynolds-number dependence. The scaling properties of these layer thicknesses are determined. Particular signi ficance is attached to the viscous/Reynolds-stress-gradient Balance layer since its thickness defines a required length scale. Multiscale analysis (necessarily incomplete) substantiates the four-layer structure in developed turbulent channel flow. In parti cular, the analysis verifies the existence of at least one intermediate layer, with its own characteristic scaling, between the traditional inner and outer layers. Other information is obtained, such as (i) the widths (in order of magnitude) of the four layers, (ii) a flattening of the Reynolds stress profile near its maximum, and (iii) the asymptotic increase rate of the peak value of the Reynolds stress as the Reynolds num ber approaches infinity. Finally, on the basis of the experimental observation that the velocity increments over two of the four layers are unbounded with increasing Reynolds num ber and have the same order of magnitude, there is additional theore tical evidence (outside traditional arguments) for the asymptotically logarithmic character of the mean velocity profile in two of the layers; and (in order of magnitude) the mean velocity increments across each of the four layers are determined. All of these results follow from a systematic train of reasoning, using the averaged Momentum Balance equation together with other minimal assumptions, such as that the mean velocity increases monotonically from the wall.
Joseph Klewicki - One of the best experts on this subject based on the ideXlab platform.
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properties of the mean Momentum Balance in polymer drag reduced channel flow
Bulletin of the American Physical Society, 2014Co-Authors: Christopher White, Yves Dubief, Joseph KlewickiAbstract:Mean Momentum equation based analysis of polymer drag-reduced channel flow is performed to evaluate the redistribution of mean Momentum and the mechanisms underlying the redistribution processes. Similar to channel flow of Newtonian fluids, polymer drag-reduced channel flow is shown to exhibit a four layer structure in the mean Balance of forces that also connects, via the mean Momentum equation, to an underlying scaling layer hierarchy. The self-similar properties of the flow related to the layer hierarchy appear to persist, but in an altered form (different from the Newtonian fluid flow), and dependent on the level of drag reduction. With increasing drag reduction, polymer stress usurps the role of the inertial mechanism, and because of this the wall-normal position where inertially dominated mean dynamics occurs moves outward, and viscous effects become increasingly important farther from the wall. For the high drag reduction flows of the present study, viscous effects become non-negligible across the entire hierarchy and an inertially dominated logarithmic scaling region ceases to exist. It follows that the state of maximum drag reduction is attained only after the inertial sublayer is eradicated. According to the present mean equation theory, this coincides with the loss of a region of logarithmic dependence in the mean profile.
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mean Momentum Balance analysis of rough wall turbulent boundary layers
Physica D: Nonlinear Phenomena, 2010Co-Authors: Faraz Mehdi, Joseph Klewicki, Christopher WhiteAbstract:Abstract Mean Momentum Balances (MMB) are carried out for zero pressure gradient rough-wall turbulent boundary layer flows. The Balance characterizes the mean dynamical mechanisms and reveals dominant terms in the governing equation, which constitutes a necessary step in the derivation of scaling behaviors. The Reynolds stress profiles in rough-wall boundary layers are, however, quite scattered and the uncertainty in the data poses challenges for educing the MMB. The present study employs a method that invokes theoretical constraints to more reliably reveal Reynolds stress gradient behaviors in the presence of data scatter. Properties of the rough-wall mean Momentum Balances are compared to those of the smooth-wall case. Important qualitative features of the layer structure that exists for the smooth-wall are shown to also exist for rough-wall boundary layers. Specifically, the present analysis reveals the existence of a stress gradient Balance layer, and thus the importance of the viscous force term well above the roughness crests. The smooth-wall Reynolds stress peak position scales in proportion with the geometric mean of inner–outer characteristic lengths. Roughness, however, imposes new dynamical length scales and evidence is provided to indicate that the scale separations between the inner length, roughness length, peak Reynolds stress length and outer length are important. The failure of the rough-wall Reynolds stress profiles to merge under smooth-wall meso-scalings clearly reveals the additional richness of the problem. Although more data are required to gain a complete characterization, the present results provide evidence that the combined roughness-Reynolds number problem exhibits significantly greater complexity than captured by the prevalent scheme for characterizing and classifying roughness regimes.
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a physical model of the turbulent boundary layer consonant with mean Momentum Balance structure
Philosophical Transactions of the Royal Society A, 2007Co-Authors: Joseph Klewicki, Tie Wei, Paul C Fife, Patrick McmurtryAbstract:Recent studies by the present authors have empirically and analytically explored the properties and scaling behaviours of the Reynolds averaged Momentum equation as applied to wall-bounded flows. The results from these efforts have yielded new perspectives regarding mean flow structure and dynamics, and thus provide a context for describing flow physics. A physical model of the turbulent boundary layer is constructed such that it is consonant with the dynamical structure of the mean Momentum Balance, while embracing independent experimental results relating, for example, to the statistical properties of the vorticity field and the coherent motions known to exist. For comparison, the prevalent, well-established, physical model of the boundary layer is briefly reviewed. The differences and similarities between the present and the established models are clarified and their implications discussed.
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properties of the mean Momentum Balance in turbulent boundary layer pipe and channel flows
Journal of Fluid Mechanics, 2005Co-Authors: Tie Wei, Paul C Fife, Joseph Klewicki, Patrick McmurtryAbstract:The properties of the mean Momentum Balance in turbulent boundary layer, pipe and channel flows are explored both experimentally and theoretically. Available highquality data reveal a dynamically relevant four-layer description that is a departure from the mean profile four-layer description traditionally and nearly universally ascribed to turbulent wall flows. Each of the four layers is characterized by a pre dominance of two of the three terms in the governing equations, and thus the mean dynamics of these four layers are unambiguously defined. The inner normalized physical extent of three of the layers exhibits significant Reynolds-number dependence. The scaling properties of these layer thicknesses are determined. Particular signi ficance is attached to the viscous/Reynolds-stress-gradient Balance layer since its thickness defines a required length scale. Multiscale analysis (necessarily incomplete) substantiates the four-layer structure in developed turbulent channel flow. In parti cular, the analysis verifies the existence of at least one intermediate layer, with its own characteristic scaling, between the traditional inner and outer layers. Other information is obtained, such as (i) the widths (in order of magnitude) of the four layers, (ii) a flattening of the Reynolds stress profile near its maximum, and (iii) the asymptotic increase rate of the peak value of the Reynolds stress as the Reynolds num ber approaches infinity. Finally, on the basis of the experimental observation that the velocity increments over two of the four layers are unbounded with increasing Reynolds num ber and have the same order of magnitude, there is additional theore tical evidence (outside traditional arguments) for the asymptotically logarithmic character of the mean velocity profile in two of the layers; and (in order of magnitude) the mean velocity increments across each of the four layers are determined. All of these results follow from a systematic train of reasoning, using the averaged Momentum Balance equation together with other minimal assumptions, such as that the mean velocity increases monotonically from the wall.
