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Direct numerical simulation is used to simulate the turbulent wake behind an accelerating axisymmetric self-propelled body in a stratified fluid. Acceleration is modelled by adding a velocity profile corresponding to net thrust to a self-propelled velocity profile resulting in a wake with excess momentum. The effect of a small to moderate amount of excess momentum on the initially momentumless self-propelled wake is investigated to evaluate if the addition of excess momentum leads to a large qualitative change in wake dynamics. Both the amount and shape of excess momentum are varied. Increasing the amount of excess momentum and/or decreasing the radial extent of excess momentum was found to increase the defect velocity, mean kinetic energy, shear in the velocity gradient and the wake width. The increased shear in the mean profile resulted in increased production of turbulent kinetic energy leading to an increase in turbulent kinetic energy and its dissipation. Slightly larger vorticity structures were observed in the late wake with excess momentum although the differences between vorticity structures in the self-propelled and 40 % excess momentum cases was significantly smaller than suggested by previous experiments. Buoyancy was found to preserve the doubly inflected velocity profile in the vertical direction, and similarity for the mean velocity and turbulent kinetic energy was found to occur in both horizontal and vertical directions. While quantitative differences were observed between cases with and without excess momentum, qualitatively similar evolution was found to occur.

This paper presents a combined experimental and numerical study of the flow characteristics of round vertical liquid jets plunging into a cylindrical liquid bath. The main objective of the experimental work consists in determining the plunging jet flow patterns, entrained air bubble sizes and the influence of the jet velocity and variations of jet falling lengths on the jet penetration depth. The instability of the jet influenced by the jet velocity and falling length is also probed. On the numerical side, two different approaches were used, namely the mixture model approach and interface-tracking approach using the level-set technique with the standard two-equation turbulence model. The numerical results are contrasted with the experimental data. Good agreements were found between experiments and the two modelling approaches on the jet penetration depth and entraining flow characteristics, with interface tracking rendering better predictions. However, visible differences are observed as to the jet instability, free surface deformation and subsequent air bubble entrainment, where interface tracking is seen to be more accurate. The CFD results support the notion that the jet with the higher flow rate thus more susceptible to surface instabilities, entrains more bubbles, reflecting in turn a smaller penetration depth as a result of momentum diffusion due to bubble concentration and generated fluctuations. The liquid average velocity field and air concentration under tank water surface were compared to existing semi-analytical correlations. Noticeable differences were revealed as to the maximum velocity at the jet centreline and associated bubble concentration. The mixture model predicts a higher velocity than the level-set and the theory at the early stage of jet penetration, due to a higher concentration of air that cannot rise to the surface and remain trapped around the jet head. The location of the maximum air content and the peak value of air holdup are also predicted differently.

After the solar wind termination shock crossings of the Voyager spacecraft, the acceleration of anomalous cosmic rays has become a very contentious subject. In this paper we examine several topics pertinent to anomalous cosmic ray oxygen acceleration and transport using a numerical cosmic ray modulation model. These include the effects of drifts on a purely Fermi I accelerated spectra, the effects of introducing higher charge states of oxygen into the modulation model, examining the viability of momentum diffusion as a re-acceleration process in the heliosheath and examining energy spectra, and intensity gradients, in the inner heliosphere during consecutive drift cycles.

General description of the interplay between the Kirkendall shift (as a special way of relaxation) and diffusion induced driving forces in diffusion intermixing of binary systems is given. It is shown that, if the Kirkendall shift is negligible, a steady state Nernts-Planck regime is established with diffusion coefficient close to the slower diffusivity, independently of the type of the diffusion induced field and also independently whether this is a single field or a combination of different fields (e.g. stress field and extra chemical potential of non-equilibrium vacancies). Deviations from parabolic kinetics are expected only before or after this steady state stage. Using the results of our previous paper, on development and relaxation of diffusion induced stresses, it is illustrated that the setting of time of the Nernst-Planck regime is very short: intermixing on the scale of few tenths of nanometer is enough to reach it. It is also illustrated that this stage is realized even in the case of asymmetric interdiffusion (in one side of the diffusion zone the diffusion is orders of magnitude higher than in the other), when the stress distribution has a more complex form (having a sharp peak at the interface). Surprisingly the steady state is longer than it would be expected from the relaxation time of Newtonian flow: This is so because the composition profile is not static but changes fast in the timescale of the stress relaxation, and thus the stress re-develops continuously.

The authors formally discuss, in the generic section of a non-linear free surface flow, the non-hydrostatic pressure and the non-uniform velocity effects using the coefficients α, β, K e and K m of...

The commonly used Eulerian or continuum model for incompressible multiphase flow is known to be unstable to perturbations for all wavenumbers, even if viscosity terms are used in the momentum equations. In the present work the model is stabilized by adding explicit artificial diffusion to the mass equations. The artificial diffusion terms lead to improved stability properties: uniform flow becomes linearly stable for large wavenumbers, and above an analytically derived threshold for the artificial diffusivity, stability for all wavenumbers is achieved. The artificial diffusivity reappears in the momentum equations, in such a way that fundamental properties of the standard equations remain valid: Galilean invariance is maintained, total mass and momentum are conserved, decay of total kinetic energy is ensured in the absence of external forces, and a flow initially at rest at hydrostatic pressure remains unchanged, even if the spatial distribution of volume fractions is nonuniform. A staggered finite volume pressure correction method using central differencing (leading to energy conserving discretization of convective and pressure terms) is presented. Application of the method to one-dimensional two-phase flow of falling particles particles confirms that the equations are stable with and unstable without artificial diffusion in the volume fraction equation.

In this study, we present a first evaluation of bounce-averaged diffusion coefficients of superluminous wave (R-X and L-O) modes at two locations: L = 6.5 and 4.5. We show that, analogous to the local diffusion coefficients, bounce-averaged momentum diffusion coefficients play a dominant role for pitch angles alpha above a critical angle alpha(c), namely, > vertical bar vertical bar > . We also demonstrate that for a Gaussian distribution of wave normal angle theta (X = tan theta). diffusion coefficients are sensitively dependent on the peak X(m). As X(m) increases, and are found to increase in cases of interest: X(m) = tan 25 degrees, tan 45 degrees and tan 65 degrees. We have estimated wave amplitudes for particular stochastic acceleration timescale for 1 MeV electrons and found that the required wave amplitudes B(te) similar to 86 to similar to 170 pT for a timescale tau = 1 day. These results indicate that superluminous wave modes may have a significant potential for both stochastic acceleration of trapped electrons (with higher pitch angles) and loss process of untrapped electrons (with smaller pitch angles). (C) 2009 Elsevier Ltd. All rights reserved.

Vegetation in natural river interacts with river flow and sediment transport. This paper proposes a two-layer theoretical model based on diffusion theory for predicting the vertical distribution of suspended sediment concentration in a flow with submerged vegetation. The suspended sediment concentration distribution formula is derived based on the sediment and momentum diffusion coefficients through the inverse of turbulent Schmidt number ( S c t ) or the parameter &eta, which is defined by the ratio of sediment diffusion coefficient to momentum diffusion coefficient. The predicted profile of suspended sediment concentration moderately agrees with the experimental data. Sensitivity analyses are performed to elucidate how the vertical distribution profile responds to different canopy densities, hydraulic conditions and turbulent Schmidt number. Dense vegetation renders the vertical distribution profile uneven and captures sediment particles into the vegetation layer. For a given canopy density, the vertical distribution profile is affected by the Rouse number, which determines the uniformity of the sediment on the vertical line. A high Rouse number corresponds to an uneven vertical distribution profile.

Heat transfer performances and flow structures of laminar impinging slot jets with power-law non-Newtonian fluids and corresponding typical industrial fluids (Carboxyl Methyl Cellulose (CMC) solutions and Xanthangum (XG) solutions) have been studied in this work. Investigations are performed for Reynolds number Re less than 200, power-law index n ranging from 0.5 to 1.5 and consistency index K varying from 0.001 to 0.5 to explore heat transfer and flow structure of shear-thinning fluid and shear-thickening fluid. Results indicate that with the increase of n, K for a given Re, wall Nusselt number increases mainly attributing to the increase of inlet velocity U. For a given inlet velocity, wall Nusselt number decreases with the increase of n and K, which mainly attributes to the increase of apparent viscosity and the reduction of momentum diffusion. For the same Re, U and Pr, wall Nusselt number decreases with the increase of n. Among the study of industrial power-law shear-thinning fluid, CMC solution with 100 ppm shows the best heat transfer performance at a given velocity. Moreover, new correlation of Nusselt number about industrial fluid is proposed. In general, for the heat transfer of laminar confined impinging jet, it is best to use the working fluid with low viscosity.

The toroidal rotation modulation and momentum transport have been investigated in the J-TEXT tokamak using a modulated electrode biasing (EB) along with measurements of the toroidal rotation (V ϕ ) by a spectrometer and a Langmuir-Mach probe array. The amplitude A v and phase delay ϕ v (relative to the phase of the biasing current, I EB) of the rotation modulation are extracted through sine-fitting approaches. It is found that the A v increases with increasing I EB and the ϕ v becomes larger when the modulation frequency increases. It has been estimated that the momentum transport time across a radial range from r/a ∼ 0.9 to 0.65 is about 10 ms, shorter than the half of modulation period (∼30 ms). Using the perturbation analysis technique, the toroidal momentum transport coefficients, including momentum diffusivity χ ϕ and convective velocity V conv, have been calculated and an inward pinch effect has been observed. In addition, the impact of the EB on the ion temperature and intrinsic rotation and the toroidal rotation difference between impurity and main ions are analyzed and discussed.

A computational fluid dynamics (CFD) analysis for a turbulent jet flow induced by a steam jet discharged into a subcooled water pool was performed for 10 s of transients to investigate whether the currently available CFD codes can be suitably used as a tool to investigate the applicability of the existing semi-analytical correlations to a condensing jet-induced turbulent jet and to analyze the thermal-hydraulic behavior, such as global circulation and local hot spot, in a condensation pool for advanced light water reactors. As for the numerical experiment, a series of sensitivity calculations was conducted systematically to elucidate the major factors which can cause different analysis results by varying the mesh distributions, numerical models for a convection term and an eddy viscosity term. The effect of a difference in the velocity and the temperature distribution in a region between the sparger and the pool wall has not been observed in the afore-mentioned sensitivity calculations. The comparison of the CFD results with the test data shows that the CFD analysis does not accurately simulate the local phenomenon of a turbulent jet existing downstream of a steam jet. It was found that the value of the turbulent intensity at the inlet of the turbulent jet region is the most important factor because it can determine the boundary of a turbulent jet through a momentum diffusion process in a radial direction. The comparison of the CFD results with the test data shows that the CFD analysis can accurately simulate the local phenomenon of a turbulent jet existing downstream of a steam jet only when the CFD analysis reflects the physics of a turbulent jet.

The momentum diffusion of atoms in the field of two counter-propagating stochastic waves, one of which reproduces the other one with a certain time delay, has been studied. It is shown that the parameters of atom-field interaction, at which the light pressure force is maximum, correspond to the increasing momentum diffusion coefficient. In the case of high-intensity field described by the stochastic field model, the momentum diffusion coefficient was found to be proportional to the square root of the field autocorrelation time. The wave function describing the inner state of atoms is modeled, by using the Monte-Carlo method. Numerical calculations are carried out for cesium atoms.

Using a realistic density model, we present a first study on the interactions between electromagnetic waves and energetic particles in the inner magnetosphere. Numerical calculations show that as the latitude λ increases, the number density ne increases, and resonant frequency range moves to lower pitch angles. During L-mode/electron and L-mode/proton interactions, the pitch angle diffusion dominates over the momentum diffusion. This indicates that L-mode waves are primarily responsible for pitch angle scattering. For R-mode/electron interaction, the momentum diffusion is found to be comparable to the pitch angle diffusion, implying that R-mode waves can play an important role in both pitch angle scattering and stochastic acceleration of electrons. For R-mode/proton interaction, diffusion coefficients locate primarily below pitch angle 60° and increase as kinetic energy increases, suggesting that R-mode waves have potential for pitch angle scattering of highly energetic (∼1 MeV) protons but cannot efficiently accelerate protons.

This paper has three objectives. The first objective is to show how the Einstein–de Broglie equation (EdB) can be extended to model and scale, via fractional scaling, both conservative and dissipative processes ranging in scale from quanta to nuclear reactors. The paper also discusses how and why a single equation and associated fractional scaling method generate for each process of change the corresponding scaling criterion. The versatility and capability of fractional scaling are demonstrated by applying it to: (a) particle dynamics, (b) conservative (Bernoulli) and dissipative (hydraulic jump) flows, (c) viscous and turbulent flows through rough and smooth pipes, and (d) momentum diffusion in a semi-infinite medium. The capability of fractional scaling to scale a process over a vast range of temporal and spatial scales is demonstrated by applying it to fluctuating processes. The application shows that the modeling of fluctuations in fluid mechanics is analogous to that in relativistic quantum field theory. Thus, Kolmogorov dissipation frequency and length are the analogs of the characteristic time and length of quantum fluctuations. The paper briefly discusses the applicability of the fractional scaling approach (FSA) to nanotechnology and biology. It also notes the analogy between FSA and the approach used to scale polymers. These applications demonstrate the power of scaling as well as the validity of Pierre-Gilles de Gennes’ ideas concerning scaling, analogies and simplicity. They also demonstrate the usefulness and efficiency of his approach to solving scientific problems. The second objective is to note and discuss the benefits of applying FSA to NPP technology. The third objective is to present a state of the art assessment of thermal-hydraulics (T/H) capabilities and needs relevant to NPP.

One of the main challenges of the atmospheric model is the proper determination of the turbulent diffusivity. In this sense, various boundary layer parametrization have been developed along of the years. For the same closure order, many times, the bigger differences between them, are concentrated in the adjustment parameters. From the adequate physical description, to find the real value of each constant is the great challenge of the models. Them, the present work compare three different parametrization for the non-dimensional relation u 2 ∗ =E , that is used as a constant in the momentum diffusion coefficient in the E - l models. In the comparison with the GABLS experiment, the results show that the constant does not have a great influence over the wind components and over the temperature. On the other hand, the constant have a fundamental role in the behavior of the turbulence kinetic energy. This is due the fact of the constant is also present in the turbulence viscous dissipation term. Finally, it is important to stress that this is a work that is in its beginning and it aims the construction of a boundary layer parameterization for climate and weather forecasting models.

Perturbative experiments have been carried out using tangential neutral beam injection (NBI) and non-resonant magnetic perturbation (NRMP) to analyze the momentum transport properties in KSTAR H-modes. Diffusive and non-diffusive terms of momentum transport are evaluated from the transient analysis. Although the operating conditions and methodologies applied in the two cases are similar, the momentum transport properties obtained show clear differences. The estimated momentum diffusivity and pinch obtained in the NBI modulation experiments is larger than that in the NRMP modulation experiments. We found that this discrepancy could be a result of uncertainties in the assumption for the analysis. By introducing time varying momentum transport coefficients depending on the temperature gradient, the linearized equation shows that if the temperature perturbation exists, the evolution of toroidal rotation perturbation could be faster than the transport rate of mean quantity, since the evolution of toroidal rotation perturbation is related to , a momentum diffusivity from perturbative analysis. This could explain the estimated higher momentum diffusivity using time independent transport coefficients in NBI experiments with higher ion temperature perturbation compared to that in NRMP modulation experiments. The differences in the momentum transport coefficient with NRMP and NBI are much reduced by considering time varying momentum transport coefficients in the time dependent transport simulation.

Full equations of convective diffusion are solved numerically for a strip-like (2D) electrodiffusion friction probe in a stream of microdisperse liquid, assuming a non-linear near-to-wall velocity profile ranging from simple shear flow (p = 1) to ideal slip (p = 0). The range of generalized Peclet number H from H = 0.01 (almost pure spatial diffusion) to H = 100 (diffusion layer with negligible longitudinal diffusion) covers all cases of possible experimental relevance. The main result is expressed as a relative deviation of actual total diffusion flux N from its diffusion-layer approximation NDLA, Ψ = N/NDLA − 1.

Semi-geostrophic theory has proved a powerful framework for understanding the dynamics of mid-latitude weather systems. However, one limitation is the lack of a realistic boundary-layer representation. Semi-geostrophic theory can be modified to include an atmospheric boundary layer by replacing the geostrophic wind with the ‘geotriptic’ (or Ekman-balanced) value in the substantive derivative and appropriately approximating the momentum diffusion term– the so-called semi-geotriptic theory. However, until now, solutions of the semi-geotriptic equations using predictor– corrector methods have not been possible for the important case of well-mixed boundary layers. Existing predictor– corrector methods require a Brunt– Vaisala frequency greater than zero to be solvable. Here we describe a method of incorporating well-mixed boundary layers into semi-geotriptic theory. We modify the hydrostatic relationship by including a small horizontal diffusion of vertical velocity. This enables the formation of a well-posed predictor– corrector method. Given well-mixed boundary layers are a ubiquitous feature of the lower atmosphere, the modification increases the usability of the model. Calculations are also performed at much higher vertical resolution than before. The revised semi-geotriptic model is compared with a hydrostatic primitive-equation model for a test case of a two-dimensional idealized diurnal cycle of a sea breeze. The performance of the revised semi-geotriptic model in the growth phase of the sea breeze is improved, as a well-mixed boundary layer is now permitted. The additional vertical resolution captures the capping inversion and the sea-breeze circulation better. The hydrostatic primitive-equation model is shown to produce inertial oscillations that persist beyond the evening decay of the boundary layer until the following morning. In contrast, the semi-geotriptic model decays following the boundary-layer state in a more realistic way. The semi-geotriptic model thus demonstrates its usefulness as a critical tool in understanding boundary-layer dynamics coupling issues in operational models. Copyright © 2010 Royal Meteorological Society and Crown Copyright.

It is shown that the radial transport of parallel momentum provides a damping mechanism for the zonal flow relevant for plasma turbulence close to the nonlinear threshold. The damping mechanism is confirmed by a “Rosenbluth-Hinton” test with a model radial momentum diffusion, in which the decay rate of the residual potential is found to be proportional to the model diffusion coefficient and in good agreement with the analytical result. Nonlinear simulations show that, when momentum transport is suppressed, stronger long wavelength zonal flow shearing occurs. The suppression of momentum transport then allows for the development of fully developed staircase structures in the E × B shear, which can suppress turbulence completely for a finite time window. No impact on shorter wavelength zonal flows is observed, in contrast to the analytical prediction which suggests a high damping rate. The latter result raises the question of the relevance the residual zonal flow plays in turbulence saturation.

The direct impact of mountain waves on the atmospheric circulation is due to the deposition of wave momentum at critical levels, or levels where the waves break. The first process is treated analytically in this study within the framework of linear theory. The variation of the momentum flux with height is investigated for relatively large shears, extending the authors’ previous calculations of the surface gravity wave drag to the whole atmosphere. A Wentzel–Kramers–Brillouin (WKB) approximation is used to treat inviscid, steady, nonrotating, hydrostatic flow with directional shear over a circular mesoscale mountain, for generic wind profiles. This approximation must be extended to third order to obtain momentum flux expressions that are accurate to second order. Since the momentum flux only varies because of wave filtering by critical levels, the application of contour integration techniques enables it to be expressed in terms of simple 1D integrals. On the other hand, the momentum flux divergence (which corresponds to the force on the atmosphere that must be represented in gravity wave drag parameterizations) is given in closed analytical form. The momentum flux expressions are tested for idealized wind profiles, where they become a function of the Richardson number (Ri). These expressions tend, for high Ri, to results by previous authors, where wind profile effects on the surface drag were neglected and critical levels acted as perfect absorbers. The linear results are compared with linear and nonlinear numerical simulations, showing a considerable improvement upon corresponding results derived for higher Ri.

The balance of material momentum is obtained by a pull-back of the balance of physical momentum to the reference configuration. The usual formulation of these balances assumes the fields involved to be continuously differentiable. At a surface of discontinuity, the mechanical balance laws are represented by jump conditions rather than differential equations. The jump condition representing the balance of material momentum is derived in an analogous manner to the continuous case. In general, there remains an imbalance term in the discontinuous version of the balance of material momentum representing a concentrated source of material momentum carried along with a shock wave. The imbalance remains nonzero in a purely hyperelastic material without any thermal properties. It is shown that the imbalance vanishes if the material is assumed thermoelastic and heat conduction is omitted. The relevance of this result for the validity of a global balance of material momentum is discussed.

Momentum correction coefficient (K) is an important parameter for the mixing process of two jet flows. In this paper, momentum correction coefficient for two jet flows mixing in a tee junction was investigated with systems of air–air, water–water and air–water in a wide region of mass ratio of flow rate. The pressure drop was analyzed, where the total pressure drop was mainly attributed to momentum exchange and friction. Based on the experimental data, pressure drop due to momentum exchange was obtained by extrapolation methods, and then the momentum correction coefficient was fitted. It turned out that the momentum correction coefficient was mainly dependent on the momentum flux ratio (M) of the two jets and almost independent with the physical properties of jet flows. The relationship between K and M was correlated as the following equation: K = 1 + 0.256 M 0.223

A β-plane multilevel quasigeostrophic channel model with interactive static stability and a simplified parameterization of atmospheric boundary layer physics is used to study the role of different boundary layer processes in eddy equilibration and their relative effect in maintaining the strong boundary layer potential vorticity (PV) gradient. The model results show that vertical thermal diffusion, along with the surface heat exchange, is primarily responsible for limiting PV homogenization by baroclinic eddies in the boundary layer. Under fixed SST boundary conditions, these two processes act as the source of the mean flow baroclinicity in the lower levels and result in stronger eddy heat fluxes. Reducing surface friction alone does not result in efficient elimination of the boundary layer PV gradient, but the equilibrium state temperature gradient is still largely influenced by surface friction and its response to changes in surface friction is not monotonic. In the regime of strong surface friction, with reduced poleward eddy heat flux, a strong temperature gradient is still retained. When the surface friction is sufficiently weak along with the stronger zonal wind, the critical level at the center of the jet drops below the surface. As a result, in the lower levels, the eddy heat flux forcing on the mean flow moves away from the center of the jet and the equilibrium state varies only slightly with the strength of the vertical momentum diffusion in the boundary layer.

We show that the transport coefficient q ˆ , describing momentum diffusion for fast jets moving in the quark-gluon plasma, receives large O(g) corrections from plasma effects which we explicitly calculate, at weak coupling. Our approach is based on an “Euclideanization” property of classical physics near the light-cone, which simplifies drastically this calculation and might open up a new possibility for the lattice study of these effects.

Specific features of the diffusion mass transfer in metals under impact mechanical action are considered. Diffusion fluxes that arise during intense plastic deformation of materials are determined. It is shown that under some conditions the diffusion of impurities from the external surface into the bulk of metal can proceed in the regime of a wave process, in which the mass transfer occurs in the form of a convective motion of atoms through the crystal lattice of the solid. The velocity of propagation of diffusion waves is determined.

An equation for diffusion impedance is derived in the terms of the lattice diffusion model based on the assumption as to the local nonequilibrium distribution of diffusing particles across the sites of different types. This equation is valid at low lattice occupation. Unlike the multiple trapping model, all site types are interpreted symmetrically. In the boundary condition, it is assumed that there is a unique relationship between the electric potential variation, on one side of the interface and variation of the generalized particle activity on the other side.

The definitions of the critical flow condition in open channel hydraulics, based on the momentum and the energy equations, differ from each other if non-hydrostatic pressure and non-uniform velocity distributions are considered. The concept of minimum energy and minimum momentum yields two distinct critical flow conditions, both in terms of their magnitude and their position. Consequently, for a given discharge, there are two singular points in the water surface profile, derived from the momentum and the energy principles, respectively. Extended momentum and energy equations for non-uniform velocity and non-hydrostatic pressure distributions are presented and the critical flow condition is generalized in relation to those conservation laws.

Suprathermal particles are ubiquitously present in the solar wind, with energies typically from ~1 keV nucleon−1 to ~a few MeV nucleon−1. Remarkably, the suprathermal particles exhibit a common spectral shape in many different circumstances; the distribution function is a power law in particle speed, with spectral index of –5. The observations cannot be explained by traditional stochastic acceleration, which yields spectra that depend on, e.g., the momentum diffusion coefficient, and thus the spectra are expected to be different in different circumstances. A theory is presented in which the particles are accelerated in thermally isolated compressional turbulence. Thermal isolation is valid in spatially homogeneous conditions in the solar wind, and when properly applied, yields suprathermal tails that always have the required spectral shape. The theory describes the time evolution of the spectrum to its equilibrium form and predicts the high-speed cutoff on the acceleration. The high-speed cutoff is shown to be in good agreement with observations of quiet-time spectra at Earth and is consistent with observations throughout the outer heliosphere.

This paper investigates the exchange of global mean angular momentum between an atmosphere and its underlying planet by a simple model. The model parameterizes four processes that are responsible for zonal mean momentum budget in the atmospheric boundary layer for a rotating planet: (i) meridional circulation that redistributes the relative angular momentum, (ii) horizontal diffusion that smoothes the prograde and retrograde winds, (iii) frictional drag that exchanges atmospheric angular momentum with the underlying planet, and (iv) internal redistribution of the zonal mean momentum by wave drag. It is shown that under a steady-state or a long-term average condition, the global relative angular momentum in the boundary layer vanishes unless there exists a preferred frictional drag for either the prograde or the retrograde zonal wind. We further show quantitatively that one cannot have either a predominant steady prograde or retrograde wind in the boundary layer of a planetary atmosphere. The parameter dependencies of the global relative angular momentum and the strength of the atmospheric circulation in the boundary layer are derived explicitly and used to explain the observational differences between the atmospheres of Earth and Venus.

The hear transfer mechanism and the constitutive models for energy boundary layer in power law fluids were investigated. Two energy transfer constitutive equations models were proposed based on the assumption of similarity of velocity field momentum diffusion and temperature field heat transfer. The governing systems of partial different equations were transformed into ordinary differential equations respectively by using the similarity transformation group. One model was assumed that Prandtl number is a constant, and the other model was assumed that viscosity diffusion is analogous to thermal diffusion. The solutions were presented analytically and numerically by using the Runge-Kutta formulas and shooting technique and the associated transfer characteristics were discussed.

Computational fluid dynamics analysis was used to investigate the added mass momentum, flow momentum and gravity effects during the constant velocity water entry of wedge-shaped sections with deadrise angles from 5° to 45°. It is shown that the added mass continues to increase for a time after chine immersion and that added mass can be estimated in terms of a constant added mass coefficient and an effective wetted width. A momentum theory is presented in which the water entry force is explained as the sum of the rate of change of added mass momentum, which becomes zero at immersion to chine depth ratios greater than about three, and the rate of change of flow momentum, which continues at deep immersions. The effect of gravity on the water entry force is given as the hydrostatic force together with the force necessary to create the potential energy in the water pile up. Hydrodynamic forces are not significantly changed by the effect of gravity on the flow fields.

The transient behavior of free convection along the vertical wire of a hot-wire apparatus has been experimentally investigated at room temperature and ambient pressure, using water and propylene glycol. The development of free convection has been studied using an ad hoc apparatus, in order to obtain the best agreement between the vertical direction and the wire. The measurements were corrected for radiation influences, and the effects induced by free convection were detected at the wire-fluid interface. The convection outcomes have been correlated to fluid properties and test conditions. A suitable time scale has been introduced, which is defined by the modified Fourier and a proper definition of the local Grashof number. The obtained correlation has been applied to data found in the literature. The possibility of describing the free convection development at the wire-fluid interface could enable the fluid properties related to momentum diffusion to be investigated by the hot-wire technique.

This study utilizes a shallow-water numerical model to investigate the influences of mountain topography on an approaching vortex on an f-plane. Systematic numerical experiments show that vortex track deflection is significantly dependent upon several parameters, namely the maximum tangential flow speed of the vortex (V max), the basic flow (U), the fluid depth (H), the radius of V max (R), the mountain height (h), and L m which, in the presence of mean flow, is represented by L y defined as the mountain half-width in the direction normal to the vortex movement. Accordingly, there exist several nondimensional parameters, the vortex Froude number, $V_{\rm max} /\sqrt {gH}$ , the basic-flow Froude number, $U/\sqrt{gH}$ , the nondimensional mountain height, h/H, and the nondimensional vortex size R/L m. The northward track deflection for a westbound vortex is significantly reduced by increased $U/\sqrt {gH}$ . However, the direction of track deflection is primarily controlled by R/L m, with respect to the nondimensional height, h/H. Leftward (facing downstream) deflection can be expected with HL m/hR > 0.5 or more strictly L m/R > 0.3, for typical conditions, h/H < 0.8. With the exclusion of explicit horizontal momentum diffusion, the vorticity budgets are essentially balanced by vorticity advection and vorticity stretching (associated with divergence) with the vorticity advection (stretching) being responsible for upstream rightward (leftward) deflection. A vortex tends to move in a clockwise path around a wider and lower mountain. With a sufficiently large h/H (high mountain), the track of a vortex becomes rightward (counter-clockwise) as a result of the more dominant vorticity advection. There is a transition of track deflection of a vortex from leftward to rightward for a decreasing mountain aspect ratio of L y /L x (where L x is the mountain half width in the direction parallel to the vortex movement) which indicates that leftward (rightward) track deflection will be more dominant for a westbound (northbound) vortex past meridionally elongated mountains, such as the Central Mountain Range (CMR) of Taiwan.

We simulate atomic ballistic transport in a standing-wave laser field in the framework of a Monte Carlo stochastic wavefunction approach in which the coherent Hamiltonian evolution is interrupted at random times by spontaneous emission events. It is shown in numerical experiments and confirmed analytically that the character of spatial and momentum diffusion of spontaneously emitting atoms changes abruptly in the atom-laser detuning regime where the deterministic Hamiltonian dynamics has been shown to be chaotic. Thus, we find a manifestation of underlying Hamiltonian chaos in the diffusive-like center-of-mass motion which can be observed in real experiments.

We present an overview of a perturbative-kinetic approach to jet propagation, energy loss, and momentum broadening in a high temperature quark-gluon plasma. The leading-order kinetic equations describe the interactions between energetic jet-particles and a non-abelian plasma, consisting of on-shell thermal excitations and soft gluonic fields. These interactions include 22 scatterings, collinear bremsstrahlung, and drag and momentum diffusion. We show how the contribution from the soft gluonic fields can be factorized into a set of Wilson line correlators on the light cone. We review recent field-theoretical developments, rooted in the causal properties of these correlators, which simplify the calculation of the appropriate Wilson lines in thermal field theory. With these simplifications lattice measurements of transverse momentum broadening have become possible, and the kinetic equations describing parton transport have been extended to next-to-leading order in the coupling g., Comment: Review to appear in QGP5, 40 pages, 12 figures

We compute the transport coefficients (drag and momentum diffusion) of the low-lying heavy baryons $\Lambda_c$ and $\Lambda_b$ in a medium of light mesons formed at the later stages of high-energy heavy-ion collisions. We employ the Fokker-Planck approach to obtain the transport coefficients from unitarized baryon-meson interactions based on effective field theories that respect chiral and heavy-quark symmetries. We provide the transport coefficients as a function of temperature and heavy-baryon momentum, and analyze the applicability of certain nonrelativistic estimates. Moreover we compare our outcome for the spatial diffusion coefficient to the one coming from the solution of the Boltzmann-Uehling-Uhlenbeck transport equation and we find a very good agreement between both calculations. The transport coefficients for $\Lambda_c$ and $\Lambda_b$ in a thermal bath will be used in a subsequent publication as input in a Langevin evolution code for the generation and propagation of heavy particles in heavy-ion collisions at LHC and RHIC energies., Comment: 26 pages, 12 figures. Title changed. Small additions and corrections. Version accepted for publication by Physical Review D journal

In discussing Newton’s law of viscosity, we have described fluid motion as flowing parallel layers which, because of viscosity, establish a velocity gradient dependent upon the shear stress applied to the fluid. This velocity gradient has been regarded as a potential or a “reason” for momentum transport from layer to layer.

A generalized formulation of the Dynamic Smagorinsky Model (DSM) is proposed as a versatile turbulent momentum diffusion scheme for Large-Eddy Simulations. The difference to previous versions of the DSM is a modified test filter range that can be chosen independently from the resolution scale to separate the impact of the test filter on the simulated flow from the impact of the resolution. The generalized DSM (gDSM) in a two-dimensional version is validated in a verification study as a horizontal momentum diffusion scheme with the Kühlungsborn Mechanistic General Circulation Model at high resolution (wavenumber 330) without hyperdiffusion. Three-day averaged results applying three different test filters in the macro-turbulent inertial range are presented and compared with analogous simulations where the standard DSM is used instead. The comparison of the different filters results in all cases in similar globally averaged Smagorinsky parameters cS≃0.35$c_S\simeq0.35$ and horizontal kinetic energy spectra. Hence, the basic assumption of scale invariance underlying the application of the gDSM to parameterize atmospheric turbulence is justified. In addition, the smallest resolved scales contain less energy when the gDSM is applied, thus increasing the stability of the simulation.

We present an ordinary case in the momentum diffusion equation for the electron spectrum evolution and investigate the energy spectra and time dependent properties of flare in Mrk 421 in the frame of a time-dependent one-zone synchrotron self-Compton model. In this model, electrons are accelerated to extra-relativistic energy through the strong magnetic turbulence and evolve with time, and non-thermal photons are produced by both synchrotron and inverse Comtpon scattering off synchrotron photons. Moreover, non-thermal photons during a pre-flare are produced by the relativistic electrons in the steady state and those during a flare are produced by the electrons whose injection rate is changed during some time interval. We apply the model to the energy spectra and time-dependent properties of flares in Mrk 421 by reproducing the pre-burst spectrum of the source and varying the injection rate in the Bohm diffusion (q=1) and the hard sphere approximation (q=2) case, respectively. Our results show that Bohm diffusion case leads to hard photon spectra, and hard sphere case approximation seems to reproduce the energy spectra and the time dependent properties of flare still better., Comment: 10 pages, 7 figures, published in MNRAS (2014MNRAS.442.3166Z)

The effects of the vertical throughflow of a non-Newtonian power-law fluid on the onset of convective instability in a horizontal porous layer are investigated. The extended Darcy’s model of momentum diffusion is employed together with the Oberbeck–Boussinesq approximation. A stationary basic solution for the vertical throughflow is determined analytically. The basic velocity and temperature fields turn out to be independent of the non-Newtonian rheology. A linear stability analysis is carried out, leading to a fourth-order eigenvalue problem. A numerical solution of the eigenvalue problem is employed to obtain the neutral stability curves and the critical Rayleigh number for the onset of instability. The governing parameters of the transition to instability are the Peclet number associated with the throughflow, and the power-law index of the fluid. These parameters influence the position of the neutral stability curve and also the critical Rayleigh number. The asymptotic cases of absolute pseudoplasticity, absolute dilatancy, and small Peclet number are discussed in detail. The latter case leads to a simple analytical solution that approximates fairly well the numerical data when the Peclet number is smaller than unity.

The structure-rheology relationship in the shear alignment of a lamellar fluid is studied using a mesoscale model which provides access to the lamellar configurations and the rheology. Based on the equations and free energy functional, the complete set of dimensionless groups that characterize the system are the Reynolds number (rho gamma L-2/mu), the Schmidt number (mu/rho D), the Ericksen number (mu(gamma)/B), the interface sharpness parameter r, the ratio of the viscosities of the hydrophilic and hydrophobic parts mu(r), and the ratio of the system size and layer spacing (L/lambda). Here, rho and mu are the fluid density and average viscosity, (gamma) over dot is the applied strain rate, D is the coefficient of diffusion, B is the compression modulus, mu(r) is the maximum difference in the viscosity of the hydrophilic and hydrophobic parts divided by the average viscosity, and L is the system size in the cross-stream direction. The lattice Boltzmann method is used to solve the concentration and momentum equations for a two dimensional system of moderate size (L/lambda = 32) and for a low Reynolds number, and the other parameters are systematically varied to examine the qualitative features of the structure and viscosity evolution in different regimes. At low Schmidt numbers where mass diffusion is faster than momentum diffusion, there is fast local formation of randomly aligned domains with ``grain boundaries,'' which are rotated by the shear flow to align along the extensional axis as time increases. This configuration offers a high resistance to flow, and the layers do not align in the flow direction even after 1000 strain units, resulting in a viscosity higher than that for an aligned lamellar phase. At high Schmidt numbers where momentum diffusion is fast, the shear flow disrupts layers before they are fully formed by diffusion, and alignment takes place by the breakage and reformation of layers by shear, resulting in defects (edge dislocations) embedded in a background of nearly aligned layers. At high Ericksen number where the viscous forces are large compared to the restoring forces due to layer compression and bending, shear tends to homogenize the concentration field, and the viscosity decreases significantly. At very high Ericksen number, shear even disrupts the layering of the lamellar phase. At low Ericksen number, shear results in the formation of well aligned layers with edge dislocations. However, these edge dislocations take a long time to anneal; the relatively small misalignment due to the defects results in a large increase in viscosity due to high layer stiffness and due to shear localization, because the layers between defects get pinned and move as a plug with no shear. An increase in the viscosity contrast between the hydrophilic and hydrophobic parts does not alter the structural characteristics during alignment. However, there is a significant increase in the viscosity, due to pinning of the layers between defects, which results in a plug flow between defects and a localization of the shear to a part of the domain.

The present status of understanding of toroidal and poloidal momentum transport in tokamaks is presented in this paper. Similar energy confinement and momentum confinement times, i.e. tau(E)/tau(phi)approximate to 1 have been reported on several tokamaks. It is more important though, to study the local transport both in the core and edge plasma separately as, for example, in the core plasma, a large scatter in the ratio of the local effective momentum diffusivity to the ion heat diffusivity chi(phi eff)/chi(i.eff) among different tokamaks can be found. For example, the value of effective Prandtl number is typically around chi(phi eff)/chi(i.eff)approximate to 0.2 on JET while still tau(E)/tau(phi)approximate to 1 holds. Perturbative NBI modulation experiments on JET have shown, however, that a Prandtl number chi(phi)/chi(i) of around 1 is valid if there is an additional, significant inward momentum pinch which is required to explain the amplitude and phase behaviour of the momentum perturbation. The experimental results, i.e. the high Prandtl number and pinch, are in good qualitative and to some extent also in quantitative agreement with linear gyro-kinetic simulations. In contrast to the toroidal momentum transport which is clearly anomalous, the poloidal velocity is usually believed to be neo-classical. However, experimental measurements on JET show that the carbon poloidal velocity can be an order of magnitude above the predicted value by the neo-classical theory within the ITB. These large measured poloidal velocities, employed for example in transport simulations, significantly affect the calculated radial electric field and therefore the E x B flow shear and hence modify and can significantly improve the simulation predictions. Several fluid turbulence codes have been used to identify the mechanism driving the poloidal velocity to such high values. CUTIE and TRB turbulence codes and also the Weiland model predict the existence of an anomalous poloidal velocity, peaking in the vicinity of the ITB and driven dominantly by the flow due to the Reynold's stress. It is worth noting that these codes and models treat the equilibrium in a simplified way and this affects the geodesic curvature effects and geodesic acoustic modes. The neo-classical equilibrium is calculated more accurately in the GEM code and the simulations suggest that the spin-up of poloidal velocity is a consequence of the plasma profiles steepening when the ITB grows, following in particular the growth of the toroidal velocity within the ITB.

A new version of the Weiland model has been used in predictive JETTO simulations of toroidal rotation. The model includes a self-consistent calculation of the toroidal momentum diffusivity (chi(phi)) which contains both diagonal and non-diagonal (pinch) contributions to the momentum flux. Predictive transport simulations of JET H-mode, L-mode and hybrid discharges are presented. It is shown that experimental temperatures and toroidal velocity were well reproduced by the simulations. The model predicts the ion heat diffusivity (chi(i)) to be larger than the momentum diffusivity and it gives Prandtl numbers (Pr = chi(phi)/chi(i)) between 0.1 and 1. The Prandtl numbers are often, depending on the plasma conditions, predicted to be significantly smaller than unity. This is in accordance with experimental findings.

Particle simulations revealed that standard quasi-linear theory cannot adequately describe the parallel and perpendicular diffusion of cosmic rays in three-dimensional magnetohydrodynamic solar wind turbulence, when the turbulence is modeled approximately as a combination of a dominant two-dimensional component and a minor slab component. Recent nonlinear theories based on a Taylor-Green-Kubo formalism, such as the nonlinear guiding center (NLGC) theory, and the weakly nonlinear theory (WNLT) proved to be much more successful. Instead, we follow a BGK-Boltzmann approach to investigate this matter. Going beyond current NLGC theory and WNLT in scope, we derived a complete cosmic-ray transport theory that includes expressions not only for parallel and perpendicular diffusion, but also for drift, convection, adiabatic energy change, and momentum diffusion. The BGK-Boltzmann approach enables one to derive tractable yet complicated expressions for the transport coefficients in both the weak and strong particle scattering limits. We show that the WNLT expressions can be recovered by combining these two limits in such a way that there is weak particle scattering along the magnetic field but strong scattering across the field. It is shown that the complex WNLT expressions can be reduced to simple analytical expressions for parallel and perpendicular diffusion that reproduce approximately the rigidity dependence of particle simulations at low to medium rigidities. These expressions also prove to be consistent with well-known expressions for perpendicular diffusion in the literature. It is discussed how large-scale gradient and curvature drifts get modified by turbulence and how stochastic particle acceleration changes when two-dimensional turbulence is dominant.

The deformation structure in terms of shear band patterns in bulk metallic glasses (BMGs) under static indentation, dynamic indentation, and dynamic scratch tests has been investigated. The evolved shear band patterns appear to be a strong function of loading rate, although the plastic regions beneath the loading surface have similarities in shape irrespective of loading type. Comparison of currently available modeling estimates with experimental measurements has revealed that these models predict the plastic zone size reasonably well at low loads but deviate considerably at higher loads. The variation in spacing of shear bands is rationalized on the basis of the shear displacement accommodated by the shear bands formed under different loading rates, which results from a proposed shear-band formation mechanism based on the momentum diffusion model.

In this paper, we study the dissipative dynamics of the Jaynes-Cummings model with phase damping in the presence of a classical homogeneous gravitational field. The model consists of a moving two-level atom simultaneously exposed to the gravitational field and a single-mode traveling radiation field in the presence of the phase damping. We present a quantum treatment of the internal and external dynamics of the atom based on an alternative su(2) dynamical algebraic structure. By making use of the super-operator technique, we obtain the solution of the master equation for the density operator of the quantum system, under the Markovian approximation. Assuming that initially the radiation field is prepared in a Glauber coherent state and the two-level atom is in the excited state, we investigate the influence of gravity on the temporal evolution of collapses and revivals of the atomic population inversion, atomic dipole squeezing, atomic momentum diffusion, photon counting statistics and quadrature squeezing of the radiation field in the presence of phase damping.

In this paper, a numerical analysis of the momentum and heat transfer of an incompressible fluid past a parallel moving sheet based on composite reference velocity U is carried out. A single set of equations has been formulated for both momentum and thermal boundary layer problems containing the following parameters: r the ratio of the free stream velocity to the composite reference velocity, σ (Prandtl number) the ratio of the momentum diffusivity of the fluid to its thermal diffusivity, and E c (E ck ) (Eckert number). The present study has been carried out in the domain 0 ≤ r ≤ 1. It is found that the direction of the wall shear changes in such an interval and an increase of the parameter r yields an increase in temperature.

The characteristics of momentum transport and plasma rotation in the toroidal direction are studied, using near-perpendicular neutral beam injection (PERP-NBI), co tangential and counter (CTR) tangential NBI in JT-60U. Diffusive and non-diffusive terms of momentum transport are evaluated from the transient analysis by using the momentum source modulation. Fast ion losses due to the toroidal field ripple, which locally induces the edge CTR rotation, are used as a novel momentum source. Parameter dependence of these transport coefficients i.e. the toroidal momentum diffusivity (?) and the convection velocity (Vconv), and the relation between momentum and heat diffusivities (?i) are investigated in L-mode plasmas systematically. The toroidal momentum diffusivity increases with increasing heating power and decreases with increasing plasma current. The relation of ? and ?i to some non-dimensional parameters is investigated. A clear dependence of ?/?i on normalized plasma pressure (?N) is observed. It is also found that toroidal rotation velocity profiles in the case with and without external torque input can be almost reproduced by ? and Vconv estimated from the transient momentum transport analysis at low ? (?N < 0.4).