Momentum Diffusion Research Articles

Energetics and mixing efficiency of lock-exchange gravity currents using simultaneous velocity and density fields

A series of laboratory experiments on energy conserving gravity currents in a lock-exchange facility are conducted for a range of Reynolds numbers, $Re= \frac{U_Fh}{\nu} =$ 485-12270. The velocity and density fields are captured simultaneously using a PIV-PLIF system. A moving average method is employed to compute the mean field and a host of turbulence statistics, namely, turbulent kinetic energy ($K$), shear production ($P$), buoyancy flux ($B$), and energy dissipation ($\epsilon$) during the slumping phase of the current. The subsequent findings are used to ascertain the quantitative values of mixing efficiency, $Ri_{f}$, Ozmidov length-scale ($L_O$), Kolmogorov length-scale ($L_\kappa$), and eddy diffusivities of momentum ($\kappa_m$) and scalar ($\kappa_\rho$). Two different forms of $Ri_{f}$ are characterized in this study, denoted by $Ri_{f}^I=\frac{B}{P}$ and $Ri_{f}^{II}=\frac{B}{B+\epsilon}$. The results cover the entire diffusive regime (3 $<Re_b<$ 10) and a portion of the intermediate regime (10 $<Re_b<$ 50), where $Re_b=\frac{\epsilon}{\nu N^2}$ is the buoyancy Reynolds number that measures the level of turbulence in a shear-stratified flow. The values of $P$, $B$, and $\epsilon$ show a marked increase at the interface of the ambient fluid and the current, owing to the development of a shear-driven mixed layer. Based on the changes in the turbulence statistics and the length scales, it is inferred that the turbulence decays along the length of the current. The mixing efficiency monotonically increases in the diffusive regime ($Re_{b}<$10), and is found to have an upper bound of $Ri_{f}^{I}\approx$ 0.15 and $Ri_{f}^{II}\approx$ 0.2 in the intermediate regime. Using the values of $Ri_{f}$, the normalized eddy diffusivity of momentum is parameterized as $\frac{\kappa_m}{\nu.Ri_{g}}$=1.2$Re_{b}$ and normalized eddy diffusivity of scalar as $\frac{\kappa_{\rho}}{\nu}$=0.2$Re_{b}$

Keeping It Cool: Much Orbit Migration, yet Little Heating, in the Galactic Disk

Abstract A star in the Milky Way’s disk can now be at a Galactocentric radius quite distant from its birth radius for two reasons: either its orbit has become eccentric through radial heating, which increases its radial action J R (“blurring”), or merely its angular momentum L z has changed and thereby its guiding radius (“churning”). We know that radial orbit migration is strong in the Galactic low-α disk and set out to quantify the relative importance of these two effects, by devising and applying a parameterized model ( ) for the distribution in the stellar disk. This model describes the orbit evolution for stars of age τ and metallicity , presuming that coeval stars were initially born on (near-)circular orbits, and with a unique at a given birth angular momentum and age. We fit this model to APOGEE red clump stars, accounting for the complex selection function of the survey. The best-fit model implies changes of angular momentum of and changes of radial action as at 8 kpc. This suggests that the secular orbit evolution of the disk is dominated by diffusion in angular momentum, with radial heating being an order of magnitude lower.

Impact of longitudinal bulk viscous effects to heavy quark transport in a strongly magnetized hot QCD medium

The effects of longitudinal bulk viscous pressure on the heavy quark dynamics have been estimated in a strongly magnetized quark-gluon plasma within the Fokker-Planck approach. The bulk viscous modification to the momentum distribution of bulk degrees of freedom has been obtained in the presence of a magnetic field while incorporating the realistic equation of state of the hot magnetized QCD medium. As the magnetic field breaks the isotropy of the medium, the analysis is done along the directions longitudinal and transverse to the field. The longitudinal bulk viscous contribution is seen to have sizable effects in the heavy quark momentum diffusion in the magnetized medium. The dependence of higher Landau levels and the equation of state on the viscous correction to the heavy quark transport has been explored in the analysis.

Stability of liquid film flow laden with the soluble surfactant sodium dodecyl sulphate: predictions versus experimental data

Gravity-driven liquid film flows laden with a soluble surfactant are considered, and aqueous solutions of sodium dodecyl sulphate (SDS) are taken as a case-study. Literature measurements of the critical Reynolds number for the onset of instability are set in perspective with predictions of linear stability theory. The theory is based on a Frumkin model of adsorption equilibrium, modified by the inclusion of finite compressibility of the adsorbed monolayer. Quantitative comparison between data and theory is first attempted in the limit of infinite wavelength. Though wave characteristics are satisfactorily predicted, the theoretical critical Reynolds number is an order of magnitude below measurements. This discrepancy is understood in terms of the large difference between momentum and mass diffusivities and indicates that the assumption of infinite wavelength is far more restrictive for the mass transfer than for the flow problem. Finite-wavelength effects are taken into account by numerical solution of the Orr–Sommerfeld eigenvalue problem, leading to predictions of maximum stabilization in good agreement with the measurements. Introduction of realistic values of monolayer compressibility improves further the agreement at high surfactant loadings. Finally, a strong stabilizing effect of salinity is confirmed.

Momentum Diffusion Near Jet Exit in a Round Jet Controlled by Half Delta-Wing Tabs

Direct numerical simulations for a round jet controlled by half delta-wing tabs are performed to elucidate the transition of turbulent diffusion near the jet exit. The aim also involves clarifying the function of the tabs in round jet control. The jet Reynolds number is set as 10,000. The number of the tab is set to 3 and 6. The results reveal that the installation of the tabs generally decreases the turbulent diffusion coefficient except immediately after the jet exit of $$x/d<1.5$$ , where x is the streamwise direction and d is the diameter of the jet exit. The magnitude relation of the turbulent diffusion coefficient between the behind-the-tab area and between-the-tabs area changes along the streamwise direction in the upstream region of $$x/d<4$$ . Also turbulent diffusion does not always follow the conventional gradient-diffusion model there. On the other hand, in the downstream region of $$x/d \ge 4$$ , the difference in terms of the turbulent diffusion coefficient disappears between the two areas. However, the jet shape is triangular in the case of three tabs due to the remaining streamwise vortices generated by the tabs. This fact leads to the larger mean velocity gradient and momentum transport in the behind-the-tab area than those in the between-the-tabs area. Conversely, in the case with six tabs, the turbulent diffusion coefficients at the two areas become almost identical in the downstream region because the jet shape approaches a round shape.

Profile of Suspended Sediment Concentration in Submerged Vegetated Shallow Water Flow

AbstractThe vertical distribution pattern of the fine suspended sediment concentration (SSC) plays an important role in the aquatic ecosystem of shallow water. To investigate the SSC profile in submerged vegetated river flow, a series of indoor flume experiments was conducted. Glass spherical balls of three different diameters (40, 77, and 90 μm) with a uniform specific gravity of 2.5 were used for the model sediments. A set of sampling devices was designed for the simultaneous measurements of SSCs at multipoints along a vertical line. Experimental results show that the SSC profile was re‐distributed in the vegetated region, gradually forming a new equilibrium pattern in the overcanopy flow layer with its maximum occurring near the canopy top. From this maximum point near the canopy top, the suspended sediment formed a dynamic balance between upward turbulent diffusion and downward gravitational settling. Meanwhile, the momentum diffusivity was observed to linearly decrease upward from the maximum‐SSC elevation toward the water surface, thereby allowing us to deduce an empirical negative linear formula. Based on the convection‐diffusion equilibrium mechanism and with assistance of the empirical formula of flow momentum diffusivity, a new form of the Rouse formula was derived for the overcanopy flow layer. In general, this equation agrees well with the measured data. Some undercalculated deviations appear in the well‐above canopy zone due to the upskewed turbulence and the weak upward secondary flow. This deviation decreases with increasing sediment diameter. The bed deposition mainly comes from the deep part of canopy‐occupied flow layer.

Numerical analysis of three-dimensional MHD flow of Casson nanofluid past an exponentially stretching sheet

The convective three dimensional electrically conducting Casson nanofluid flow over an exponentially stretching sheet embedded in a saturated porous medium and subjected to thermal as well as solutal slip in the presence of externally applied transverse magnetic field (force-at-a-distance) is studied. The heat transfer phenomenon includes the viscous dissipation, Joulian dissipation, thermal radiation, contribution of nanofluidity and temperature dependent volumetric heat source. The study of mass diffusion in the presence of chemically reactive species enriches the analysis. The numerical solutions of coupled nonlinear governing equations bring some earlier reported results as particular cases providing a testimony of validation of the present study. The important findings are reported as Casson fluid contributes to accelerate the processes of momentum diffusivity but decelerates the thermal diffusivity. The effects of respective Biot numbers in temperature and concentration distributions are significant whereas cross effects are not. Further, the existence of chemical reaction stabilizes the characteristics of rate coefficients at the surface.

Unified theory of vibrational spectra in hard amorphous materials

The phonon spectra of solids, described through the measurable vibrational density of states (VDOS), provide a wealth of information about the underlying atomic structure and bonding, and they determine fundamental macroscopic properties such as specific heat, thermal conductivity and superconductivity. In amorphous solids, structural disorder generates a number of poorly understood phenomena that are absent in crystals. Starting from an effective field theory description which accounts for disorder in terms of momentum diffusion, we provide a unified theoretical description of the VDOS of amorphous materials. The theory provides an excellent description of the simulated/experimental VDOS of two quite different materials (silica glass and amorphous Si) with very few non-trivial fitting parameters. In particular, the phonons speeds and diffusive linewidths obtained from the fits are fully consistent with the tabulated values from experiments. This semi-analytical approach solves the long-standing problem of describing and explaining the features of the VDOS and Raman spectra of amorphous solids in relation with the underlying acoustic dispersion relations and acoustic attenuation. Furthermore, it can be used in a reverse-engineered way to estimate phonon dispersion relations, acoustic attenuation and dynamic structure factors from a simple fitting of the VDOS with the presented model.

Rebuttal on “A mathematical model on depth-averaged β-factor in open-channel turbulent flow” Environmental Earth Sciences 77:253 (2018)

In a recent paper published in Environmental Earth Sciences, Jain et al. (Environ Earth Sci 77:253, 2018) proposed an interesting study about the $$\beta$$-factor (the inverse of the turbulent Schmidt number, i.e. the ratio of momentum diffusivity to mass diffusivity in a turbulent flow). They proposed an equation for the depth-averaged $$\beta$$-factor which was used in the Rouse equation to calculate concentration profiles of suspended sediments in open-channel turbulent flows. Despite the interest, the study shows a weakness related to some inconsistencies and contradictions in the method. The main result should be improved. In this note, the weakness in this study will be pointed out. Some used equations are in contradiction with the initial assumptions. The Rouse equation is a solution of the steady-state one-dimensional convection–diffusion equation with a parabolic eddy viscosity which is based on a logarithmic velocity profile. In the same study, Jain et al. (2018) used two different mixing length equations, parabolic and linear relations. The parabolic mixing length and a constant mixing velocity are in contradiction with the used exponential-type eddy viscosity profile. The used equation for coefficient $$\gamma$$ is based on the finite mixing length model and the related assumptions of a linear eddy viscosity and a logarithmic velocity distribution (Nielsen and Teakle in Phys Fluids 16(7):2342–2348, 2004) which are in contradiction with the used exponential-type eddy viscosity profile and velocity distribution. An improved approach and new equations for the depth-averaged $$\beta$$-factor are proposed. The first is based on the equation for the coefficient $$A$$ proposed by Jain et al. (2018) and a second based on a linear function for $$A$$ which gives an equation for $$\beta$$ similar to that of van Rijn (J Hydraul Eng ASCE 1104(11):1613–1641, 1984).

Combined effects of partial slip and variable diffusion coefficient on mass and heat transfer subjected to chemical reaction

This article is a generalization of already published work and investigates the combined effects of chemical reaction, partial slip, temperature and concentration, jumps on the transport of heat energy and solute of variable mass conductance in a fluid of temperature dependent viscosity and thermal conductivity. Publish benchmark (Hayat et al 2015 Partial slip effects in flow over nonlinear stretching surface Appl. Math. Mech. 36 1513–26) is the special case of present work. It is also important to highlight that partial slip effects in the presence of variable diffusion coefficients are investigated first time. It is found that the distractive chemical reaction accelerates the rate of diffusion of solute. However, diffusion rate is decelerated by constructive chemical reaction. The concentration of solute in the liquid regime increases as the mass diffusion increases due to the rise in temperature. It is also observed that the diffusion of momentum of wall in fluid of constant viscosity is faster than the diffusion of momentum fluid of viscosity varying under rise in temperature. Further, an increase in thermal conductivity due to rise in temperature causes an enhancement in rate of heat conduction from wall into the fluid. Eventually, temperature of fluid rises.

Diffusion behaviors of energy and momentum for 1D single-walled carbon nanotubes

The single-walled carbon nanotube (CNT) is a quasi-1D material with ultra high thermal conductivity. It is known that the heat conduction is closely related with the energy diffusion and the information of heat conduction can be obtained by examining the energy diffusion behavior. The correlated energy distribution CE(i,t) calculated in diffusion process gives the whole spatial distribution of energy spreading at every correlation time which is much better than the traditional heat conduction method where only a number of thermal conductivity is provided. In previous study the anomalous super-diffusion of energy has been reported for CNT via a non-equilibrium diffusion method. Here we apply the more sophisticate equilibrium diffusion method to investigate the energy diffusion behavior in CNT with much longer length up to m with much higher accuracy. At room temperature, the super-diffusion of energy described by the mean square displacement of energy is found to be not far away from ballistic diffusion which is consistent with the experimentally measured ultra high thermal conductivity for CNT. With the equilibrium diffusion method, the diffusion of momentum has also been performed for CNT and ballistic diffusion is found which can be viewed as a support for anomalous super energy diffusion. The momentum diffusion can also give accurate information of sound velocity which is determined as m s−1 at room temperature. In particular, the very weak temperature coefficient of sound velocity can be obtained as m (. The normalized temperature coefficient of sound velocity can be related with the normalized temperature coefficient of Raman frequency shifts experimentally measured as . The obtained value via the momentum diffusion method is consistent with the experimental measurements.

Stellar Migration in Galaxy Disks Using the Chirikov Diffusion Rate

Abstract We are reexamining the problem of stellar migration in disk galaxies from a diffusion perspective. We use for the first time the formulation of the diffusion rates introduced by Chirikov, applied to both energy, E, and angular momentum, L z , in self-consistent N-body experiments. We limit our study to the evolution of stellar disks well after the formation of the bar, in a regime of adiabatic evolution. We show that distribution functions of Chirikov diffusion rates have similar shapes, regardless of the simulations, but different slopes for energy and angular momentum. Distribution functions of derived diffusion timescales, T D , also have the same form for all simulations, but are different for T D (E) and T D (L z ). Diffusion timescales are strongly dependent on L z . in a L z range roughly delimited by the set of stellar bar resonances (between the ultraharmonic resonance and the outer Lindblad resonance). Only particles with low L z have , i.e., the simulation length. In terms of mass fraction, 35%–42% turn out to diffuse energy in a characteristic timescale shorter than 10 Gyr, i.e., simulations length, while 60%–64% undergo the diffusion of the angular momentum on the same timescale. Both the diffusion of L z and E are important to grasp the full characterization of the radial migration process, and we show that depending on the spatial region considered, one or the other diffusion dominates.

Anomalous energy diffusion in two-dimensional nonlinear lattices.

Heat transport in one-dimensional (1D) momentum-conserved lattices is generally assumed to be anomalous, thus yielding a power-law divergence of thermal conductivity with system length. However, whether heat transport in a two-dimensional (2D) system is anomalous or not is still up for debate because of the difficulties involved in experimental measurements or due to the insufficiently large simulation cell size. Here we simulate energy and momentum diffusion in the 2D nonlinear lattices using the method of fluctuation correlation functions. Our simulations confirm that energy diffusion in the 2D momentum-conserved lattices is anomalous and can be well described by the Lévy-stable distribution. As is expected, we verify that 2D nonlinear lattices with on-site potentials exhibit normal energy diffusion, independent of the dimension. Contrary to the hypothesis of a 1D system, we further clarify that anomalous heat transport in the 2D momentum-conserved system cannot be corroborated by the momentum superdiffusion any longer. Our findings offer some valuable insights into mechanisms of thermal transport in 2D system.

Atom femto trap: experimental realization

In this work, we demonstrate the trapping of rubidium (Rb) atoms in a pulsed optical dipole trap formed by femtosecond laser radiation with a pulse duration as small as 70 fs. The atom localization in such trap strongly depends on the heating of the atoms caused by the momentum diffusion due to the dipole force fluctuations. The atom femto traps can be used for localization of atoms others than alkaline and alkaline earth atomic elements by conversation of pulsed laser radiation of visible or near infrared to UV spectral.

Viscous Fluid Flowing around the Plate: Turbulence

Diffusion of momentum gives rise to viscosity. This article presents a solution in the explicit form of the equation of the momentum diffusion for a viscous fluid flowing around a plate taking into account deceleration. Three characteristic regions of a viscous flow have been described: the mantle, the body of the boundary layer, the viscous sublayer. In the mantle, the effect of viscosity is significant at a considerable distance from the plate. The momentum diffusion is focused in the body of the boundary layer. The diffusion force that produces the momentum of force giving rise to eddies is localized in the viscous sublayer. At the beginning of the plate, a moment of force twists the liquid along the flow, creating eddies that roll along the plate. For this reason, they are pressed against the surface of the plate. But at some distance from the beginning of the plate, the moment of force changes its orientation to the opposite and twists the vortices in the opposite direction, causing the vortices to roll along the plate against the flow. This causes the liquid to detach from the surface of the plate. This is the beginning of turbulence. The diameter of the vortex produced in the viscous sublayer is small being of the order of the thickness of the viscous sublayer. The vortex possesses a large angular velocity. Due to the momentum diffusion and the effect of the eddies combined in passing along the plate, its diameter increases up to the size of the thickness of the boundary layer and even more, whereas its angular velocity decreases down to the values really observed. The value of the critical Reynolds number of the transition from the laminar flow to the turbulent one has been found, and it agrees with the experimental data. The value of the shear stress produced by the viscous fluid on the plate surface has also been obtained. The way of measurement of the friction coefficient characterizing the effect of the plate on the flow has been proposed. It has been shown that the boundary condition of adhesion to the surface of a body flown around, that is applied in the estimation of viscous flows, contradicts the real processes of the flow.

A fractional and analytic investigation of thermo-diffusion process on free convection flow: an application to surface modification technology

It is worth noted that soft and hard inchromizing entirely depends upon high temperature on materials. Due to this fact, thermal diffusion process can enhance the life expectancy of tools based on surface modification technology. The main objective of this investigation is to explore the thermo-diffusion effects on unsteady-free convection flow in the presence of magnetic field. For developing the governing equations of thermal diffusion process in terms of fractional differentiation, a modern approach of Atangana–Baleanu differential operator is invoked for knowing the memory effects on thermal diffusion process. The temperature, velocity, and concentration are obtained through analytical calculation via Laplace and Fourier sine transform methods. A parametric study is focused for hidden phenomenon of thermo-diffusion process which exhibits typical and rheological properties such as optimal temperature ranges, temperature resistance, increase or decrease of temperature, and few others. Finally, the characteristics of thermal diffusion process are presented graphically based on some physical parameters such as heat transfer (Grashof number), heat capacity (Prandtl number), enthalpy (Dufour number), momentum and mass diffusivity (Schmidt number), magnetization (magnetic field), and few other embedded parameters.

CFD-based analysis of entropy generation in turbulent double diffusive natural convection flow in square cavity

The present study concerns the problem of natural and double diffusive natural convection inside differentially heated cavity filled with a binary mixture composed of air and carbon dioxide (CO2). Temperature and CO2 concentration gradients are imposed on both perpendicular left and right walls. Simulations have been performed using the CFD commercial code ANSYS Fluent by solving continuity, momentum, energy and species diffusion equations. Numerical results obtained have been compared to data from the literature for both natural convection thermosolutal cases under laminar and turbulent regimes. For turbulent runs the RNG k-ε model has been selected. A good agreement has been noted between the different types of data for both cases for Rayleigh number ranging between 103 and 1010 and buoyancy ratio between -5 and +5. Entropy generation rates due to thermal, viscous and diffusive effects have been calculated in post processing for all cases.

Effect of couple stresses on the rheology and dynamics of linear Maxwell viscoelastic fluids

The constitutive analog of the linear Maxwell viscoelastic fluid model with the explicit addition of couple stresses is derived from thermodynamic first principles. Furthermore, the concepts of the recently proposed “Consistent Couple Stress theory” are considered to fully determine the rheological description of the fluid model. Finally, the resulting linear momentum equations are used to investigate the couple stress modulated flow dynamics of a few simple flow configurations. The plots of the variations in the elastic behavior of the fluid due to the presence of couple stresses show that the couple stress acts in addition to the conventional force-stress to increase the diffusion of momentum and thereby enhance the dampening of the elastic deformations in the equivalent spring-dashpot interpretation of the linear Maxwell viscoelastic fluid.

Experimental investigation of lower hybrid current drive induced plasma rotation on the experimental advanced superconducting tokamak

Rotation and its shear can reduce the magnetohydrodynamic instabilities and enhance the confinement. The LHCD has been proposed as a possible means of rotation driving on a future fusion reactor. Exploring the mechanisms of LHCD rotation driving on the current tokamaks can provide important reference for future reactors. On EAST, it was previously shown that 2.45 GHz LHCD can drive plasma toroidal rotation and the change of edge plasma rotation leads the co-current core rotation to increase. At higher frequency, 4.6 GHz lower hybrid wave can more effectively drive co-current plasma toroidal rotation. On EAST, at the lower current, the effects of different LHCD power on plasma toroidal rotation are analyzed. Higher power LHCD has a better driving efficiency. The effect of safety factor (&lt;i&gt;q&lt;/i&gt;) profile on toroidal rotation is also presented. The LHCD can change the profile of safety factor due to current drive. It is found that when the power exceeds 1.4MW, the &lt;i&gt;q&lt;/i&gt; profile remains unchanged and the rotation changes only very slightly with LHCD power, suggesting that the current profile is closely related to rotation. In order to further analyze the dynamic process of plasma toroidal rotation driven by lower hybrid current drive on EAST, the toroidal momentum transport due to LHCD is deduced by using the modulated LHCD power injection. Based on the momentum balance equation, the toroidal momentum diffusion coefficient (&lt;i&gt;χ&lt;/i&gt;&lt;i&gt;&lt;sub&gt;φ&lt;/sub&gt;&lt;/i&gt;) and the toroidal momentum pinch coefficient (&lt;i&gt;V&lt;/i&gt;&lt;sub&gt;pinch&lt;/sub&gt;) are obtained by the method of separation of variables and Fourier analysis for the region where the external momentum source can be ignored. It is found that the momentum diffusion coefficient (&lt;i&gt;χ&lt;/i&gt;&lt;sub&gt;&lt;i&gt;φ&lt;/i&gt;&lt;/sub&gt;) and momentum pinch coefficient (&lt;i&gt;V&lt;/i&gt;&lt;sub&gt;pinch&lt;/sub&gt;) tend to increase from the core to the outer region. This is consistent with the characteristic that the toroidal rotation velocity first changes in the outer region and then propagates to the core when the toroidal rotation is driven by LHCD.

Vertical Distribution of Suspended Sediments above Dense Plants in Water Flow

Plants in natural water flow can improve water quality by adhering and absorbing the fine suspended sediments. Dense plants usually form an additional permeable bottom boundary for the water flow over it. In the flow layer above dense plants, the flow velocity generally presents a zero-plane-displacement and roughness-height double modified semi-logarithmic profile. In addition, the second order shear turbulent moment (or the Reynolds stress) are different from that found in non-vegetated flow. As a result, the turbulent momentum diffusivity of flow and thus the diffusivity of sediment will shift, which will cause the vertical profile of suspended sediment and the corresponding Rouse formula deform. A set of physical experiments with three different diameters of fine suspended sediments was conducted in an indoor water flume. These experiments investigated a new distribution pattern of suspended sediment and the correspondingly deformed Rouse formula in the flow layer over the dense plants. Experimental results showed that above the dense plants, the shear turbulent momentum of flow presented a plant-height modified negative linear profile, which has been proposed by a previous study, and the vertical distribution of fine suspended sediments presented an equilibrium pattern. Based on the plant-modified profiles of flow velocity and the shear turbulent momentum a new zero-plane and plant-height double modified Rouse formula were analytically derived. This double-parameter modified Rouse formula agrees well with the measured profile of suspended sediment concentration experimentally observed in the present study. By adjusting the Prandtl–Schmidt number, i.e., the ratio of sediment diffusivity to flow diffusivity, the double-parameter modified Rouse formula can be applied to submerged dense plant occupied flow.