Momentum Diffusion Research Articles

Black Hole Scrambling from Hydrodynamics

We argue that the gravitational shock wave computation used to extract the scrambling rate in strongly coupled quantum theories with a holographic dual is directly related to probing the system's hydrodynamic sound modes. The information recovered from the shock wave can be reconstructed in terms of purely diffusionlike, linearized gravitational waves at the horizon of a single-sided black hole with specific regularity-enforced imaginary values of frequency and momentum. In two-derivative bulk theories, this horizon "diffusion" can be related to late-time momentum diffusion via a simple relation, which ceases to hold in higher-derivative theories. We then show that the same values of imaginary frequency and momentum follow from a dispersion relation of a hydrodynamic sound mode. The frequency, momentum, and group velocity give the holographic Lyapunov exponent and the butterfly velocity. Moreover, at this special point along the sound dispersion relation curve, the residue of the retarded longitudinal stress-energy tensor two-point function vanishes. This establishes a direct link between a hydrodynamic sound mode at an analytically continued, imaginary momentum and the holographic butterfly effect. Furthermore, our results imply that infinitely strongly coupled, large-N_{c} holographic theories exhibit properties similar to classical dilute gases; there, late-time equilibration and early-time scrambling are also controlled by the same dynamics.

Change of flow structure and heat transfer performance of photosensitive micellar solutions with light irradiation

Heat transfer enhancement in the low Reynolds number condition is increasingly required with the perpetual attempt to integrate and miniaturize electronic devices. The authors have suggested the application of photo-rheological fluid, whose rheological properties change by external photic stimulus, to a coolant of small heat exchangers. High heat transfer state and low pressured drop state can be switched by light irradiation to the fluid according to the demand for heat transfer enhancement. This study investigated how the change of viscoelasticity of photosensitive micellar solutions by light irradiation relates to flow structure and heat transfer performance. Flow visualization and heat transfer measurement were conducted using an aqueous solution of surfactant and counterions (cetyl-trimethyl-ammonium bromide/sodium salicylate/ortho-methoxy cinnamic acid) with different light irradiation time in serpentine channels. The results showed that the decrease of the viscoelasticity with light irradiation caused the decrease in heat transfer rate and pressure drop. In the flow visualization, two types of secondary vortex, i.e., a single large-scaled vortex and a pair of counter-rotating vortices, were observed. As the light irradiation time increased, flow unsteadiness diminished, and the frequency in the appearance of a single vortex and fast flow near wall decreased. The decrease in heat transfer rate and pressure drop with light irradiation was ascribed to the deterioration of fluid mixing by flow unsteadiness, the reduction of momentum and thermal diffusion by the decrease in near-wall velocity gradient, and the decrease in the strength of a pair of vortices.

The impact of slip conditions on magnetohydrodynamics radiating fluid beyond an exponentially extended sheet

A mathematical model is performed to analyse the magnetohydrodynamics (MHD) fluid flow and transmission of heat in the case of an exponentially extended sheet. The system is supressed by thermal radiation, which is constituted in the energy equation. The boundary contains velocity, thermal and mass slips. Similarity transformation is applied, to convert the governing equations (continuity, momentum, energy and mass diffusion equations) into ordinary differential equations (ODE). Then, the purpose of numerical shooting method is to perform the solutions in the ODE part. Finally, results are presented in the forms of table and graphs (skin friction coefficient, heat transfer rate, concentration gradient at the plate, and the profiles of velocity, temperature, concentration and concentration gradient) for various values of controlling parameters. The consequences of the controlling parameters on the system are described in details.

A new approach to evaluate the impact of thermophysical properties of nanofluids on heat transfer and pressure drop

In this paper, an experimental and numerical study was conducted to evaluate the impacts of momentum and thermal diffusivity comparing to the thermal conductivity of various types of nanofluids on turbulent forced convection heat transfer. 1%, 2%, and 3% volumetric concentrations of different nanofluids such as Al2O3-DW, SiO2-DW, and Cu-DW were considered in this study and their properties were evaluated numerically at the flow inlet temperature of 30 °C. The experimental works were conducted with distilled water as a working fluid to validate the 2-D numerical model. A two-dimensional domain was constructed using ANSYS-Fluent package, and the standard k–ε turbulence model was employed to solve the continuity, momentum, and energy equations. The flow was maintained in the Reynolds range between 6000 and 12,000, and the data obtained experimentally were validated by results from empirical correlations. The numerical solutions for the average Nusselt number and pressure drop presents a good agreement with the experimental results as the average error was less than 5% for both the cases of heat transfer and pressure loss data. The results showed that Al2O3-DW nanofluid has the best enhancement in convection heat transfer coefficient compared with the DW and other nanofluids of the same concentration while Cu-DW nanofluids shown the lowest enhancement though it shown the highest value of thermal conductivity. Also, the results showed that the product of kinematic and dynamic viscosities had the greatest effect on pressure drop in the fluid domain.

Study of subgrid-scale velocity models for reacting and nonreacting flows

A study is conducted to identify advantages and limitations of existing large-eddy simulation (LES) closures for the subgrid-scale (SGS) kinetic energy using a database of direct numerical simulations (DNS). The analysis is conducted for both reacting and nonreacting flows, different turbulence conditions, and various filter sizes. A model, based on dissipation and diffusion of momentum (LD-D model), is proposed in this paper based on the observed behavior of four existing models. Our model shows the best overall agreements with DNS statistics. Two main investigations are conducted for both reacting and nonreacting flows: (i) an investigation on the robustness of the model constants, showing that commonly used constants lead to a severe underestimation of the SGS kinetic energy and enlightening their dependence on Reynolds number and filter size; and (ii) an investigation on the statistical behavior of the SGS closures, which suggests that the dissipation of momentum is the key parameter to be considered in such closures and that dilatation effect is important and must be captured correctly in reacting flows. Additional properties of SGS kinetic energy modeling are identified and discussed.

Avaliação da dependência dos parâmetros de ajuste de um modelo E − l com a estratificação térmica estável

One of the main challenges of the atmospheric model is the proper determination of the turbulent diffusivity. In this sense, variousboundary 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 u2 ∗=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 windcomponents 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 studies of toroidal momentum transport in KSTAR H-mode and the effect of ion temperature perturbation

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.

Scale-Invariant Formulation of Momentum Diffusion for High-Resolution Atmospheric Circulation Models

A new version of the dynamic Smagorinsky model is presented that applies for nonisotropic momentum diffusion in high-resolution atmospheric circulation models. While the horizontal mixing length is computed in accordance with scale invariance in the mesoscale regime of the horizontal energy cascade, the associated dynamic vertical mixing length (DVML) is based on a recently developed scale invariance criterion and represents an application of the scaling laws of stratified macroturbulence. The DVML is validated in high-resolution simulations with the Kühlungsborn mechanistic general circulation model, using triangular spectral truncation at wavenumber 330 and a vertical level spacing of about 200 m in the upper troposphere. For a proper choice of the test filter, the model simulates a realistic horizontal kinetic energy spectrum in the troposphere along with a realistic intensity of the Lorenz energy cycle. This result is obtained without any hyperdiffusion, and it depends only little on whether the vertical mixing length is prescribed or set to the DVML. The globally averaged Smagorinsky parameter is about c S ≅ 0.53. The latitude–height cross sections show that c S maximizes in regions of strong mesoscale kinetic energy.

The influence of massive black hole binaries on the morphology of merger remnants

Massive black hole (MBH) binaries, formed as a result of galaxy mergers, are expected to harden by dynamical friction and three-body stellar scatterings, until emission of gravitational waves (GWs) leads to their final coalescence. According to recent simulations, MBH binaries can efficiently harden via stellar encounters only when the host geometry is triaxial, even if only modestly, as angular momentum diffusion allows an efficient repopulation of the binary loss cone. In this paper, we carry out a suite of N-body simulations of equal-mass galaxy collisions, varying the initial orbits and density profiles for the merging galaxies and running simulations both with and without central MBHs. We find that the presence of an MBH binary in the remnant makes the system nearly oblate, aligned with the galaxy merger plane, within a radius enclosing 100 MBH masses. We never find binary hosts to be prolate on any scale. The decaying MBHs slightly enhance the tangential anisotropy in the centre of the remnant due to angular momentum injection and the slingshot ejection of stars on nearly radial orbits. This latter effect results in about 1% of the remnant stars being expelled from the galactic nucleus. Finally, we do not find any strong connection between the remnant morphology and the binary hardening rate, which depends only on the inner density slope of the remnant galaxy. Our results suggest that MBH binaries are able to coalesce within a few Gyr, even if the binary is found to partially erase the merger-induced triaxiality from the remnant.

String-like collective motion in the α- and β-relaxation of a coarse-grained polymer melt.

Relaxation in glass-forming liquids occurs as a multi-stage hierarchical process involving cooperative molecular motion. First, there is a "fast" relaxation process dominated by the inertial motion of the molecules whose amplitude grows upon heating, followed by a longer time α-relaxation process involving both large-scale diffusive molecular motion and momentum diffusion. Our molecular dynamics simulations of a coarse-grained glass-forming polymer melt indicate that the fast, collective motion becomes progressively suppressed upon cooling, necessitating large-scale collective motion by molecular diffusion for the material to relax approaching the glass-transition. In each relaxation regime, the decay of the collective intermediate scattering function occurs through collective particle exchange motions having a similar geometrical form, and quantitative relationships are derived relating the fast "stringlet" collective motion to the larger scale string-like collective motion at longer times, which governs the temperature-dependent activation energies associated with both thermally activated molecular diffusion and momentum diffusion.

Precipitation loss of Van Allen radiation belt electrons by hiss waves outside the plasmasphere

Plasmaspheric hiss waves have been frequently invoked to explain the slow loss of the radiation belt electrons. However, the effect of hiss waves outside the plasmasphere on the radiation belt electrons remains unclear. Here, on the basis of Van Allen Probes observations and quasilinear simulations, we show that the hiss waves outside the plasmasphere are able to cause the significant precipitation loss of energetic electrons on a timescale of 1 day. In the event of interest, the hiss wave power spectra density reached up to \(10^{-6}~\mbox{nT}^{2}/\mbox{Hz}\), and the obtained pitch-angle diffusion coefficients are found to be \(10^{2}\)–\(10^{4}\) times larger than the momentum and cross diffusion coefficients. During a period of 1 day, the modeled hiss waves caused the depletion of 300–500 keV electrons by up to 10 times. These results suggest that the hiss waves outside the plasmasphere should be taken into account in the future radiation belt modeling.

QCD shear viscosity at (almost) NLO

We compute the shear viscosity of QCD with matter, including almost all next-to-leading order corrections — that is, corrections suppressed by one power of g relative to leading order. We argue that the still missing terms are small. The next-to-leading order corrections are large and bring η/s down by more than a factor of 3 at physically relevant couplings. The perturbative expansion is problematic even at T ≃ 100 GeV. The largest next-to-leading order correction to η/s arises from modifications to the widehat{q} parameter, which determines the rate of transverse momentum diffusion. We also explore quark number diffusion, and shear viscosity in pure-glue QCD and in QED.

The Effect of Area Ratio Change Via Increased Hole Length for Shaped Film Cooling Holes With Constant Expansion Angles

Shaped film cooling holes are used as a cooling technology in gas turbines to reduce metal temperatures and improve durability, and they generally consist of a small metering section connected to a diffuser that expands in one or more directions. The area ratio (AR) of these holes is defined as the area at the exit of the diffuser, divided by the area at the metering section. A larger AR increases the diffusion of the coolant momentum, leading to lower average momentum of the coolant jet at the exit of the hole and generally better cooling performance. Cooling holes with larger ARs are also more tolerant of high blowing ratio conditions, and the increased coolant diffusion typically better prevents jet lift-off from occurring. Higher ARs have traditionally been accomplished by increasing the expansion angle of the diffuser while keeping the overall length of the hole constant. The present study maintains the diffuser expansion angles and instead increases the length of the diffuser, which results in longer holes. Various ARs have been examined for two shaped holes: one with forward and lateral expansion angles of 7 deg (7-7-7 hole) and one with forward and lateral expansion angles of 12 deg (12-12-12 hole). Each hole shape was tested at numerous blowing ratios to capture trends across various flow rates. Adiabatic effectiveness measurements indicate that for the baseline 7-7-7 hole, a larger AR provides higher effectiveness, especially at higher blowing ratios. Measurements also indicate that for the 12-12-12 hole, a larger AR performs better at high blowing ratios but the hole experiences ingestion at low blowing ratios. Steady Reynolds-averaged Navier–Stokes simulations did not accurately predict the levels of adiabatic effectiveness, but did predict the trend of improving effectiveness with increasing AR for both hole shapes. Flowfield measurements with particle image velocimetry (PIV) were also performed at one downstream plane for a low and high AR case, and the results indicate an expected decrease in jet velocity due to a larger diffuser.

Alternating currents and shear waves in viscous electronics

Strong interaction among charge carriers can make them move like viscous fluid. Here we explore alternating current (AC) effects in viscous electronics. In the Ohmic case, incompressible current distribution in a sample adjusts fast to a time-dependent voltage on the electrodes, while in the viscous case, momentum diffusion makes for retardation and for the possibility of propagating slow shear waves. We focus on specific geometries that showcase interesting aspects of such waves: current parallel to a one-dimensional defect and current applied across a long strip. We find that the phase velocity of the wave propagating along the strip respectively increases/decreases with the frequency for no-slip/no-stress boundary conditions. This is so because when the frequency or strip width goes to zero (alternatively, viscosity go to infinity), the wavelength of the current pattern tends to infinity in the no-stress case and to a finite value in a general case. We also show that for DC current across a strip with no-stress boundary, there only one pair of vortices, while there is an infinite vortex chain for all other types of boundary conditions.

Resonant Scattering of Radiation Belt Electrons by Off‐Equatorial Magnetosonic Waves

AbstractFast magnetosonic (MS) waves are commonly regarded as electromagnetic waves that are characteristically confined within ±3° of the geomagnetic equator. We report two typical off‐equatorial MS events observed by Van Allen Probes, that is, the 8 May 2014 event that occurred at the geomagnetic latitudes of 7.5°–9.2° both inside and outside the plasmasphere with the wave amplitude up to 590 pT and the 9 January 2014 event that occurred at the latitudes of—(15.7°–17.5°) outside the plasmasphere with a smaller amplitude about 81 pT. Detailed test particle simulations quantify the electron resonant scattering rates by the off‐equatorial MS waves to find that they can cause the pitch angle scattering and momentum diffusion of radiation belt electrons with equatorial pitch angles < ~75° or < ~58° (depending on the wave latitudinal coverage) on timescales of a day. Subsequent two‐dimensional Fokker‐Planck diffusion simulations indicate that the strong off‐equatorial MS waves are capable of efficiently transporting high pitch angle electrons to lower pitch angles to facilitate the formation of radiation belt electron butterfly distributions for a broad energy range from ~100 keV to >1 MeV within an hour. Our study clearly demonstrates that the presence of off‐equatorial MS waves, in addition to equatorial MS waves, can contribute importantly to the dynamical variations of radiation belt electron fluxes and their pitch angle distribution.

On the phase lag of turbulent dissipation in rotating tidal flows

Field observations of rotating tidal flows in a shallow tidally swept sea reveal that a notable phase lag of both shear production and turbulent dissipation increases with height above the seafloor. These vertical delays of turbulent quantities are approximately equivalent in magnitude to that of squared mean shear. The shear production approximately equals turbulent dissipation over the phase-lag column, and thus a main mechanism of phase lag of dissipation is mean shear, rather than vertical diffusion of turbulent kinetic energy. By relating the phase lag of dissipation to that of the mean shear, a simple formulation with constant eddy viscosity is developed to describe the phase lag in rotating tidal flows. An analytical solution indicates that the phase lag increases linearly with height subjected to a combined effect of tidal frequency, Coriolis parameter and eddy viscosity. The vertical diffusion of momentum associated with eddy viscosity produces the phase lag of squared mean shear, and resultant delay of turbulent quantities. Its magnitude is inhibited by Earth's rotation. Furthermore, a theoretical formulation of the phase lag with a parabolic eddy viscosity profile can be constructed. A first-order approximation of this formulation is still a linear function of height, and its magnitude is approximately 0.8 times that with constant viscosity. Finally, the theoretical solutions of phase lag with realistic viscosity can be satisfactorily justified by realistic phase lags of dissipation.

Damping of zonal modes through turbulent momentum transport

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.

Delusions in Theoretical Hydrodynamics

Theoretical hydrodynamics may lead one into serious delusions. This article is focused on three of them. First, using flowing around a sphere as an example it is shown that the known potential solutions of the flow-around problems are not unique and there exist nonpotential solutions. A nonpotential solution has been obtained for flowing around a sphere. A general solution of the problem of flowing around an arbitrary surface has been obtained in the quadrature form. To single out a physically realisable solution among a great number of others, it is necessary to add supplementary conditions to the known boundary ones, in particular, to find a solution with the minimum total energy. The hypothesis explaining the reason for stalled flows by viscosity is erroneous. When considering a flow-around problem one should use stalled and broken solutions of the continuity equation along with the continuous ones. If the minimum total energy is achieved by the continuous solution, it is a continuous flow that will be implemented. If it is achieved by the broken solution, a stalled flow will be realised. Second, the hydrodynamics of a flow is considered exclusively at each point of it. Differential equations are used to describe the flows that are written for a randomly small volume of a flow, i.e., for a point. The integral characteristics of a flow and its inertial properties are neglected in the consideration, which results in the misunderstanding of the mechanism of the formation of a vortex. The reason for the formation of vortices is related to viscosity, which is a mistake. The formation of vortices is the result of the inhomogeneity of the acceleration field and the inertial properties of a flow. Third, the fictitious values of viscous stresses are used in hydrodynamics. As a matter of fact, viscosity is the momentum diffusion and it should be described by the diffusion equation included into the Euler system of equations for a viscous fluid. The momentum diffusion leads to the necessity of including the volume momentum sources produced by diffusion into the continuity equation and excluding the viscosity forces from the equation of motion. The problem of a viscous fluid flowing around a thin plate has been solved analytically, the velocity profiles satisfying the experiment have been obtained. The superfluidity of helium is not its property. It is the interaction of helium with a streamlined surface that is responsible for the mechanism of superfluidity. At low temperatures when the quantum properties are most pronounced the momentum transfer from the helium atoms to the streamlined wall becomes impossible, since the value of the energy transferred in the collision of a helium atom with that of the wall is smaller than the permitted quantum of energy. This mechanism takes place in the case of a flow in capillaries. Under a hydrodynamic flow-around superfluidity does not manifest due to the occurrence of stalled flows. The hypothesis of the disappearance of the viscous stresses at low temperatures is erroneous. The viscous stresses cannot disappear since they do not exist in nature. The theory of representing superfluidity as a phase transition accompanied by the formation of the combined viscous and nonviscous phases is a mistake.

Reinvestigation on mixing length in an open channel turbulent flow

The present study proposes a model on vertical distribution of streamwise velocity in an open channel turbulent flow through a newly proposed mixing length, which is derived for both clear water and sediment-laden turbulent flows. The analysis is based on a theoretical consideration which explores the effect of density stratification on the streamwise velocity profile. The derivation of mixing length makes use of the diffusion equation where both the sediment diffusivity and momentum diffusivity are taken as a function of height from the channel bed. The damping factor present in the mixing length of sediment-fluid mixture contains velocity and concentration gradients. This factor is capable of describing the dip-phenomenon of velocity distribution. From the existing experimental data of velocity, the mixing length data are calculated. The pattern shows that mixing length increases from bed to the dip-position, having a larger value at dip-position and then decreases up to the water surface with a zero value thereat. The present model agrees well with these data sets and this behavior cannot be described by any other existing model. Finally, the proposed mixing length model is applied to find the velocity distribution in wide and narrow open channels. The derived velocity distribution is compared with laboratory channel data of velocity, and the comparison shows good agreement.

Stability limits of the single relaxation-time advection–diffusion lattice Boltzmann scheme

In many cases, multi-species and/or thermal flows involve large discrepancies between the different diffusion coefficients involved — momentum, heat and species diffusion. In the context of classical passive scalar lattice Boltzmann (LB) simulations, the scheme is quite sensitive to such discrepancies, as relaxation coefficients of the flow and passive scalar fields are tied together through their common lattice spacing and time-step size. This in turn leads to at least one relaxation coefficient, [Formula: see text] being either very close to 0.5 or much larger than unity which, in the case of the former (small relaxation coefficient), has been shown to cause instability. The present work first establishes the stability boundaries of the passive scalar LB method in the sense of von Neumann and as a result shows that the scheme is unconditionally stable, even for [Formula: see text], provided that the nondimensional velocity does not exceed a certain threshold. Effects of different parameters such as the distribution function and lattice speed of sound on the stability area are also investigated. It is found that the simulations diverge for small relaxation coefficients regardless of the nondimensional velocity. Numerical applications and a study of the dispersion–dissipation relations show that this behavior is due to numerical noise appearing at high wave numbers and caused by the inconsistent behavior of the dispersion relation along with low dissipation. This numerical noise, known as Gibbs oscillations, can be controlled using spatial filters. Considering that noise is limited to high wave numbers, local filters can be used to control it. In order to stabilize the scheme with minimal impact on the solution even for cases involving high wave number components, a local Total Variation Diminishing (TVD) filter is implemented as an additional step in the classical LB algorithm. Finally, numerical applications show that this filter eliminates the unwanted oscillations while closely reproducing the reference solution.