The turbulent/nonturbulent interface in penetrative convection

The effect of buoyancy on the turbulent/nonturbulent interface (TNTI) and viscous superlayer are studied by performing direct numerical simulation of penetrative convection. In this flow, rising turbulent thermals alternate with unmixed fluid entrained from above, forming a TNTI between the turbulent and irrotational flow regions. We detect the TNTI using a broad range of enstrophy iso-levels, from the very low levels of the outer fringes of the turbulent flow region to high levels located in the turbulent flow region. We study the local entrainment velocity v_n by which the TNTI propagates outwards relative to the fluid flow while entraining unmixed fluid into the turbulent region. The relative entrainment velocity is decomposed into a viscous, an inertial and a baroclinic torque term, respectively. For low enstrophy levels we find a viscous superlayer (VSL) where viscous diffusion dominates, while inertial and baroclinic torque terms are small. It is only for higher iso-levels in the buffer region of the TNTI, which extends from the edge of the VSL to the threshold for which v_n = 0, that the inertial enstrophy production term plays a significant role. Penetrative convection does not feature a turbulent core where v_n > 0 (i.e. inward moving enstrophy isosurfaces) that has been previously identified in other entraining flows such as jets or gravity currents. Surprisingly, the baroclinic torque remains inactive throughout the whole range of enstrophy iso-levels. The smallness of the baroclinic torque against viscous effects in the TNTI is supported by a dimensional argument which predicts that at high Reynolds number the baroclinic torque term will be negligible.     

Effects of viscous fluid on wave propagation in carbon nanotubes

In this Letter, the effects of the viscous fluid on the propagation characteristics of elastic waves in carbon nanotubes are studied. Based on the nonlocal continuum theory, the small scales effects are also considered. The equations of wave motion are derived and the dispersion relation is presented. Numerical simulations are performed with the consideration of different scale coefficients to discuss the influence of the viscous fluid. From the results, it can be observed that the dispersion relation can be changed by the fluid viscosity obviously. Moreover, due to the fluid viscosity, the wave frequency will be reduced to a low region and the elastic wave behaviors can be significantly influenced by the viscous fluid velocity.     

流体黏性及表面张力对气泡运动特性的影响

基于气泡边界层理论,引入黏性修正,采用边界积分法,考虑黏性效应和表面张力在单气泡以及双气泡耦合作用过程中的影响.首先将建立的数值模型与Rayleigh-Plesset的解析解进行对比,发现二者符合良好,验证了数值模型的有效性;在此基础上,建立考虑流体弱黏性效应的双气泡耦合模型,研究流体黏性和表面张力作用下,气泡表面变形、射流速度、流场能量转换等物理量的变化规律;最后研究雷诺数和韦伯数对于气泡脉动特性的影响规律.结果表明,流体黏性会抑制气泡脉动和气泡射流发展,降低气泡半径和射流速度;表面张力不改变气泡脉动幅值,但缩短了脉动周期,提升气泡势能.     

Motion of dark solitons in trapped bose-einstein condensates

We use a multiple time scale boundary layer theory to derive the equation of motion for a dark (or grey) soliton propagating through an effectively one-dimensional cloud of Bose-Einstein condensate, assuming only that the background density and velocity vary slowly on the soliton scale. We show that solitons can exhibit viscous or radiative acceleration (antidamping), which we estimate as slow but observable on experimental time scales.     

Boundary layer theory modified for analysis of wave flow on the surface of a viscous liquid finite-thickness layer resting on a hard bottom

The theory of a boundary layer that is adjacent to the surface of an indefinitely deep viscous liquid and caused by its periodic motion is modified for analysis of finite-amplitude flow motion on the charged surface of a viscous conductive finite-thickness liquid layer resting on a hard bottom (the thickness of the layer is comparable to the wavelength). With the aim of adequately describing the viscous liquid flow, two boundary layers are considered: one at the free surface and the other at the hard bottom. The thicknesses of the boundary layers are estimated for which the difference between an exact solution and a solution to a model problem (stated in terms of the modified theory) may be set with a desired accuracy in the low-viscosity approximation. It is shown that the presence of the lower (bottom) boundary layer should be taken into account (with a relative computational error no more than 0.001) only if the thickness of the viscous layer does not exceed two wavelengths. For thicker layers, the bottom flow may be considered potential. In shallow liquids (with a thickness of two tenths of the wavelength or less), the upper (near-surface) and bottom layers overlap and the eddy flow entirely occupies the liquid volume. As the surface charge approaches a value that is critical for the onset of instability against the electric field negative pressure, the thicknesses of both layers sharply grow.     

Crossover between 2D and 3D fluid dynamics in the diffusion of islands in ultrathin freely suspended smectic films

The Stokes paradox, that moving a disk at finite velocity through an infinite two-dimensional (2D) viscous fluid requires no force, leads, via the Einstein relation, to an infinite diffusion coefficient D for the disk. Saffman and Delbrück proposed that if the 2D fluid is a thin film immersed in a 3D viscous medium, then the film should behave as if it were of finite size, and D～ -ln(aη'), where a is the inclusion radius and η' is the viscosity of the 3D medium. By studying the Brownian motion of islands in freely suspended smectic liquid crystal films a few molecular layers thick, we verify this dependence using no free parameters, and confirm the subsequent prediction by Hughes, Pailthorpe, and White of a crossover to 3D Stokes-like behavior when the diffusing island is sufficiently large.     

On the breakdown of stationary motion of a domain wall in bilayer uniaxial magnetic films with different signs of the gyromagnetic ratio in layers

The motion of an isolated domain wall in bilayer uniaxial magnetic films with a gyromagnetic ratio of different sign in the layers is studied by numerically solving the Slonczewski equations. The gyromagnetic ratio and the thickness of the layers are varied, and threshold values of the field and velocity of the domain wall at which a breakdown of its stationary motion takes place are calculated. It is shown that, for a specific relationship between the thickness and the gyromagnetic ratio of the layers, the field and the velocity for the breakdown of the stationary motion of the domain wall increase infinitely.     

Nonlinear vibration of viscoelastic embedded-DWCNTs integrated with piezoelectric layers-conveying viscous fluid considering surface effects

This article studies the nonlinear vibration of viscoelastic embedded nano-sandwich structures containing of a double walled carbon nanotube (DWCNT) integrated with two piezoelectric Zinc oxide (ZnO) layers. DWCNT and ZnO layers are subjected to magnetic and electric fields, respectively. This system is conveying viscous fluid and the related force is calculated by modified Navier–Stokes relation considering slip boundary condition and Knudsen number. Visco–Pasternak model with three parameters of the Winkler modulus, shear modulus, and damp coefficient is used for simulation of viscoelastic medium. The nano-structure is simulated as an orthotropic Timoshenko beam (TB) and the effects of small scale, structural damping and surface stress are considered based on Eringen's, Kelvin-voigt and Gurtin–Murdoch theories. Energy method and Hamilton's principle are employed to derive motion equations which are then solved using differential quadrature method (DQM). The detailed parametric study is conducted, focusing on the combined effects of small scale effect, fluid velocity, thickness of piezoelectric layer, boundary condition, surface effects, van der Waals (vdW) force on the frequency and critical velocity of nano-structure. Results indicate that the frequency and critical velocity increases with assume of surface effects.     

Layer-scale optical chirality of liquid-crystalline phases

We present a model for the optical chirality of layered liquid-crystalline phases. The model demonstrates that uniform stacking of chiral layers can lead to significant collective optical rotation, even in the absence of a superlayer helix. We predict the optical rotation of the B2 phases of bent-core liquid crystals, which can have optical rotation as large as 1000 times the molecular optical activity.     

Simulation of Viscous Flows Around a Moving Airfoil by Field Velocity Method with Viscous Flux Correction

Based on the field velocity method, a novel approach for simulating unsteady pitching and plunging motion of an airfoil is presented in this paper. Responses to pitching and plunging motions of the airfoil are simulated under different conditions. The obtained results are compared with those of moving grid method and good agreement is achieved. In the conventional field velocity method, the Euler solver is usually used to simulate the movement of the airfoil. However, when viscous effect is considered, unsteady Navier-Stokes equations have to be solved and the viscous flux correction must be taken into account. In this work, the viscous flux correction is introduced into the conventional field velocity method when non-uniform grid speed distribution is occurred. Numerical experiments for the flow around NACA0012 airfoil showed that the proposed approach can well simulate viscous moving boundary flow problems.     

The KdV-Burgers equation in speed gradient viscous continuum model

Based on the microscopic two velocity difference model, a macroscopic model called speed viscous continuum model is developed to describe traffic flow. The relative velocities are added to the motion equation, which leads to viscous effects in continuum model. The viscous continuum model overcomes the backward travel problem, which exists in many higher-order continuum models. Nonlinear analysis shows that the density fluctuation in traffic flow leads to density waves. Near the onset of instability, a small disturbance could lead to solitons described by the Korteweg-de Vries-Burgers (KdV-Burgers) equation, which is seldom found in other traffic flow models, and the soliton solution is derived.     

Phenomenology of Rayleigh-Taylor turbulence

I analyze the advanced mixing regime of the Rayleigh-Taylor incompressible turbulence in the small Atwood number Boussinesq approximation. The prime focus of my phenomenological approach is to resolve the temporal behavior and the small-scale spatial correlations of velocity and temperature fields inside the mixing zone, which grows as proportional, variant t(2). I show that the "5/3"-Kolmogorov scenario for velocity and temperature spectra is realized in three spatial dimensions with the viscous and dissipative scales decreasing in time, proportional, variant t(-1/4). The Bolgiano-Obukhov scenario is shown to be valid in two dimensions with the viscous and dissipative scales growing, proportional, variant t(1/8).     

Self-propelled particles with fluctuating speed and direction of motion in two dimensions

We study general aspects of active motion with fluctuations in the speed and the direction of motion in two dimensions. We consider the case in which fluctuations in the speed are not correlated to fluctuations in the direction of motion, and assume that both processes can be described by independent characteristic time scales. We show the occurrence of a complex transient that can exhibit a series of alternating regimes of motion, for two different angular dynamics which correspond to persistent and directed random walks. We also show additive corrections to the diffusion coefficient. The characteristic time scales are also exposed in the velocity autocorrelation, which is a sum of exponential forms.     

Viscous effects on motion and heating of electrons in inductivelycoupled plasma reactors

A transport model is developed for nonlocal effects on motion and heating of electrons in inductively coupled plasma reactors. The model is based on the electron momentum equation derived from the Boltzmann equation, retaining anisotropic stress components which in fact are viscous stresses. The resulting model consists of transport equations for the magnitude of electron velocity oscillation and terms representing energy dissipation due to viscous stresses in the electron energy equation. In this model, electrical current is obtained in a nonlocal manner due to viscous effects, instead of Ohm's law or the electron momentum equation without viscous effects, while nonlocal heating of electrons is represented by the viscous dissipation. Computational results obtained by two-dimensional numerical simulations show that nonlocal determination of electrical current indeed is important, and viscous dissipation becomes an important electron heating mechanism at low pressures. It is suspected that viscous dissipation in inductively coupled plasma reactors in fact represents stochastic heating of electrons, and this possibility is exploited by discussing physical similarities between stochastic heating and energy dissipation due to the stress tensor     

基于扩散速度方法粘性流场的离散涡数值模拟

基于扩散速度方法粘性流场的离散涡数值模拟吴文权，李春，卜千里（上海机械学院上海２０００９３）关键词：扩散速度模型，粘性流场，离散涡方法。ＮＵＭＥＲＩＣＡＬＳＩＭＵＬＡＴＩＯＮＯＦＶＩＳＣＯＵＳＦＬＯＷＦＩＥＬＤＳＵＳＩＮＧＤＩＦＦＵＳＩＯＮＶＥＬＯＣ...     

Effect of side walls on the motion of a viscous fluid induced by an infinite plate that applies an oscillating shear stress to the fluid

The velocity field corresponding to the unsteady motion of a viscous fluid between two side walls perpendicular to a plate is determined by means of the Fourier transforms. The motion of the fluid is produced by the plate which after the time t = 0, applies an oscillating shear stress to the fluid. The solutions that have been obtained, presented as a sum of the steady-state and transient solutions satisfy the governing equation and all imposed initial and boundary conditions. In the absence of the side walls they are reduced to the similar solutions corresponding to the motion over an infinite plate. Finally, the influence of the side walls on the fluid motion, the required time to reach the steady-state, as well as the distance between the walls for which the velocity of the fluid in the middle of the channel is unaffected by their presence, are established by means of graphical illustrations.     

Modification of the boundary layer theory for analysis of wave motions in a cylindrical jet of a viscous liquid

The existent concepts of the boundary layer near the free surface of a viscous liquid, which is related to its periodic motion, are modified with the aim of analyzing the finite-amplitude wave motion on the surface of a thick charged jet of a viscous conducting liquid. To describe the flow in the boundary layer, a model problem is proposed that is simpler in statement compared with the complete problem and the solution of which uses the governing properties of the exact solution obtained in the low-viscosity asymptotics: the form of the dispersion relation, wave profile, and rate of velocity field viscous damping with time. An estimate is made of the boundary layer thickness at which the discrepancy between the exact solution and solution to the model problem (stated in terms of the theory proposed) falls into a given interval in the low-viscosity asymptotics. The domain of applicability of the modified theory is determined.     

On calculation of the rate of mass transfer by periodic waves propagating over the surface of a viscous liquid

A generalization of the Stokes classical drift model describing mass transfer by periodic waves propagating over the surface of an infinitely deep incompressible liquid to the case of a viscous liquid is constructed. An analytic expression is proposed for the velocity of an additional flow into which the liquid is involved by horizontal viscous shear stresses emerging between adjacent horizontal layers of the liquid participating in the drift.     

Application of integral transforms to a description of the Brownian motion by a non-Markovian random process

The one-dimensional Brownian motion and the Brownian motion of a spherical particle in an infinite medium are described by the conventional methods and integral transforms considering the entrainment of surrounding particles of the medium by the Brownian particle. It is demonstrated that fluctuations of the Brownian particle velocity represent a non-Markovian random process. A harmonic oscillator in a viscous medium is also considered within the framework of the examined model. It is demonstrated that for rheological models, random dynamic processes are also non-Markovian in character. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 66–74, February, 2009.     

Negative differential viscosity in magnetic suspensions

Recent experiments have shown that the dependence of the macroscopic viscous stress on the mean velocity gradient during the Couette flow of concentrated magnetic suspensions in an external magnetic field is N-shaped. As the field strength is decreased, the amplitude of the N-shaped curve decreases and in the absence of the field, the stress monotonically increases with the shear velocity. A model is proposed to explain the shape of the rheological curve. The model assumes that the magnetic field initiates the formation of dense aggregates in a suspension, which connect the opposite walls of a measurement cell. In the Couette flow, the friction of aggregates on the cell walls causes their deviation from the applied magnetic field through an angle determined by the velocity of the relative motion of the walls. For large enough velocities, the aggregates are detached from the wall and are destroyed by viscous forces. It is shown that the friction of aggregates on cell walls results in the initial increasing and decreasing part of the N-shaped rheogram, while the flow after the detachment of aggregates corresponds to its right increasing part.