粘性涡方法在多圆柱绕流数值模拟中的应用

用粘性涡方法求解了涡量速度形式的二维不可压缩Navier—Stokes方程．利用分步方法分别求解无粘的对流运动和粘性扩散，粘性扩散用随机走步方法来处理，利用涡量交换技术来满足无滑移边界条件，同时为进一步减少计算量，在求解对流速度时，采用了多极子展开法加速技术使得计算量由N2的量级减少到NlogN的量级．数值模拟了单圆柱和双圆柱纵向排列的绕流流场．     

Fluctuations of energy flux in wave turbulence

We report that the power driving gravity and capillary wave turbulence in a statistically stationary regime displays fluctuations much stronger than its mean value. We show that its probability density function (PDF) has a most probable value close to zero and involves two asymmetric roughly exponential tails. We understand the qualitative features of the PDF using a simple Langevin-type model.     

Time-dependent and outflow boundary conditions for Dissipative Particle Dynamics

We propose a simple method to impose both no-slip boundary conditions at fluid-wall interfaces and at outflow boundaries in fully developed regions for Dissipative Particle Dynamics (DPD) fluid systems. The procedure to enforce the no-slip condition is based on a velocity-dependent shear force, which is a generalized force to represent the presence of the solid-wall particles and to maintain locally thermodynamic consistency. We show that this method can be implemented in both steady and time-dependent fluid systems and compare the DPD results with the continuum limit (Navier-Stokes) results. We also develop a force-adaptive method to impose the outflow boundary conditions for fully developed flow with unspecified outflow velocity profile or pressure value. We study flows over the backward-facing step and in idealized arterial bifurcations using a combination of the two new boundary methods with different flow rates. Finally, we explore the applicability of the outflow method in time-dependent flow systems. The outflow boundary method works well for systems with Womersley number of O(1), i.e., when the pressure and flowrate at the outflow are approximately in-phase.     

Dynamics of coin tossing is predictable

The dynamics of the tossed coin can be described by deterministic equations of motion, but on the other hand it is commonly taken for granted that the toss of a coin is random. A realistic mechanical model of coin tossing is constructed to examine whether the initial states leading to heads or tails are distributed uniformly in phase space. We give arguments supporting the statement that the outcome of the coin tossing is fully determined by the initial conditions, i.e. no dynamical uncertainties due to the exponential divergence of initial conditions or fractal basin boundaries occur. We point out that although heads and tails boundaries in the initial condition space are smooth, the distance of a typical initial condition from a basin boundary is so small that practically any uncertainty in initial conditions can lead to the uncertainty of the results of tossing.     

New evolution equations for the joint response-excitation probability density function of stochastic solutions to first-order nonlinear PDEs

By using functional integral methods we determine new evolution equations satisfied by the joint response-excitation probability density function (PDF) associated with the stochastic solution to first-order nonlinear partial differential equations (PDEs). The theory is presented for both fully nonlinear and for quasilinear scalar PDEs subject to random boundary conditions, random initial conditions or random forcing terms. Particular applications are discussed for the classical linear and nonlinear advection equations and for the advection–reaction equation. By using a Fourier–Galerkin spectral method we obtain numerical solutions of the proposed response-excitation PDF equations. These numerical solutions are compared against those obtained by using more conventional statistical approaches such as probabilistic collocation and multi-element probabilistic collocation methods. It is found that the response-excitation approach yields accurate predictions of the statistical properties of the system. In addition, it allows to directly ascertain the tails of probabilistic distributions, thus facilitating the assessment of rare events and associated risks. The computational cost of the response-excitation method is order magnitudes smaller than the one of more conventional statistical approaches if the PDE is subject to high-dimensional random boundary or initial conditions. The question of high-dimensionality for evolution equations involving multidimensional joint response-excitation PDFs is also addressed.     

Curvature of lagrangian trajectories in turbulence

We report measurements of the curvature of Lagrangian trajectories in an intensely turbulent laboratory water flow measured with a high-speed particle-tracking system. The probability density function (PDF) of the instantaneous curvature is shown to have robust power-law tails. We propose a model for the instantaneous curvature PDF, assuming that the acceleration and velocity are uncorrelated Gaussian random variables, and show that our model reproduces the tails of our measured PDFs. We also predict the scaling of the most probable vorticity magnitude in turbulence, assuming Heisenberg-Yaglom scaling. Finally, we average the curvature along trajectories and show that, by removing the effects of large-scale flow reversals, the filtered curvature reveals the turbulent features.     

湍流边界层内流向涡的数值模拟研究

采用准二维共振三波作为湍流边界层近壁区相干结构初值,用直接数值模拟方法计算了流动从二维结构发展到三维结构并且伴随流向涡生成的整个过程,分析结果显示流向涡对湍流动能和质量传输有着重要作用,是湍流边界层相干结构的重要特征和运动形式.     

Scalar dispersion by coherent structures in uniformly sheared flow generated in a water tunnel

In order to investigate the role of coherent structures as mechanisms of scalar dispersion, we studied measurements of a passive scalar plume released in a uniformly sheared turbulent flow generated in a water tunnel. The flow had homogeneous turbulence properties in the measurement domain and contained hairpin vortices similar to those in boundary layers, and so was an ideal test bed to study the effects of coherent structures on turbulent dispersion, free from the effects of inhomogeneities or boundaries. Measurements of the velocity and concentration fields were acquired simultaneously using stereo particle image velocimetry and planar laser-induced fluorescence. We found that dye was preferentially located far away from vortices and was less likely to appear in close proximity to vortices, which is attributed to the high dissipation at the periphery of the vortices. However, we also found that dye was not directly correlated with the uniform momentum zones in the flow, suggesting a more complex relationship exists between these zones, the locations of vortices, and dye transport. Considering scalar flux events rather than simply the presence of dye as our condition of interest, a conditional eddy analysis demonstrated that hairpin vortices are responsible for the large scalar flux events as well as the large Reynolds stress events in the flow. The fact that the Reynolds stress was correlated with the scalar flux further confirmed that coherent structures are dominant mechanisms for scalar transport. Furthermore, we found that the scalar flux vector was preferentially inclined by 155° and ?25° with respect to the streamwise direction, and was thus approximately orthogonal to the planes of the legs of the most common upright and inverted hairpin structures in the flow. These findings demonstrate that coherent structures play an important and intricate role in turbulent diffusion.     

Immersed boundary method for the simulation of 2D viscous flow based on vorticity–velocity formulations

A new immersed boundary method based on vorticity–velocity formulations for the simulation of 2D incompressible viscous flow is proposed in present paper. The velocity and vorticity are respectively divided into two parts: one is the velocity and vorticity without the influence of the immersed boundary, and the other is the corrected velocity and the corrected vorticity derived from the influence of the immersed boundary. The corrected velocity is obtained from the multi-direct forcing to ensure the well satisfaction of the no-slip boundary condition at the immersed boundary. The corrected vorticity is derived from the vorticity transport equation. The third-order Runge–Kutta for time stepping, the fourth-order finite difference scheme for spatial derivatives and the fourth-order discretized Poisson for solving velocity are applied in present flow solver. Three cases including decaying vortices, flow past a stationary circular cylinder and an in-line oscillating cylinder in a fluid at rest are conducted to validate the method proposed in this paper. And the results of the simulations show good agreements with previous numerical and experimental results. This indicates the validity and the accuracy of present immersed boundary method based on vorticity–velocity formulations.     

Effects of dimples on laminar boundary layers

A series of direct numerical simulations of the flow past a flat plate with two and eight rows of dimples in a staggered arrangement is carried out. The Reynolds number based on the boundary layer thickness and freestream velocity near the inflow plane is 1000 and the dimples are spherical with a depth to diameter ratio of 0.1. The incoming flow is laminar and the boundary layer thickness before the dimples is half the dimple depth. At this low Reynolds number the flow is expected to remain laminar over a smooth flat plate. The presence of the dimples triggers instabilities that cause significant momentum transport. It is shown that the shear layer that forms as the flow separates over the first two rows of dimple becomes unstable and sheds coherent vortex sheets. The vortex sheets become unstable and are transformed into packets of horseshoe vortices. When these vortices evolve over a flat plate or over a series of dimples the flow dynamics are very different with important changes in momentum transport across the boundary layer.     

New features of CS solitons and the formation of vortices

This work investigates, mainly by means of flow visualization, experimental aspects of nonlinear stages, aiming at the K-regime in boundary layer transition. Soliton-like coherent structures (CS solitons) and a new physical mechanism for the formation of vortices along the border of the CS soliton are found.     

Controlling density fluctuations in wall-bounded dissipative particle dynamics systems

Dissipative Particle Dynamics (DPD) simulations of wall-bounded flows exhibit density fluctuations that depend strongly on the no-slip boundary condition and increase with the level of coarse graining. We develop an adaptive model for wall-particle interactions that eliminates such oscillations and can target prescribed density profiles. Comparisons are made with ideal no-slip boundary conditions and molecular dynamics simulations. The new model is general and can be used in other coarse-grained particle methods.     

Anisotropic geophysical vortices

A survey is made of many types of coherent vortices in the Earth's ocean and atmosphere. These vortices often occur with strong, environmentally induced anisotropy in their velocity and vorticity fields. We propose a definition of the essential characteristics of coherent vortices and formulate hypotheses concerning their dynamical role in complex, anisotropic fluid motions. Finally, we analyze numerical solutions both for uniformly rotating, stably stratified three-dimensional flow and for two-dimensional flow for the phenomena of enstrophy cascade and dissipation, intermittency, isotropy in the appropriate coordinate frame, coherent vortex emergence, vortex population dynamics, and approach to a nonturbulent end state.     

Nanorheology: An investigation of the boundary condition at hydrophobic and hydrophilic interfaces

It has been shown that the flow of a simple liquid over a solid surface can violate the so-called no-slip boundary condition. We investigate the flow of polar liquids, water and glycerol, on a hydrophilic Pyrex surface and a hydrophobic surface made of a Self-Assembled Monolayer of OTS (octadecyltrichlorosilane) on Pyrex. We use a Dynamic Surface Force Apparatus (DSFA) which allows one to study the flow of a liquid film confined between two surfaces with a nanometer resolution. No-slip boundary conditions are found for both fluids on hydrophilic surfaces only. Significant slip is found on the hydrophobic surfaces, with a typical length of one hundred nanometers. Received 21 December 2001 and Received in final form 3 August 2002 RID="a" ID="a"e-mail: ccottin@dpm.univ-lyon1.fr RID="b" ID="b"Present address.     

Tunable-slip boundaries for coarse-grained simulations of fluid flow

On the micro- and nanoscale, classical hydrodynamic boundary conditions such as the no-slip condition no longer apply. Instead, the flow profiles exhibit "slip" at the surface, which is characterized by a finite slip length (partial slip). We present a new, systematic way of implementing partial-slip boundary conditions with arbitrary slip length in coarse-grained computer simulations. The main idea is to represent the complex microscopic interface structure by a spatially varying effective viscous force. An analytical equation for the resulting slip length can be derived for planar and for curved surfaces. The comparison with computer simulations of a DPD (dissipative particle dynamics) fluid shows that this expression is valid from full slip to no slip.     

Double-diffusive radiative magnetic mixed convective slip flow with Biot and Richardson number effects

This paper investigates combined heat and mass transfer by mixed magneto-convective flow of an electrically conducting flow along a moving radiating vertical flat plate with hydrodynamic slip and thermal convective boundary conditions. The governing transport equations are converted into a system of coupled nonlinear ordinary differential equations with prescribed boundary conditions using similarity variables developed by Lie group theory. The transformed nondimensional boundary value problem is then solved numerically with MAPLE13 quadrature. Excellent correlation with previous nonmagnetic, no-slip studies is achieved. Surface shear stress function and local Nusselt number (heat transfer gradient at the wall) are increased with Richardson number, whereas local Sherwood number is found to initially decrease then subsequently increase. The “thermally thick” scenario (Biot number > 0.1) is investigated and increasing Biot number is observed to enhance shear stress function (skin friction), local Nusselt number, and local Sherwood number. Increasing thermal radiation flux increases thermal boundary layer thickness as does increasing the magnetic field effect. Increasing hydrodynamic slip parameter reduces skin friction but enhances local Nusselt and Sherwood numbers. The study has applications in high-temperature polymeric synthesis and magnetic field flow control.     

Persistence problem in two-dimensional fluid turbulence

We present a natural framework for studying the persistence problem in two-dimensional fluid turbulence by using the Okubo-Weiss parameter Λ to distinguish between vortical and extensional regions. We then use a direct numerical simulation of the two-dimensional, incompressible Navier-Stokes equation with Ekman friction to study probability distribution functions (PDFs) of the persistence times of vortical and extensional regions by employing both Eulerian and Lagrangian measurements. We find that, in the Eulerian case, the persistence-time PDFs have exponential tails; by contrast, this PDF for Lagrangian particles, in vortical regions, has a power-law tail with an exponent θ=2.9±0.2.     

Arnold's method for asymptotic stability of steady inviscid incompressible flow through a fixed domain with permeable boundary

The flow of an ideal fluid in a domain with a permeable boundary may be asymptotically stable. Here the permeability means that the fluid can flow into and out of the domain through some parts of the boundary. This permeability is a principal reason for the asymptotic stability. Indeed, the well-known conservation laws make the asymptotic stability of an inviscid flow impossible, if the usual no flux condition on a rigid wall (or on a free boundary) is employed. We study the stability problem using the direct Lyapunov method in the Arnold's form. We prove the linear and nonlinear Lyapunov stability of a two-dimensional flow through a domain with a permeable boundary under Arnold's conditions. Under certain additional conditions, we amplify the linear result and prove the exponential decay of small disturbances. Here we employ the plan of the proof of the Barbashin-Krasovskiy theorem, established originally only for systems with a finite number of degrees of freedom. (c) 2002 American Institute of Physics.     

Energy dissipating structures produced by walls in two-dimensional flows at vanishing viscosity

We perform numerical experiments of a dipole crashing into a wall, a generic event in two-dimensional incompressible flows with solid boundaries. The Reynolds number (Re) is varied from 985 to 7880, and no-slip boundary conditions are approximated by Navier boundary conditions with a slip length proportional to Re(-1). Energy dissipation is shown to first set up within a vorticity sheet of thickness proportional to Re(-1) in the neighborhood of the wall, and to continue as this sheet rolls up into a spiral and detaches from the wall. The energy dissipation rate integrated over these regions appears to converge towards Re-independent values, indicating the existence of energy dissipating structures that persist in the vanishing viscosity limit.     

Rate-dependent slip of Newtonian liquid at smooth surfaces

Newtonian fluids were placed between molecularly smooth surfaces whose spacing was vibrated at spacings where the fluid responded as a continuum. Hydrodynamic forces agreed with predictions from the no-slip boundary condition only provided that flow rate (peak velocity normalized by spacing) was low, but implied partial slip when it exceeded a critical level, different in different systems, correlated with contact angle (surface wettability). With increasing flow rate and partially wetted surfaces, hydrodynamic forces became up to 2-4 orders of magnitude less than expected by assuming the no-slip boundary condition that is commonly stated in textbooks.