Formation of ripples over a sand bed submitted to a turbulent shear flow

We investigate the process of ripple formation when a sand bed is submitted to a steady and turbulent liquid flow. The sand transport dynamics is described in terms of a simple relaxation law which accounts for the fact that the transport rate does not adapt instantaneously to its equilibrium value. The equilibrium sand flux is evaluated using a standard law based on the estimation of the flow shear stress calculated at the sand bed surface. The latter is estimated from an analytical resolution of the flow over a deformed sand bed which is based on the Jackson and Hunt calculation [J.C.R. Hunt, Quart. J. R. Met. Soc. 101, 929 (1975)]. Within this model, we investigate the stability of the sand bed and are able to derive analytical scaling laws for the wavelength and phase velocity of the most dangerous mode. In the deep flow limit, the model predicts the occurrence of a single mode of instability corresponding to the formation of ripples. Predictions of our model are compared with previous models and available experimental data.     

Ripple formation in weakly turbulent flow

The formation of granular ripples under liquid shear flow in an annular channel is studied experimentally. The erodible granular bed is subject to weakly turbulent flows without a defined sharp boundary layer close to the granular bed. The flow field and the degree of turbulence is characterized quantitatively by using a particle image velocimeter and a laser-Doppler velocimeter, respectively. A new range of particle Reynolds numbers at the lower limit of the Shields diagram were explored. Quantitative measurements of the granular flow on the surface reveal that the threshold for particle motion coincides within the order of one percent with the threshold for ripple formation. In fully developed ripples it was found that on the leeward side of the ripples regions of low-velocity gradients exist where granular motion is scarce, indicating that the coupling between the ripples is mainly caused by the flow field of the liquid.     

Inertial range scaling of laminar shear flow as a model of turbulent transport

Asymptotic scaling behavior, characteristic of the inertial range, is obtained for a fractal stochastic system proposed as a model for turbulent transport.Research supported in part by the U.S. Department of Energy, contract DE-FG02-90ER25084Research supported in part by the U.S. Department of Energy, contract DE-FG02-90ER25084, the National Science Foundation, grant DMS-8901884, the Army Research Office, grant DAAL03-K-0017     

Experimental investigation on laminar separation control for flow over a two-dimensional bump

The laminar boundary layer separation flow over a two-dimensional bump controlled by synthetic jets is experimentally investigated in a water channel with hydrogen-bubble visualisation and particle image velocimetry (PIV) techniques. The two-dimensional synthetic jet is applied near the separation point. Two Reynolds numbers (Re = 700 and 1120) based on the bump height and free-stream velocity are adopted in this experiment, and seven different excitation frequencies at each Reynolds number are considered, focusing on the separation control as well as the vortex dynamics. The experimental results show that the optimal control can only be achieved within some excitation frequencies at both Reynolds numbers. However, beyond this range, further increasing the excitation frequency leads to an increase in the separation region. The proper orthogonal decomposition (POD) technique and vortex identification by swirling strength (Λ_ci) are applied for the deeper analysis of the separated flow. The reconstructed Λ_ci field by the first four POD modes is used and vortex lock-on phenomenon is observed. It is found that the negative synthetic jet vortex with clockwise rotation draws the separated wake shear layer as it is convected downstream, and then they syncretise together. Thus, the new vortex is induced and shedding downstream periodically.     

Long-time behavior of sand ripples induced by water shear flow

The formation of sand ripples under water shear flow in a narrow annular channel and the approach of the ripple pattern towards a steady state were studied experimentally. Four results are obtained: i) The mean amplitude, the average drift velocity and the mean sediment transport rate of the evolving bed shape are strongly related. A quantitative characterization of this relation is given. ii) The ripple pattern reaches a stationary state with a finite ripple amplitude and wavelength. The time needed to reach the state depends on the shear stress and may be several days. iii) The onset of ripple formation is determined by the bed shear stress, but it seems neither to depend on the grain diameter nor on the depth of the water layer. iv) The ripple amplitude, drift velocity and sediment transport in this stationary state depend on the grain size. This dependency is neither captured by the particle Reynolds number nor by the Shields parameter: an empirical scaling law is presented instead.     

Long-time behavior of sand ripples induced by water shear flow

The European Physical Journal E - The formation of sand ripples under water shear flow in a narrow annular channel and the approach of the ripple pattern towards a steady state were studied...     

Transition to turbulence in a shear flow

We analyze the properties of a 19-dimensional Galerkin approximation to a parallel shear flow. The laminar flow with a sinusoidal shape is stable for all Reynolds numbers Re. For sufficiently large Re additional stationary flows occur; they are all unstable. The lifetimes of finite amplitude perturbations shows a fractal dependence on amplitude and Reynolds number. These findings are in accord with observations on plane Couette flow and suggest a universality of this transition scenario in shear flows.     

超声速层流/湍流压缩拐角流动结构的实验研究

在Ma=3.0的超声速风洞中, 分别对上游边界层为超声速层流和湍流, 压缩角度为25°和28°的压缩拐角流动进行了实验研究. 采用纳米粒子示踪平面激光散射(NPLS)技术获得了流场整体和局部区域的精细结构, 边界层、剪切层、分离激波、回流区和再附激波等典型结构清晰可见, 测量了超声速层流压缩拐角壁面的压力系数. 从时间平均的流场结构中测量出分离激波、再附激波的角度和再附后重新发展的边界层的增长情况, 通过分析时间相关的流场NPLS图像, 可以发现流场结构随时间的演化特性. 实验结果表明: 在25°的压缩角度下, 超声速层流压缩拐角流动发生了典型的分离, 边界层迅速增长失稳转捩, 并引起一道诱导激波, 流场中出现了K-H涡、剪切层和微弱压缩波结构, 而超声速湍流压缩拐角流动没有出现分离, 湍流边界层始终表现为附着状态; 在28° 的压缩角度下, 超声速层流压缩拐角流动进一步分离, 回流区范围明显扩大, 诱导激波、分离激波向上游移动, 再附激波向下游移动, 分离区流动结构复杂, 相比之下, 超声速湍流压缩拐角流动的回流区范围明显较小, 边界层增长缓慢, 流场中没有出现诱导激波、K-H涡和压缩波, 流动分离区域的结构也相对简单, 但分离激波的强度则明显更强. 关键词： 压缩拐角 层流 湍流 流动结构     

Initiation and evolution of current ripples on a flat sand bed under turbulent water flow

We investigate the formation and dynamics of sand ripples under a turbulent water flow. Our experiments were conducted in an open flume with spherical glass beads between 100 and 500μm in diameter. The flow Reynolds number is of the order of 10 000 and the particle Reynolds number of the order of 1 to 10. We study the development of ripples by measuring their wavelength and amplitude in course of time and investigate the influence of the grain size and the flow properties. In particular, we demonstrate two different regimes according to the grain size. For fine grains, a slow coarsening process (i.e., a logarithmic increase of the wavelength and amplitude) takes place, while for coarser grains, this process occurs at a much faster rate (i.e., with a linear growth) and stops after a finite time. In the later case, a stable pattern is eventually observed. Besides, we carefully analyze the wavelength of ripples in the first stages of the instability as a function of the grain size and the shear velocity of the flow, and compare our results with other available experimental data and with theoretical predictions based on linear stability analyses.     

Instability of a lamellar phase under shear flow: formation of multilamellar vesicles

The formation of closed-compact multilamellar vesicles (referred to in the literature as the "onion texture") obtained upon shearing lamellar phases is studied using small-angle light scattering and cross-polarized microscopy. By varying the shear rate gamma;, the gap cell D, and the smectic distance d, we show that: (i) the formation of this structure occurs homogeneously in the cell at a well-defined wave vector q(i), via a strain-controlled process, and (ii) the value of q(i) varies as (dgamma;/D)(1/3). These results strongly suggest that formation of multilamellar vesicles may be monitored by an undulation (buckling) instability of the membranes, as expected from theory.     

Fluctuation background due to incompressible disturbances in laminar shear flows

The incompressible fluctuation background in laminar shear flows with a smooth velocity profile is investigated. Concrete calculations are performed for parallel Couette flow using nonmodal analysis of the linear dynamics of the disturbances. Nonmodal analysis makes it possible to grasp phenomena that could not be grasped in the early investigations, and thereby makes it possible to represent the fluctuation background in a completely new light: In incompressible shear flows the spatial spectral energy density of the fluctuation background is anisotropic, and furthermore in certain regions of wave-number space it is higher than that of the thermal noise. It is also shown that in the stationary state of the nonequilibrium system studied there exists a new, indirect channel for thermalization of the energy of the mean flow—energy is constantly transferred from the mean flow into the spatial Fourier harmonics of vortex pertubations and ultimately into heat. Possible manifestations of the fluctuation background described in this paper are listed. Zh. éksp. Teor. Fiz. 112, 1664–1674 (November 1997)     

Coupling effect of Brownian motion and laminar shear flow on colloid coagulation:a Brownian dynamics simulation study

Simultaneous orthokinetic and perikinetic coagulations(SOPCs) are studied for small and large Peclet numbers(P e) using Brownian dynamics simulation.The results demonstrate that the contributions of the Brownian motion and the shear flow to the overall coagulation rate are basically not additive.At the early stages of coagulation with small Peclet numbers,the ratio of overall coagulation rate to the rate of pure perikinetic coagulation is proportional to P 1/2 e,while with high Peclet numbers,the ratio of overall coagulation rate to the rate of pure orthokinetic coagulation is proportional to P 1/2 e.Moreover,our results show that the aggregation rate generally changes with time for the SOPC,which is different from that for pure perikinetic and pure orthokinetic coagulations.By comparing the SOPC with pure perikinetic and pure orthokinetic coagulations,we show that the redistribution of particles due to Brownian motion can play a very important role in the SOPC.In addition,the effects of redistribution in the directions perpendicular and parallel to the shear flow direction are different.This perspective explains the behavior of coagulation due to the joint effects of the Brownian motion(perikinetic) and the fluid motion(orthokinetic).     

Electro–magnetic control of shear flow over a cylinder for drag reduction and lift enhancement

In this paper, the electro-magnetic control of a cylinder wake in shear flow is investigated numerically. The effects of the shear rate and Lorentz force on the cylinder wake, the distribution of hydrodynamic force, and the drag/lift phase diagram are discussed in detail. It is revealed that Lorentz force can be classified into the field Lorentz force and the wall Lorentz force and they affect the drag and lift forces independently. The drag/lift phase diagram with a shape of ＂8＂ consists of two closed curves, which correspond to the halves of the shedding cycle dominated by the upper and lower vortices respectively. The free stream shear （K 〉 0） induces the diagram to move downward and leftward, so that the average lift force directs toward the downside. With the upper Lorentz force, the diagram moves downwards and to the right by the field Lorentz force, thus resulting in the drag increase and the lift reduction, whereas it moves upward and to the left by the wall Lorentz force, leading to the drag reduction and the lift increase. Finally the diagram is dominated by the wall Lorentz force, thus moving upward and leftward. Therefore the upper Lorentz force, which enhances the lift force, can be used to overcome the lift loss due to the free stream shear, which is also obtained in the experiment.     

An Exner-based coupled model for two-dimensional transient flow over erodible bed

Transient flow over erodible bed is solved in this work assuming that the dynamics of the bed load problem is described by two mathematical models: the hydrodynamic model, assumed to be well formulated by means of the depth averaged shallow water equations, and the Exner equation. The Exner equation is written assuming that bed load transport is governed by a power law of the flow velocity and by a flow/sediment interaction parameter variable in time and space. The complete system is formed by four coupled partial differential equations and a genuinely Roe-type first order scheme has been used to solve it on triangular unstructured meshes. Exact solutions have been derived for the particular case of initial value Riemann problems with variable bed level and depending on particular forms of the solid discharge formula. The model, supplied with the corresponding solid transport formulae, is tested by comparing with the exact solutions. The model is validated against laboratory experimental data of different unsteady problems over erodible bed.     

MHD laminar thin-film flow along a vertcal wall

An accelerating magnetohydrodynamic laminar flow of an electrically conducting fluid under the influence of gravity and in presence of transverse magnetic field is investigated in the paper. Using a cubic polynomial for the velocity profile inside the boundary layer, the momentum integral equation is solved numerically by Runge-Kutta method to determine the boundary layer thickness and the corresponding film thickness is then calculated for the entrance region. The effect of magnetic field on these solutions is shown in graphical form.List of symbols u, v local velocity components - p pressure - density - kinematic viscosity - viscosity= - electrical conductivity - g acceleration due to gravity - U _s (x) inviscid core velocity - h(x) film thicknes - (x) boundary layer thickness - M Hartmann number - B ₀ external magnetic field The authors remain thankful to the referee for some helpful criticisms.     

The pulsating laminar flow in a rectangular channel

The finite difference method is used to solve the task of the developed pulsating laminar flow in a rectangular channel. The optimum of the difference scheme parameters was determined. Data on the amplitude and phase of the longitudinal velocity oscillations, the hydraulic and friction drag coefficients, the shear stress on the wall have been obtained. Using the dimensionless value of the frequency pulsations two characteristic regimes — the quasisteady-state regime and the high-frequency regime have been identified. In the quasi-steady-state regime, the values of all hydrodynamic quantities at each instant of time correspond to the velocity value averaged over the cross section at a given moment of time. It is shown that in the high-frequency regime, the dependences on the dimensionless oscillation frequency of oscillating components of hydrodynamic quantities are identical for rectilinear channels with a different cross-sectional form (round pipe, flat and a rectangular channels). The effect of the aspect ratio of the rectangular channel sides channel on the pulsating flow dynamics has been analyzed.     

Dynamo quenching due to shear flow

We provide a theory of dynamo (alpha effect) and momentum transport in three-dimensional magnetohydrodynamics. For the first time, we show that the alpha effect is reduced by the shear even in the absence of magnetic field. The alpha effect is further suppressed by magnetic fields well below equipartition (with the large-scale flow) with different scalings depending on the relative strength of shear and magnetic field. The turbulent viscosity is also found to be significantly reduced by shear and magnetic fields, with positive value. These results suggest a crucial effect of shear and magnetic field on dynamo quenching and momentum transport reduction, with important implications for laboratory and astrophysical plasmas, in particular, for the dynamics of the Sun.     

Wall shear stress from single almost spherical and long Taylor bubbles in laminar upward tube flow

An experimental electrodiffusional technique with eight double probes is used to detect perturbation of the wall shear stress by a single bubble in laminar upward tube flow. Small almost spherical and long Taylor bubbles are tested. The wall shear stress perturbations by bubbles have a complex structure. It is possible to define three components of perturbation caused by a small bubble. The perturbation by Taylor bubble contains only two components due to the main flow symmetry around the bubble. An unexpectedly long shear stress pulsations zone is registered behind the Taylor bubbles.