Generation of secondary instability modes in the interaction of a Tollmien-Schlichting wave with isolated roughness

The infinite plane channel flow arising from the impingement of a plane instability wave of finite amplitude on isolated three-dimensional wall roughness is considered. The problem of the transformation of perturbations developing on the roughness in growing modes of secondary instability is solved. This problem describes the development of perturbations leading to the occurrence of a turbulent wedge. Simple relations describing the flow at large distances from the roughness are obtained. From these relations it follows that the angle at the vertex of the turbulent wedge is determined by the amplitude of the impinging wave, while the value of the perturbations generated is proportional to the roughness volume.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 28–38, May–June, 1995.The work was carried out with the financial support of the Russian Foundation for Fundamental Research (project No. 93-013-17613).     

Scalar transport from a point source in flows over wavy walls

Simultaneous measurements of the velocity and concentration field in fully developed turbulent flows over a wavy wall are described. The concentration field originates from a low-momentum plume of a passive tracer. PLIF and digital particle image velocimetry are used to make spatially resolved measurements of the structure of the scalar distribution and the velocity. The measurements are performed at three different Reynolds numbers of Re _b = 5,600, Re _b = 11,200 and Re _b = 22,400, respectively, based on the bulk velocity u _b and the total channel height 2h. The velocity field and the scalar field are investigated in a water channel with an aspect ratio of 12:1, where the bottom wall of the test section consists of a train of sinusoidal waves. The wavy wall is characterized by the amplitude to wavelength ratio α = 0.05 and the ratio β between the wave amplitude and the half channel height where β = 0.1. The scalar is released from a point source at the wave crest. For the concentration measurements, Rhodamine B is used as tracer dye. At low to moderate Reynolds number, the flow field is characterized through a recirculation zone which develops after the wave crest. The recirculation zone induces high intensities of the fluctuations of the streamwise velocity and wall-normal velocity. Furthermore, large-scale structures are apparent in the flow field. In previous investigations it has been shown that these large-scale structures meander laterally in flows over wavy bottom walls. The investigations show a strong effect of the wavy bottom wall on the scalar mixing. In the vicinity of the source, the scalar is transported by packets of fluid with a high scalar concentration. As they move downstream, these packets disintegrate into filament-like structures which are subject to strong gradients between the filaments and the surrounding fluid. The lateral scale of the turbulent plume is smaller than the lateral scale of the large-scale structures in the flow field and the plume dispersion is dominated by the structures in the flow field. Due to the lateral meandering of the large-scale structures of the flow field, also the scalar plume meanders laterally. Compared to turbulent plumes in plane channel flows, the wavy bottom wall enhances the mixing effect of the turbulent flow and the spreading rate of the scalar plume is increased.     

Numerical modeling of gravity currents in inclined channels

The mixing and wave formation processes in gravity currents induced by the rupture of a vertical dam initially separating a heavy and a light liquid are studied for different channel inclination angles. The calculations are performed using the LES and RANS models. It is shown that when the heavy liquid moves down the channel slope, the longitudinal and transverse internal waves break and form turbulent mixing zones. When the heavy liquid ascends the slope, the wavy motion mode predominates.     

激波在不同三角楔面内传播特性的数值研究

激波在收缩管内的反射与聚焦会形成高温高压区,点燃可燃混合气并诱导爆轰,因此对爆轰发动机的点火具有重要意义。本文基于二维N-S方程,结合五阶WENO格式,对马赫数为6的正激波在三角形楔面内的反射与聚焦现象进行了数值研究。结果表明,楔面顶角的变化对激波的反射类型以及聚焦均有明显的影响:随着顶角的增加,激波的反射类型从马赫反射向过渡马赫反射和双马赫反射转变,且壁面上的前向射流更加明显;三波点第一次碰撞产生的高温高压区足够满足可燃混合气体的点火条件,且其温度与压力值随顶角的增加而增大;当激波在楔面上发生临界双马赫反射时,温度与压力达到最大;当顶角增加到一定值时,激波在楔面反射转变为常规反射,不会产生激波对碰,因而没有高温高压区。     

Distinctive features of heat transfer in the region of a gas curtain formed on injection of extraneous gas

New effects on a permeable surface on gas injection are detected on the basis of the numerical modeling of a turbulent boundary layer. It is shown, in particular, that in the gas curtain region the surface temperature can be considerably lower than the injected gas temperature. This effect manifests itself particularly strongly for gas mixtures with low Prandtl numbers.     

Breaking bore: Physical observations of roller characteristics

In an estuary, a tidal bore is a hydraulic jump in translation generated at the leading edge of the flood tide during the early flood tide under spring macrotidal conditions in a narrow funnelled channel. After formation, the bore is traditionally analysed as a hydraulic jump in translation and its leading edge is characterised by a breaking roller for Fr₁ > 1.3–1.5. Herein new unsteady experiments were conducted to investigate in details the upstream propagation of breaking bore roller. The toe perimeter shape fluctuated rapidly with transverse distance and time. A characteristic transverse wave length of the toe perimeter was observed. Both the standard deviation of toe perimeter location and characteristic transverse wave length were comparable to field observations. The celerity of the roller toe fluctuated rapidly with time and space. The instantaneous longitudinal profile of the roller free-surface showed significant temporal and spatial fluctuations. Although the bore propagation may be analysed in an integral form in first approximation, the rapid fluctuations in roller toe perimeter and free-surface profiles indicated a strongly three-dimensional turbulent flow motion.     

Orthogonal wavelet analysis of counter gradient transport phenomena in turbulent asymmetric channel flow

In this paper four families of orthogonal wavelets are applied to analyze the turbulent counter gradient transport phenomena in fully developed asymmetric channel flows. The results show that: (1) In the instance of counter gradient transport, the principal scale of the coherent structure is responsible for the strong local counter gradient transport; (2) Counter gradient transport phenomena have a strong effect on the intermittency of turbulence; (3) Non-Gaussian part of the principal coherent structure is essential for counter gradient transport phenomena.The project supported by the National Natural Science Foundation of China (10272071, 10472063)     

Numerical modeling of cohesive sediments dynamics in estuaries: Part I—Description of the model and simulations in the Po River Estuary

The present work contributes to the numerical modeling of complex turbulent multiphasic fluid flows occurring in estuarine channels. This research finds its motivation in the increasing need for efficient management of estuaries by taking into account the complex turbulent stratified flows encountered in estuaries and costal zones. A time‐dependent, 3D finite element model of suspended sediment transport taking into account the effects of cohesiveness between sediments is presented. The model estuary is the forced time‐dependent winds, time elevation at open boundaries and river discharge. To cope with the stiffness problems a decoupling method is employed to solve the shallow‐water equations of mass conservation, momentum and suspended sediment transport with the conventional hydrostatic pressure. The decoupling method partitions a time step into three subcycles according to the physical phenomena. In the first sub‐cycle the pure hydrodynamics including the k–ε turbulence model is solved, followed by the advection–diffusion equations for pollutants (salinity, temperature, suspended sediment concentration, (SSC)), and finally the bed evolution is solved. The model uses a mass‐preserving method based on the so‐called Raviart–Thomas finite element on the unstructured mesh in the horizontal plane, while the multi‐layers system is adopted in vertical with the conventional conforming finite element method, with the advantage that the lowermost and uppermost layers of variable height allow a faithful representation of the time‐varying bed and free surface, respectively. The model has been applied to investigate the SSC and seabed evolution in Po River Estuary (PRE) in Italy. The computed results mimic the field data well. Copyright © 2007 John Wiley & Sons, Ltd.     

柱形汇聚几何中内爆驱动金属界面不稳定性

采用自研的高保真度爆轰与冲击动力学程序,对柱形汇聚几何中内爆驱动金属材料界面不稳定性的动力学行为,进行了数值模拟研究。结果表明,首次冲击后至约12 μs,界面发展以RM（Richtmyer-Meshkov）不稳定性为主;12 μs后至冲击波聚心反弹加载前,界面聚心运动处于加速减速状态,界面发展由RT (Rayleigh-Taylor)不稳定性主导;冲击波聚心反弹加载后,界面发展又由RM不稳定性主导。另外,还研究了初始条件（初始振幅、初始波长、钢壳初始厚度和几何构型）对柱形内爆驱动金属材料界面不稳定性的影响。结果显示:初始振幅较大时振幅增长也较大;初始波长较小（模数较大）时振幅增长较小,而且存在一个截止波长;钢壳厚度会抑制扰动增长,也存在一个截止厚度;几何汇聚效应会使扰动增长速度更快。     

On the determination of the tidal amplitude in a river estuary having an irregular topography

A method based upon the balance of mechanical energy is used to calculate the local tidal amplitude in a river estuary. The technique permits the specification of an irregular topography and variable coefficient of eddy viscosity in the landward direction. Numerical calculations are performed for a river having the approximate dimensions of the Thames between Southend and Teddington. The fitting of the topography involves the specification of the mean width and depth by a suitable functional law along the river. The parametric representation of the turbulence may be quantified by prescribing that the local eddy viscosity be proportional to the local mean depth. The resulting evaluations are then used to assess the effect upon the tidal dynamics of nonuniformities in the topography and structure of the turbulence.     

Structure of turbulent two-dimensional channel flow with strongly heated wall

A laser Doppler velocimeter and a resistance thermometer were used to study velocity and temperature statistics in a strongly heated turbulent two-dimensional channel flow, with the wall temperature up to 700 °C and a Reynolds number of 14,000. Normalized mean velocity and mean temperature profiles were not significantly affected by the wall heating. Turbulent intensities of temperature fluctuation were also insensitive to the heat flux. However, turbulent intensities of velocity fluctuation were suppressed in the region away from the wall, whereas those near the wall were not changed noticeably by the wall heating. This phenomenon was explained by the balance of three parameters: turbulent production, viscous dissipation and intermittency.     

Experiments on the linear instability of flow in a wavy channel

The effects of wall corrugation on the stability of wall-bounded shear flows have been examined experimentally in plane channel flows. One of the channel walls has been modified by introduction of the wavy wall model with the amplitude of 4% of the channel half height and the wave number of 1.02. The experiment is focused on the two-dimensional travelling wave instability and the results are compared with the theory [J.M. Floryan, Two-dimensional instability of flow in a rough channel, Phys. Fluids 17 (2005) 044101 (also: Rept. ESFD-1/2003, Dept. of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, Canada, 2003)]. It is shown that the flow is destabilized by the wall corrugation at subcritical Reynolds numbers below 5772, as predicted by the theory. For the present corrugation geometry, the critical Reynolds number is decreased down to about 4000. The spatial growth rates, the disturbance wave numbers and the distribution of disturbance amplitude measured over such wavy wall also agree well with the theoretical results.     

Separation control by vortex generator devices in a transonic channel flow

An experimental study was conducted in a transonic channel to control by mechanical vortex generator devices the strong interaction between a shock wave and a separated turbulent boundary layer. Control devices—co-rotating and counter-rotating vane-type vortex generators—were implemented upstream of the shock foot region and tested both on a steady shock wave and on a forced shock oscillation configurations. The spanwise spacing of vortex generator devices along the channel appeared to be an important parameter to control the flow separation region. When the distance between each device is decreased, the vortices merging is more efficient to reduce the separation. Their placement upstream of the shock wave is determinant to ensure that vortices have mixed momentum all spanwise long before they reach the separation line, so as to avoid separation cells. Then, vortex generators slightly reduced the amplitude of the forced shock wave oscillation by delaying the upstream displacement of the leading shock.     

Wave turbulence and intermittency in directional wave fields

The evolution of surface gravity waves is driven by nonlinear interactions that trigger an energy cascade similarly to the one observed in hydrodynamic turbulence. This process, known as wave turbulence, has been found to display anomalous scaling with deviation from classical turbulent predictions due to the emergence of coherent and intermittent structures on the water surface. In the ocean, waves are spread over a wide range of directions, with a consequent attenuation of the nonlinear properties. A laboratory experiment in a large wave facility is presented to discuss the sensitivity of wave turbulence on the directional properties of model wave spectra. Results show that the occurrence of coherent and intermittent structures become less likely with the broadening of the wave directional spreading. There is no evidence, however, that intermittency completely vanishes.     

Scale properties of turbulent transport and coherent structure in stably stratified flows

The empirical mode decomposition (EMD) is used to study the scale properties of turbulent transport and coherent structures based on velocity and temperature time series in stably stratified turbulence. The analysis is focused on the scale properties of intermittency and coherent structures in different modes and the contributions of energy-contained coherent structures to turbulent scalar counter-gradient transport (CGT). It is inferred that the velocity intermittency is scattered to more modes with the development of the stratified flow, and the intermittency is enhanced by the vertical stratification, especially in small scales. The anisotropy of the field is presented due to different time scales of coherent structures of streamwise and vertical velocities. There is global counter-gradient heat transport close to the turbulence-generated grid, and there is local counter-gradient heat transport at certain modes in different positions. Coherent structures play a principal role in the turbulent vertical transport of temperature.     

Evaluation of tidal residual currents in a wide estuary,using a finite element method

From the linearized, time-independent, constant depth, shallow water tidal equations in an f-plane for a two-layer estuary, two independent modal Helmholtz equations are derived. These modal equations are solved using a fifth-degree finite element technique. The first and second space derivatives of the complex modal tidal elevations, and thus the modal currents and their first derivatives, are evaluated directly from the solution at each node of the finite element mesh. The Stokes drift, which is the major part of the residual tidal flow, is evaluated from these nodal values of the currents and their derivatives. Good agreement is obtained with the exact analytical solution for a wedge-shaped estuary with a wedge angle of π/3, using a mesh of 64 equilateral triangles with sides approximately 1/10 of the wavelength 2πC₂/σ of a Kelvin wave solution for the short-wavelength mode.     

Electrohydrodynamic peristaltic flow of a viscoelastic Oldroyd fluid with a mild stenosis: Application of an endoscope

The effect of a vertical alternating current, electric field, and heat transfer on a peristaltic flow of a dielectric viscoelastic Oldroyd fluid is studied. This analysis involves uniform and nonuniform annuli having a mild stenosis. The analytical solutions of equations of motion are based on the perturbation technique. This technique depends on two parameters: amplitude ratio and small wave number. Numerical calculations are performed to obtain the effects of several parameters, such as the electrical Rayleigh number, temperature gradient, Reynolds number, wave number, maximum height of stenosis, and Weissenberg numbers, on the distributions of velocity, temperature, electric potential, and wall shear stress. It is found that the above-mentioned distributions in the case of a convergent tapered tube are larger than those in the case of a non-tapered one as well as a diverging tapered tube.     

Investigation of Groundwater Contaminant Discharge into Tidally Influenced Surface-Water Bodies: Experimental Results

An investigation of the effect of tidally influenced water elevations on the concentration of groundwater contaminants discharging to a surface-water body is studied using a one-dimensional homogeneous sand column. A constant water level is imposed upstream, and the downstream water level is controlled by a wave generator that controls the hydraulic head to mimic a 12-h tidal fluctuation. The experimental results demonstrate that the tidal fluctuations in the downstream reservoir result in a decrease in average contaminant concentration at the point of discharge to the tidally influenced surface-water body. The further upstream an observation well is located, the smaller the amplitude of the concentration oscillation. Fourier analysis suggests that the dominant frequency of the pressure at different locations along the length of the column is identically two cycles per day and that the concentration data have a dominant frequency of two cycles per day, but also exhibit harmonics.     

Behaviour of liquid films and flooding in counter-current two-phase flow. Part 2. Flow in annuli and rod bundles

Experiments are described on the gas velocity at the onset of flooding and the maximum height of the wavy liquid film flowing downwards on a rod surface. On the basis of a simple analysis for a large amplitude wave on the liquid film, a flooding condition relating the maximum wave height to the gas velocity at the onset of flooding is derived. The values predicted by this condition show a good agreement with the measured results.An equivalent diameter of the channel is defined for the flooding velocity. Applying this diameter, the present data for annuli and rod bundles are well correlated by the same empirical equation as that for flow in circular tubes presented previously.