An engineering model for countercurrent flow under wind-induced waves and current

A general model for the phase-averaged velocity field in wind-induced countercurrent flow is proposed. The influence of waves on the time-averaged velocity is accounted for by introducing a skewness factor in a parabolic eddy viscosity model. The skewness factor represents the net effect of the wavy surface in the engineering model for velocity. The coherent velocity components are described separately by an orbital velocity obtained from linear wave theory and are added to the time-averaged components to give a complete model for the phase-averaged velocity field. The proposed model collapses to the standard model for deep-water conditions, but is also shown to yield the correct behavior for intermediate conditions. Moreover, the bed shear stress, derived from the proposed velocity model, is also shown to be in agreement with experiments.     

Numerical modelling of horizontal sediment-laden jets

Sediment-laden turbulent flows are commonly encountered in natural and engineered environments. It is well known that turbulence generates fluctuations to the particle motion, resulting in modulation of the particle settling velocity. A novel stochastic particle tracking model is developed to predict the particle settling out and deposition from a sediment-laden jet. Particle velocity fluctuations in the jet flow are modelled from a Lagrangian velocity autocorrelation function that incorporates the physical mechanism leading to a reduction of settling velocity. The model is first applied to study the settling velocity modulation in a homogeneous turbulence field. Consistent with basic experiments using grid-generated turbulence and computational fluid dynamics (CFD) calculations, the model predicts that the apparent settling velocity can be reduced by as much as 30 % of the stillwater settling velocity. Using analytical solution for the jet mean flow and semi-empirical RMS turbulent velocity fluctuation and dissipation rate profiles derived from CFD predictions, model predictions of the sediment deposition and cross-sectional concentration profiles of horizontal sediment-laden jets are in excellent agreement with data. Unlike CFD calculations of sediment fall out and deposition from a jet flow, the present method does not require any a priori adjustment of particle settling velocity.     

Improved formulae of velocity distributions along the vertical and transverse directions in natural rivers with the sidewall effect

The distribution of flow velocity is a basis for the research into the transport of flow and sediment in natural rivers. Characteristics of velocity distribution in narrow-deep natural rivers are different from those in wide-shallow open channels, and the effect of sidewalls on the distribution of flow velocity is considerable, which leads to a large transverse gradient of the depth-averaged velocity, with the maximum velocity occurring below the water surface. Based on the Reynolds equation of turbulence flow and the analysis of the features of velocity distribution in natural rivers, improved formulae with two empirical parameters α and β have been proposed for the velocity distributions along the vertical and transverse directions, with the effect of sidewalls being considered, through solving the definite solution problem by the method of variable separation. The proposed formulae were validated fully through comparisons between the calculated and measured velocity profiles and depth-averaged velocities at several sections in the Yangtze and Baitarani Rivers, with close agreement between them being obtained. The formula of velocity distribution along the transverse direction in natural rivers with the sidewall effect was also compared with previous studies, and the calculation accuracy of this formula at a section with a narrow-deep geometry was higher than the accuracy of the previous equations. It is confirmed that the proposed formulae can reproduce well the distribution characteristics of flow velocity along the vertical and transverse directions in narrow-deep natural rivers, with a more wide application in practice.     

Analytical model for vertical velocity profiles in flows with submerged shrub-like vegetation

An analytical solution for the vertical profiles of the horizontal velocity of channel flow with submerged shrub-like vegetation is investigated in this paper. At first, a shape function is proposed to fit the diameter change of different types of shrub-like vegetation. Using the momentum theorem and the mixing-length turbulence model, an analytical solution for the vertical profile of the horizontal velocity within the vegetation is obtained. The velocity distribution of the whole column is determined in tandem with the logarithmic velocity profile above the vegetation. The solution is compared with experimental data in excellent agreement. The results show that the flow above the vegetation has a logarithmic velocity profile while the flow within the vegetation is impacted greatly by the shape and density of vegetation. The flows within shrub-like vegetations are non-uniform and vary inversely with the shrub diameter.     

Turbulent velocity profile in fully-developed open channel flows

The determination of velocity profile in turbulent narrow open channels is a difficult task due to the significant effects of the anisotropic turbulence that involve the Prandtl’s second type of secondary flow occurring in the cross section. With these currents the maximum velocity appears below the free surface that is called dip phenomenon. The well-known logarithmic law describes the velocity distribution in the inner region of the turbulent boundary layer but it is not adapted to define the velocity profile in the outer region of narrow channels. This paper relies on an analysis of the Navier–Stokes equations and yields a new formulation of the vertical velocity profile in the center region of steady, fully developed turbulent flows in open channels. This formulation is able to predict time averaged primary velocity in the outer region of the turbulent boundary layer for both narrow and wide open channels. The proposed law is based on the knowledge of the aspect ratio and involves a parameter C_Ar depending on the position of the maximum velocity (ξ_dip). ξ_dip may be derived, either from measurements or from an empirical equation given in this paper. A wide range of longitudinal velocity profile data for narrow open channels has been used for validating the model. The agreement between the measured and the computed velocities is rather good, despite the simplification used.     

Turbulent entrainment into fluid mud gravity currents

The entrainment of ambient water into non-Newtonian fluid mud gravity currents was investigated in this study. Constant volume release gravity currents were generated in a lock-exchange tank for a wide range of experimental conditions. A technique similar to the so-called light attenuation technique was used to find the boundary of the current, allowing for the calculation of both temporal and bulk entrainment parameters (in terms of the temporal and bulk entrainment velocities, respectively). It was found that the temporal entrainment velocity is dependent on different parameters in the different propagation phases. The slumping phase begins with an adjustment zone (henceforth, non-established zone) in which the temporal entrainment velocity is not a function of the current front velocity, followed by the established zone in which the temporal entrainment velocity is a function of the current front velocity. This dependence of the temporal entrainment velocity on the current front velocity carries through to the inertia-buoyancy phase. As expected, temporal entrainment velocity in the viscous-buoyancy phase was negligible in comparison to average entrainment velocity in the other phases. It is observed that the temporal entrainment characteristics in the non-established zone is governed by the competition between the entrainment-inhibiting density stratification effects and the entrainment-favouring effects of the Kelvin–Helmholtz billows that are quantified by the Richardson number and the Reynolds number of the gravity current, respectively. In the established zone, Reynolds number effects were observed to dominate over Richardson number effects in dictating temporal entrainment characteristics. A parameterization for the temporal entrainment velocity for non-Newtonian fluid mud gravity currents is developed based upon the experimental observations. This study also found that the bulk entrainment characteristics for the non-Newtonian fluid mud gravity currents can be parameterized by the Newtonian bulk entrainment parameterizations that rely solely on a bulk Richardson number. Interestingly, it was found that the non-Newtonian characteristics of the gravity current have little to no effect on the entrainment of the Newtonian ambient fluid.     

Mobility of free surface in different liquids and its influence on water striders locomotion

Dynamics of the surface layer in different liquids is examined by means of infrared thermography of the surface and simultaneous velocity fields measurements using surface and infrared Particle Image Velocimetry. This technique allows measurements and comparison of two velocity fields—at the surface and at small depth about 50–200 μm. In distilled water the velocity fields at the surface and at small depth exhibit significant dissimilarity. The flow field below the surface is essentially 3D, whereas the surface flow is characterized by vanishing 2D divergence of velocity, indicating predominantly planar motion. In contrast, in ethanol–butanol mixture two velocity fields are well correlated, both corresponding to 3D flow with continuous surface renewal. Thermal patterns, observed at the surface, and the flow field structure in different liquids are associated with different boundary conditions for velocity at the surface. Water surface is seldom renewed, which inhibits heat and mass exchange between the liquid and atmosphere. However, absence of vertical advection also enables organisms to live within the surface layer, to stand and walk on the free surface. This is illustrated by the difficulties a water strider faces on the surface of ultrapure water, which exhibits Marangoni convection.     

A modification of the classical Ekman model accounting for the Stokes drift and stratification effects

A modification of the classical Ekman model of oceanic wind-driven currents including the Stokes drift and stratification effects is discussed. The modification is formulated as an application of turbulence mechanics accounting for the curvature effect of velocity fluctuation streamlines. It is shown that similar to the Stokes drift effect, the presence of a density jump layer (pycnocline) decreases the veering of the flow velocity vector at the surface from the direction of the wind stress. It is shown also that in the pycnocline the decrease of the norm of the velocity vector as well as its rotation with depth is smaller than in the regions adjacent to the pycnocline. If the Stokes drift and stratification effects are neglected, the model reduces to the classical Ekman solution with the coefficient of the turbulent shear viscosity replaced by an effective viscosity coefficient. The vertical distributions of velocity predicted by the modified model are compared with the velocity data measured in the Drake Passage and within the Long-Term Upper Ocean Study (LOTUS) in the North Atlantic.     

Effects of stream hydraulic conditions on foraging strategies of false dace, Pseudorasbora parva, in the lentic ecosystem

The effects of current velocity on the foraging behavior of false dace, Pseudorasbora parva, were examined in a zero velocity (stagnant) condition, and at four flow rates (5, 7, 11 and 16 cm per second). In stagnant water, the fish displayed a cruise-searching pattern, but they used a drift-feeding foraging tactic in flowing water. The shape of the transverse field of reaction field was elliptical in the stagnant condition, whereas their downward regions were restricted under the flowing conditions. The fish had a blind spot oriented directly in front of their reaction field. Although the relative swimming speed (with considering the against current velocity) increased with increasing flow velocity, the absolute search speed (ignore the against current velocity) showed about 1.2 fish body length per second at stagnant water and low flow velocity. The results of feeding rates showed stop-and wait (driff-feeding) foraging strategy is more efficient in flowing water because prey drift directly towards the fish and prey easily detected.     

Drift velocity in sediment-laden downward jets

Environmental Fluid Mechanics - The drift velocity, defined as the velocity of individual phase relative to the water–sediment mixture, is a key variable in two-phase mixture model. In this...     

Characteristics of surface layer turbulence in coastal area of Qatar

A characterization of the atmospheric surface layer in coastal region of Qatar is presented in the present paper. The micrometeorological data is collected in the New Doha International Airport (25.25N, 51.62E), at a pier 500 m into the ocean by deploying tower based instruments during the month of June-2011. The normalized variance of the three components of velocity and temperature are studied within the framework of Monin–Obukhov similarity theory. The normalized variances of stream wise and transverse velocity at near-neutral condition are found to be consistent with the reported values from measurement sites around the world, but the normalized variance of vertical velocity at near-neutral condition is found to be consistently lower in the present case. The dependency of the normalized velocity variances with buoyancy parameter indicates a higher growth rate of variances, compared to other investigations. The non-dimensional variance of temperature matches well with the past investigations, but the correlation between vertical velocity and temperature indicates higher magnitude for the present location.     

Streamwise velocity profiles in coastal currents

The ability to model marine currents can be a powerful device for many planning activities, for which the knowledge of the velocity field is of pivotal importance, such as the evaluation of current-induced loading on maritime structures or the diffusion and dispersion of polluted flow discharges. Observations of time-averaged velocity profiles, taken with a vessel mounted acoustic Doppler current profiler during a monitoring survey program in the seas of Southern Italy, are analysed in this paper. The measurements were taken under non-breaking conditions, offshore the surf zone, with the aim of reproducing the vertical trends of the streamwise velocity by means of standard theoretical laws. To evaluate also the possible influence of stratification on the current velocity profile shape, together with velocity measurements water temperature and salinity were also measured at the same time and locations, by means of a CTD recorder. The examined surveys referred to different time periods and sites, to guarantee a general validity of deductions. On the basis of the experiments, we verified the actual existence of a log-layer and concluded that the upper limit of the region in which the log law is applicable extends well beyond the inner region. Moreover, the deviations of the measured velocity from the logarithmic profiles above the height of the log layer is consistent with the effects of stratification. The parameters of the log law were estimated, depending on both flow dynamics and stratification in the target area. As a second step, in the most superficial and stratified layer, the velocity profiles were modelled by means of a power law, which fitted the measured data well. According to previous studies, the power law parameters result Reynolds number dependent by means of a new proposed formulation. Finally, the bottom stress and the bottom drag coefficient were investigated.     

Mechanism of the intermittent motion of two-phase debris flows

A typical two-phase debris flow exhibits a high and steep flow head consisting of rolling boulders and cobbles with intermittent or fluctuating velocity. The relative motion between the solid phase and the liquid phase is obvious. The motion of a two-phase debris flow depends not only on the rheological properties of the flow, but also on the energy transmission between the solid and liquid phases. Several models have been developed to study two-phase debris flows. An essential shortcoming of most of these models is the omission of the interaction between the two phases and identification of the different roles of the different materials in two-phase debris flows. The tracer particles were used for the velocity of solid phase and the velocity of liquid phase was calculated by the water velocity on the surface of the debris flow in the experiments. This paper analyzed the intermittent feature of two-phase debris flows based on videos of debris flows in the field and flume experiments. The experiments showed that the height of the head of the two-phase debris flow increased gradually in the initiation stage and reached equilibrium at a certain distance from the start of the debris flow. The height growth and the velocity of the flow head showed fluctuating characteristics. Model equations were established and the analyses proved that the average velocity of the two-phase debris flow head was proportional to the flood discharge and inversely proportional to the volume of the debris flow head.     

Idealized study on cohesive sediment flux by tidal asymmetry

The flux of cohesive sediment in an estuary is determined by many factors, including tidal asymmetry, wave effect, fluvial influence, phase difference between tidal velocity and tidal level fluctuations, sediment properties, flocculation, bed erodibility, bathymetry effect and other nonlocal effects. Our capability in predicting sediment fluxes in tide-dominant environments is critical to the morphodynamics and water quality of estuaries. Due to the difficulties in carrying out detailed measurement of sediment flux with high spatial and temporal resolutions, an one-dimensional-vertical (1DV) numerical model for cohesive sediment transport, previously verified and calibrated with field measured cohesive sediment concentration data, is utilized here to study some of the aforementioned factors in affecting tidal-driven sediment fluxes in idealized condition. Tidal-averaged sediment flux is shown to be correlated with tidal velocity skewness with a linear relationship. This linear relationship is different from that of non-cohesive sediment and it is demonstrated here to be mainly due to variable critical shear stress implemented for the mud bed in order to parameterize consolidation. The reason that tidal velocity skewness causes tidal-averaged residual sediment transport is shown to be due to nonlinear intra-tidal interactions between flow velocity and sediment concentration. Moreover, the effects of nonlinear intra-tidal interaction between tidal velocity and tidal level fluctuations is shown to mainly cause seaward transport, which is the most significant under progressive wave system (phase difference 90°) and almost negligible for standing wave system (phase difference 0°).     

Flow structure of unconfined turbidity currents interacting with an obstacle

Driven by a growing importance to engineered structures, investigating the flow characteristics of turbidity currents interacting with a basal obstruction has become popular over the last three decades. However, research has focused on confined studies or numerical simulations, whereas in situ turbidity currents are typically unconfined. The present study investigates experimentally the velocity and turbulence structure of an unconfined turbidity current, in the immediate regions surrounding a rectangular obstacle. Initial density of the current, and substrate condition is varied. Through a novel technique of installing ultrasonic probes within the obstacle, the presence of a velocity recirculation region immediately upstream and downstream of the obstacle is revealed and confirmed with high-resolution imagery. This was found to be comparable to previous confined studies, suggesting that stream-wise velocity profile structure is somewhat independent of confinement. The obstacle was found to reduce velocity and turbulence intensity maxima downstream of the obstacle when compared with unobstructed tests.     

Numerical simulation for impacts of hydrodynamic conditions on algae growth in Chongqing Section of Jialing River, China

Hydrodynamic conditions are important factors for planktonic algae growth, through introducing two parameters which express the optimal velocity and the velocity range for planktonic algae growth, a new velocity factor was put forward for the formula of growth rate. Therefore, the two-dimensional unsteady ecological dynamic model for algae growth was established to analyze the effects of hydrodynamic conditions on algae growth in Chongqing Reach of Jialing River in China. The temporal and spatial distribution of Chlorophyll-a (Chl-a) concentration was simulated numerically for various water levels, under climate conditions in period of high frequency for algae blooms of Three Gorges Reservoir and nutrition status at present in the research reach. The corresponding locations and areas of likely algae blooms were analyzed and forecasted. The results showed that about 0.04 m s⁻¹ was the optimal velocity for algae growth, and the occurrence of algae blooms in large scale is almost impossible because of relatively high water flow velocity for Jialing River.     

Fourier analysis of the roll-up and merging of coherent structures in shallow mixing layers

The current study investigates the role of nonlinearity in the development of two-dimensional coherent structures (2DCS) in shallow mixing layers. A nonlinear numerical model based on the depth-averaged shallow water equations is used to investigate temporal shallow mixing layers, where the mapping from temporal to spatial results is made using the velocity at the center of the mixing layer. The flow is periodic in the stream-wise direction and the transmissive boundary conditions are used in the cross-stream boundaries to prevent reflections. The numerical results are examined with the aid of Fourier decomposition. Results show that the previous success in applying local linear theory to shallow mixing layers does not imply that the flow is truly linear. Linear stability theory is confirmed to be only valid within a short distance from the inflow boundary. Downstream of this linear region, nonlinearity becomes important for the roll-up and merging of 2DCS. While the energy required for the merging of 2DCS is still largely provided by the velocity shear, the merging mechanism is one where nonlinear mode interaction changes the velocity field of the subharmonic mode and the gradient of the along-stream velocity profile which, in turn, changes the magnitude of the energy production of the subharmonic mode by the velocity shear implicitly. The nonlinear mode interaction is associated with energy up-scaling and is consistent with the inverse energy cascade which is expected to occur in shallow shear flows. Current results also show that such implicit nonlinear interaction is sensitive to the phase angle difference between the most unstable mode and its subharmonic. The bed friction effect on the 2DCS is relatively small initially and grows in tandem with the size of the 2DCS. The bed friction also causes a decrease in the velocity gradient as the flow develops downstream. The transition from unstable to stable flow occurs when the bed friction balances the energy production. Beyond this point, the bed friction is more dominant and the 2DCS are progressively damped and eventually get annihilated. The energy production by the velocity shear plays an important role from the upstream end all the way to the point of transition to stable flow. The fact that linear stability theory is valid only for a short distance from the inflow boundary suggests that some elements of nonlinearity is incorporated in the mean velocity profile in experiments by the averaging process. The implicit nature of nonlinear interaction in shallow mixing layers and the sensitivity of the nonlinear interaction to phase angle difference between the most unstable mode and its subharmonic allows local linear theory to be successful in reproducing features of the instability such as the dominant mode of the 2DCS and its amplitude.     

Design and Testing of a Turbulence Probe for Harsh Flows

The force of wind on the ground created by turbulent eddies is commonly used to describe the horizontal flux of material during wind erosion. Here we present the Murdoch Turbulence Probe, an instrument for use in both clean and eroding flows which uses pressure differences to measure the three components of wind velocity. Correlation techniques calculate the forces near the ground and turbulence statistics in nearly real time, including turbulent velocity fluctuations from less than 0.1 Hz to 200 Hz, mean flow velocities, Reynolds stresses as well as the integral length and time scales. In the portable wind-tunnel used by Agriculture Western Australia, turbulence statistics were recorded over stable surfaces and in blowing sand from the initiation of erosion up to the time the sand supply was exhausted. Estimates of the friction velocity derived from the turbulence probe were compared with estimates obtained from the wind speed profile measured with a rake of pitot and static tubes. The Murdoch Turbulence Probe appears to work well in sandblasting conditions. Relative turbulence intensities ranged from 0.11 to 0.2 and are in close agreement with values in the literature. The ratio of the turbulence to the friction velocity (3 to 3.2) is at the high end of the reported range. The Reynolds stress measurements agree closely with predictions of the threshold friction velocities of the sand and estimates from the wind speed profile with a von Kármán constant of about 0.3, lower than the commonly accepted value of 0.4. We suggest that the wind-tunnel profile represents the `outer layer' of the boundary-layer that may best be described by a `Wake Law' or `Defect Law'. At about 54 mm above the surface, the friction velocity decreases from 0.64 m/s to 0.39 m/s and the mean velocity increases from 9.6 m/s to 11.6 m/s as the supply of sand is depleted. In addition to the friction velocity, other scales may be necessary to characterise the overriding effect of the wind and in extending wind-tunnel results to the field.     

利用电泳萃取技术从有机溶液中回收染料

本文以正丁醇作为有机溶剂,水作为萃取剂,依据染料在两相体系中的分配关系,选择了几种油溶性较好的染料,实验研究了电泳萃取过程所能达到的萃取效果及电压、两相流速变化对萃取率及传质通量的影响。实验结果表明,萃取率和传质通量随电压的增大而增大,在施加足够大的电压的情况下,萃取率可达９０％以上,有机相流速改变对驻效果有显著影响,有机相流速增大萃取率减小,传质通量可能存在极大值,水相流速改变对萃取效果影响不大     

Determination of the entrainment coefficient of a pure plume using the salt-bath technique

Environmental Fluid Mechanics - The entrainment coefficient of the pure plume, the ratio of the radial velocity of the entraining fluid at the edge of the plume to the axial velocity, is...