Compound channel flow with a longitudinal transition in hydraulic roughness over the floodplains

Flows in a compound open-channel (two-stage geometry with a main channel and adjacent floodplains) with a longitudinal transition in roughness over the floodplains are experimentally investigated in an 18 m long and 3 m wide flume. Transitions from submerged dense vegetation (meadow) to emergent rigid vegetation (wood) and vice versa are modelled using plastic grass and vertical wooden cylinders. For a given roughness transition, the upstream discharge distribution between main channel and floodplain (called subsections) is also varied, keeping the total flow rate constant. The flows with a roughness transition are compared to flows with a uniformly distributed roughness over the whole length of the flume. Besides the influence of the downstream boundary condition, the longitudinal profiles of water depth are controlled by the upstream discharge distribution. The latter also strongly influences the magnitude of the lateral net mass exchanges between subsections, especially upstream from the roughness transition. Irrespective of flow conditions, the inflection point in the mean velocity profile across the mixing layer is always observed at the interface between subsections. The longitudinal velocity at the main channel/floodplain interface, denoted \(U_{int}\), appeared to be a key parameter for characterising the flows. First, the mean velocity profiles across the mixing layer, normalised using \(U_{int}\), are superimposed irrespective of downstream position, flow depth, floodplain roughness type and lateral mass transfers. However, the profiles of turbulence quantities do not coincide, indicating that the flows are not fully self-similar and that the eddy viscosity assumption is not valid in this case. Second, the depth-averaged turbulent intensities and Reynolds stresses, when scaled by the depth-averaged velocity \(U_{d,int}\) exhibit two plateau values, each related to a roughness type, meadow or wood. Lastly, the same results hold when scaling by \(U_{d,int}\) the depth-averaged lateral flux of momentum due to secondary currents. Turbulence production and magnitude of secondary currents are increased by the presence of emergent rigid elements over the floodplains. The autocorrelation functions show that the length of the coherent structures scales with the mixing layer width for all flow cases. It is suggested that coherent structures tend to a state where the magnitude of velocity fluctuations (of both horizontal vortices and secondary currents) and the spatial extension of the structures are in equilibrium.     

Influence of Downstream Control and Limited Depth on Flow Hydrodynamics of Impinging Buoyant Jets

Much study has been performed on the mixing properties of submerged, turbulent buoyant jets. It is safe to say that the problem of estimating dilution rates in vertical buoyant jets spreading in an `infinitely deep' ambient water has been more than adequately resolved by previous researchers. However, the majority of environmental applications involve discharges into ambient waters of finite depths in which a bounding surface serves to re-direct the impinging buoyant jet horizontally into a radial spreading layer. Previous research indicates that this impinging jet undergoes additional mixing before buoyancy stabilizes vertical mixing and confines the spreading layer to the vicinity of the bounding surface. Unfortunately, the conceptualization and subsequent mathematical modeling of this additional mixing phenomenon is surrounded by considerable amount of disagreement between researchers. The purpose of this study is to provide, by means of velocity and concentration profile measurements, independent experimental evidence for the existence of a critical flow state immediately downstream of the active mixing zone in the horizontally flowing, radial flow that forms after impingement. It is further shown that this critical flow state must be expressed in terms of a composite Froude Number that takes into account the possibility of a non-zero exchange layer flow. Finally, the influence of the presence of a sill-like topographic downstream control on the criticality of the radial flow immediately downstream of the active mixing zone is also investigated.     

A hydromechanical principle for particle retention in Mytilus edulis and other ciliary suspension feeders

It is generally thought that the laterofrontal cirri of the bivalve gill act as filters that retain suspended particles in the through current and transfer the particles onto the frontal surface of the gill filaments. In Mytilus edulis calculations indicated that if water passed between the branching cilia of the cirri that are assumed to constitute the filter the pressure drop needed would amount to about 10 times the actual pressure drop across the whole gill. Thus, instead of acting as filters the laterofrontal cirri seem to move water. Presumably, the cirri together with the frontal cilia produce the water currents along the frontal surface of the gill filaments. Particle retention in the bivalve gill implies the transfer of suspended particles from the current of water about to enter an interfilamentar space into a neighbouring frontal surface current. The complex three-dimensional pattern of flow that arises where the 2 systems of current meet is characterized by steep velocity gradients. Particles that enter such steep, steady velocity gradients become exposed to transverse forces that cause the particles to migrate perpendicularly to the direction of flow. Whether particles enter the surface current, i.e. are retained, or they stay within the through current andescape, depends primarily upon particle size, and upon the steepness and height of the gradients within the boundary zone between the surface current and through current. Further studies are needed to evaluate the capacities and relative importance of this hydromechanical particle-trapping mechanism in suspension feeding bivalves. It is suggested that in downstream particle-retaining systems, e.g. on the tentacles of polychaetes and entoprocts, velocity gradients between through currents and surface currents also act as the particle-collecting mechanism.     

A Simple Model to Determine In Situ Mixing Height Growth from Surface Measurements

A generic In Situ Mixing Height Growth (IMG) model, capable of predicting the real-time growth of the mixed layer and its diurnal evolution from routinely observed simple surface meteorological is developed. The algorithm for the determination of temporally growing daytime mixing height includes both convective and mechanical turbulence contributions. It accounts for neutral as well as height varying potential temperature gradients above the mixed layer. For thermally stable and mechanically dominated unstable night time Atmospheric Boundary Layer (ABL) the module uses similarity formulae based on the wind velocity [1]), the Monin—Obukhov length [2], and the Coriolis parameter. In the convective case simple slab model is integrated, based on initial lapse rate and the surface heat flux. The lapse rate is evaluated on the basis of vertical atmospheric stability, surface type and surface temperature. This differentiates the IMG model from other existing mixing height models that need initial measured lapse rate for calculation. IMG model is site specific as it calculates the radiative incoming heat flux depending on the solar declination estimates based on-site latitude and longitude. The IMG model is applied to calculate mixing height for India by using surface data (viz. wind speed, surface temperature, surface type) from 152 surface meteorological stations. Results have been evaluated with radiosonde mixing height data procured from 18 upper air stations. Sensitivity analysis of the model with respect to various parameters is performed. The model is formulated after reviewing presently available radiosonde mixing height data in India and can satisfactorily provide an alternative means of estimating mixing height for air pollution dispersion models.     

Velocity measurements in inclined negatively buoyant jets

Experiments were performed with a particle tracking velocimetry system to investigate the behaviour of inclined negatively buoyant jets with source angles of 15°, 30°, 45°, 60°, 65°, 70°, and 75° in stationary ambient conditions. Velocities were measured in a plane aligned with the central axis of the flow and the experiments were designed such that the flow did not interact with boundaries in the region were the flow behaviour was measured. The results of this study complement previous research, which has largely focused on the mean geometric characteristics and the mean dilution of the discharged fluid. Geometric characteristics, spreading rates, and time-averaged (mean) centreline velocity results are compared with relevant experimental results from previous studies and integral model predictions. Axial and transverse mean velocity profiles at maximum height and the return point provide additional insights into the detrainment of discharged fluid due to the unstable density gradient on the inner side of the flow.     

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.     

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.     

Mixing dynamics of turbidity currents interacting with complex seafloor topography

Direct Numerical Simulations are employed to investigate the mixing dynamics of turbidity currents interacting with seamounts of various heights. The mixing properties are found to be governed by the competing effects of turbulence amplification and enhanced dissipation due to the three-dimensional topography. In addition, particle settling is seen to play an important role as well, as it affects the local density stratification, and hence the stability, of the current. The interplay of these different mechanisms results in the non-monotonic dependence of the mixing behavior on the height of the seamount. Regions of dilute lock fluid concentration generally mix more intensely as a result of the seafloor topography, while concentrated lock fluid remains relatively unaffected. For long times, the strongest mixing occurs for intermediate bump heights. Particle settling is seen to cause turbidity currents to mix more intensely with the ambient than gravity currents.     

Influence of the secondary motions on pollutant mixing in a meandering open channel flow

This paper presents large eddy simulation of turbulent flow in a meandering open channel with smooth wall and rectangular cross-section. The Reynolds number based on the channel height is 40,000 and the aspect ratio of the cross-section is 4.48. The depth-averaged mean stream-wise velocity agree well to experimental measurements. In this specific case, two interacting cells are formed that swap from one bend to the other. Transport and mixing of a pollutant is analysed using three different positions of release, e.g. on the inner bank, on the outer bank and on the centre of the cross section. The obtained depth-average mean concentration profiles are reasonably consistent with available experimental data. The role of the secondary motions in the mixing processes is the main focus of the discussion. It is found that the mixing when the scalar is released on the centre of the cross-section is stronger and faster than the mixing of the scalar released on the sides. When the position of release is close to a bank side, the mixing is weaker and a clear concentration of scalar close to the corresponding side-wall can be observed in both cases.     

Parameterization of the roughness length over the sea in forced and free convection

In the condition of free convection, the Charnock relation is inadequate. In this paper we extend the Charnock relation to include the effect of free convection on the roughness length. As a result, the singularity in the Monin–Obukhov similarity theory can be avoided. This paper shows two approaches to derive the roughness length formula in the forced and free convections. The first approach is based on the mixing length theory and the use of the observational data of the vertical velocity variance. We introduce a new vertical velocity scale based on the vertical velocity variance; this velocity variance is well behaved in the atmospheric boundary layer and easy to obtain from field experiments. The second approach is based on the theoretical framework of Sykes et al. (Q R Met Soc, 119: 409–421). From that framework, we develop a theory to obtain the roughness length formula. The results of these two approaches are in agreement with each other. In the past, a multiplication factor associated with free convection was considered to be a constant. This paper shows that this multiplication factor is, in fact, also dependent on the depth of the mixing height. In previous studies, experimental works were often conducted without taking into account the depth of the mixing height. Not taking into account the mixing height in the estimation of the roughness length in free convection would result in an inaccurate estimate of the roughness length and hence the drag coefficient. An erratum to this article can be found at     

Hydrodynamics and bed stability of open channel flows with submerged foliaged plants

In this work we investigate experimentally and numerically the flow structure around foliaged plants deployed in a channel with gravels on the bed under submerged and barely submerged conditions. Velocity and Reynolds stress were measured by using a NORTEK Vectrino profiler. Visual observation shows that the initial motion of gravels is easier to be triggered under the condition of flow with barely submerged vegetation. This is confirmed by the measured velocity, Reynolds stress and total kinetic energy (TKE) profiles. The velocity exhibits a speed up in the near-bed region, and the associated Reynolds stress and TKE increase there. A 3D numerical model is then verified against the experiments and used to investigate systematically the effect of degree of submergence of foliaged plants on the channel bed shear stress. The results show that the maximum bed shear stress occurs when the foliage is situated slightly below the water surface, which can enhance channel bed instability.     

Wave mixing rise inferred from Lyapunov exponents

We study the horizontal surface mixing and the transport induced by waves in a coastal environment. A comparative study is addressed by computing the Lagrangian coherent structures, via Finite Size Lyapunov Exponents, that arise in two different numerical settings: with and without wave coupled to currents. In general, we observe that mixing is increased in the area due to waves. Besides, the methodology presented here is tested by deploying a set of eight Lagrangian drifters at different locations. This dynamical approach is shown as a valuable tool to extract information about transport, mixing and residence embedded in the Eulerian time dependent velocity fields obtained from numerical models.     

Deducing an upper bound to the horizontal eddy diffusivity using a stochastic Lagrangian model

We present a method for estimating the upper bound of the horizontal eddy diffusivity using a non-stationary Lagrangian stochastic model. First, we identify a mixing barrier using a priori evidence (e.g., aerial photographs or satellite imagery) and using a Lagrangian diagnostic calculated from observed or modeled spatially non-trivial, time-dependent velocities [for instance, the relative dispersion (RD) or finite time Lyapunov exponent (FDLE)]. Second, we add a stochastic component to the observed (or modeled) velocity field. The stochastic component represents sub-grid stochastic diffusion and its mean magnitude is related to the eddy diffusivity. The RD of Lagrangian trajectories is computed for increasing values of the eddy diffusivity until the mixing barrier is no longer present. The value at which the mixing barrier disappears provides a dynamical estimate of the upper bound of the eddy diffusivity. The erosion of the mixing barrier is visually observed in numerical simulations, and is quantified by computing the kurtosis of the RD at each value of the eddy diffusivity. We demonstrate our method using the double gyre circulation model and apply it to high frequency (HF) radar observations of surface currents in the Gulf of Eilat.     

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.     

The structure of turbulence near a tall forest edge: the backward-facing step flow analogy revisited

Flow disturbances near tall forest edges are receiving significant attention in diverse disciplines including ecology, forest management, meteorology, and fluid mechanics. Current theories suggest that near a forest edge, when the flow originates from a forest into a large clearing, the flow retains its forest canopy turbulence structure at the exit point. Here, we propose that this framework is not sufficiently general for dense forested edges and suggest that the flow shares several attributes with backward-facing step (BFS) flow. Similar analogies, such as rotor-like circulations, have been proposed by a number of investigators, though the consequences of such circulations on the primary terms in the mean momentum balance at the forest clearing edge have rarely been studied in the field. Using an array of three triaxial sonic anemometers positioned to measure horizontal and vertical gradients of the velocity statistics near a forest edge, we show that the flow structure is more consistent with an intermittent recirculation pattern, rather than a continuous rotor, whose genesis resembles the BFS flow. We also show that the lateral velocity variance, v'2, is the moment that adjusts most slowly with downwind distance as the flow exits from the forest into the clearing. Surprisingly, the longitudinal and vertical velocity variances (u'2 and w'2) at the forest edge were comparable in magnitude to their respective values at the center of a large grass-covered forest clearing, suggesting rapid adjustment at the edge. Discussions on how the forest edge modifies the spectra and co-spectra of momentum fluxes, effective mixing length, and static pressure are also presented.     

Surface signatures of submerged heated jet

The flow induced at the surface of a water body by a submerged heated horizontal turbulent jet was investigated experimentally with the aim of developing parameterizations for surface mean temperature/velocity fields. The jet nozzle diameter was fixed, the depth of the jet beneath the free surface was varied, and two jet Reynolds numbers (5020, 11300) were considered. The surface temperature was measured using a highly sensitive infrared camera, and the near-surface horizontal velocity field was measured using particle image velocimetry. The experimental results were explained using a model based on similarity solutions with variable turbulent viscosity. While classical Schlichting’s solution with constant turbulent viscosity predicts complete similarity for transverse velocity/temperature distributions only in a plane that coincides with the flow axis, the present solution predicts similarity in an arbitrary plane parallel to the flow axis, which was confirmed using data collected at the surface. Comparisons of present data with available previous results also showed general agreement.     

The Structure of the Shear Layer in Flows over Rigid and Flexible Canopies

Flume experiments were conducted with rigid and flexible model vegetation to study the structure of coherent vortices (a manifestation of the Kelvin–Helmholtz instability) and vertical transport in shallow vegetated shear flows. The vortex street in a vegetated shear layer creates a pronounced oscillation in the velocity profile, with the velocity near the top of a model canopy varying by a factor of three during vortex passage. In turn, this velocity oscillation drives the coherent waving of flexible canopies. Relative to flows over rigid vegetation, the oscillation in canopy geometry has the effect of decreasing the amount of turbulent vertical momentum transport in the shear layer. Using a waving plant to determine phase in the vortex cycle, each vortex is shown to consist of a strong sweep at its front (during which the canopy is most deflected), followed by a weak ejection at its rear (when the canopy height is at a maximum). Whereas in unobstructed mixing layers the vortices span the entire layer, they encompass only 70% of the flexibly obstructed shear layer studied here.     

Integral Model for Turbulent Buoyant Jets in Unbounded Stratified Flows Part 2: Plane Jet Dynamics Resulting from Multiport Diffuser Jets

An integral model for the plane buoyant jet dynamics resulting from the interaction of multiple buoyant jet effluxes spaced along a diffuser line is considered as an extension of the round jet formulation that was proposed in Part I. The receiving fluid is given by an unbounded ambient environment with uniform density or stable density stratification and under stagnant or steady sheared current conditions. Applications for this situation are primarily for submerged multiport diffusers for discharges of liquid effluents into ambient water bodies, but also for multiple cooling tower plumes and building air-conditioning. The CorJet model formulation describes the conservation of mass, momentum, buoyancy and scalar quantities in the turbulent jet flow in the plane jet geometry. It employs an entrainment closure approach that distinguishes between the separate contributions of transverse shear and of internal instability mechanisms, and contains a quadratic law turbulent pressure force mechanism. But the model formulation also includes several significant three-dimensional effects that distinguish actual diffuser installations in the water environment. These relate to local merging processes from the individual multiple jets, to overall finite length effects affecting the plume geometry, and to bottom proximity effects given by a “leakage factor” that measures the combined affect of port height and spacing in allowing the ambient flow to pass through the diffuser line in order to provide sufficient entrainment flow for the mixing downstream from the diffuser. The model is validated in several stages: First, comparison with experimental data for the asymptotic, self-similar stages of plane buoyant jet flows, i.e. the plane pure jet, the pure plume, the pure wake, the advected line puff, and the advected line thermal, support the choice of the turbulent closure coefficients contained in the entrainment formulation. Second, comparison with data for many types of non-equilibrium flows with a plane geometry support the proposed functional form of the entrainment relationship, and also the role of the pressure force in the jet deflection dynamics. Third, the observed behavior of the merging process from different types of multiport diffuser discharges in both stagnant and flowing ambient conditions and with stratification appears well predicted with the CorJet formulation. Fourth, a number of spatial limits of applicability, relating to terminal layer formation in stratification or transition to passive diffusion in a turbulent ambient shear flow, have been proposed. In sum, the CorJet integral model appears to provide a mechanistically sound, accurate and reliable representation of complex buoyant jet mixing processes, provided the condition of an unbounded receiving fluid is satisfied.     

Experimental study of the concentration field of discharge from a boat propeller

Engines in boats and ships using total loss lubrication deposit a significant proportion of their lubricant and fuel directly into the water. Their impact on the Australian coastline and marine ecosystems is of great concern. The purpose of this study was to document the velocity and concentration field characteristics of a submerged swirling water jet emanating from a propeller in order to provide information on its fundamental characteristics. The properties of the jet were examined far enough downstream to be relevant to the eventual modelling of the mixing problem. Measurements of the velocity and concentration field were performed in a turbulent jet generated by a model boat propeller (0.02 m diameter) within a 0.4 m-wide and 0.15 m-deep flume, operating at 1,500 and 3,000 rpm in a weak co-flow of 0.04 m/s. The measurements were carried out in the Zone of Established Flow up to 50 propeller diameters downstream of the propeller. Results pertaining to radial distribution, self-similarity, standard deviation growth, maximum value decay and integral fluxes of velocity and concentration fitted with empirical correlations. Furthermore, propeller-induced mixing and pollutant source concentration from a two-stroke engine were estimated.