Instabilities in non-rotating and rotating shallow shear flows

Numerical simulations for the wave radiation effect on the linear and nonlinear instabilities of rotating and non-rotating shallow flows are conducted using shallow-water equations. At a low convective Froude number, the results of the instabilities is a string of eddies. The coalescence between the neighbouring eddies decides the transverse mixing of the shallow shear flow. At a higher convective Froude number, the development of the shear flow is characterized by wave radiation and the production of shocklets. The radiation of waves in the non-rotating shallow flow is a phenomenon analogous to the radiation of sound in gas dynamics. In the rotating flow on the other hand, the shallow-flow instabilities are intensified due to rotational interference within a window of instability over a narrow range of Rossby numbers.     

Visualization of the internal flow properties and the material exchange interface in an entraining viscous Newtonian gravity current

In order to simulate a simple entraining geophysical flow, a viscous Newtonian gravity current is released from a reservoir by a dam-break and flows along a rigid horizontal bed until it meets a layer of entrainable material of finite depth, identical to the current. The goal is to examine the entrainment mechanisms by observing the interaction between the incoming flow and the loose bed. The sole parameter varied is the initial volume of the gravity current, thus altering its height and velocity. The gravity current plunges or spills into the entrainable bed and the velocity of the flow front becomes linear with time. The bed material is directly affected: motion is generated in the fluid far downstream of, and in that lying beneath the encroaching front. Shear bands are identified, separating horizontal flow downstream from flow with a strong vertical component close to the step. Downstream of the step the flow is horizontal and stratified, with no slip on the bottom boundary and very low shear near the surface. Between these two regions may lie transitional zones with linear velocity profiles, separated by horizontal bands of high shear; the number of transitional zones in the cross-section varies with the initial volume of the dam-break.     

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°).     

Hydrodynamics and contaminant transport on a degraded bed at a 90-degree channel confluence

Channel confluences at which two channels merge have an important effect on momentum exchange and contaminant diffusion in both natural rivers and artificial canals. In this study, a three-dimensional numerical model, which is based on the Reynolds Averaged Navier–Stokes equations and Reynolds Stress Turbulence model, is applied to simulate and compare flow patterns and contaminant transport processes for different bed morphologies. The results clearly show that the distribution of contaminant concentrations is mainly controlled by the shear layer and two counter-rotating helical cells, which in turn are affected by the discharge ratio and the bed morphology. As the discharge ratio increases, the shear flow moves to the outer bank and the counter-clockwise tributary helical cell caused by flow deflection is enlarged, leading the mixing happens near the outer bank and the mixing layer distorted. The bed morphology can induce shrinkage of the separation zone and increase of the clockwise main channel helical cell, which is initiated by the interaction between the tributary helical cell and the main channel flow and strengthened by the deep scour hole. The bed morphology can also affect the distortion direction of the mixing layer. Both a large discharge ratio and the bed morphology could lead to an increase in mixing intensity.     

Eddy diffusivity: a single dispersion analysis of high resolution drifters in a tidal shallow estuary

In an estuary, mixing and dispersion resulting from turbulence and small scale fluctuation has strong spatio-temporal variability which cannot be resolved in conventional hydrodynamic models while some models employs parameterizations large water bodies. This paper presents small scale diffusivity estimates from high resolution drifters sampled at 10 Hz for periods of about 4 h to resolve turbulence and shear diffusivity within a tidal shallow estuary (depth <3 m). Taylor’s diffusion theorem forms the basis of a first order estimate for the diffusivity scale. Diffusivity varied between 0.001 and 0.02 m²/s during the flood tide experiment. The diffusivity showed strong dependence (R² > 0.9) on the horizontal mean velocity within the channel. Enhanced diffusivity caused by shear dispersion resulting from the interaction of large scale flow with the boundary geometries was observed. Turbulence within the shallow channel showed some similarities with the boundary layer flow which include consistency with slope of 5/3 predicted by Kolmogorov’s similarity hypothesis within the inertial subrange. The diffusivities scale locally by 4/3 power law following Okubo’s scaling and the length scale scales as 3/2 power law of the time scale. The diffusivity scaling herein suggests that the modelling of small scale mixing within tidal shallow estuaries can be approached from classical turbulence scaling upon identifying pertinent parameters.     

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.     

Spatial–temporal structure of mixing interface turbulence at two large river confluences

Converging flows at stream confluences often produce highly turbulent conditions. The shear layer/mixing interface that develops within the confluence hydrodynamic zone (CHZ) is characterized by complex patterns of three-dimensional flow that vary both spatially and temporally. Previous research has examined in detail characteristics of mean flow and turbulence along mixing interfaces at small stream confluences and laboratory junctions; however few, if any, studies have examined these characteristics within mixing interfaces at large river confluences. This study investigates the structure of mean velocity profiles as well as spatial and temporal variations in velocity, backscatter intensity, and temperature within the mixing interfaces of two large river confluences. Velocity, temperature, and backscatter intensity data were obtained at stationary locations within the mixing interfaces and at several cross sections within the CHZ using acoustic Doppler current profilers. Results show that mean flow within the mixing interfaces accelerates over distance from the junction apex. Turbulent kinetic energy initially increases rapidly over distance, but the rate of increase diminishes downstream. Hilbert–Huang transform analysis of time series data at the stationary locations shows that multiple dominant modes of fluctuations exist within the original signals of velocity, backscatter intensity, and temperature. Frequencies of the largest dominant modes correspond well with predicted frequencies for shallow wake flows, suggesting that mixing-interface dynamics include wake vortex shedding—a finding consistent with spatial patterns of depth-averaged velocities at measured cross sections. Spatial patterns of temperature and backscatter intensity show that the converging flows at both confluences do not mix substantially, indicating that turbulent structures within the mixing interfaces are relatively ineffective at producing mixing of the flows in the CHZ.     

Does the canopy mixing layer model apply to highly flexible aquatic vegetation? Insights from numerical modelling

Vegetation is a characteristic feature of shallow aquatic flows such as rivers, lakes and coastal waters. Flow through and above aquatic vegetation canopies is commonly described using a canopy mixing layer analogy which provides a canonical framework for assessing key hydraulic characteristics such as velocity profiles, large-scale coherent turbulent structures and mixing and transport processes for solutes and sediments. This theory is well developed for the case of semi-rigid terrestrial vegetation and has more recently been applied to the case of aquatic vegetation. However, aquatic vegetation often displays key differences in morphology and biomechanics to terrestrial vegetation due to the different environment it inhabits. Here we investigate the effect of plant morphology and biomechanical properties on flow–vegetation interactions through the application of a coupled LES-biomechanical model. We present results from two simulations of aquatic vegetated flows: one assuming a semi-rigid canopy and the other a highly flexible canopy and provide a comparison of the associated flow regimes. Our results show that while both cases display canopy mixing layers, there are also clear differences in the shear layer characteristics and turbulent processes between the two, suggesting that the semi-rigid approximation may not provide a complete representation of flow–vegetation interactions.     

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.     

Shallow wake behind exposed wood-induced bar in a gravel-bed river

Recent theoretical research indicates that dynamics of shallow flows can be strongly affected by waves developing on the free surface. In this study a shallow wake with an oblique pressure wave behind a model of a tree-centered emergent bar is investigated in a gravel-bed river. A bar was constructed in a shallow river reach with nearly uniform flow. The structure of flow was assessed with an array of velocimeters. Flow visualization with a solute of fluorescent dye complemented the measurements and provided qualitative information on the wake behavior. This study indicates that quantitative criteria for shallow wakes classification developed in laboratory setups are not straightforward in explaining the field results. According to the wake stability criteria, the expected dynamics for examined wake flow is a vortex street (VS) type. Contrary to this expectation, measurements and visualizations in this study show that mean momentum differential and turbulent vortices in the wake decrease stronger than expected in VS type and therefore the wake should be classified as unsteady bubble type with a weak downstream instability. Analysis of velocity differential dynamics in the examined shallow wake suggests that the bed friction alone is insufficient to explain the inconsistency of VS criterion whereas accounting for advective fluxes driven by inhomogeneous pressure field leads to a correct prediction of the wake behavior.     

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.     

Stokes drift through corals

Motivated by shallow ocean waves propagating over coral reefs, we investigate the drift velocities due to surface wave motion in an effectively inviscid fluid that overlies a saturated porous bed of finite depth. Previous work in this area either neglects the large-scale flow between layers (Phillips in Flow and reactions in permeable rocks, Cambridge University Press, Cambridge, 1991) or only considers the drift above the porous layer (Monismith in Ann Rev Fluid Mech 39:37–55, 2007). Overcoming these limitations, we propose a model where flow is described by a velocity potential above the porous layer and by Darcy’s law in the porous bed, with derived matching conditions at the interface between the two layers. Both a horizontal and a novel vertical drift effect arise from the damping of the porous bed, which requires the use of a complex wavenumber k. This is in contrast to the purely horizontal second-order drift first derived by Stokes (Trans Camb Philos Soc 8:441–455, 1847) when working with solely a pure fluid layer. Our work provides a physical model for coral reefs in shallow seas, where fluid drift both above and within the reef is vitally important for maintaining a healthy reef ecosystem (Koehl et al. In: Proceedings of the 8th International Coral Reef Symposium, vol 2, pp 1087–1092, 1997; Monismith in Ann Rev Fluid Mech 39:37–55, 2007). We compare our model with field measurements by Koehl and Hadfield (J Mar Syst 49:75–88, 2004) and also explain the vertical drift effects as documented by Koehl et al. (Mar Ecol Prog Ser 335:1–18, 2007), who measured the exchange between a coral reef layer and the (relatively shallow) sea above.

     

Environmental Impact of Undular Tidal Bores in Tropical Rivers

A tidal bore impacts significantly on the estuarine ecosystem, although little is known on the flow field, mixing and sediment motion beneath tidal bores. In the absence of detailed systematic field measurements, a quasi-steady flow analogy was applied to investigate undular tidal bores with inflow Froude numbers between 1.25 and 1.6. Experimental results indicated that rapid flow redistributions occur beneath the free-surface undulations, with significant variations in bed shear stress between wave crests and troughs. Dynamic similarity was used to predict detailed flow characteristics of undular tidal bores. The effects of periodic loading on river sediments, scour of river bed and flow mixing behind the bore are discussed. A better understanding of these processes will contribute to better management practices in tidal bore affected rivers, including the Styx and Daly rivers in tropical Australia.     

Markovian–Octant analysis based stable turbulent shear stresses in near-bed bursting phenomena of vortex settling chamber

The coherent structure in near-bed turbulent boundary layer of vortex chamber, particularly the bursting events and their associated shear stresses play the main role in sediment flushing process and consequently the trap efficiency of the vortex settling chamber. Hence, three-dimensional velocity measurements were made at 48 points near the bed of physical model of vortex chamber by using Micro-ADV. The pattern of sediment deposition at the bed of vortex settling chamber reveals three separate regions formed by three predominant currents of inlet flow, flushing flow and outlet over flow. Additionally, due to the instability and three-dimensional nature of the bursting events near the bed of chamber, the new method of Markovian–Octant analysis was applied to study the different classes of near-bed stable shear stresses of vortex chamber in three dimensions. Moreover, the role of each class of stable shear stresses on Sediment transport mechanism at the bed of vortex chamber is investigated.     

Formation of tidal starting-jet vortices through idealized barotropic inlets with finite length

This paper presents a surface particle image velocimetry study to investigate the dynamics of shallow starting-jet dipoles formed by tidal flow through inlets and their interaction with vorticity formed at the inlet channel lateral boundaries. Vortical structure in the flow field is identified using a local swirl strength criterion evaluated from the two-dimensional flow field. The starting jet dipole vortices and vortices formed as the lateral boundary layers are expelled during flow reversal are characterized by their trajectory, size, and circulation. Using these quantities, a model is developed to predict the size and strength of the expelled lateral boundary layer vortices based on the inlet velocity, channel length, and width of the lateral boundary layer. The expelled boundary layer vortices are found to disrupt the formation of the primary tidal jet dipole through two mechanisms. First, because the boundary layer vortices themselves form a dipole with each half of the starting-jet dipole, the starting-jet vortices are pulled apart and advected away from the inlet mouth early in the tidal cycle, resulting in a reduction in the spin-up time and the amount of vorticity input during starting-jet vortex formation. Second, the advection of each dipole away from the inlet disconnects each starting-jet vortex from the starting jet; hence, the vortices are not fed by fluid in the jet or energized by shear in the jet boundary layers. These influences of the lateral boundary layer on the starting-jet vortices’ formation and propagation are found to be a function of the channel length L, maximum velocity U, and tidal period T, resulting in a predictive value to characterize their trajectory, strength, and evolution.     

Blockage of saline intrusions in restricted,two-layer exchange flows across a submerged sill obstruction

Results are presented from a series of large-scale experiments investigating the internal and near-bed dynamics of bi-directional stratified flows with a net-barotropic component across a submerged, trapezoidal, sill obstruction. High-resolution velocity and density profiles are obtained in the vicinity of the obstruction to observe internal-flow dynamics under a range of parametric forcing conditions (i.e. variable saline and fresh water volume fluxes; density differences; sill obstruction submergence depths). Detailed synoptic velocity fields are measured across the sill crest using 2D particle image velocimetry, while the density structure of the two-layer exchange flows is measured using micro-conductivity probes at several sill locations. These measurements are designed to aid qualitative and quantitative interpretation of the internal-flow processes associated with the lower saline intrusion layer blockage conditions, and indicate that the primary mechanism for this blockage is mass exchange from the saline intrusion layer due to significant interfacial mixing and entrainment under dominant, net-barotropic, flow conditions in the upper freshwater layer. This interfacial mixing is quantified by considering both the isopycnal separation of vertically-sorted density profiles across the sill, as well as calculation of corresponding Thorpe overturning length scales. Analysis of the synoptic velocity fields and density profiles also indicates that the net exchange flow conditions remain subcritical (G < 1) across the sill for all parametric conditions tested. An analytical two-layer exchange flow model is then developed to include frictional and entrainment effects, both of which are needed to account for turbulent stresses and saline entrainment into the upper freshwater layer. The experimental results are used to validate two key model parameters: (1) the internal-flow head loss associated with boundary friction and interfacial shear; and (2) the mass exchange from the lower saline layer into the upper fresh layer due to entrainment.     

Experimental investigation of bubbly flow and turbulence in hydraulic jumps

Many environmental problems are linked to multiphase flows encompassing ecological issues, chemical processes and mixing or diffusion, with applications in different engineering fields. The transition from a supercritical flow to a subcritical motion constitutes a hydraulic jump. This flow regime is characterised by strong interactions between turbulence, free surface and air–water mixing. Although a hydraulic jump contributes to some dissipation of the flow kinetic energy, it is also associated with increases of turbulent shear stresses and the development of turbulent eddies with implications in terms of scour, erosion and sediment transport. Despite a number of experimental, theoretical and numerical studies, there is a lack of knowledge concerning the physical mechanisms involved in the diffusion and air–water mixing processes within hydraulic jumps, as well as on the interaction between the free-surface and turbulence. New experimental investigations were undertaken in hydraulic jumps with Froude numbers up to Fr = 8.3. Two-phase flow measurements were performed with phase-detection conductivity probes. Basic results related to the distributions of void fraction, bubble frequency and mean bubble chord length are presented. New developments are discussed for the interfacial bubble velocities and their fluctuations, characterizing the turbulence level and integral time scales of turbulence representing a “lifetime” of the longitudinal bubbly flow structures. The analyses show good agreement with previous studies in terms of the vertical profiles of void fraction, bubble frequency and mean bubble chord length. The dimensionless distributions of interfacial velocities compared favourably with wall-jet equations. Measurements showed high turbulence levels. Turbulence time scales were found to be dependent on the distance downstream of the toe as well as on the distance to the bottom showing the importance of the lower (channel bed) and upper (free surface) boundary conditions on the turbulence structure.     

Evaluating the dimensionality and significance of “active periods” in turbulent environmental flows defined using Lipshitz/Hölder regularity

Active periods within perturbed boundary-layer flows are considered in terms of the local roughness of measured velocity time series and defined in terms of Hölder/Lipshitz exponents. Such events are associated with the passage of energetic, coherent flow structures and are responsible for exerting high turbulent stresses because of the rapid changes in velocity that occur at such times. A method is proposed for assessing the effective dimensionality of such active periods, as well as their significance to the flow field, for a particular choice of flow metric. The method is applied to the turbulent flow through a confluence flow geometry, with velocity samples acquired close to the bed of the channel in a zone of complex mixing. The dimensionality of the active periods is consistent with the observed patterns of sediment entrainment from the bed, with the significance of the active periods decaying away from the erosional zone.     

Kelvin–Helmholtz instability in the presence of variable viscosity for mudflow resuspension in estuaries

The temporal stability of a parallel shear flow of miscible fluid layers of different density and viscosity is investigated through a linear stability analysis and direct numerical simulations. The geometry and rheology of this Newtonian fluid mixing can be viewed as a simplified model of the behavior of mudflow at the bottom of estuaries for suspension studies. In this study, focus is on the stability and transition to turbulence of an initially laminar configuration. A parametric analysis is performed by varying the values of three control parameters, namely the viscosity ratio, the Richardson and Reynolds numbers, in the case of initially identical thickness of the velocity, density and viscosity profiles. The range of parameters has been chosen so as to mimic a wide variety of real configurations. This study shows that the Kelvin–Helmholtz instability is controlled by the local Reynolds and Richardson numbers of the inflection point. In addition, at moderate Reynolds number, viscosity stratification has a strong influence on the onset of instability, the latter being enhanced at high viscosity ratio, while at high Reynolds number, the influence is less pronounced. In all cases, we show that the thickness of the mixing layer (and thus resuspension) is increased by high viscosity stratification, in particular during the non-linear development of the instability and especially pairing processes. This study suggests that mud viscosity has to be taken into account for resuspension parameterizations because of its impact on the inflection point Reynolds number and the viscosity ratio, which are key parameters for shear instabilities.     

Characteristics of flow structure of free-surface flow in a partly obstructed open channel with vegetation patch

Free-surface flows over patchy vegetation are common in aquatic environments. In this study, the hydrodynamics of free-surface flow in a rectangular channel with a bed of rigid vegetation-like cylinders occupying half of the channel bed was investigated and interpreted by means of laboratory experiments and numerical simulations. The channel configurations have low width-to-depth aspect ratio (1.235 and 2.153). Experimental results show that the adjustment length for the flow to be fully developed through the vegetation patch in the present study is shorter than observed for large-aspect-ratio channels in other studies. Outside the lateral edge of the vegetation patch, negative velocity gradient (\(\partial \overline{u}/\partial z < 0\)) and a local velocity maximum are observed in the vertical profile of the longitudinal velocity in the near-bed region, corresponding to the negative Reynolds stress (\(- \overline{{u^{\prime}w^{\prime}}} < 0\)) at the same location. Assuming coherent vortices to be the dominant factor influencing the mean flow field, an improved Spalart–Allmaras turbulence model is developed. The model improvement is based on an enhanced turbulence length scale accounting for coherent vortices due to the effect of the porous vegetation canopy and channel bed. This particular flow characteristic is more profound in the case of high vegetation density due to the stronger momentum exchange of horizontal coherent vortices. Numerical simulations confirmed the local maximum velocity and negative gradient in the velocity profile due to the presence of vegetation and bed friction. This in turn supports the physical interpretation of the flow processes in the partly obstructed channel with vegetation patch. In addition, the vertical profile of the longitudinal velocity can also be explained by the vertical behavior of the horizontal coherent vortices based on a theoretical argument.