Using surface drifter observations to measure tidal vortices and relative diffusion at Aransas Pass,Texas

Tidal vortices play an important role in the flushing of coastal regions. At the mouth of a tidal inlet, the input of circulation by the ebb tide may force the formation of a starting-jet dipole vortex. The continuous ebb jet current also creates a periodic sequence of secondary vortices shed from the inlet mouth. In each case, these tidal vortices have a shallow aspect ratio, with a lateral extent much greater than the water depth. These shallow vortices affect the transport of passive tracers, such as nutrients and sediment from the estuary to the ocean and vice versa. Field observation of tidal vortices primarily relies on ensemble averaging over several vortex events that are repeatable in space and can be sampled by a fixed Eulerian measurement grid. This paper presents an adaptive approach for locating and measuring within tidal vortices that propagate offshore near inlets and advect along variable trajectories set by the wind-driven currents. A field experiment was conducted at Aransas Pass, Texas to measure these large-scale vortices. Locations of the vortices produced during ebb tide were determined using near real-time updates from surface drifters deployed near or within the inlet during ebb tide, and the paths of towed acoustic Doppler current profiler (ADCP) transects were selected by analysis of the drifter observations. This method allowed ADCP transects to be collected within ebb generated tidal vortices, and the paths of the drifters indicated the presence of both the starting-jet dipole and the secondary vortices of the unstable ebb tidal jet. Drifter trajectories were also used to estimate the size of each observed vortex as well as the statistics of relative diffusion offshore of Aransas Pass. The field data confirmed the starting-jet spin-up time (time until the vortex dipole begins to propagate offshore) measured in the laboratory by Bryant et al. [6] and that the Strouhal condition of \(St=0.2\) predicts the shedding of secondary vortices from the inlet mouth. The size of the rotational core of the vortex is also shown to be approximated physically by the inlet width or by \(0.02UT\) , where U is the maximum velocity through the inlet channel and T is the tidal period, and confirms results found in laboratory experiments by Nicolau del Roure et al. [23]. Additionally, the scale of diffusion was approximately 1–15 km and the apparent diffusivity was between 2–130  \(m^2/s\) following Richardsons law.     

Analysis of the velocity field in a large rectangular channel with lateral shockwave

In this work the authors describe the main characteristics of the velocity field of hydraulic jumps in a very large channel where lateral shockwaves occur. Experiments were carried out at the Coastal Engineering Laboratory of the Water Engineering and Chemistry Department of the Technical University of Bari (Italy). Extensive flow velocity measurements were investigated in order to have a clearer understanding of both hydraulic jump development and lateral shockwave formation in a very large channel. Eight experiments were performed in a 4m wide rectangular channel; the experiments differed in the inlet Froude number F ₀ and the jump type. Seven tests were carried out with undular jumps and one with a roller jump. The flow velocity and the flow free surface measurements were taken using a two-dimensional Acoustic Doppler Velocimeter (ADV) and an ultrasonic profiler, respectively. The experimental results can be summarized as follow: (i) the formation of well developed lateral shockwaves similar to those of oblique jumps were observed; (ii) the comparison of the experimental and theoretical data shows that the classic shockwave theory is sufficiently confirmed in the analyzed range of Reynolds number, taking into account the experimental errors and the difference between the theoretical and experimental assumptions; (iii) the transversal flow velocity profiles in the recirculating zone show a good agreement with the numerical simulations presented in literature in the case of a separated turbulent boundary layer over a flat plate. This conclusion enables us to confirm the hypothesis that the lateral shockwaves in the channel are the result of a boundary layer which, as observed, forms on the channel sidewalls.     

A mesoscale vortex in a small stratified lake

A mesoscale vortex structure in the small stratified Lake Stechlin has been revealed by field experiments with satellite-tracked quasi-lagrangian drifters. The vortex with a radius of about 200 m drifted at 300 m/day along the western bight of the lake with nearly constant rotation speed of 3 cpd. Analysis of kinematical properties of the vortex motion demonstrates solid body character of rotation. Extrapolation of the vortex drift trajectory over the period preceding the observations combined with data on local winds and seiche dynamics has allowed tracing the vortex fate from its generation point. The normal modes analysis of the internal seiching in the lake reveals the vortex generation mechanism to be the interaction of certain seiche modes with local bottom topography and suggests generation of the mesoscale vortices to be the a regular feature of the lake circulation. Analysis of vorticity suggests additional energy supply to rotational flow, possibly from inverse cascading of small-scale turbulent motions—a feature typical for quasi-2D turbulence. The vortices can play an important role in the energy transport from basin-scale motions to small-scale boundary mixing. They can also contribute significantly to the horizontal heterogeneity of phyto- and zooplankton distribution as well as to the transport of dissolved matter such as nutrients between littoral and profundal areas. The topographically generated traveling vortices represent an analog of the synoptic eddies in the Ocean and in the Atmosphere, whereas their role in the lake hydrodynamics is practically unknown.     

Vertical dense jet in flowing current

The discharge of brackish water, as a dense jet in a natural water body, by the osmotic power plants, undergoes complex mixing processes and has significant environmental impacts. This paper focuses on the mixing processes that develop when a dense round jet outfall perpendicularly enters a shallow flowing current. Extensive experimental measurements of both the salinity and the velocity flow fields were conducted to investigate the hydrodynamic jet behavior within the ambient current. Experiments were carried out in a closed circuit flume at the Coastal Engineering Laboratory (LIC) of the Technical University of Bari (Italy). The salinity concentration and velocity fields were analyzed, providing a more thorough knowledge about the main features of the jet behavior within the ambient flow, such as the jet penetration, spreading, dilution, terminal rise height and its impact point with the flume lower boundary. In this study, special attention is given to understand and confirm the conjecture, not yet experimentally demonstrated, of the development and orientation of the jet vortex structures. Results show that the dense jet is almost characterized by two distinct phases: a rapid ascent phase and a gradually descent phase. The measured flow velocity fields definitely confirm the formation of the counter-rotating vortices pair, within the jet cross-section, during both the ascent and descent phases. Nevertheless, the experimental results show that the counter-rotating vortices pair of both phases (ascent and descent) are of opposite rotational direction.     

Experimental study of recirculating flows generated by lateral shock waves in very large channels

Due to the lack of data on hydraulic-jump dynamics in very large channels, the present paper describes the main characteristics of the velocity field and turbulence in a large rectangular channel with a width of 4 m. Although a hydraulic jump is always treated as a wave that is transversal to the channel wall, in the case of this study it has a trapezoidal front shape, first starting from a point at the sidewalls and then developing downstream in an oblique manner, finally giving rise to a trapezoidal shape. The oblique wave front may be regarded as a lateral shockwave that arises from a perturbation at a certain point of the lateral wall and travels obliquely toward the centreline of the channel. The experimental work was carried out at the Coastal Engineering Laboratory of the Water Engineering and Chemistry Department of the Technical University of Bari (Italy). In addition to the hydraulic jump formation, a large recirculating flow zone starts to develop from the separating point of the lateral shock wave and a separate boundary layer occurs. Intensive measurements of the streamwise and spanwise flow velocity components along one-half width of the channel were taken using a bidimensional Acoustic Doppler Velocimeter (ADV). The water surface elevation was obtained by means of an ultrasonic profiler. Velocity vectors, transversal velocity profiles, turbulence intensities and Reynolds shear stresses were all investigated. The experimental results of the separated boundary layer were compared with numerical predictions and related work presented in literature and showed good agreement. The transversal velocity profiles indicated the presence of adverse pressure gradient zones and the law of the wall appears to govern the region around the separated boundary layer.     

Interaction of North Brazil Current rings with the Lesser Antilles Arc and Barbados Island: laboratory experiments and observations

The interaction of North Brazil Current (NBC) rings with the Lesser Antilles Arc (LAA) and the Barbados Island (BI) is addressed by experimental modeling and observations. Our results compare well with previous experimental results and numerical simulations. Several sizes, intensities and two different vorticity profiles (non-isolated and initially isolated vortices) were tested. Three regimes were found namely: (1) the vortex surrounds the BI and its translational motion (TM) stops North of BI; (2) the vortex passes through the corridor between the LAA and the BI by reducing its size; and (3) The vortex stopped at the entrance to the corridor South of the BI. Isolated vortices were prone to stopped North of the BI. Apparently the intensity in the outer vorticity ring has an influence on the fate of the NBC ring. Non-isolated vortices can also stop its TM North of the BI because when in \(\beta\) plane they develop an outer ring similar to the isolated vortices. From these results we conclude that intense and big NBC rings are likely to stop its TM North of the BI. Medium and moderate vortices stops its TM South of the BI and they reduce their size until they are able to pass through the corridor between the LAA and the BI. Mild vortices of all sizes stop South of the corridor, close to the BI and the LAA. Drifter trajectories and Sea Surface Height altimetry confirm the results.     

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.     

Turbulent secondary flows in wall turbulence: vortex forcing,scaling arguments,and similarity solution

Spanwise surface heterogeneity beneath high-Reynolds number, fully-rough wall turbulence is known to induce a mean secondary flow in the form of counter-rotating streamwise vortices—this arrangement is prevalent, for example, in open-channel flows relevant to hydraulic engineering. These counter-rotating vortices flank regions of predominant excess(deficit) in mean streamwise velocity and downwelling(upwelling) in mean vertical velocity. The secondary flows have been definitively attributed to the lower surface conditions, and are now known to be a manifestation of Prandtl’s secondary flow of the second kind—driven and sustained by spatial heterogeneity of components of the turbulent (Reynolds averaged) stress tensor (Anderson et al. J Fluid Mech 768:316–347, 2015). The spacing between adjacent surface heterogeneities serves as a control on the spatial extent of the counter-rotating cells, while their intensity is controlled by the spanwise gradient in imposed drag (where larger gradients associated with more dramatic transitions in roughness induce stronger cells). In this work, we have performed an order of magnitude analysis of the mean (Reynolds averaged) transport equation for streamwise vorticity, which has revealed the scaling dependence of streamwise circulation intensity upon characteristics of the problem. The scaling arguments are supported by a recent numerical parametric study on the effect of spacing. Then, we demonstrate that mean streamwise velocity can be predicted a priori via a similarity solution to the mean streamwise vorticity transport equation. A vortex forcing term has been used to represent the effects of spanwise topographic heterogeneity within the flow. Efficacy of the vortex forcing term was established with a series of large-eddy simulation cases wherein vortex forcing model parameters were altered to capture different values of spanwise spacing, all of which demonstrate that the model can impose the effects of spanwise topographic heterogeneity (absent the need to actually model roughness elements); these results also justify use of the vortex forcing model in the similarity solution.     

Vertical Buoyant Jets in a Linearly Stratified Ambient Cross-Stream

In this study a numerical simulation is performed to investigate the effect of ambient density stratification on the characteristic of a vertical buoyant jet in a stably linearly stratified ambient cross-stream. Based on the ensemble integral method, the theoretical formulation for such a flow field consists of a set of elliptic Reynolds-averaged equations incorporating with the k– transport equations for the turbulence closure. An oscillating motion can be observed in the computed jet trajectory, and the corresponding alternative variation of dominant quantities for the induced momentum and buoyancy of the jet are examined by direct integration on a cross-section along the jet axis. The influences on the jet development both by the ambient cross-stream and the stratification are investigated. The oscillation characteristic shows that a linear relation holds between the wavenumber of jet trajectory, crossflow velocity and the Brunt–Väisälä frequency of ambient stratification. Computational results indicate that the formation of the secondary and a third pairs of vortices, which are not induced in the unstratified environment, causes the jet flow oscillation from its maximum height-of-rise in the flowing direction. The ambient stratification prohibits the growth of the plume radius and reduces the mixing rate as well as the plume rise. The developed flow indicates the transformation of entrainment mechanism in stratified crossflow.     

Hydrodynamics and turbulence in emergent and sparsely vegetated open channel flow

This present study reports the results of an experimental study characterizing thorough variation of turbulent hydrodynamics and flow distribution in emergent and sparsely vegetated open channel flow. An emergent and rigid sparse vegetation patch with regular spacing between stems along the flow and transverse directions was fixed in the central region of the cross-section of open channel. Experiments were conducted in subcritical flow conditions and velocity measurements were obtained with an acoustic Doppler Velocimetry system. Large variations of the turbulence intensities, Reynolds shear stress, turbulent kinetic energy and vortical motions are found in and around the vegetation patch. At any cross-section through the interior of the vegetation patch, streamwise velocity decreases with increase in streamwise length and the velocity profiles converge from the log-law to a linear profile with increasing slope. Time-averaged lateral and vertical velocities inside the vegetation patch increase with increasing streamwise distance and converge from negative values to positive values. Turbulence intensities interior of the sparse vegetation patch are more than those of without the vegetation patch. Similar to the trend of streamwise velocity profiles inside the vegetation, turbulence intensities and longitudinal-normal Reynolds shear stress profile decreases with streamwise direction. In the interior of the vegetation patch and downstream of the trailing edge, turbulent kinetic energy profiles are exhibiting irregular fluctuations and the maximum values are occurring in the outer layer. Analysis of flow distribution confirms sparse vegetation patch is inducing a serpentine flow pattern in its vicinity. At the leading edge, flow is rushing towards the right hand sidewall, and at the trailing edge, flow is turning to the left hand sidewall. In between the leading and trailing edges, the streamlines are following a zig-zag fashion at varied degree along the streamwise and lateral directions. Immediate upstream of the leading edge and in the interior of the vegetation patch, vortex motion is clearly visible and the vortices are stretched along the width of the channel with streamwise direction.     

Development of a rotorcraft dust-emission parameterization using a CFD model

Flights of rotorcraft over the desert floor can result in significant entrainment of particulate matter into the atmospheric boundary layer. Continuous or widespread operation can lead to local and regional impacts on visibility and air quality. To account for this pollutant source in air quality models, a parameterization scheme is needed that addresses the complex vertical distribution of dust ejected from the rotorcraft wake into the atmospheric surface layer. A method to parameterize the wind and turbulence fields and shear stress at the ground is proposed here utilizing computational fluid dynamics and a parameterized rotor model. Measurements taken from a full scale experiment of rotorcraft flight near the surface are compared to the simulation results in a qualitative manner. The simulation is shown to adequately predict the forward detachment length of the induced ground jet compared to the measured detachment lengths. However, the simulated ground vortex widths and vorticity deviate substantially from the measured values under a range of flight speeds. Results show that the method may be applicable for air quality modeling assuming slow airspeeds of the rotorcraft, with advance ratios of 0.005–0.02.     

Study of flow formed by three coplanar impinging pipe jets at inclination angles of 30° and 45°

This paper presents an experimental study of the interactions of three fully-submerged, coplanar impinging jets issued from long pipes. The jets were neutrally buoyant and were arranged symmetrically about the axis of a central jet, with two side jets set to intersect with the central jet at two inclination angles (30° and 45°) and three Reynolds numbers (4240, 6400 and 8000). Measurements of the flow fields were performed using particle image velocimetry to examine the flow structures in various planes, i.e., the jet axis plane (X–Y), the jet normal plane (X–Z) and the cross-sectional plane (Y–Z). This flow configuration results in pronounced interactions among the three jets, and hence better mixing than that of a canonical single pipe jet as illustrated by augmented centreline velocity decay, spreading rate and turbulence level. The jets at the inclination angle of 45° impinge and mix more rapidly than those at 30°. For each case, the flow is highly 3-dimensional, and jet development displayed several distinct regions (converging, merging and combining) along the streamwise direction. The expansion of flow in the X–Y plane is similar to the shape of a hyperbola with necking formed immediately downstream of the impinging point, whereas that in the X–Z plane assumes the shape of a parabola with an open rim exhibiting a pronounced velocity deficit in the central part of the combining flow. Self-similarity of streamwise mean velocity is explored in the combining region of the flow on the two planes of symmetry (X–Y and X–Z). Flow development in the combining region is dominated by large-scale vortical structures, including von Kárman-like spanwise vortices in the X–Y plane and secondary circulation in the form of two pairs of counter-rotating streamwise vortices in the Y–Z plane.     

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.     

Turbulence and aeration in hydraulic jumps: free-surface fluctuation and integral turbulent scale measurements

In an open channel, a change from a supercritical to subcritical flow is a strong dissipative process called a hydraulic jump. Herein some new measurements of free-surface fluctuations of the impingement perimeter and integral turbulent time and length scales in the roller are presented with a focus on turbulence in hydraulic jumps with a marked roller. The observations highlighted the fluctuating nature of the impingement perimeter in terms of both longitudinal and transverse locations. The results showed further the close link between the production and detachment of large eddies in jump shear layer, and the longitudinal fluctuations of the jump toe. They highlighted the importance of the impingement perimeter as the origin of the developing shear layer and a source of vorticity. The air–water flow measurements emphasised the intense flow aeration. The turbulent velocity distributions presented a shape similar to a wall jet solution with a marked shear layer downstream of the impingement point. The integral turbulent length scale distributions exhibited a monotonic increase with increasing vertical elevation within 0.2 < L_z/d₁ < 0.8 in the shear layer, where L_z is the integral turbulent length scale and d₁ the inflow depth, while the integral turbulent time scales were about two orders of magnitude smaller than the period of impingement position longitudinal oscillations.     

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.     

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.     

A numerical (LES) investigation of a shallow-water, mid-latitude, tidally-driven boundary layer

We investigate turbulent mixing in a tidally driven, mid-latitude, shallow-water basin. The study is carried out numerically at a laboratory-scale, using large-eddy simulation. We compared the results of the simulation with those of a correspondent purely oscillatory flow (Stokes boundary layer). The effect of rotation on the flow dynamics is twofold. First, rotation gives rise to a mean spanwise flow that concurs to redistribute the turbulent energy among the Reynolds stresses, in particular between the horizontal directions, thus increasing the mixing across the water column and thickening the layer where developed turbulence is observable. Second, the presence of the horizontal component of the background vorticity (latitude effect) breaks the symmetry between the two semi-cycles of the oscillation, since turbulence results suppressed/enhanced during the first/second semi-cycle. These two effects significantly modify the turbulent characteristics with respect to the purely oscillating flow, although the mechanisms that generates turbulence present similar features. The qualitative agreement between our results and some measurements carried out in two sites with characteristics similar to the case analyzed suggests that the outcomes here provided may be of general use for the analysis of mid-latitude, neutrally stratified, shallow-water basins mainly driven by semi-diurnal tidal currents.     

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.     

Undular tidal bores: effect of channel constriction and bridge piers

A tidal bore may occur in a macro-tidal estuary when the tidal range exceeds 4.5–6 m and the estuary bathymetry amplifies the tidal wave. Its upstream propagation induces a strong mixing of the estuarine waters. The propagation of undular tidal bores was investigated herein to study the effect of bridge piers on the bore propagation and characteristics. Both the tidal bore profile and the turbulence generated by the bore were recorded. The free-surface undulation profiles exhibited a quasi-periodic shape, and the potential energy of the undulations represented up to 30% of the potential energy of the tidal bore. The presence of the channel constriction had a major impact on the free-surface properties. The undular tidal bore lost nearly one third of its potential energy per surface area as it propagated through the channel constriction. The detailed instantaneous velocity measurements showed a marked effect of the tidal bore passage suggesting the upstream advection of energetic events and vorticity “clouds” behind the bore front in both channel configurations: prismatic and with constriction. The turbulence patches were linked to some secondary motions and the proposed mechanisms were consistent with some field observations in the Daly River tidal bore. The findings emphasise the strong mixing induced by the tidal bore processes, and the impact of bridge structures on the phenomenon.     

Mixing layer in open-channel junction flows

When two open-channel flows merge in a three-branch subcritical junction, a mixing layer appears at the interface between the two inflows. If the width of the downstream channel is equal to the width of each inlet channel, this mixing layer is accelerated and is curved due to the junction geometry. The present work is dedicated to simplified geometries, considering a flat bed and a \(90^{\circ }\) angle where two configurations with different momentum ratios are tested. Due to the complex flow pattern in the junction, the so-called Serret–Frenet frame-axis based on the local direction of the velocity must be employed to characterize the flow pattern and the mixing layer as Cartesian and cylindrical frame-axes are not adapted. The analysis reveals that the centerline of the mixing layer, defined as the location of maximum Reynolds stress and velocity gradient, fairly fits the streamline separating at the upstream corner, even though a slight shift of the mixing layer towards the center of curvature is observed. The shape of the mixing layer appears to be strongly affected by the streamwise acceleration and the complex lateral confinement due to the side walls and the corners of the junction, leading to a streamwise increase of the mean velocity along the centerline and a decrease of the velocity difference. This results in a specific streamwise evolution of the mixing layer width, which reaches a plateau in the downstream region of the junction. Finally, the evaluation of the terms in the Reynolds-Averaged-Navier–Stokes equations reveals that the streamwise and normal acceleration and the pressure gradient remain dominant, which is typical of accelerated and rotational flows.