Turbulence fields in the lee of two‐dimensional transverse dunes simulated in a wind tunnel

The turbulence field of airflow in the lee of a dune has significant impacts on dune dynamics and related processes. We used particle image velocimetry in a wind tunnel simulation to obtain detailed velocity measurements in the lee of two‐dimensional transverse dune models, then used the results to analyse their turbulence fields. The dune models used in this study had a single lee angle of 30°, and a total of six stoss angles: 3°, 5°, 10°, 15°, 20° and 25°. We used vorticity, turbulence intensity, Reynolds stress and turbulent kinetic energy to characterize the turbulence fields. These parameters were functions of stoss angle, wind velocity, distance from the dune crest and height above the ground surface. The stoss angles could generally be divided into two groups based on the profiles of mean velocity, turbulence and Reynolds stress. Stoss angles of 3° and 5° usually had similar profiles, and angles of 15°, 20° and 25° formed a second group with similar profiles. The profiles for the stoss angle of 10° were usually transitional and were intermediate between the two groups. Vorticity, Reynolds stress and turbulent kinetic energy increased monotonically with increasing free‐stream wind velocity, but their variations with respect to the stoss angle were complex. The stoss angles of 15° and 20° had the maximum values of these three parameters, thus these angles may have special significance in dune development given the characteristics of the mean velocity fields and turbulence fields they produce within the lee airflow. It is the streamwise velocity component and its turbulence that determine the surface shear stress. Copyright © 2008 John Wiley and Sons, Ltd.     

3D Lagrangian modelling of saltating particles diffusion in turbulent water flow

A 3D Lagrangian model of the saltation of solid spherical particles on the bed of an open channel flow, accounting for turbulence-induced mechanisms, is proposed and employed as the key tool of the study. The differences between conventional 2D models and a proposed 3D saltation model are discussed and the advantages of the 3D model are highlighted. Particularly, the 3D model includes a special procedure allowing generation of 3D flow velocity fields. This procedure is based on the assumption that the spectra of streamwise, vertical and transverse velocity components are known at any distance from the bed. The 3D model was used to identify and quantify effects of turbulence on particle entrainment and saltation. The analysis of particle trajectories focused on their diffusive nature, clarifying: (i) the effect of particle mobility parameter; (ii) the effect of bed topography; and (iii) the effect of turbulence. Specifically, the results of numerical simulations describing the abovementioned effects on the change in time of the variance are presented. In addition, the change in time of the skewness and kurtosis, which are likely to reflect the turbulence influence on the spread of particles, are also shown. Two different diffusion regimes (local and intermediate) for each of the investigated flow conditions are confidently identified.     

Planetary Boundary Layer Flows in the Atmosphere and the Ocean at the Equator

—The boundary layer flows created by the frictional dissipation of the wind speed at the surface in the atmosphere and by surface wind stress in the ocean at the equator and in the equatorial region, are obtained by taking the influence of the surface friction on the zonal velocity as being balanced by vertical transport for the long-term mean flow and by a corresponding time variation for time-dependent flow fields. Solutions are expressed in terms of the velocities in zonal and vertical directions and the divergence of the horizontal current in the two media. It is found that under the ever present easterly flow in the lower atmosphere, the boundary layer flow in the atmosphere is convergence and ascending motion in the lower troposphere, and divergence at the surface and uplift in ocean, and in reverse directions for the westerly flow. Similar results are obtained for time-dependent wind fields and they give way to the steady asymptotic solutions when the period of the variation exceeds 10 months.     

On the origin of jets in the ocean

We show a mechanism whereby the jets result during the development of β-plumes (i.e., low-frequency Rossby waves that establish gyre circulations) in a model of ocean-basin circulation. The energy originates in baroclinic meanders of circulation at the eastern boundary of the ocean. Eddies are intimately related and occur as a result of the instability of this process. This mechanism does not rely on the existence of the small-scale turbulence to establish zonal flows. Zonal jets can then be amplified by eddies arranged in certain order in the flow. The underlying dynamics include the propagation of linear and nonlinear basin scale Rossby waves. The related barotropic theory for these waves is developed here. We demonstrate the radiative development of jets and β-plumes in a laboratory experiment using a rotating fluid with a paraboloidal free surface. The dynamical fields are measured by the laboratory analog of the satellite altimetry.     

Numerical simulation of surf–swash zone motions and turbulent flow

A two-dimensional numerical model was presented for the simulation of wave breaking, runup and turbulence in the surf and swash zones. The main components of the model are the Reynolds-Averaged Navier–Stokes equations describing the average motion of a turbulent flow, a k–ε turbulence closure model describing the transformation and dissipation processes of turbulence and a volume of fluid technique for tracking the free surface motion. Nearshore wave evolution on a sloping bed, the velocity field and other wave characteristics were investigated. First, the results of the model were compared with experimental results for different surf zone hydrodynamic conditions. Spilling and plunging breakers were simulated and the numerical model investigated for different wave parameters. The turbulence field was also considered and the spatial and time-dependent variations of turbulence parameters were discussed. In the next stage of the study, numerical results were compared with two sets of experimental data in the swash zone. Generally, there is good agreement except for turbulence predictions near the breaking point where the model does not represent well the physical processes. On the other hand, turbulence predictions were found to be excellent for the swash zone. The model provides a precise and efficient tool for the simulation of the flow field and wave transformations in the nearshore, especially in the swash zone. The numerical model can simulate the surface elevation of the vertical shoreline excursion on sloping beaches, while swash–swash interactions within the swash zone are accounted for.     

Wind mixing of a stratified shear flow

The response of a shear flow to an imposed wind stress is studied both theoretically and by means of a numerical turbulence model. It is shown that for small initial gradient Richardson numbers (Ri₀ ≲ 4/3) a tail wind causes the slab velocity of the upper mixed layer to decrease. The theory is based on the assumption that during the wind-induced entrainment process the overall Richardson number will adjust to a quasi-constant value (Ri_u ≈ 2/3). The turbulence model is the so-called k-ɛ model. It is calibrated to five conditions by tuning only one constant. The details of the deepening process and the density and velocity distributions of the upper mixed layer during this anomalous behavior are thus made clear. The results imply that the common practice of estimating the total current velocity by vector addition of the original velocity and the wind-induced velocity (calculated from models based on an ocean at rest) may lead to an overestimation of the current speed.     

Velocity and turbulence variations at the edge of saltmarshes

Saltmarsh vegetation significantly influences tidal currents and sediment deposition by decelerating the water velocity in the canopy. In order to complement previous field results, detailed profiles of velocity and turbulence were measured in a laboratory flume. Natural Spartina anglica plants were installed in a 3 m length test section in a straight, recirculating flume. Different vegetation densities, water depths and surface velocities were investigated. The logarithmic velocity profile, which existed in front of the vegetation, was altered gradually to a skimming-flow profile, typical for submerged saltmarsh vegetation. The flow reduction in the denser part of the canopy also induced an upward flow (the current was partially deflected by the canopy). The skimming flow was accompanied by a zone of high turbulence co-located with the strongest velocity gradient. This gradient moved upward and the turbulence increased with distance from the edge of the vegetation. Below the skimming flow, the velocity and the turbulence were low. The structure of the flow in the canopy was relatively stable 2 m into the vegetation. The roughness length (z₀) of the vegetation depends only on the vegetation characteristics, and is not sensitive to the current velocity or the water depth. Both the reduced turbulence in the dense canopy and the high turbulence at the top of the canopy should increase sediment deposition. On the other hand, the high turbulence zone just beyond the vegetation edge and the oblique upward flow may produce reduced sedimentation; a phenomenon that was observed near the vegetation edge in the field.     

Numerical modelling of wind effects on breaking waves in the surf zone

Wind effects on periodic breaking waves in the surf zone have been investigated in this study using a two-phase flow model. The model solves the Reynolds-averaged Navier–Stokes equations with the k ? ?? turbulence model simultaneously for the flows both in the air and water. Both spilling and plunging breakers over a 1:35 sloping beach have been studied under the influence of wind, with a focus during wave breaking. Detailed information of the distribution of wave amplitudes and mean water level, wave-height-to-water-depth ratio, the water surface profiles, velocity, vorticity, and turbulence fields have been presented and discussed. The inclusion of wind alters the air flow structure above water waves, increases the generation of vorticity, and affects the wave shoaling, breaking, overturning, and splash-up processes. Wind increases the water particle velocities and causes water waves to break earlier and seaward, which agrees with the previous experiment.     

Geophysical flows with anisotropic turbulence and dispersive waves: flows with stable stratification

The quasi-normal scale elimination (QNSE) is an analytical spectral theory of turbulence based upon a successive ensemble averaging of the velocity and temperature modes over the smallest scales of motion and calculating corresponding eddy viscosity and eddy diffusivity. By extending the process of successive ensemble averaging to the turbulence macroscale one eliminates all fluctuating scales and arrives at models analogous to the conventional Reynolds stress closures. The scale dependency embedded in the QNSE method reflects contributions from different processes on different scales. Two of the most important processes in stably stratified turbulence, internal wave propagation and flow anisotropization, are explicitly accounted for in the QNSE formalism. For relatively weak stratification, the theory becomes amenable to analytical processing revealing just how increasing stratification modifies the flow field via growing anisotropy and gravity wave radiation. The QNSE theory yields the dispersion relation for internal waves in the presence of turbulence and provides a theoretical reasoning for the Gargett et al. (J Phys Oceanogr 11:1258–1271, 1981) scaling of the vertical shear spectrum. In addition, it shows that the internal wave breaking and flow anisotropization void the notion of the critical Richardson number at which turbulence is fully suppressed. The isopycnal and diapycnal viscosities and diffusivities can be expressed in the form of the Richardson diffusion laws thus providing a theoretical framework for the Okubo dispersion diagrams. Transitions in the spectral slopes can be associated with the turbulence- and wave-dominated ranges and have direct implications for the transport processes. We show that only quasi-isotropic, turbulence-dominated scales contribute to the diapycnal diffusivity. On larger, buoyancy dominated scales, the diapycnal diffusivity becomes scale independent. This result underscores the well-known fact that waves can only transfer momentum but not a scalar and sheds a new light upon the Ellison–Britter–Osborn mixing model. It also provides a general framework for separation of the effects of turbulence and waves even if they act on the same spatial and temporal scales. The QNSE theory-based turbulence models have been tested in various applications and demonstrated reliable performance. It is suggested that these models present a viable alternative to conventional Reynolds stress closures.     

An analysis of the characteristics of rough bed turbulent shear stresses in an open channel

Entrainment of sediment particles from channel beds into the channel flow is influenced by the characteristics of the flow turbulence which produces stochastic shear stress fluctuations at the bed. Recent studies of the structure of turbulent flow has recognized the importance of bursting processes as important mechanisms for the transfer of momentum into the laminar boundary layer. Of these processes, the sweep event has been recognized as the most important bursting event for entrainment of sediment particles as it imposes forces in the direction of the flow resulting in movement of particles by rolling, sliding and occasionally saltating. Similarly, the ejection event has been recognized as important for sediment transport since these events maintain the sediment particles in suspension. In this study, the characteristics of bursting processes and, in particular, the sweep event were investigated in a flume with a rough bed. The instantaneous velocity fluctuations of the flow were measured in two-dimensions using a small electromagnetic velocity meter and the turbulent shear stresses were determined from these velocity fluctuations. It was found that the shear stress applied to the sediment particles on the bed resulting from sweep events depends on the magnitude of the turbulent shear stress and its probability distribution. A statistical analysis of the experimental data was undertaken and it was found necessary to apply a Box-Cox transformation to transform the data into a normally distributed sample. This enabled determination of the mean shear stress, angle of action and standard error of estimate for sweep and ejection events. These instantaneous shear stresses were found to be greater than the mean flow shear stress and for the sweep event to be approximately 40 percent greater near the channel bed. Results from this analysis suggest that the critical shear stress determined from Shield's diagram is not sufficient to predict the initiation of motion due to its use of the temporal mean shear stress. It is suggested that initiation of particle motion, but not continuous motion, can occur earlier than suggested by Shield's diagram due to the higher shear stresses imposed on the particles by the stochastic shear stresses resulting from turbulence within the flow.     

Robust classification for the joint velocity‐intermittency structure of turbulent flow over fixed and mobile bedforms

Two datasets of turbulence velocities collected over different bedform types under contrasting experimental conditions show similarity in terms of velocity‐intermittency characteristics and suggest a universality to the velocity‐intermittency structure for flow over bedforms. One dataset was obtained by sampling flow over static bedforms in different locations, and the other was based on a static position but mobile bedforms. A flow classification based on the velocity‐intermittency behaviour is shown to reveal some differences from that based on an analysis of Reynolds stresses, boundary layer correlation and turbulent kinetic energy. This may be attributed to the intermittency variable, which captures the local effect of individual turbulent flow structures. Locations in the wake region or the outer layer of the flow are both shown to have a velocity‐intermittency behaviour that departs from that for idealized wakes or outer layer flow because of the superposition of localized flow structures generated by bedforms. The combined effect of this yields a velocity‐intermittency structure unique to bedform flow. The use of a time series of a single velocity component highlights the potential power of our approach for field, numerical and laboratory studies. The further validation of the velocity‐intermittency method for non‐idealized flows undertaken here suggests that this technique can be used for flow classification purposes in geomorphology, hydraulics, meteorology and environmental fluid mechanics. © 2014 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.     

Diagnosing vertical motion in the Equatorial Atlantic

Estimating the vertical velocity (w) in the oceanic upper-layers is a key issue for understanding the cold tongue development in the Eastern Equatorial Atlantic. In this methodological paper, we develop an expanded and general formulation of the vertical velocity equation based on the primitive equation (PE) system, in order to gain new insight into the physical processes responsible for the Equatorial and Angola upwellings. This approach is more accurate for describing the real ocean than simpler considerations based on just the wind-driven patterns of surface layer divergence. The w-sources/forcings are derived from the PE w-equation and diagnosed from a realistic ocean simulation of the Equatorial Atlantic. Sources of w are numerous and express the high complexity of terms related to the turbulent momentum flux, to the circulation and to the mass fields, some of them depending explicitly on w and others not. The equatorial upwelling is found to be mainly induced by the (i) the zonal turbulent momentum flux, (ii) the curl of turbulent momentum flux and (iii) the imbalance between the circulation and the pressure fields. The Angola upwelling in the eastern part of the basin is controlled by strong curl of turbulent momentum flux. A strong cross-regulation is evidenced between the w-forcings independent of w and dependent on w, which suggests an equatorial balanced-dynamics. The w-forcing depending on w represents the negative feedback of the ocean to the w-forcing independent of w: in the equatorial band, this adjustment is led by non-linear processes and by vortex stretching outside.     

Influence of Zostera marina canopies on unidirectional flow,hydraulic roughness and sediment movement

Seagrasses develop extensive or patchy underwater meadows in coastal areas around the world, forming complex, highly productive ecosystems. Seagrass canopies exert strong effects on water flow inside and around them, thereby affecting flow structure, sediment transport and benthic ecology. The influence of Zostera marina canopies on flow velocity, turbulence, hydraulic roughness and sediment movement was evaluated through laboratory experiments in 2 flumes and using live Z. marina and a mobile sand bed. Profiles of instantaneous velocities were measured and sediment movement was identified upstream, within and downstream of patches of different sizes and shoot density and at different free-stream velocities. Flow structure was characterised by time-averaged velocity, turbulence intensity and Turbulent Kinetic Energy (TKE). When velocity data were available above the canopy, they were fitted to the Law of the Wall and shear velocities and roughness lengths were calculated. When a seagrass canopy was present, three layers were distinguishable in the water column: (1) within canopy represented by low velocities and high turbulence; (2) transition zone around the height of the canopy, where velocities increased, turbulence decreased and TKE was high; and (3) above canopy where velocities were equal or higher than free-stream velocities and turbulence and TKE were lower than below. Shoot density and patch-width influenced this partitioning of the flow when the canopy was long enough (based on flume experiments, at least more than 1 m-long). The enhanced TKE observed at the canopy/water interface suggests that large-scale turbulence is generated at the canopy surface. These oscillations, likely to be related to the canopy undulations, are then broken down within the canopy and high-frequency turbulence takes place near the bed. This turbulence ‘cascade’ through the canopy may have an important impact on biogeochemical processes. The velocity above the canopy generally followed a logarithmic profile. Roughness lengths were higher above the canopy than over bare sand and increased with increasing distance from the leading edge of the canopy; however, they were still small (<1 cm) compared to other studies in the literature. Within and downstream of the canopy, sediment movement was observed at velocities below the threshold of motion. It was likely caused by the increased turbulence at those positions. This has large implications for sediment transport in coastal zones where seagrass beds develop.     

Structure of flow over alluvial bedforms: an experiment on linking field and laboratory methods

This paper presents results of a field study designed to examine the structure of flow over mobile and fixed bedforms in a natural stream and to compare the results with findings of previous laboratory studies within the framework of double time–space averaging approach. Measurements of turbulence were obtained in a small river in Illinois, USA, over a fine spatial grid of sampling points above a mobile sandy bedform and its artificially moulded replica. Flow structure over the artificial bedform is similar to that observed in laboratory studies, but is markedly different from the flow structure over natural bedforms. These differences are most pronounced in the roughness sublayer, whereas flow in the logarithmic layer over natural and artificial sand waves is fairly similar and exhibits spatial uniformity. The double time–space averaged distributions of turbulence statistics conform to the multilayer model of flow structure over bedforms. Mean velocity distributions indicate neither classical flow recirculation nor substantial reduction of velocities in the lee of bedform crests. However, vertical patterns of turbulence statistics over depth suggest that stacked wakes similar to those observed in laboratory studies exist above the bedforms. Thus, despite the absence of flow separation, wake development seems to be induced by the systematic influence of upstream bedforms on the vertical structure of turbulence. Copyright © 2006 John Wiley & Sons, Ltd.     

Homogeneous planar and two-dimensional mean-field antidynamo theorems with zero mean flow

In an electrically conducting fluid, two types of turbulence with a preferred direction are distinguished: planar turbulence, in which every velocity in the turbulent ensemble of flows has no component in the given direction; and two-dimensional turbulence, in which every velocity in the turbulent ensemble is invariant under translation in the preferred direction. Under the additional assumptions of two-scale and homogeneous turbulence with zero mean flow, the associated magnetohydrodynamic alpha- and beta-effects are derived in the second-order correlation approximation (SOCA) when the electrically conducting fluid occupies all space. Limitations of the SOCA are well known, but alpha- and beta-effects of a turbulent flow are useful in interpreting the dynamo effects of the turbulence. Two antidynamo theorems, which establish necessary conditions for dynamo action, are shown to follow from the special structures of these alpha- and beta-effects. The theorems, which are analogues of the laminar planar velocity and two-dimensional antidynamo theorems, apply to all turbulent ensembles with the prescribed alpha- and beta-effects, not just the planar and two-dimensional ensembles. The mean magnetic field is general in the planar theorem but only two-dimensional in the two-dimensional theorem. The two theorems relax the previous restriction to turbulence which is both two-dimensional and planar. The laminar theorems imply decay of the total magnetic field for any velocity of the associated turbulent ensemble. However, the mean-field theorems are not fully consistent with the laminar theorems because further conditions beyond those arising from the turbulence must be imposed on the beta-effect to establish decay of the mean magnetic field. In particular, negative turbulent magnetic diffusivities must be restricted. It is interesting that there is no inconsistency in the alpha-effects. The failure of the SOCA with the two-scale approximation to simply preserve the laminar antidynamo theorems at the beta-effect level is a further demonstration of the restricted validity of the theory and shows that negative diffusivity effects derived by approximation methods must be treated cautiously.     

A flume experiment to examine underwater sound generation by flowing water

The hydrogeomorphology and ecology of rivers and streams has been subject of intensive research for many decades. However, hydraulically-generated acoustics have been mostly neglected, even though this physical attribute is a robust signal in fluvial ecosystems. Physical generated underwater sound can be used to quantify hydro-geomorphic processes, to differentiate among aquatic habitat types, and it has implications on the behavior of organisms. In this study, acoustic signals were quantified in a flume by varying hydro-geomorphic drivers and the related turbulence and bubble formation. The acoustic signals were recorded using two hydrophones and analyzed using a signal processing software, over 31 third-octave bands (20 Hz–20 kHz), and then combined in 10 octave bands. The analytical method allowed for a major improvement of the signal-to-noise ratio, therefore greatly reducing the uncertainty in our analyses. Water velocity, relative submergence, and flow obstructions were manipulated in the flume and the resultant acoustic signals recorded. Increasing relative submergence ratio and water velocity were important for reaching a turbulence threshold above which distinct sound levels were generated. Increases in water velocity resulted in increased sound levels over a wide range of frequencies. The increases in sound levels due to relative submergence of obstacles were most pronounced in midrange frequencies (125 Hz–2 kHz). Flow obstructions in running waters created turbulence and air bubble formation, which again produced specific sound signatures.     

Decaying grid turbulence experiments in a stratified fluid: flow measurements and statistics

Laboratory experiments of decaying grid stratified turbulence were performed in a two-layer fluid and varying the stratification intensity. Turbulence was generated by towing an array of cylinders in a square vessel and the grid was moved at a constant velocity along the total vertical extent of the tank. In order to investigate the influence of the stratification intensity on the turbulence decay, both 2C-PIV and stereo PIV were used to provide time resolved velocity fields in the horizontal plane and the out-of-plane velocity. As expected, a faster decay of the turbulence level along the vertical axis and the collapse in a quasi-horizontal motion increased with the buoyancy frequency, N. In order to characterise the decay process we investigated the time evolution of the vortex statistics, the turbulence scales and the kinetic energy and enstrophy of the horizontal flow. The exponents recovered in the corresponding scaling laws were compared with the theoretical predictions and with reference values obtained in previous experimental studies. Both the spectral analysis and the evolution of characteristic length scales indicate that, in the examined range of N, the dynamics is substantially independent of the stratification intensity. The results obtained were explained in terms of the scaling analysis of decaying turbulence in strongly stratified fluids introduced by Brethouwer et al. (J Fluid Mech 585:343–368.  https://doi.org/10.1017/S0022112007006854, 2007).