Showing papers in "Acta Geophysica in 2008"

Flow and transport in channels with submerged vegetation

Abstract: This paper reviews recent work on flow and transport in channels with submerged vegetation, including discussions of turbulence structure, mean velocity profiles, and dispersion. For submerged canopies of sufficient density, the dominant characteristic of the flow is the generation of a shear-layer at the top of the canopy. The shear-layer generates coherent vortices by Kelvin-Helmholtz (KH) instability. These vortices control the vertical exchange of mass and momentum, influencing both the mean velocity profile, as well as the turbulent diffusivity. For flexible canopies, the passage of the KH vortices generates a progressive wave along the canopy interface, termed monami. The KH vortices formed at the top of the canopy penetrate a distance δe into the canopy. This penetration scale segregates the canopy into an upper layer of rapid transport and a lower layer of slow transport. Flushing of the upper canopy is enhanced by the energetic shear-scale vortices. In the lower layer turbulence is limited to length-scales set by the stem geometry, and the resulting transport is significantly slower than that of the upper layer.

Stable-boundary-layer regimes from the perspective of the low-level jet

Abstract: This paper reviews results from two field studies of the nocturnal stable atmospheric boundary layer (SBL) over the Great Plains of the United States. Data from a scanning remote-sensing system, a High-Resolution Doppler Lidar (HRDL), provided measurements of mean and turbulent wind components at high spatial and temporal resolution through the lowest 500–1000 m of the atmosphere. This data set has allowed the characteristics of the low-level jet (LLJ) maximum (speed, height, direction) to be documented through entire nights. LLJs form after sunset and produce strong shear in the layer below the LLJ maximum or nose, which is a source of turbulence and mixing in the SBL. Simultaneous HRDL measurements of turbulence quantities related to turbulence kinetic energy (TKE) has allowed the turbulence in the subjet layer to be related to LLJ properties. Turbulence structure was found to be a function of the bulk stability of the subjet layer. For the strong-LLJ (> 15 m s−1), weakly stable cases the strength of the turbulence is proportional to the strength of the LLJ. For these cases with nearly continuous turbulence in the subjet layer, low-level jet scaling, in which lengths are scaled by the LLJ height and velocity variables are scaled by the LLJ speed, was found to be appropriate. For the weak-wind (< 5 m s−1 in the lowest 200 m), very stable boundary layer (vSBL), the boundary layer was found to be very shallow (sometimes < 10 m deep), and turbulent fluxes between the earth’s surface and the atmosphere were found to be essentially shut down. For more intermediate wind speeds and stabilities, the SBL shows varying degrees of intermittency due to various mechanisms, including shearinstability and other gravity waves, density currents, and other mesoscale disturbances.

An inconvenient “truth” about using sensible heat flux as a surface boundary condition in models under stably stratified regimes

Abstract: In single column and large-eddy simulation studies of the atmospheric boundary layer, surface sensible heat flux is often used as a boundary condition. In this paper, we delineate the fundamental shortcomings of such a boundary condition in the context of stable boundary layer modelling and simulation. Using an analytical approach, we are able to show that for reliable model results of the stable boundary layer accurate surface temperature prescription or prediction is needed. As such, the use of surface heat flux as a boundary condition should be avoided in stable conditions.

Flow analysis in a channel with flexible vegetation using double-averaging method

Abstract: The paper addresses the problem of the resistance due to vegetation in an open channel flow, characterized by partially and fully submerged vegetation formed by colonies of bushes. The flow is characterized by significant spatial variations of velocity between vertical profiles that make the traditional approach based on time averaging of turbulent fluctuations inconvenient. A more useful procedure, based on time and spatial averaging (Double-Averaging Method) is applied for the flow field analysis and characterization. The vertical distribution of mean velocity and turbulent stresses at different spatial locations has been measured with a 3D Acoustic Doppler Velocimeter (ADV) for two different vegetation densities where fully submerged real bushes (salix pentandra) have been used. Velocity measurements were completed together with the measurements of drag exerted on the flow by bushes at different flow depths. The analysis of velocity measurements allows depicting the fundamental characteristics of both the mean flow field and turbulence. The experimental data show that the contribution of form-induced stresses to the momentum balance cannot be neglected. The mean velocity profiles and the spatially averaged turbulent intensity profiles allow inferring that the vegetation density is a driving parameter for the development of a mixing layer at the canopy top in the case of submerged vegetation. Moreover, the net upward turbulent momentum flux, evaluated with the methodology proposed by Lu and Willmarth (1973), appears to be damped for increased vegetation density; this finding can rationally explain the reduction of the suspended sediment transport capacity typically observed in free surface flows over a vegetated bed.

Form induced stresses over rough gravel-beds

Abstract: This paper presents an analysis of spatial flow heterogeneity over rough gravel beds for shallow flows in terms of form induced stresses. Data from experiments specifically designed with the intention to analyze the flow data with the double-averaging methodology are used to investigate the nature of form induced stresses. It is shown that spatial flow heterogeneity is small at greater distances to the roughness tops (z100), increases slightly towards z100, and increases significantly below z100. Form induced stresses determined over the same bed and with the same slope are found to be independent of discharge. The influence of the number of measuring verticals on the magnitude of form induced stresses is discussed. The distributions of form induced stresses − are used to define the geodetic level of the roughness crest for rough, irregular beds from hydraulic data.

Boundary layer characteristics and turbulent exchange mechanisms in highly complex terrain

Abstract: The Mesoscale Alpine Programme’s Riviera project investigated the turbulence structure and related exchange processes in an Alpine valley by combining a detailed experimental campaign with high-resolution numerical modelling. The present contribution reviews published material on the Riviera Valley’s boundary layer structure and discusses new material on the near-surface turbulence structure. The general conclusion of the project is that despite the large spatial variability of turbulence characteristics and the crucial influence of topography at all scales, the physical processes can accurately be understood and modelled. Nevertheless, many of the “text book characteristics” like the interaction between the valley and slope wind systems or the erosion of the nocturnal valley inversion need reconsideration, at least for small non-ideal valleys like the Riviera Valley. The project has identified new areas of research such as post-processing methods for turbulence variables in complex terrain and new approaches for the surface energy balance when advection is non-negligible. The exchange of moisture and heat between the valley atmosphere and the free troposphere is dominated by local “secondary” circulations due to the curvature of the valley axis. Because many curved valleys exist, and operational models still have rather poor resolution, parameterization of these processes may be required.

Flow structure over square bars at intermediate submergence: Large Eddy Simulation study of bar spacing effect

Abstract: Turbulent open-channel flow over 2D roughness elements is investigated numerically by Large Eddy Simulation (LES). The flow over square bars for two roughness regimes (k-type roughness and transitional roughness between d-type and k-type) at a relative submergence of H/k = 6.5 is considered, where H is the maximum water depth and k is the roughness height. The selected roughness configurations are based on laboratory experiments, which are used for validating numerical simulations. Results from the LES, in turn, complement the experiments in order to investigate the time-averaged flow properties at much higher spatial resolution. The concept of the double-averaging (DA) of the governing equations is utilized to quantify roughness effects at a range of flow properties. Double-averaged velocity profiles are analysed and the applicability of the logarithmic law for rough-wall flows of intermediate submergence is evaluated. Momentum flux components are quantified and roughness effect on their vertical distribution is assessed using an integral form of the DA-equations. The relative contributions of pressure drag and viscous friction to the overall bed shear stress are also reported.

Transitional, entraining, cloudy, and coastal boundary layers

Abstract: Atmospheric boundary layers are marvelously varied and complex. Recent research has examined some of that variety. Boundary layers over land undergo drastic changes throughout the day as the sun rises and sets, and as clouds form and dissipate. Air is entrained at the top of the boundary layer at varying rates. As air moves over the coast, the boundary layer reacts to changes in surface forcing. All of these changes affect pollutant transport and weather formation. In this paper, research attempting to understand transitional, cloud-topped, and coastal boundary layers, and boundary-layer top entrainment, is reviewed.

Nocturnal basin low-level jets: an integrated study

Abstract: Low-level jets (LLJs) are a very common feature in the nocturnal stably stratified boundary layer. Many factors can intervene in their generation, linked basically to effects of baroclinity. A special kind of low-level jets is composed by the nocturnal katabatic and basin flows, generated over terrain slopes. A study of observed LLJs in the Duero Basin is shown here, combining observational data and modelling experiments. Normalized in respect to the maximum wind height, the dynamic characteristics of the jets are similar: a two-layer system, with a stably stratified layer below the jet maximum and a near neutral layer above, with a very stable layer separating them at the level of the wind maximum. There is vertical mixing above and below the jet, and the connection between these layers takes place occasionally in a very turbulent manner.

Effects of wind shear on the atmospheric convective boundary layer structure and evolution

Abstract: The article reviews past accomplishments and recent advances in conceptual understanding, numerical simulation, and physical interpretation of the wind shear phenomena in the atmospheric convective boundary layer.

Double-averaging methodology and its application to turbulent flow in and above vegetation canopies

Abstract: Double averaged equations for atmospheric boundary layer flows are introduced as natural extensions of single averaged Reynolds equations. We show that in circumstances where double averaged equations are needed, the two fundamental properties of Reynolds averaging are violated. First, we consider double-averaging in free air turbulence, where the aim is to separate coherent motions from background turbulence. We illustrate the different properties of the main operators that have been used and the physical meaning of the terms that result. Second, in canopy flows, the multiply connected nature of the canopy airspace leads to a different set of departures from the standard Reynolds equations. We establish the physical meaning of the extra terms that arise. Finally we briefly discuss the problems, both practical and theoretical, that arise when we use double averaged equations to interpret real data.

The spatial organisation of time-averaged streamwise velocity and its correlation with the surface topography of water-worked gravel beds

Abstract: An examination was made into the spatial pattern of time-averaged streamwise velocity in the near-bed region over two water-worked gravel beds. Laboratory observations revealed that there is considerable spatial variability in velocity. It was organised into streamwise streaks of high-speed fluid which were overlain by spots of low-speed fluid. This spatial pattern was found to be consistently and heavily dependent on relative submergence. The spatial pattern of velocity was shown to have little linear coherence with bed surface topography at the grain-scale. It suggested that for flows above the two beds studied here, bed surface topography at the grain-scale exerted less of an influence on the spatial organisation of time-averaged streamwise velocities than relative submergence.

Turbulent measurements in the stable atmospheric boundary layer during SHEBA: ten years after

Abstract: This paper surveys results of the comprehensive turbulent measurements in the stable boundary layer (SBL) made over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) in the Beaufort Gyre from October 1997 through September 1998. Turbulent fluxes and mean meteorological data were continuously measured and reported hourly at five levels on a 20-m main SHEBA tower. Eleven months of measurements during SHEBA cover a wide range of stability conditions, from the weakly unstable regime to very stable stratification, and allow studying the SBL in detail. A brief overview of the SBL regimes, the flux-profile relationships, the turbulent Prandtl number, and other parameters obtained during SHEBA is given. The traditional Monin–Obukhov approach, z-less scaling, and gradient-based scaling are evaluated and discussed based on the data from SHEBA.

Comparison of source parameters estimated in the frequency and time domains for seismic events at the Rudna copper mine, Poland

Abstract: Source parameters estimated in the frequency domain for 100 selected seismic events from the Rudna copper mine, with moment magnitude ranging from 1.4 to 3.6, were collected to study their scaling relations and to compare them with the parameters estimated in the time domain. The apparent stress and static stress drop, corrected for the limited bandwidth recording, increase slightly in a similar manner with increasing seismic moment. The ratio of apparent stress to static stress drop, a measure of radiation efficiency, is practically constant and its mean value is close to 0.1. For 37 seismic events, with moment magnitude between 1.9 and 3.4, source parameters were estimated in the time domain from relative source time functions, that displayed unilateral rupture propagation, and their rupture velocity could be estimated. It ranges from 0.23 to 0.80 of shear wave velocity and is almost independent of seismic moment. The fault length, estimated from the average source pulse width and rupture velocity, is clearly dependent on seismic moment and is smaller than the source radius estimated from the corner frequency on the average by about 25 percent. There is no correlation between the values of static stress drop estimated in the frequency and time domains, but the time domain stress drop is in general similar to that estimated in the frequency domain. The apparent stress increases with increasing rupture velocity, and the ratio of apparent stress to static stress drop seems also to depend on rupture velocity.

Rupture model of the great AD 365 Crete earthquake in the southwestern part of the Hellenic Arc

Abstract: An M8.3 earthquake struck the southwestern part of the Hellenic Arc, near the Island of Crete, in AD 365, generating a tsunami that affected almost the entire eastern Mediterranean region. Taking into account that the time history of seismicity in this region is fairly complete for such earthquakes in the historical catalog, which can be dated as back as the 5th century B.C., there is no indication that this segment of plate boundary has been fully ruptured again. The seismic hazard associated with this part of the Hellenic Arc necessitates the evaluation of the rupture characteristics of this great event. The constraint of the faulting geometry was initially achieved by using information from seismicity, and the focal mechanisms of earthquakes that occurred during the instrumental period. A rupture model for this great earthquake is constructed by assuming an elastic medium and calculating the theoretical surface displacements for various fault models that are matched with the observed surface deformation gleaned from historical reports. The resulted fault model concerns thrust faulting with a rupture length of 160 km and a seismic moment of 5.7 × 1028 dyn·cm, an average slip of 8.9 m and a corresponding moment magnitude equal to 8.4, in excellent agreement with the macroseismic estimation. The absence of such events recurrence is an indication of the lack of complete seismic coupling that is common in subduction zones, which is in accordance with the back arc spreading of the Aegean microplate and with previous results showing low coupling for extensional strain of the upper plate.

Micro- and macro-dispersive fluxes in canopy flows

Abstract: Resolving every detail of the three-dimensional canopy morphology and its underlying topography remains untenable when modeling high Reynolds number geophysical flows. How to represent the effects of such a complex morphological variability and any concomittant topographic variability into one-dimensional bulk flow representation remains a fundamental challenge to be confronted in canopy turbulence research. Theoretically, planar averaging to the scale of interest should be applied to the time-averaged mean momentum balance; however, such averaging gives rise to covariance or dispersive terms produced by spatial correlations of time-averaged quantities that remain ‘unclosed’ or require parameterization. When the averaging scale is commensurate with few canopy heights, these covariances can be labeled as ‘micro-dispersive’ stresses. When averaging is intended to eliminate low-wavenumber topographic variations, we refer to these covariances as ‘macro-dispersive’ terms. Two flume experiments were used to explore the magnitude and sign of both micro- and macro-dispersive fluxes relative to their conventional Reynolds stresses counterparts: a rod-canopy with variable roughness density and a dense rod canopy situated on gentle hilly terrain. When compared to the conventional momentum flux, the micro-dispersive fluxes in the lowest layers of sparse canopies can be significant (∼50%). For dense canopies, the dispersive terms remain negligible when compared to the conventional momentum fluxes throughout. For the macro-dispersive fluxes, model calculations suggest that these terms can be neglected relative to the Reynolds stresses for a deep canopy situated on a narrow hill. For the region in which topographic variations can interact with the pressure, both model calculations and flume experiments suggest that the macro-dispersive fluxes cannot be neglected, and their value can be 20% of the typical Reynolds stresses.

Electrical structure of the upper mantle beneath Central Europe: Results of the CEMES project

Abstract: In the years 2001–2003, we accomplished the experimental phase of the project CEMES by collecting long-period magnetotelluric data at positions of eleven permanent geomagnetic observatories situated within few hundreds kilometers along the south-west margin of the East European Craton. Five teams were engaged in estimating independently the magnetotelluric responses by using different data processing procedures. The conductance distributions at the depths of the upper mantle have been derived individually beneath each observatory. By averaging the individual cross-sections, we have designed the final model of the geoelectrical structure of the upper mantle beneath the CEMES region. The results indicate systematic trends in the deep electrical structure of the two European tectonic plates and give evidence that the electrical structure of the upper mantle differs between the East European Craton and the Phanerozoic plate of west Europe, with a separating transition zone that generally coincides with the Trans-European Suture Zone.

Double-average characteristics of sediment motion in one-dimensional bed load

Abstract: The sediment transport process on a flat bed was investigated experimentally, with reference to the relationship between the average solid discharge and the concentration and velocity of the moving grains. The instantaneous values of the quantities were measured and, therefore, it was possible to quantify the contribution of the temporal fluctuations of concentration and velocity to the resulting average sediment transport rate. Recognizing that the sediment transport process is an episodic phenomenon, an intermittency factor was defined and its contribution to the solid discharge, typically implicit in earlier formulations of the sediment flux, was highlighted. Conceptual analyses of the spatial scale dependence of the quantities were also made.

Effects of shear in the convective boundary layer: analysis of the turbulent kinetic energy budget

Abstract: Effects of convective and mechanical turbulence at the entrainment zone are studied through the use of systematic Large-Eddy Simulation (LES) experiments. Five LES experiments with different shear characteristics in the quasi-steady barotropic boundary layer were conducted by increasing the value of the constant geostrophic wind by 5 m s-1 until the geostrophic wind was equal to 20 m s-1. The main result of this sensitivity analysis is that the convective boundary layer deepens with increasing wind speed due to the enhancement of the entrainment heat flux by the presence of shear. Regarding the evolution of the turbulence kinetic energy (TKE) budget for the studied cases, the following conclusions are drawn: (i) dissipation increases with shear, (ii) the transport and pressure terms decrease with increasing shear and can become a destruction term at the entrainment zone, and (iii) the time tendency of TKE remains small in all analyzed cases. Convective and local scaling arguments are applied to parameterize the TKE budget terms. Depending on the physical properties of each TKE budget contribution, two types of scaling parameters have been identified. For the processes influenced by mixed-layer properties, boundary layer depth and convective velocity have been used as scaling variables. On the contrary, if the physical processes are restricted to the entrainment zone, the inversion layer depth, the modulus of the horizontal velocity jump and the momentum fluxes at the inversion appear to be the natural choices for scaling these processes. A good fit of the TKE budget terms is obtained with the scaling, especially for shear contribution.

Absorbing Boundary Conditions in a Fourth-order Accurate SH-wave Staggered Grid Finite Difference Algorithm

Abstract: This article presents the implementation of two well known absorbing boundary conditions in a fourth-order accurate staggered grid SH-wave finite difference (FD) algorithm with variable grid size, in a very simplified manner. Based on simulated results, it was confirmed that the Clayton and Engquist absorbing boundary condition causes edge-reflections in case of larger angle of incidence of body waves on the model edges. The results of various numerical experiments revealed that the Israeli and Orszag sponge boundary condition is efficient enough to avoid edge-reflections for any angle of incidence of the body. We recommend the use of both the Clayton and Engquist and Israeli and Orszag absorbing boundary conditions simultaneously to avoid any edge-reflections.

Particle simulations of dispersion using observed meandering and turbulence

Abstract: A Lagrangian stochastic particle model driven by observed winds from a network of 13 sonic anemometers is used to simulate the transport of contaminates due to meandering of the mean wind vector and diffusion by turbulence. The turbulence and the meandering motions are extracted from the observed velocity variances using a variable averaging window width. Such partitioning enables determination of the separate contributions from turbulence and meandering to the total dispersion. The turbulence is described by a Markov Chain Monte Carlo process based on the Langevin equation using the observed turbulence variances. The meandering motions, not the turbulence, are primarily responsible for the 1-h averaged horizontal dispersion as measured by the travel time dependence of the particle position variances. As a result, the 1-h averaged horizontal concentration patterns are often characterized by streaks and multi-modal distributions. Time series of concentration at a fixed location are highly nonstationary even when the 1-h averaged spatial distribution is close to Gaussian. The results show that meandering dominates the travel-time dependence of the horizontal dispersion under all atmospheric conditions: weak and strong winds, and unstable and stable stratification.

Rough-bed flows in geophysical, environmental, and engineering systems: Double-Averaging Approach and its applications

Abstract: Rough-wall turbulent flows represent a ubiquitous feature of many natural systems and man-made structures and therefore they have attracted significant attention from mathematicians, physicists, engineers, and Earth scientists, who have extensively studied these flows for more than eighty years. However, in spite of a fairly long research history and significant progress made towards their description and understanding, accurate prediction and control of rough-wall flows are still unsolved problems and thus additional research efforts and new approaches are required. One of these approaches, the so-called Double-Averaging Methodology (DAM), is the topic of this Special Issue.

Double-averaged velocity profiles over fixed dune shapes

Abstract: Spatially averaged profiles of time averaged velocity, using integrals over thin horizontal slabs (Cartesian double average), are employed in characterizing the flow over fixed dune shapes. For comparison the spatial averaging method of Smith and McLean (1977) that averages along lines at constant distance from the local bed elevation is also investigated. The Cartesian double averaged profiles of the inverse of the velocity shear are nearly constant below the crest elevation, but increase rapidly above the crest level. This results in velocity profiles that increase linearly with distance from the bed below the crest. Above the crest it can be argued that the velocity increases logarithmically, but a power law profile can also be argued. Spatially averaged eddy viscosity profiles are calculated by multiplying the average Reynolds stress by the inverse shear. The resulting profile is more complex than the uniform flow counterpart.

Finite difference modeling of seismic wave propagation in monoclinic media

Abstract: Reported in the present paper are the results of the study of propagation of SH waves in the plane of mirror symmetry of a monoclinic multilayered medium with displacement normal to the plane. Dispersion equation has been obtained analytically ussing Haskell’s matrix method, while the finite-difference method has been employed to model the SH-wave propagation to study its phase and group velocities.

Simulating time-histories and pseudo-spectral accelerations from the 1992 Cairo earthquake at the proposed El-Fayoum New City Site, Egypt

Abstract: El-Fayoum New City represents one of the new urban settlements that are recently erected all over Egypt. Because seismic recordings are not available, I used the stochastic method to simulate the largest damaging earthquake from the closest seismic source to the proposed area of the city. To verify the method and its computed results in Egypt, a study termed “method verification” was performed. I found that the October 12, 1992, earthquake (Mb = 5.8) that occurred southwest of Cairo in the vicinity of the Dahshour region, at the coordinates 29.77°N, 31.07°E, is a significant earthquake to the city. The parameters of the path from the hypocenter of the event to the city were taken into consideration. To determine the site parameters, a shallow seismic refraction survey was carried out in the studied area. Accordingly, I simulated time-histories and pseudo-spectral accelerations from the October 12, 1992, earthquake at the location of seismic profiles. Finally, it is demonstrated that the site is characterized by high ground motion amplification factors, producing a high ground motion acceleration value.

On the significance of form-induced stress in rough wall turbulent boundary layers

Abstract: This paper presents a review of recent experimental and numerical studies which deal with the analysis of form-induced stress in rough wall turbulent boundary layers. The aim of the paper is to assess the importance of this stress for various rough wall geometries and flow conditions. Analysis of the significance of form-induced stress is first performed by comparing its magnitude with the magnitude of Reynolds stress for each data set available in literature. Then, by selecting a special set of data, we analyze the comparison between the gradients of both stresses. We point out that the comparison of stress gradients gives a different perspective on the role of form-induced stress in rough wall boundary layers.

Swarms in Andaman Sea, India — a seismotectonic analysis

Abstract: The seismotectonic characteristics of 1983–1984, 1993 and 2005 swarms in Andaman Sea are analysed. These swarms are characterised by their typical pulsating nature, oval shaped geometry and higher b values. The migration path of the swarms from north to south along the Andaman Spreading Ridge is documented. While the first two swarms are located along existing mapped rift segments, the 2005 swarm appears to have generated a new rift basin along 8°N. The analysis and supporting evidences suggest that these swarms were generated by intruding magmatic dyke along the weak zones in the crust, followed by rifting, spreading and collapse of rift walls. CMT solutions for 2005 swarm activity indicate that intrusion of magmatic dyke in the crustal weak zone is documented by earthquakes showing strike slip solution. Subsequent events with normal fault mechanism corroborate the rift formation, collapse and its spreading.

Changes of GPR spectra due to the presence of hydrocarbon contamination in the ground

Abstract: The location of hydrocarbon contamination in the ground using the GPR method is based mainly on information taken from reflected signals. In the cases investigated in Polish contaminated sites, such signals were very seldom recorded. A long time after spillage, contamination takes the form of plumes with different size and distribution, which depends on geological and hydraulic properties of the ground. In this paper, it is shown that the set of hydrocarbon plumes should be described with a stochastic model, and such plumes may generate the scattered waves which cause changes in the power spectra. It has been observed that the power spectra of GPR signals over contaminated areas are quite different from such spectra over clear ones. These differences were discussed in this paper on the basis of theoretical analysis, numerical modelling and the results of GPR terrain surveys.

Turbulent kinetic energy budget in a gravel-bed channel flow

Abstract: The present experimental investigation focuses on the characteristics of near bed turbulence in a fully rough, uniform open-channel flow over a gravel-type bed. Due to bed topography small scale heterogeneity, the flow is not uniform locally in the near bed region and a double averaging methodology is applied over a length scale much larger than the gravel size. The double-averaged Turbulent Kinetic Energy (TKE) budget derived in the context of the present flow over a gravel bed differs from the TKE budget written for flow over a vegetation canopy. The non-constant shape of the roughness function measured in our gravel bed leads to an additional bed-induced production term which is null for vertical roughness elements, such as simplified vegetation elements.

Double-averaged velocity and stress distributions for hydraulically-smooth and transitionally-rough turbulent flows

Abstract: We analyse experimental measurements of turbulent open-channel flow over hydraulically-smooth and transitionally-rough beds using the double-averaging methodology. Oil with a viscosity of 15×10−6 m2/s is used instead of water so that transitional-range roughness Reynolds numbers can be achieved with large (11.1 mm) roughness elements, allowing spatial variations in the mean velocity field to more easily be measured. Distributions of double-averaged velocities, turbulence intensities, form-induced intensities, and viscous, Reynolds, form-induced and total shear stresses are studied with comparisons made between distributions for hydraulically-smooth, transitionally-rough, and fully-rough boundaries. Measured streamwise turbulence intensities for all experiments peaked at a constant distance from the bed (z++d+ = 15) when elevation scale is adjusted using the zero-plane displacement d for the logarithmic velocity distribution. This collapse suggests that turbulence intensity distributions may be useful in assessing appropriate values of d for transitionally-rough and fully-rough boundaries. Form-induced normal and shear stresses above the roughness tops were found to collapse towards a common curve independent of roughness Reynolds number.