An erosion criterion for gravel-bed rivers

A theoretically-based erosion criterion is developed for gravel-bed rivers which incorporates the effect of both grain geometry and turbulent velocity fluctuations. It is derived from a balance of instantaneous drag, lift, and gravity forces operating on individual grains and is calculated for spherical grains arranged in three distinct geometries. To accommodate the temporal variation in bed shear stress, the model includes a stochastic element based on the characteristics of turbulence derived from the flume evidence of McQuivey (1973a, b). In terms of the Shields parameter, results show reasonable agreement with the range of observations quoted from the field and with the experimental data of Fenton and Abbott (1977). Finally, the argument is generalized to cover applications in the wider context of field conditions including a range of grain sizes and flow conditions.     

Small scale turbulent diffusion determined with underwater flow visualization

Dye plumes were generated at three depths in the seasonal thermocline between 7 and 11 m, 22 km south of Key West on 21 August 1980 and photographed at about 10 second intervals with an underwater camera system. Eleven pairs of consecutive pictures are analyzed to determine the mean current vertical shear and the width of the plumes by positioning reference points relative to the rod attached to the camera system. The relative distances of reference points are calibrated with the stereophotogrammetric method for one pair. The eddy diffusivity is calculated by use of a model of turbulent diffusion developed byTaylor (1921). Its values range from 5 to 25 cm²s^–1 for the plume widths ranging from 33 to 132 cm. The Richardson number is calculated for each pair of pictures with the vertical density gradient estimated from temperature profiles. Its values are higher than the critical value of 0.25 except for one case. The diffusivity was higher by orders of magnitude than the molecular one and indicates the presence of turbulence together with billow like features of the plumes in spite of high Richardson numbers. This suggests that the billow turbulence might be caused by effects of surface gravity waves and not by the Kelvin-Helmholtz instability.     

Further Studies Of Atmospheric Turbulence In Layers Near The Surface: Scaling The Tke Budget Above The Roughness Sublayer

The second of two experimental studies of the TKE budget conducted on sites of different roughness is described, and results are compared. The first took place within a shallow layer above a small field of mostly bare, cultivated soil; the second was carried out above a roughness sublayer of significant depth on an extensive plain of tall dry grass. Budget terms observed in the second study were scaled with a modified u which compensated for effects of an unusually large stress gradient and ensured that the _m functions would be collinear. By showing that the modification becomes negligible in smaller gradients, it is demonstrated that in normal conditions, budgets observed above significant roughness sublayers should be normalized by scaling in terms of the unreduced Reynolds stress at the sublayer's upper surface. This procedure is shown to be consistent with the expectation that TKE budgets in layers near the surface all scale in fundamentally the same way.Other findings include: (1) the fact that most _m functions previously reported are not quite collinear is attributed to a type of overspeeding known to affect three-cup anemometers; (2) revised _m functions, collinear and largely free of the effects of overspeeding, are determined from a well-established characteristic of the linear _m relation for the stable case; (3) data that define collinear _m functions can also be represented with single hyperbolic curves; (4) dissipation is found to be 10 to 15% too small to balance total TKE production in unstable and neutral conditions and to decrease with increasing z/L in thestable regime; and (5) new relations for based on the observed behaviour of the dissipation deficit provide an improved closure for the set of equations that express the budget terms as functions of _m and z/L.     

Turbulence Closures In Neutral Boundary Layer Over Complex Terrain

In this work, three turbulence closure models, Mellor andYamada level 2.5, E - l and E - implemented in a circulation model, are compared in neutral condition over complex terrain. They are firstly applied to a one-dimensional case on flat terrain and then to a schematic two-dimensional valley. The simulation results, in terms of wind field and turbulent kinetic energy, are tested against measurements from a wind-tunnel experiment. The empirical constants defining the characteristic length scales of the closures are modified based on turbulence parameters estimated in the experiment. The formulation of the diffusion coefficients is analysed to explain the differences among the various closures in the simulation results. Regarding the mean flow, both on flat and complex terrain, all the closures yield satisfactory results. Concerning the turbulent kinetic energy, the best results are obtained by E - l and E - closures.     

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.     

Analysis And Simulation Of Surface-Layer Winds Using Multiplicative Cascade Models With Self-Similar Probability Densities

Statistical analysis techniques based on multiplicative cascades are investigated for use with surface-layer wind data sets collected in the atmospheric boundary layer over flat farm land. The data were found to exhibit multiscaling statistics, allowing the surface-layer winds to be simulated with the use of multiplicative random cascades. The study found evidence that, for the surface-layer at least, these cascade models (andhence the methods of multifractal analysis) should be applied in separate ways to the microscale inertial range, and the mesoscale. This is at odds with the view found in the existing literature, which proposes a `universal multifractal' model to replace the widely held view that there exists separate microscale, mesoscale and synoptic scales for which the processes governing each are different. At least two separate ranges of scaling are suggested for surface-layer wind data, corresponding to the microscale inertial range and the mesoscale. For the case of the mesoscale range, a self-similar distribution of weighting factors was found for the wind speed data themselves, rather than for an intermediate (dissipation) field, as is required for themicroscale data.     

A SIMPLIFIED APPROACH TO MODELING 3D SEDIMENT-LADEN TURBULENT FLOWS

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A Physically-Based Turbulent Velocity Time Series Decomposition

Single-point, three-component turbulent velocity time series data obtained in the atmospheric boundary layer over the ocean reveal coherent structures that are consistent with a model of a steady linearly varying spatial velocity field that translates past the measurement point at constant velocity. The kinematic model includes both strain and rotation rates and has implications regarding vortex generation, vortex pairing, vortex break-up, and stability. While the complete specification of the dimensions, spatial velocity gradients, and translational velocity of the linear coherent structure (LCS) cannot be made from the single-point, three-component measurements, the model LCS velocity time series can be determined from least- squares fits to the data. The total turbulent kinetic energy is used to find in the record the initial and final times of a model LCS in the data, i.e., the time interval over which a model LCS is passing over the anemometer. Maxima in the kinetic energy removed from the data (by subtraction of the model LCS velocity functions from the data) are used to identify the most-energetic model LCSs. These model LCS velocity functions replicate the essential large-scale features of the time series of the three-component velocity fluctuations, most noticeably in the streamwise component. The model LCS decomposition was used to perform a scale analysis of the data, which was compared to the usual Fourier method. Time intervals of model LCSs were found successively in the data, after subtracting the previous fits. This process resulted in a series of 'levels with a number of LCSs found at each level. About six levels account for most of the kinetic energy. The model also allows the computation of the Reynolds stress components, for which six levels also are sufficient. The recomposition of the time series on a LCS-by-LCS basis compares well with the mode-by-mode Fourier recomposition for the average momentum fluxes and kinetic energy.     

Modification Of The Standard ∈-Equation For The Stable Abl Through Enforced Consistency With Monin–Obukhov Similarity Theory

A condition is derived for consistency of the standard-equation with Monin–Obukhov (MO) similarity theory of thestably-stratified surface layer. The condition is derivedby extending the procedure used to derive the analogous condition forneutral theory to stable stratification. It is shown that consistencywith MO theory requires a function of flux Richardson number, Ri_f, to be absorbed into either of two closure parameters, c ₁ or c ₂.Inconsistency, on the other hand, results if constant values of these are maintained for all Ri_f, as is done in standardapplication of the equation, and the large overpredictions ofturbulence found in such application to the one-dimensionalstable atmospheric boundary layer (1D-SBL) are traced to thisinconsistency. Guided by this, we formulate a MO-consistent-equation by absorbing the aforementioned function intoc ₁, and combine this with a Level-2.5 second-orderclosure model for vertical eddy viscosity and diffusivities.Numerical predictions of the 1D-SBL by the modified model converge to a quasi-steady state, rectifying the predictive failure of the standard -equation for the case.Quasi-steady predictions of non-dimensional variables agree stronglywith Nieuwstadt's theory. Qualitative accuracy of predictionsis inferred from comparisons to field data, large-eddy simulationresults and Rossby-number similarity relationships.     

The Control Of Coherent Eddies In Vegetation Canopies: Streamwise Structure Spacing, Canopy Shear Scale And Atmospheric Stability

An analogy has been established between a plane mixing layer and the atmospheric flow near the top of a vegetation canopy. It is based on a common feature, a strong inflection in the mean velocity profile, responsible for hydrodynamical instabilities that set the pattern for the coherent eddies and determine the turbulence length scales. In an earlier study, this analogy was tested using a small data set from thirteen experiments, all in near-neutral conditions. It provided a good prediction of the streamwise spacing _w of the dominant canopy eddies (evaluated from time series of vertical velocity) that appears to depend on a shear length scale L_s = U(h)/U'(h), where h is canopy height, U is mean velocity and U' the vertical gradient dU/dz. The present analysis utilizes an extensive data set of approximately 700 thirty-minute runs, from six experiments on two forest sites and a maize crop, with a large range of stability conditions. _w was estimated for each run using the wavelet transform as an objective, automated detection method. First, the variations of _w and L_s with atmospheric stability are discussed. Neutral and unstable values exhibit a large scatter whereas in stable conditions both variables decrease with increasing stability. It is subsequently found that _w is directly related to L_s, in a way close to the neutral prediction _w /h = 8.1L_s/h.The Strouhal number S_tr = L_s /_w is then shown to vary with atmospheric stability, weakly in unstable conditions, more significantly in stable conditions. Altogether these results suggest that, to some extent, the plane mixing-layer analogy can be extended to non-neutral conditions. It is argued that the primary effect of atmospheric stability, at least in stable conditions, is to modify the shear length scale L_s through changes in U(h) and U'(h), which in turn determines the streamwise spacing of the active, coherent motions.