Effect of non‐uniformity of flow on velocity and turbulence intensities over a cobble‐bed

Non‐uniform flows encompassing both accelerating and decelerating flows over a cobble‐bed flume have been experimentally investigated in a flume at a scale of intermediate relative submergence. Measurements of mean longitudinal flow velocity u, and determinations of turbulence intensities u′, v′, w′, and Reynolds shear stress ?u_fw_f have been made. The longitudinal velocity distribution was divided into the inner zone close to the bed and the outer zone far from the bed. In the inner zone of the boundary layer (near the bed) the velocity profile closely followed the ‘Log Law’; however, in the outer zone the velocity distribution deviated from the Log Law consistently for both accelerating and decelerating flows and the changes in bed slopes ranging from ?2% to + 2% had no considerable effect on the outer zone. For a constant bed slope (S = ±0·015), the larger the flow rate, the smaller the turbulence intensities. However, no detectable pattern has been observed for u′, v′ and w′ distributions near the bed. Likewise, for a constant flow rate (Q = 0·040 m³/s), with variation in bed slope the longitudinal turbulent intensity profile in the longitudinal direction remained concave for both accelerating and decelerating flows; whereas vertical turbulent intensity (w′) profile presented no specific form. The results reveal that the positions of maximum values of turbulence intensities and the Reynolds shear stress depend not only on the flow structure (accelerating or decelerating) but also on the intermediate relative submergence scale. Copyright © 2009 John Wiley & Sons, Ltd.     

Model of vibrational level populations of Herzberg states of oxygen molecules at heights of the lower thermosphere and mesosphere

The paper presents a model of the kinetics of electronically excited O₂(c¹Σ_u⁻,v), O₂(A′³Δ_u,v), O₂(A³Σ_u⁺,v) molecules at heights of the lower thermosphere and mesosphere with allowance for electronic excitation transfer processes during molecular collisions. The model is used to calculate the relative O₂(A³Σ_u⁺,v) and O₂(A′³Δ_u,v) populations at heights of 80–110 km. The calculated populations are compared with the available literature results on experimental estimates, and good agreement is obtained. It is shown how the increase in the quenching rates of the considered states by oxygen atoms affects the calculation results.     

Shear velocity estimates in rough‐bed open‐channel flow

Shear velocity u_* is an important parameter in geophysical flows, in particular with respect to sediment transport dynamics. In this study, we investigate the feasibility of applying five standard methods [the logarithmic mean velocity profile, the Reynolds stress profile, the turbulent kinetic energy (TKE) profile, the wall similarity and spectral methods] that were initially developed to estimate shear velocity in smooth bed flow to turbulent flow over a loose bed of coarse gravel (D₅₀ = 1·5 cm) under sub‐threshold conditions. The analysis is based on quasi‐instantaneous three‐dimensional (3D) full depth velocity profiles with high spatial and temporal resolution that were measured with an Acoustic Doppler Velocity Profiler (ADVP) in an open channel. The results of the analysis confirm the importance of detailed velocity profile measurements for the determination of shear velocity in rough‐bed flows. Results from all methods fall into a range of ± 20% variability and no systematic trend between methods was observed. Local and temporal variation in the loose bed roughness may contribute to the variability of the logarithmic profile method results. Estimates obtained from the TKE and Reynolds stress methods reasonably agree. Most results from the wall similarity method are within 10% of those obtained by the TKE and Reynolds stress methods. The spectral method was difficult to use since the spectral energy of the vertical velocity component strongly increased with distance from the bed in the inner layer. This made the choice of the reference level problematic. Mean shear stress for all experiments follows a quadratic relationship with the mean velocity in the flow. The wall similarity method appears to be a promising tool for estimating shear velocity under rough‐bed flow conditions and in field studies where other methods may be difficult to apply. This method allows for the determination of u_* from a single point measurement at one level in the intermediate range (0·3 < h < 0·6). Copyright © 2013 John Wiley & Sons, Ltd.     

Velocity distribution in a gradually accelerating free surface flow

This study investigates the interaction of the vertical velocity v and the streamwise velocity u in a gradually accelerating flow. The analytical result shows that the momentum of uv driven by the mean velocities in a non-uniform flow is not negligible. This additional momentum directly results in the concave profiles of Reynolds shear stress in gradually accelerating flows, a departure from the expected linear profile. Consequently, this momentum causes the maximum velocity to be located below the free surface, i.e., the dip-phenomenon. This paper investigated the interactions of the Reynolds shear stress, non-zero vertical velocity and dip-phenomenon, it is found that the non-zero vertical velocity causes the dip-phenomenon. The approach is tested using the experimental data of Song and others, and good agreements between the predicted and measured velocity profiles have been achieved.     

Macroturbulent coherent structures in an ice‐covered river flow using a pulse‐coherent acoustic Doppler profiler

The aim of this work is to compare macroturbulent coherent structures (MCS) geometry and organization between ice covered and open channel flow conditions. Velocity profiles were obtained using a Pulse‐Coherent Acoustic Doppler Profiler in both open channel and ice‐covered conditions. The friction imposed by the ice cover results in parabolic shaped velocity profiles. Reynolds stresses in the streamwise (u) and vertical (v) components of the flow show positive values near the channel bed and negative values near the ice cover, with two distinctive boundary layers with specific turbulent signatures. Vertically aligned stripes of coherent flow motions were revealed from statistics applied to space‐time matrices of flow velocities. In open channel conditions, the macroturbulent structures extended over the entire depth of the flow whereas they were discontinued and nested close to the boundary walls in ice‐covered conditions. The size of MCS is consequently reduced in scale under an ice cover. The average streamwise length scale is reduced from 2.5 to 0.4Y (u) and from 1.5 to 0.4Y (v) where Y is the flow depth. In open channel conditions, the vertical extent of MCS covers the entire flow depth, whereas the vertical extent was in the range 0.58Y–1Y (u) and 0.81Y–1Y (v) in ice‐covered conditions. Under an ice cover, each boundary wall generates its own set of MCS that compete with each other in the outer region of the flow, enhancing mixing and promoting the dissipation of coherent structures. Copyright © 2012 John Wiley & Sons, Ltd.     

Laboratory flume studies of microflow environments of aquatic plants

The microflow environments of aquatic plants with reference to Myriophyllum and Hydrilla are simulated in a laboratory flume. A Nix Streamflow microflow meter was used to measure the mean velocity profiles of flow at different densities of plants, flow ranges and measurement positions. Each mean velocity profile consists of three hydrodynamic regimes (i.e. within‐canopy zone, above‐canopy zone and a transitional zone between them), which indicate the presence of two benthic boundary layers (internal and external ones). Out of 38 measured mean velocity profiles, most do not fit a logarithmic relationship. The following hydrodynamic parameters are used in characterizing the flow regimes: local shear velocity (u_*), roughness length (z_o), canopy roughness Reynolds number (Re_*), bed shear stress (τ_o) and laminar sublayer (σ). Copyright © 2002 John Wiley & Sons, Ltd.     

Superhelicity,helicity and potential vorticity

Abstract

‘‘Helicity'’ density H ≡ u · ω and other pseudo-scalar fields such as P ≡ ω · Vlnρ (which is related to Ertel potential vorticity) are useful quantities in theoretical fluid dynamics and magneto-fluid dynamics. Here u denotes the Eulerian flow velocity relative to the chosen frame of reference, ω ≡ V × u is the corresponding relative vorticity and ρ the mass density of the fluid. A general expression is readily obtained for ?H/?t (where t denotes time) in terms of P and the ‘‘superhelicity'’ density S ≡ ω · V × ω which, in fluids of low viscosity, has its highest values in boundary layers. One need for such a relationship became evident during an attempt to interpret the findings of laboratory experiments on thermal convection in rotating fluids in containers of various geometrical shapes and topological characteristics.

In electrodynamics an analogous expression can be found relating the time rate of change of ‘‘magnetic helicity'’ A · B to ‘‘magnetic superhelicity'’ B · ? × B (where B · ? × A is the magnetic field) and a scalar quantity analogous to P which involves non-Ohmic contributions to the relationship between the electric current density and the electric field.     

Field studies on factors affecting very fine and ultra fine particulate organic matter deposition in low‐gradient sand‐bed streams

The knowledge on particle deposition in streams is mainly based on investigations in mountain streams. No data exist from low‐gradient sand‐bed streams that largely differ in the morphological and hydraulic factors proposed to affect deposition. To identify physical control on particle deposition in low‐gradient streams, we assessed deposition of very fine and ultra fine organic particulate matter in 18 sand‐bed stream reaches. We added particles derived from lake sediment and assessed the mean transport distance S_P and the deposition velocity v_dep. Additionally, reach hydraulics were estimated by injections of a conservative solute tracer (NaCl). Among the low‐gradient streams, particle deposition kinetics were variable but similar to deposition in mountain streams. S_P was solely related to the flow velocity. This relation was confirmed when comprising published data on deposition of fine organic particles. An association between particle deposition and transient storage factors was insignificant. We found significance of the transient storage to S_P only for repeated measures within a single reach, when flow velocity and benthic conditions were nearly constant. Measured v_dep/v_fall ratios were much larger than unity in most reaches. Evidence from this relation suggests that the vertical transport of very fine and ultra fine organic particulate matter through the water column was caused mainly by vertical mixing. Copyright © 2006 John Wiley & Sons, Ltd.     

Detection and reconstruction of large‐scale coherent flow structures in gravel‐bed rivers

Large‐scale flow structures (LSFS) in the streamwise direction are important features of gravel‐bed river flows, because they may contribute to sediment transport and gas exchange. In the present study, these structures are detected using Huang's empirical mode decomposition and reconstructed with phase‐averaging techniques based on a Hilbert transform of the velocity signal. The analysis is based on the fluctuating component of 15 quasi‐instantaneous velocity profiles measured with a three‐dimensional (3D) acoustic Doppler velocity profiler (ADVP) in an armoured gravel‐bed river with a low relative submergence of 2.9 (ratio between flow depth and bed grain diameter). LSFS were identified in most of the measured profiles and consistently showed similar features. We were able to characterize the geometry of these large‐scale coherent structures: the front has a vertical linear shift in the time domain and a vertical profile corresponding to a first quarter moon with the apex situated at z/h ≈ 0.4. In the vertical, the front scales with flow depth h, and in the streamwise direction, LSFS scale with three to seven times the mean flow depth. On the bed, the effect of LSFS is a periodic non‐linear variation of the friction velocity on average between 0.90 and 1.10 times the mean value. A model for the friction velocity cycle resulting from LSFS oscillation is presented. Copyright © 2014 John Wiley & Sons, Ltd.     

Nonlinear development of phase-mixed alfvén waves

Abstract

We derive an equation governing the nonlinear propagation of a linearly polarized Alfvén wave in a two-dimensional, anisotropic, slightly compressible, highly magnetized, viscous plasma, where nonlinearities arise from the interaction of the Alfvén wave with fast and slow magnetoacoustic waves. The phase mixing of such a wave has been suggested as a mechanism for heating the outer solar atmosphere (Heyvaerts and Priest, 1983).

We find that cubic wave damping dominates shear linear dissipation whenever the Alfvén wave velocity amplitude δv_y exceeds a few times ten metres per second. In the nonlinear regime, phase-mixed waves are marginally stable, while non-phase-mixed waves of wavenumber k_a are damped over a timescale k_uRe ₀|δ v_y/v_A |^?2, Re ₀ being the Reynolds number corresponding to the Braginskij viscosity coefficient η₀ and v_A the Alfvén speed. Dissipation is most effective where β = (v_s /v_A) ² ≈ 1, v_s being the speed of sound.     

Aeolian sediment flux decay: Non-linear behaviour on developing deflation lag surfaces

Wind tunnel simulations of the effect of non-erodible roughness elements on sediment transport show that the flux ratio q/q_s, shear velocity U*, and roughness density λ are co-dependent variables. Initially, the sediment flux is enhanced by kinetic energy retention in relatively elastic collisions that occur at the roughness element surfaces, but at the same time, the rising surface coverage of the immobile elements reduces the probability of grain ejection. A zone of strong shearing stress develops within 0·03 to 0·04 m of the rough bed because of a relative straightening of velocity profiles which are normally convex with saltation drag. This positive influence on fluid entrainment is opposed by declining shear stress partitioned to the sand bed. Similarly, because the free stream velocity U_f is fixed while U_* increases, velocity at height z and particle momentum gain from the airstream decline, leading eventually to lower numbers of particles ejected on average at each impact. When the ratio of the element basal area to frontal area σ is approximately equal to 3·5, secondary flow effects appear to become significant, so that the dimensionless aerodynamic roughness parameter Z₀/h and shear stress on the exposed sand bed T_s decrease. It is at this point that grain supply to the airstream and saltation drag appear to be significantly reduced, thereby intensifying the reduction in U_*. The zone of strong fluid shear near the bed dissipates.     

Sediment transport in high‐speed flows over a fixed bed: 2. Particle impacts and abrasion prediction

Single bed load particle impacts were experimentally investigated in supercritical open channel flow over a fixed planar bed of low relative roughness height simulating high‐gradient non‐alluvial mountain streams as well as hydraulic structures. Particle impact characteristics (impact velocity, impact angle, Stokes number, restitution and dynamic friction coefficients) were determined for a wide range of hydraulic parameters and particle properties. Particle impact velocity scaled with the particle velocity, and the vertical particle impact velocity increased with excess transport stage. Particle impact and rebound angles were low and decreased with transport stage. Analysis of the particle impacts with the bed revealed almost no viscous damping effects with high normal restitution coefficients exceeding unity. The normal and resultant Stokes numbers were high and above critical thresholds for viscous damping. These results are attributed to the coherent turbulent structures near the wall region, i.e. bursting motion with ejection and sweep events responsible for turbulence generation and particle transport. The tangential restitution coefficients were slightly below unity and the dynamic friction coefficients were lower than for alluvial bed data, revealing that only a small amount of horizontal energy was transferred to the bed. The abrasion prediction model formed by Sklar and Dietrich in 2004 was revised based on the new equations on vertical impact velocity and hop length covering various bed configurations. The abrasion coefficient k_v was found to be vary around k_v ~ 10⁵ for hard materials (tensile strength f_t > 1 MPa), one order of magnitude lower than the value assumed so far for Sklar and Dietrich's model. Copyright © 2017 John Wiley & Sons, Ltd.     

Near-bed mass flux profiles in aeolian sand transport: high-resolution measurements in a wind tunnel

Vertical profiles of the streamwise mass flux of blown sand in the near-bed (< 17 mm) region are analysed from high-resolution measurements made using an optical sensor in a wind tunnel. This analysis is complemented by detailed measurements of mass flux and mean velocity profiles throughout the boundary layer depth (0·17 m) using passive, chambered sand traps of small dimensions and armoured thermal anemometers, respectively. The data permit a preliminary analysis of the relations between the observed forms of the profiles of near-bed fluid stress and horizontal mass flux within a carefully conditioned boundary layer. Profiles of mass flux density are found to be characterized by three regions of differing gradient with transitions at about 2 mm and 19 mm above the bed. The exponential decay of mass flux with height is confirmed for elevations above 19 mm, and when plotted as a function of u_*²/g (a parameter of mean vertical trajectory height in saltation), the gradient of mass flux in this region scales with the wake-corrected friction velocity (u), where u > 0·30 m s⁻¹. A separate near-bed region of more intense transport below 19 mm is identified which carries 80 per cent of the total mass flux. This region is evident in some previous field and wind tunnel data but not in profiles simulated by numerical models. Ventilated passive sand traps underestimate mass flux in this region by 37 per cent. At slow or moderate wind speeds a third significant region below 2 mm is observed. These regions are likely to be related to grain populations in successive saltation, low-energy ejections and intermittent bed contact, respectively. Optical measurements reveal locally high grain concentrations at some elevations below 5 mm; these heights scale with transport rate, mass flux gradient and wind speed. Copyright © 1999 John Wiley & Sons, Ltd.     

Observations of bedforms on a dissipative macrotidal beach

Field measurements of wave ripples and megaripples were made with a Sand Ripple Profiler in the surf and shoaling zones of a sandy macrotidal dissipative beach at Perranporth, UK in depths 1–6 m and significant wave heights up to 2.2 m. A frequency domain partitioning approach allowed quantification of height (η), length (λ) and migration rate of ripples and megaripples. Wave ripples with heights up to 2 cm and wavelengths ～20 cm developed in low orbital velocity conditions (u _m?<?0.65 m/s) with mobility number ψ?<?25. Wave ripple heights decreased with increasing orbital velocity and were flattened when mean currents were >0.1 m/s. Wave ripples were superimposed on top of megaripples (η?=?10 cm, λ?=?1 m) and contributed up to 35 % of the total bed roughness. Large megaripples with heights up to 30 cm and lengths 1–1.8 m developed when the orbital velocity was 0.5–0.8 m/s, corresponding to mobility numbers 25–50. Megaripple heights and wavelengths increased with orbital velocity but reduced when mean current strengths were >0.15 m/s. Wave ripple and megaripple migrations were generally onshore directed in the shoaling and surf zones. Onshore ripple migration rates increased with onshore-directed (+ve) incident wave skewness. The onshore migration rate reduced as offshore-directed mean flows (undertow) increased in strength and reached zero when the offshore-directed mean flow was >0.15 m/s. The migration pattern was therefore linked to cross-shore position relative to the surf zone, controlled by competition between onshore-directed velocity skewness and offshore-directed mean flow.     

Characteristics of turbulence over the semi-fixed desert area north of Xinjiang,China

As the largest fixed and semi-fixed desert in China, the Gurbantünggüt Desert undergoes a long period of snow cover in the winter and the rapid growth of ephemeral plants in the spring, presenting obvious seasonal changes in the underlying desert surface type, which can lead to variation in the turbulence of the near-surface boundary layer turbulence over the desert. In this study, gradient tower data and eddy covariance data from 2017 were analysed to investigate the turbulence characteristics of the different surface boundary layers in the hinterland of the Gurbantünggüt Desert. The results indicate that stable atmospheric conditions in the desert occur exclusively during the early morning and at night in the desert, and the onset and duration of this stable state varies seasonally. Two regimes of intermittent turbulence occur during the night, a weak turbulent regime that occurs when the wind speed is less than the threshold and a strong turbulent regime when the wind speed exceeds the threshold, and different wind speed thresholds were observed at each level. These parameters follow a seasonal pattern of summer (July) > spring (April) > autumn (October) > winter (January) in terms of magnitude. The mean turbulence intensities of the along-wind, cross-wind and vertical wind are 0.5, 0.47 and 0.14, respectively, with I_u > I_v > I_w. The normalized standard deviation of the wind velocity components (σ_u, σ_v and σ_w) generally satisfies a 1/3 power-law relation. Our results show that the night-time turbulence regime classification for the Gurbantünggüt Desert strongly depends on meteorological and orographic features, and the intermittent turbulent events have the non-stationarity of the flow in common. The results can contribute to the study of land surface processes, climate change and desertification in inland arid desert areas.     

USING SPECTRAL ANALYSIS TO DETECT SENSOR NOISE AND CORRECT TURBULENCE INTENSITY AND SHEAR STRESS ESTIMATES FROM EMCM FLOW RECORDS

Electromagnetic current meters (EMCMs) are frequently used to gather turbulent velocity records in rivers and estuaries. Experience has shown that, on occasion, the output of these sensors can be affected by contamination from various noise sources. These noises may be limited to narrow bands of frequencies and thus fail to produce conspicuous increases in observed signal variance. Such ‘narrow-band’ noises can be difficult to identify from simple inspection of signal traces or variance levels, yet degrade estimates of turbulence statistics, in particular covariances (used to calculate Reynolds shear stress). This paper demonstrates the usefulness of spectral analysis to detect and characterize narrow-band noise components in turbulent flow records. Statistical principles underlying the use of spectral analysis for noise detection are briefly reviewed. Examples of u and v velocity spectra and cospectra are then presented from actual EMCM velocity records from flume and field deployments that were found to be contaminated by such noises. The sensitivity of the shear stress estimates to even minor noise levels is demonstrated. The use of spectral analysis to correct variance (turbulence intensity) and covariance (shear stress) estimates obtained from records contaminated by narrow-band noise is also illustrated.     

Estimating the mean speed of laminar overland flow using dye injection‐uncertainty on rough surfaces

A common method for estimating mean flow speeds in studies of surface runoff is to time the travel of a dye cloud across a measured flow path. Motion of the dye front reflects the surface flow speed, and a correction must be employed to derive a value for the profile mean speed, which is always lower. Whilst laminar flow conditions are widespread in the interrill zone, few data are available with which to establish the relationship linking surface and profile mean speeds, and there are virtually none for the flow range 100 < Re < 500 (Re = Reynolds number) which is studied here. In laboratory experiments on a glued sand board, mean flow speeds were estimated from both dye speeds and the volumetric flow relation v = Q/ wd with d measured using a computer‐controlled needle gauge at 64 points. In order to simulate conditions applicable to many dryland soils, the board was also roughened with plant litter and with ceramic tiles (to simulate surface stone cover). Results demonstrate that in the range 100 < Re < 500, there is no consistent relation between surface flow speeds and the profile mean. The mean relationship is v = 0·56 v _surf, which departs significantly from the theoretical smooth‐surface relation v = 0·67 v _surf, and exhibits a considerable scatter of values that show a dependence on flow depth. Given the inapplicability of any fixed conversion factor, and the dependence on flow depth, it is suggested that the use of dye timing as a method for estimating v be abandoned in favour of precision depth measurement and the use of the relation v = Q/ wd , at least within the laminar flow range tested. Copyright © 2001 John Wiley & Sons, Ltd.     

A theoretical investigation of bed-form shapes

The deformation of movable boundaries under the action of an applied turbulent shear stress is well known. The resulting bed forms often are highly organized and nearly two-dimensional, which makes them an intriguing focus of study considering that they are generated in both steady and oscillatory turbulent flows. Many past studies share a common approach in which an infinitesimal perturbation is prescribed and the resulting growth or decay patterns are examined. In this approach, the bed forms are usually sinusoidal and the perturbation analysis does not provide a theoretical prediction of equilibrium bed-form geometry. An alternative approach is suggested here in which the forcing terms (pressure and stress) are prescribed parametrically and the governing equations are solved for the flow velocity and the associated boundary deformation. Using a multilayered approach, in which the bottom boundary layer is divided into a discrete, yet, arbitrary number of finite layers, analytical solutions for the horizontal current and bed profile are derived. The derivations identify two nondimensional parameters, p₀/u₀² and ₀/kh₀u₀², which modulate the amplitude of the velocity fluctuations and boundary deformation. For the case of combined pressure and stress divergence anomalies, the magnitude of the front face and lee slopes exhibit an asymmetry that is consistent with observed bed forms in steady two-dimensional flows.Responsible Editor: Jens Kappenberg     

Computational fluid dynamics modelling of boundary roughness in gravel‐bed rivers: an investigation of the effects of random variability in bed elevation

Results from a series of numerical simulations of two‐dimensional open‐channel flow, conducted using the computational fluid dynamics (CFD) code FLUENT, are compared with data quantifying the mean and turbulent characteristics of open‐channel flow over two contrasting gravel beds. Boundary roughness effects are represented using both the conventional wall function approach and a random elevation model that simulates the effects of supra‐grid‐scale roughness elements (e.g. particle clusters and small bedforms). Results obtained using the random elevation model are characterized by a peak in turbulent kinetic energy located well above the bed (typically at y/h = 0·1–0·3). This is consistent with the field data and in contrast to the results obtained using the wall function approach for which maximum turbulent kinetic energy levels occur at the bed. Use of the random elevation model to represent supra‐grid‐scale roughness also allows a reduction in the height of the near‐bed mesh cell and therefore offers some potential to overcome problems experienced by the wall function approach in flows characterized by high relative roughness. Despite these benefits, the results of simulations conducted using the random elevation model are sensitive to the horizontal and vertical mesh resolution. Increasing the horizontal mesh resolution results in an increase in the near‐bed velocity gradient and turbulent kinetic energy, effectively roughening the bed. Varying the vertical resolution of the mesh has little effect on simulated mean velocity profiles, but results in substantial changes to the shape of the turbulent kinetic energy profile. These findings have significant implications for the application of CFD within natural gravel‐bed channels, particularly with regard to issues of topographic data collection, roughness parameterization and the derivation of mesh‐independent solutions. Copyright © 2001 John Wiley & Sons, Ltd.