Flow Layer Thickness Research Articles

Comprehensive Field Study of Swash-Zone Processes. II: Sheet Flow Sediment Concentrations during Quasi-Steady Backwash

Sheet flow sediment concentration profiles were measured in natural conditions for the first time as part of a comprehensive field study on swash-zone hydrodynamics and sediment transport. Three conductivity concentration profilers (CCPs) measured the sediment concentration profile in the sheet flow layer with a 1-mm resolution in the swash zone of a dissipative beach. This paper focuses on sheet flow during quasi-steady backwash events generated by infragravity motion when the effects of phase lags, surface-generated turbulence, and accelerations are small. The sheet flow sediment concentration profile has a linear shape in the lower section of the profile and a power-law shape in the upper section, with the transition occurring at sediment volume fractions of 0.20–0.30. The shape of the concentration profile is self-similar for measured sheet flow layer thicknesses ranging from 6 to 18 mm. Because of the self-similarity, a single concentration profile curve can be used to describe the normalized profile for the entire range of sheet thicknesses, leading to improved estimates of the sheet flow layer thickness in a simple analytical model. The sheet flow layer thickness and sheet load, the sediment mass mobilized in the sheet flow layer, are well correlated with the hydrodynamic forcing represented by the mobility number (r2=0.60 for sheet thickness and r2=0.53 for sheet load).

Viscous potential flow analysis of peripheral heavy ion collisions

The conditions for the development of a Kelvin-Helmholtz instability (KHI) for the quark-gluon plasma (QGP) flow in a peripheral heavy ion collision is investigated. The projectile and target side particles are separated by an energetically motivated hypothetical surface, characterized with a phenomenological surface tension. In such a view, a classical potential flow approximation is considered and the onset of the KHI is studied. The growth rate of the instability is computed as a function of phenomenological parameters characteristic for the QGP fluid: viscosity, surface tension, and flow layer thickness.

Parameters and scalings for dry and immersed granular flowing layers in rotating tumblers

The scaling properties of the continuous flowing layer in a quasi-2D circular tumbler half filled with a granular material are studied experimentally in the presence of three different interstitial fluids (air, water, and glycerine). In the dry case, the dimensionless flowing layer thickness δ(0)/d scales with the dimensionless flow rate Q(dry)(*) = Q/(dsqrt[gd]), where Q is the flow rate, d is the particle diameter, and g is the acceleration due to gravity, in agreement with previous studies. However, unlike previous studies, we show that the exponent for the power-law relation between the two depends on the range of Q(dry)(*) Meanwhile, the angle of repose increases linearly with Q(dry)(*). In the immersed case, the interstitial fluid changes the relevant time scales, which can be accommodated by considering the fluid properties. The result is that there are two different expressions for the dimensionless flow rate in the immersed flow; one corresponding to a free fall regime for a large Stokes number, and one corresponding to a viscous regime at small Stokes number. On this basis, a single dimensionless flow rate that incorporates both buoyancy and viscous friction is proposed. The effect of side walls is also investigated. For dry flows and those immersed in water, the thickness of the flowing layer decreases while the slope of the free surface increases as the gap separating the walls becomes smaller. For immersed granular flows with glycerine as the interstitial fluid, however, the ratio of the thickness of the flowing layer to the bead diameter is independent of the distance the between the side walls because viscous effects dominate.

Effects of Partial Slip on the Analytic Heat and Mass Transfer for the Incompressible Viscous Fluid of a Porous Rotating Disk Flow

The present paper is concerned with a class of exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous fluid flow motion due to a porous disk rotating with a constant angular speed about its axis. The recent study (Turkyilmazoglu, 2009, “Exact Solutions for the Incompressible Viscous Fluid of a Porous Rotating Disk Flow,” Int. J. Non-Linear Mech., 44, pp. 352–357) is extended to account for the effects of partial flow slip and temperature jump imposed on the wall. The three-dimensional equations of motion are treated analytically yielding derivation of exact solutions for the flow and temperature fields. Explicit expressions representing the flow properties influenced by the slip as well as a uniform suction and injection are extracted, including the velocity, vorticity and temperature fields, shear stresses, flow and thermal layer thicknesses, and Nusselt number. The effects of variation in the slip parameters are better visualized from the formulae obtained.

Experimental study of the turbulent boundary layer in acceleration-skewed oscillatory flow

AbstractExperiments have been conducted in a large oscillatory flow tunnel to investigate the effects of acceleration skewness on oscillatory boundary layer flow over fixed beds. As well as enabling experimental investigation of the effects of acceleration skewness, the new experiments add substantially to the relatively few existing detailed experimental datasets for oscillatory boundary layer flow conditions that correspond to full-scale sea wave conditions. Two types of bed roughness and a range of high-Reynolds-number, $\mathit{Re}\ensuremath{\sim} O(1{0}^{6} )$, oscillatory flow conditions, varying from sinusoidal to highly acceleration-skewed, are considered. Results show the structure of the intra-wave velocity profile, the time-averaged residual flow and boundary layer thickness for varying degrees of acceleration skewness, $\ensuremath{\beta} $. Turbulence intensity measurements from particle image velocimetry (PIV) and laser Doppler anemometry (LDA) show very good agreement. Turbulence intensity and Reynolds stress increase as the flow accelerates after flow reversal, are maximum at around maximum free-stream velocity and decay as the flow decelerates. The intra-wave turbulence depends strongly on $\ensuremath{\beta} $ but period-averaged turbulent quantities are largely independent of $\ensuremath{\beta} $. There is generally good agreement between bed shear stress estimates obtained using the log-law and using the momentum integral equation, and flow acceleration skewness leads to high bed shear stress asymmetry between flow half-cycles. Turbulent Reynolds stress is much less than the shear stress obtained from the momentum integral; analysis of the stress contributors shows that significant phase-averaged vertical velocities exist near the bed throughout the flow cycle, which lead to an additional shear stress, $\ensuremath{-} \rho \tilde {u} \tilde {w} $; near the bed this stress is at least as large as the turbulent Reynolds stress.

The influence of thickness and ammonia flow rate on the properties of AlN layers

Undoped AlN layers have been grown on c-plane sapphire substrates by metal-organic chemical vapor deposition in order to study the effects of ammonia (NH3) flow rate and layer thickness on the structural quality and surface morphology of AlN layers by high-resolution X-ray diffraction, scanning electron microscopy, and atomic force microscopy. Lower NH3 flow rate improves crystallinity of the symmetric (0002) plane in AlN layers. Ammonia flow rate is also correlated with surface quality; pit-free and smooth AlN surfaces have been obtained at a flow rate of 70 standard cm3 per minute. Thicker AlN films improve the crystallinity of the asymmetric (101̄2) plane.

Relaxation dynamics of water-immersed granular avalanches

We study water-immersed granular avalanches in a long rectangular cell of small thickness. By video means, both the angle of the granular pile and the velocity profiles of the grains across the depth are recorded as a function of time. These measurements give access to the instantaneous granular flux. By inclining the pile at initial angles larger than the maximum angle of stability, avalanches are triggered and last for a long time, up to several hours for small grains, during which both the slope angle and the granular flux relax slowly. We show that the relaxation is quasi-steady so that there is no inertia: the relaxation at a given time is controlled only by the slope angle at that time. This allows us to adapt a frictional model developed recently for dry or water-immersed grains flowing in stationary conditions. This model succeeds well in reproducing our unsteady avalanche flows, namely the flowing layer thickness, the granular flux and the temporal relaxation of the slope. When a water counter-flow is applied along the pile, the granular avalanches are slowed down and behave as if granular friction were increased by an amount proportional to the water flow. All these findings are also reproduced well with the same friction model by taking into account the additional fluid force.

Mobile layer thickness in sheet flow beneath random waves

The erosion depth and the sheet flow layer thickness represent two characteristic parameters for transport processes in oscillatory sheet flow. Formulas for these parameters under regular waves have been applied to obtain characteristic statistical values under random waves. The applicability of the method for practical purposes is illustrated by two examples using data typical for field conditions at water depths of 70 m (Ekofisk location in the North Sea) and 15 m, respectively. Two fictive storms based on the Dohmen-Janssen and Hanes [Dohmen-Janssen, C.M., Hanes, D.M., 2005. Sheet flow and suspended sediment due to wave groups in a large wave flume. Cont. Shelf Res. 25, 333–347] data from large scale wave flume tests have also been utilized to demonstrate how the return period of the sheet flow layer thickness observed in their experiments can be estimated.

Creeping granular motion under variable gravity levels

In a rotating tumbler that is more than one-half filled with a granular material, a core of material forms that should ideally rotate with the tumbler. However, the core rotates slightly faster than the tumbler (precession) and decreases in size (erosion). The precession and erosion of the core provide a measure of the creeping granular motion that occurs beneath a continuously flowing flat surface layer. Since the effect of gravity on the subsurface flow has not been explored, experiments were performed in a 63% to 83% full granular tumbler mounted in a large centrifuge that can provide very high g-levels. Two colors of 0.5 mm glass beads were filled side by side to mark a vertical line in the 45 mm radius quasi-two-dimensional tumbler. The rotation of the core with respect to the tumbler (precession) and the decrease in the size of the core (erosion) were monitored over 250 tumbler revolutions at accelerations between 1g and 12g. The flowing layer thickness is essentially independent of the g-level for identical Froude numbers, and the shear rate in the flowing layer increases with increasing g-level. The degree of core precession increases with the g-level, while the core erosion is essentially independent of the g-level. Based on a theory for core precession and erosion, the increased precession is likely a consequence of the higher shear rate. Core erosion, on the other hand, is related to the creep region decay constant, which is connected with slow diffusion in the bed and unaffected by gravity.

Solids back-mixing in CFB boilers

The furnaces of circulating fluidized bed (CFB) boilers have substantially lower height-to-width ratios than most of the laboratory CFB risers from which experimental investigations on riser fluid dynamics are published. Therefore, it is uncertain whether literature expressions for prediction of the distribution of solids and the thickness of the wall layers, derived from investigations in laboratory units, are applicable to boilers. In this work, data from laboratory units are compared with boiler data, and the accuracy of literature expressions for prediction of solids distribution, solids flow and wall layer thickness is reviewed. It is found that the height-to-width ratio does have a significant impact on the flow properties. Correlations based on experiments in laboratory units show poor agreement when applied to boilers. Modifications of literature expressions for prediction of solids flow and solids distribution are proposed, and an improved expression is formulated for prediction of the thickness of the wall layer.

Deposition of SiOx diffusion barriers on flexible packaging materials by PECVD

This study focuses on the water vapor permeability of plasma enhanced chemical vapor deposited (PECVD) silicon oxide (SiOx) films. A batch reactor equipped with a 2.45 GHz slot antenna plasma source and a 13.56 MHz-biased substrate holder, was used to conduct the experiments. The remote microwave and the direct radio frequency plasma source can be operated separately or in dual mode. An oxygen plasma was generated and hexamethyldisiloxane (HMDSO) used as monomer. The SiO2-like films were deposited onto 12 μm PET film. An increase of RF-power input, oxygen-to-monomer flow rate ratio, layer thickness or decrease of process pressure was found to enhance the gas barrier performance. Compared to uncoated PET films, a maximum reduction of more than a factor of 150 has been achieved for water vapor transmission rate.

Layer thicknesses and velocities of wave overtopping flow at seadikes

Seadikes often fail due to wave overtopping and a failure of the landward slope. Therefore, these aspects have to be taken into account for the design of seadikes. In present design, the calculation of the crest height of seadikes is essentially based on using a design water level and the corresponding wave run-up height. An average overtopping rate is generally considered for wave overtopping which can not account for the stresses and other effects due to extreme individual overtopping events. Landward slope design is more or less based on experience. It can be concluded from failure analysis that dike failures on the landward slope are rather initiated by individual overtopping events, in particular by the related overtopping flow velocities and layer thicknesses which are relevant for the prediction of erosion, infiltration and slip failure. Therefore, overtopping flow velocities and layer thicknesses are required in addition to average overtopping rates as hydraulic boundary conditions for the geotechnical stability analysis of seadikes. The objective of the present paper is the theoretical and experimental determination of overtopping flow velocities and layer thicknesses on the seaward slope, the dike crest and the landward slope of a seadike. Overtopping parameters are derived on the basis of small scale model tests which are required for the design of the landward slope and to avoid dike failures by wave overtopping in the future. For the prediction of the layer thicknesses and the velocities of the overtopping flow on the seaward slope, the dike crest and the landward slope, a set of theoretical formulas is derived and validated by hydraulic scale model tests.

Sheet flow and suspended sediment due to wave groups in a large wave flume

A series of sand bed experiments was carried out in the Large Wave Flume in Hannover, Germany as a component of the SISTEX99 experiment. The experiments focussed on the dynamic sediment response due to wave group forcing over a flat sand bed in order to improve understanding of cross-shore sediment transport mechanisms and determine sediment concentrations, fluxes and net transport rates under these conditions. Sediment concentrations were measured within the sheet flow layer (thickness in the order of 10 grain diameters) and in the suspension region (thickness in the order of centimetres). Within the sheet flow layer, the concentrations are highly coherent with the instantaneous near-bed velocities due to each wave within the wave group. However, in the suspension layer concentrations respond much more slowly to changes in near-bed velocity. At several centimetres above the bed, the suspended sediment concentrations vary on the time scale of the wave group, with a time delay relative to the peak wave within the wave group. The thickness of the sheet flow changes with time. It is strongly coherent with the wave forcing, and is not influenced by the history or sequence of the waves within the group. The velocity of the sediment was also measured within the sheet flow layer some of the time (during the larger wave crests of the group), and the velocity of the fluid was measured at several cm above the sheet flow layer. The grain velocity and concentration estimates can be combined to estimate the sediment flux. The estimates were found to be consistent with previous measurements under monochromatic waves. Under these conditions, without any significant mean current, the sediment flux within the sheet flow layer was found to greatly exceed the sediment flux in the suspension layer. As a result, net transport rates under wave groups are similar to those under monochromatic waves.

Observations and models of lateral hydrothermal circulation on a young ridge flank: Numerical evaluation of thermal and chemical constraints

We used a two‐dimensional coupled heat and fluid flow model to investigate large‐scale, lateral heat and fluid transport on the eastern flank of the Juan de Fuca Ridge. Cool seawater in the natural system is inferred to enter basement where it is exposed close to the spreading center and flow laterally beneath thick sediments, causing seafloor heat flow to be depressed relative to that input at the base of the plate. The flow rate, and thus the properties of permeable basement (the flow layer), controls the efficiency of lateral heat transport, as quantified through numerical modeling. We simulated forced flow in this layer by pumping water through at a fixed rate and quantified relations between flow rate, thickness of the permeable basement, and the extent of suppression of seafloor heat flow. Free flow simulations, in which fluid flow was not forced, match heat flow constraints if nonhydrostatic initial conditions are used and flow layer permeabilities are set to the high end of observed values (10−11 to 10−9 m2). To match seafloor heat flow observations, the models required lateral specific discharge of 1.2 to 40 m/yr for flow layer thicknesses of 600 to 100 m, respectively. The models also replicate differences in fluid pressures in basement, and the local distribution of pressures above and below hydrostatic. Estimated lateral flow rates are 10× to 1000× greater than estimates based on radiocarbon ages of basement pore waters. Estimated lateral flow rates based on thermal and chemical constraints can be reconciled if diffusion from discrete flow zones into less permeable stagnant zones in the crust is considered.

Experimental study of granular surface flows via a fast camera: A continuous description

Depth averaged conservation equations are written for granular surface flows. Their application to the study of steady surface flows in a rotating drum allows to find experimentally the constitutive relations needed to close these equations from measurements of the velocity profile in the flowing layer at the center of the drum and from the flowing layer thickness and the static/flowing boundary profiles. The velocity varies linearly with depth, with a gradient independent of both the flowing layer thickness and the static/flowing boundary local slope. The first two closure relations relating the flow rate and the momentum flux to the flowing layer thickness and the slope are then deduced. Measurements of the profile of the flowing layer thickness and the static/flowing boundary in the whole drum explicitly give the last relation concerning the force acting on the flowing layer. Finally, these closure relations are compared to existing continuous models of surface flows.

Mobile‐bed effects in oscillatory sheet flow

Field observations often show a considerable variation in mean grain size along the coastal profile. Under high waves in shallow water, bed ripples are washed out, and sheet flow becomes the dominant transport mode: large amounts of sand are transported in a thin layer close to the bed, i.e., the sheet flow layer. This paper focuses on grain size influences on transport processes in oscillatory sheet flow. Experiments were carried out in the Large Oscillating Water Tunnel (LOWT) of Delft Hydraulics, in which near‐bed orbital velocities in combination with a net current can be simulated at full scale. Three uniform sands with different mean grain size were used. It was found that in contradiction to expressions found in literature, both the erosion depth and the sheet flow layer thickness are larger for fine sand (D50 = 0.13 mm) than for coarser sand (D50 ≥ 0.21 mm). Measured time‐averaged velocity and concentration profiles indicate that the presence of a sheet flow layer leads to an increased flow resistance and to damping of turbulence and that these effects are stronger for a thicker sheet flow layer (i.e., for fine sand). These mobile‐bed effects are analyzed further by comparing the measurements with the results of a one‐dimensional vertical advection‐diffusion boundary layer model. Simulating the mobile‐bed effects in the model by introducing an increased roughness height and a reduced turbulent eddy viscosity showed that the roughness height is of the order of the sheet flow layer thickness and that turbulence damping increases for a decreasing grain size.

On scaling relations in time‐dependent mantle convection and the heat transfer constraint on layering

We present a series of simulations of the mantle convection process based upon an axisymmetric numerical model and highlight a wide range of results in which scaling emerges. For the more challenging simulations it was found necessary to employ a finite difference mesh with uneven grid spacing in the radial coordinate, and we present the appropriate transformed field equations that are required to implement a model of this kind. The statistics of mass flux events transiting the 660‐km phase transition are calculated for a large number of high‐resolution calculations, and some of these are shown to display scale invariance properties in the high Rayleigh number regime. We also present a new parameterized model of convection and demonstrate its success in predicting the manner in which many of the bulk properties of the convection process scale with convection control parameters. Results are also presented which demonstrate that quantities such as heat flow, characteristic velocity, and thermal boundary layer thickness scale with the mean viscosity even in time‐dependent simulations in which the effects of phase transitions, depth‐varying viscosity, and internal heating are active. The heat flow scaling exponent is seen to decrease in magnitude with increasing internal heating rate and Clapeyron slope of the 660‐km phase transition, but it is shown to be insensitive to depth variation of viscosity. Heat flow is seen to be reduced only modestly as the degree of layering increases unless layering is extreme. These calculations clearly demonstrate that in order for the surface heat flow predicted by the model to equal that characteristic of Earth, the mean viscosity of the mantle that controls the convection process must be considerably higher than the viscosity inferred on the basis of postglacial rebound and/or the flow must be significantly layered by the endothermic phase transition at 660 km depth. If mantle viscosity may be assumed to be Newtonian, in which case the creep resistance that controls rebound and convection must be the same, this constitutes a strong argument for the importance of layering. The force of this argument depends upon the existence of an accurate estimate of the temperature at the core‐mantle boundary which has only recently become available.

Convection in a long cavity with differentially heated end walls

The fluid-filled long cavity with differentially heated end walls is a common and simple model for flows both in the environment and in technical applications. A delineation of the flow regime showing confined flowing layers from those showing cavity-filling counter currents is provided. Theoretical considerations yield a description of the flowing layer thickness and an approximate value for the longitudinal temperature gradient in the core of the tank. This way, a good description of the major features in the long cavity is achieved, which is confirmed by experimental data.

Detailed analysis of carrier transport in InAs0.3Sb0.7 layers grown on GaAs substrates by metalorganic chemical-vapor deposition

InAs0.3Sb0.7 layers with mirrorlike morphology have been grown on GaAs substrates by low-pressure metalorganic chemical vapor deposition. A room-temperature electron Hall mobility of 2×104 cm2/V s has been obtained for a 2-μm-thick layer. Low-temperature resistivity of the layers depended on TMIn flow rate and layer thickness. Hall mobility decreased monotonically with decreasing temperature below 300 K. A 77 K conductivity profile has shown an anomalous increase in the sample conductivity with decreasing thickness except in the near vicinity of the heterointerface. In order to interpret the experimental data, the effects of different scattering mechanisms on carrier mobility have been calculated, and the influences of the lattice mismatch and surface conduction on the Hall measurements have been investigated by applying a three-layer Hall-effect model. Experimental and theoretical results suggest that the combined effects of the dislocations generated by the large lattice mismatch and strong surface inversion may lead to deceptive Hall measurements by reflecting typical n-type behavior for a p-type sample, and the measured carrier concentration may considerably be affected by the surface conduction up to near room temperature. A quantitative analysis of dislocation scattering has shown significant degradation in electron mobility for dislocation densities above 107 cm−2. The effects of dislocation scattering on hole mobility have been found to be less severe. It has also been observed that there is a critical epilayer thickness (∼1 μm) below which the surface electron mobility is limited by dislocation scattering.

Sea-floor dynamic processes as the possible cause of correlations between paleoclimatic and paleomagnetic indices in deep-sea sedimentary cores

Recent publications showing correlations between the variation of intensity of magnetization (J) and paleomagnetic inclination I on the one hand, and diverse paleoclimatic indices on the other, have been interpreted to represent direct cause and effect relationships between climate and geomagnetism. It is proposed that several sea-floor dynamic processes, which are climatically variable, are at least equally feasible causes of the observed correlations. Thus, for variation in J, it is a simple matter to invoke variations in such factors as the magnetic particle size fraction below 50 microns, carbonate content, or laminar flow layer thickness, all of which can change with climate. For variation in I, climatically related variation of the velocity gradient in the laminar flow layer can be employed to explain the correlation. Prior to accepting the suggested geomagnetic control of climate as real, it is recommended that simple measurements of the temporal and geographic variation in fabric and composition of the deep-sea sediments involved should be carried out, as a check for the effect of bottom dynamic processes.