Threshold of sediment motion under unidirectional currents

Carefully selected data for the threshold of sediment movement under unidirectional flow conditions have been utilized to re-examine the various empirical curves that are commonly employed to predict this threshold. After a review of the existing data, we employed only that data obtained from open channel flumes with parallel sidewalls where flows were uniform and steady over flattened beds of unigranular, rounded sediments. Without these restrictions, an unmanageable amount of scatter is introduced. This selected data is used to develop a modified Shields-type threshold diagram that extends the limits of the original diagram by three orders of magnitude in the grain-Reynolds number. The equally general but more easily employed Yalin diagram for sediment threshold is also examined. Although the Shields and Yalin diagrams are general in that they apply to a wide range of different liquids, in both cases somewhat different curves are obtained for threshold under air than for the liquids. The often used empirical curves of the friction velocity u_*, the velocity 100 cm above the bed u₁₀₀, the bottom stress θ_t, and Shields’ relative stress θ_t, all versus the grain diameter D, are limited in their ranges of application to certain combinations of grain density, fluid density, fluid viscosity and gravity. These conditions must be selected before the curves are generated from either the more general Shields or Yalin curves. For example, on the basis of the data selected for use in this paper, empirical threshold relationships for quartz density material in water are where the velocity u₁₀₀ measured 100 cm above the sediment bed is given in cm/sec and the grain diameter D is in cm. The limitations on any of the threshold relationships are severe. These limitations should be properly understood so that the empirical curves and relationships are not improperly employed.     

Point defects and cation tracer diffusion in (Ti<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> Fe<Subscript><Emphasis Type="Italic">1−x</Emphasis></Subscript>)<Subscript>3−δ</Subscript>O<Subscript>4</Subscript>. II. Cation tracer diffusion

 Cation tracer diffusion coefficients, D_Me ^*, for Me=Fe, Mn, Co and Ti, were measured using radioactive isotopes in the spinel solid solution (Ti _x Fe _1−x )_3−δO₄ as a function of the oxygen activity. Experiments were performed at different cationic compositions (x=0, 0.1, 0.2 and 0.3) at 1100, 1200, 1300 and 1400 °C. The oxygen activity dependence of all data for D_Me ^* at constant temperature and cationic composition can be described by equations of the type D_Me ^*=D^∘ _Me[V]. C_V·a _O2 ^2/3+D_Me[I] ^∘·a _O2 ^−2/3·D_Me[V] ^∘ and D_Me[I] ^∘ are constants and C_V is a factor of the order of unity which decreases with increasing δ. All log D_Me ^* vs. loga _O2 curves obtained for different values of x and for different temperatures go through a minimum due to a change in the type of point defects dominating the cation diffusion with oxygen activity. Cation vacancies prevail for the cation diffusion at high oxygen activities while cation interstitials become dominant at low oxygen activities. At constant values of x, D_Me[V] ^∘ decreases with increasing temperature while D_Me[I] ^∘ increases.     

Empirical constraints on closure temperatures from a single diffusion coefficient

The elucidation of thermal histories by geochronological and isotopic means is based fundamentally on solid-state diffusion and the concept of closure temperatures. Because diffusion is thermally activated, an analytical solution of the closure temperature (T _c ^*) can only be obtained if the diffusion coefficient D of the diffusion process is measured at two or more different temperatures. If the diffusion coefficient is known at only one temperature, however, the true closure temperature (T _c ^*) cannot be calculated analytically because there exist an infinite number of possible (apparent) closure temperatures (Tˉ _c ) which can be generated by this single datum. By introducing further empirical constraints to limit the range of possible closure temperatures, however, mathematical analysis of a modified form of the closure temperature equation shows that it is possible to make both qualitative and quantitative estimates of T _c ^* given knowledge of only one diffusion coefficient D _M measured at one temperature T _M . Qualitative constraints of the true closure temperature T _c ^* are obtained from the shapes of curves on a graph of the apparent T _c (Tˉ _c ) vs. activation energy E, in which each curve is based on a single diffusion coefficient measurement D _M at temperature T _M . Using a realistic range of E, the concavity of the curve shows whether T _M is less than, approximately equal to, or greater than T _c ^*. Quantitative estimates are obtained by considering two dimensionless parameters [ln êRT^ _c vs. T _c ^*/T _M ] derived from these curves. When these parameters are plotted for known argon diffusion data and for a given diffusion size and cooling rate, it is found that the resultant curves are almost identical for all of the commonly dated K–Ar minerals – biotite, phlogopite, muscovite, hornblende and orthoclase – in spite of differences in their diffusion parameters. A common curve for Ar diffusion can be derived by least-squares fitting of all the Ar diffusion data and provides a way of predicting a “model” closure temperature T _cm from a single diffusion coefficient D _M at temperature T _M . Preliminary diffusion data for a labradorite lead to a T _cm of 507 ± 17 °C and a corresponding activation energy of about 65 kcal/mol, given a grain size of 200 μm and a cooling rate of 5 °C/Ma. Curves for He diffusion in silicates (augite, quartz and sanidine) also overlap to a significant degree, both among themselves and with the Ar model curve, suggesting that a single model curve may be a good representation of noble gas closure temperatures in silicates. An analogous model curve for a selection of ¹⁸O data can also be constructed, but this curve differs from the Ar model curve. A single model curve for cationic species does not appear to exist, however, suggesting that chemical bonding relationships between the ionic size/charge and crystal structure may influence the closure temperatures of diffusing cations. An indication of the degree of overlap among the various curves for Ar, He, ¹⁸O and cations is also obtained by considering the dimensionless parameter E/RT _c ^*; for the noble gases and ¹⁸O, E/RT _c ^* values for the respective minerals are very similar, whereas for cations, there is significant dispersion. Given these constraints, this may be a potential method of estimating closure temperatures for certain diffusing species when there are limited diffusion data. Received: 1 July 1999 / Accepted: 24 March 2000     

Ca–Mg diffusion in diopside: tracer and chemical inter-diffusion coefficients

We have experimentally determined the tracer diffusion coefficients (D*) of ⁴⁴Ca and ²⁶Mg in a natural diopside (~Di₉₆) as function of crystallographic direction and temperature in the range of 950–1,150 °C at 1 bar and f(O₂) corresponding to those of the WI buffer. The experimental data parallel to the a*, b, and c crystallographic directions show significant diffusion anisotropy in the a–c and b–c planes, with the fastest diffusion being parallel to the c axis. With the exception of logD*(²⁶Mg) parallel to the a* axis, the experimental data conform to the empirical diffusion “compensation relation”, converging to logD ~ −19.3 m²/s and T ~ 1,155 °C. Our data do not show any change of diffusion mechanism within the temperature range of the experiments. Assuming that D* varies roughly linearly as a function of angle with respect to the c axis in the a–c plane, at least within a limited domain of ~20° from the c-axis, our data do not suggest any significant difference between D*(//c) and D*(⊥(001)), the latter being the diffusion data required to model compositional zoning in the (001) augite exsolution lamellae in natural clinopyroxenes. Since the thermodynamic mixing property of Ca and Mg is highly nonideal, calculation of chemical diffusion coefficient of Ca and Mg must take into account the effect of thermodynamic factor (TF) on diffusion coefficient. We calculate the dependence of the TF and the chemical interdiffusion coefficient, D(Ca–Mg), on composition in the diopside–clinoenstatite mixture, using the available data on mixing property in this binary system. Our D*(Ca) values parallel to the c axis are about 1–1.5 log units larger than those Dimanov et al. (1996). Incorporating the effect of TF, the D(Ca–Mg) values calculated from our data at 1,100–1,200 °C is ~0.6–0.7 log unit greater than the experimental quasibinary D((Ca–Mg + Fe)) data of Fujino et al. (1990) at 1 bar, and ~0.6 log unit smaller than that of Brady and McCallister (1983) at 25 kb, 1,150 °C, if our data are normalized to 25 kb using activation volume (~4 and ~6 cm³/mol for Mg and Ca diffusion, respectively) calculated from theoretical considerations.     

Discriminating between pore‐filling load and bed‐structure load: a new porosity‐based method,exemplified for the river Rhine

Sediments contained in the river bed do not necessarily contribute to morphological change. The finest part of the sediment mixture often fills the pores between the larger grains and can be removed without causing a drop in bed level. The discrimination between pore‐filling load and bed‐structure load, therefore, is of practical importance for morphological predictions. In this study, a new method is proposed to estimate the cut‐off grain size that forms the boundary between pore‐filling load and bed‐structure load. The method evaluates the pore structure of the river bed geometrically. Only detailed grain‐size distributions of the river bed are required as input to the method. A preliminary validation shows that the calculated porosity and cut‐off size values agree well with experimental data. Application of the new cut‐off size method to the river Rhine demonstrates that the estimated cut‐off size decreases in a downstream direction from about 2 to 0·05 mm, covariant with the downstream fining of bed sediments. Grain size fractions that are pore‐filling load in the upstream part of the river thus gradually become bed‐structure load in the downstream part. The estimated (mass) percentage of pore‐filling load in the river bed ranges from 0% in areas with a unimodal river bed, to about 22% in reaches with a bimodal sand‐gravel bed. The estimated bed porosity varies between 0·15 and 0·35, which is considerably less than the often‐used standard value of 0·40. The predicted cut‐off size between pore‐filling load and bed‐structure load (D_c,p) is fundamentally different from the cut‐off size between wash‐load and bed‐material load (D_c,w), irrespective of the method used to determine D_c,p or D_c,w. D_c,w values are in the order of 10^?1 mm and mainly dependent on the flow characteristics, whereas D_c,p values are generally much larger (about 10⁰ mm in gravel‐bed rivers) and dependent on the bed composition. Knowledge of D_c,w is important for the prediction of the total sediment transport in a river (including suspended fines that do not interact with the bed), whereas knowledge of D_c,p helps to improve morphological predictions, especially if spatial variations in D_c,p are taken into account. An alternative to using a spatially variable value of D_c,p in morphological models is to use a spatially variable bed porosity, which can also be predicted with the new method. In addition to the morphological benefits, the new method also has sedimentological applications. The possibility to determine quickly whether a sediment mixture is clast‐supported or matrix‐supported may help to better understand downstream fining trends, sediment entrainment thresholds and variations in hydraulic conductivity.     

Experimental determination of cation diffusivities in aluminosilicate garnets

Data from experimentally-induced diffusion profiles at approximately 40 Kbar, 1,300–1,500° C in spessartine-almandine couples and a pyrope-almandine couple at 40 Kbar, 1,440° C, described in Part I, were used to derive tracer diffusion coefficients (D ^*) of Fe, Mn and Mg in garnet. The experimental data were fitted by numerical simulations that model multicomponent, compositionally-dependent difussion, including the effects of nonideal thermodynamic mixing. The simulations use the formalism of irreversible thermodynamics and an eigenvector technique of solution. We were able to fit the asymmetrical spessartine-almandine profiles using constant D ^* and either the Darken/Hartley-Crank or Manning-Lasaga models relating D ^* and interdiffusion coefficients, and both models yielded D _Mg ^* consistent with the direct measurement of D _Mg ^* in by Cygan and Lasaga (1985) at lower temperatures (750–900° C). The results (equations 4.1–4.3 and Table 1) indicate that D _Fe ^* D _Mg ^* <D _Mn ^* and Q _FeQ _Mg>Q _Mn, where Q is the activation energy. In contrast, the asymmetry of pyrope-almandine profiles is too great to fit with either tracer model assuming constant D ^* and indicates that D _Mg ^* is similar to its value in spessartine-almandine couples but D _Fe ^* is an order of magnitude less. The fit also suggests that D _Ca ^* < D _Fe ^* Mg ^* in pyrope-almandine couples. Synthesis of data from the two types of diffusion couples suggests that D _Mg ^* is insensitive to compositional changes, whereas D _Fe ^* is affected by Mn/Mg and Fe/Mg ratios and probably by other factors. These compositional effects on tracer coefficients are compatible with those documented by Morioka (1983) for cation diffusion in olivine.     

Measurements of sand transport by wind on a natural beach

Bagnold's (1954) and Kawamura's (1951) formulae may be used for the calculation of the sand movement on a natural beach, provided the shear stress velocity U_* > 0·D4 m/s. Great discrepancies have been found between calculated and measured sand transport rates for U_* < 0·D4 m/s, mainly because of the capillary forces acting on a wet beach. The measured critical shear velocity U_*c at the beginning of sand movement on a clean dry beach agrees very well with that predicted by Bagnold's formula. On a dry beach where the sand grains are stuck together, U_*c was found to be about 10% higher. On a wet beach U_*c appeared to depend on the moisture content of the surface layer. Grain size is a determining parameter in the U_*c-moisture content relation. When the angle a between the wind direction at sea and the dune face is between 15° and 85° the streamlines of the wind will bend in the vicinity of the dune face. In consequence this may influence the direction of sediment movement.     

Laboratory Validation of Ultra-Soft Soil Deformation Model

Ultra-soft soil with high moisture content will experience large strain deformation under one-dimensional compression with little or no gain in effective stress. Such deformation behaviour does not comply with Terzaghi’s effective stress gain theory. The e-log s_v^￠ \sigma_{v}^{\prime } relationship of ultra-soft soil is non-linear with large compression index in the first order of log cycle. This paper proposes three compression indices (C_c1^* C_{c1}^{*} , C_c2^* C_{c2}^{*} and C_c3^* C_{c3}^{*} ) for stresses covering three log cycles. Good prediction of settlement magnitude is possible with these newly proposed compression parameters for ultra-soft soil. In addition, implicit finite difference model applying the large strain theory is also proposed and validated with results from laboratory measurements. The time factor curves for ultra-soft soil with large strain compression are also proposed and validated.     

Suspended Matter,Chl-a,CDOM, Grain Sizes,and Optical Properties in the Arctic Fjord-Type Estuary,Kangerlussuaq, West Greenland During Summer

Optical constituents as suspended particulate matter (SPM), chlorophyll (Chl-a), colored dissolved organic matter (CDOM), and grain sizes were obtained on a transect in the arctic fjord-type estuary Kangerlussuaq (66°) in August 2007 along with optical properties. These comprised diffuse attenuation coefficient of downwelling PAR (K _d(PAR)), upwelling PAR (K _u(PAR)), particle beam attenuation coefficient (c _p), and irradiance reflectance R(−0, PAR). PAR is white light between 400 and 700 nm. The estuary receives melt water from the Greenland Inland Ice and stations covered a transect from the very high turbid melt water outlet to clear marine waters. Results showed a strong spatial variation with high values as for suspended matter concentrations, CDOM, diffuse attenuation coefficient K _d(PAR), particle beam attenuation coefficients (c _p), and reflectance R(−0, PAR) at the melt water outlet. Values of optical constituents and properties decreased with distance from the melt water outlet to a more or less constant level in central and outer part of the estuary. There was a strong correlation between inorganic suspended matter (SPMI) and diffuse attenuation coefficient K _d(PAR) (r ² = 0.92) and also for particle beam attenuation coefficient (c _p; r ² = 0.93). The obtained SPMI specific attenuation—K _d^*(PAR) = 0.13 m² g⁻¹ SPMI—and the SPMI specific particle beam attenuation—c _p^* = 0.72 m² g⁻¹—coefficients were about two times higher than average literature values. Irradiance reflectance R(−0, PAR) was comparatively high (0.09−0.20) and showed a high (r ² = 0.80) correlation with K _u(PAR). Scattering dominated relative to absorption—b(PAR)/a(PAR) = 12.3. Results strongly indicated that the high values in the optical properties were related to the very fine particle sizes (mean = 2–6 μm) of the suspended sediment. Data and results are discussed and compared to similar studies from both temperate and tropical estuaries.     

Dust emission and transport in Mali, West Africa

Vertical dust fluxes were measured in the Inland Delta region of the Niger River, Mali, West Africa, during April-June, 1989 and 1990. Measurements of dust flux represent, for the most part, non-dust storm conditions or ‘dust haze’ periods. The observed concentration versus height relationships are similar to data presented by other investigators. The relationship between wind shear velocity (u_*, m s^?1) and vertical dust flux (F, μg m^?2 s^?1) can be described by a relationship in which F is proportional to u_*⁴. However, there is considerable scatter within the data set which is attributable to textural controls and surface conditions. The vertical dust fluxes measured in Mali are compared to dust fluxes measured in Texas, USA, and Yukon Territories, Canada. The significantly different values for the constant of proportionality (a) in the F α a u_*⁴ relationship for these geographically diverse areas is a function of surficial controls on the release of sediments to the air stream. Dust concentrations measured in Mali were found to be uniformly high and in general exceed WHO health standards for acceptable total suspended particulate loadings. As a result background dust may be considered a long term stress on health for the people of this region of Mali.     

Holocene hydrological variability of Lake Ladoga,northwest Russia,as inferred from diatom oxygen isotopes

This article presents a new comprehensive assessment of the Holocene hydrological variability of Lake Ladoga, northwest Russia. The reconstruction is based on oxygen isotopes of lacustrine diatom silica (δ¹⁸O_diatom) preserved in sediment core Co 1309, and is complemented by a diatom assemblage analysis and a survey of modern isotope hydrology. The data indicate that Lake Ladoga has existed as a freshwater reservoir since at least 10.8 cal. ka BP. The δ¹⁸O_diatom values range from +29.8 to +35.0‰, and relatively higher δ¹⁸O_diatom values around +34.7‰ between c. 7.1 and 5.7 cal. ka BP are considered to reflect the Holocene Thermal Maximum. A continuous depletion in δ¹⁸O_diatom since c. 6.1 cal. ka BP accelerates after c. 4 cal. ka BP, indicating Middle to Late Holocene cooling that culminates during the interval 0.8–0.2 cal. ka BP, corresponding to the Little Ice Age. Lake‐level rises result in lower δ¹⁸O_diatom values, whereas lower lake levels cause higher δ¹⁸O_diatom values. The diatom isotope record gives an indication for a rather early opening of the Neva River outflow at c. 4.4–4.0 cal. ka BP. Generally, overall high δ¹⁸O_diatom values around +33.5‰ characterize a persistent evaporative lake system throughout the Holocene. As the Lake Ladoga δ¹⁸O_diatom record is roughly in line with the 60°N summer insolation, a linkage to broader‐scale climate change is likely.     

Trace-element partitioning between garnet,clinopyroxene and Fe-rich picritic melts at 3 to 7 GPa

We have determined mineral-melt partition coefficients (D values) for 20 trace elements in garnet-pyroxenite run products, generated in 3 to 7 GPa, 1,425–1,750°C experiments on a high-Fe mantle melt (97SB68) from the Paraná-Etendeka continental-flood-basalt (CFB) province. D values for both garnet (∼Py₆₃Al₂₅Gr₁₂) and clinopyroxene (∼Ca_0.2Mg_0.6Fe_0.2Si₂O₆) show a large variation with temperature but are less dependent on pressure. At 3 GPa, D ^cpx/liq values for pyroxenes in garnet-pyroxenite run products are generally lower than those reported from Ca-rich pyroxenes generated in melting experiments on eclogites and basalts (∼Ca_0.3–0.5Mg_0.3–0.6Fe_0.07–0.2Si₂O₆) but higher than those for Ca-poor pyroxenes from peridotites (∼Ca_0.2Mg_0.7Fe_0.1Si₂O₆). D ^grt/liq values for light and heavy rare-earth elements are ≤0.07 and >0.8, respectively, and are similar to those for peridotitic garnets that have comparable grossular but higher pyrope contents (Py_70–88Al_l7–20Gr_8–14). 97SB68 D _LREE^grt/liq values are higher and D _HREE^grt/liq values lower than those for eclogitic garnets which generally have higher grossular contents but lower pyrope contents (Py_20–70Al_10–50Gr_10–55). D values agree with those predicted by lattice strain modelling and suggest that equilibrium was closely approached for all of our experimental runs. Correlations of D values with lattice-strain parameters and major-element contents suggest that the wollastonite component and pyrope:grossular ratio exert major controls on 97SB68 clinopyroxene and garnet partitioning, respectively. These are controlled by the prevailing pressure and temperature conditions for a given bulk-composition. The composition of co-existing melt was found to have a relatively minor effect on 97SB68 D values. The variations in D values displayed by different mantle lithologies are subtle and our study confirms previous investigations which have suggested that the modal proportions of garnet and clinopyroxene are by far the most influential factor in determining incompatible trace-element concentrations in mantle melts. The trace-element partition coefficients we have determined may be used to place high-pressure constraints on garnet-pyroxenite melting models.     

Steady state saltation in air

Coupled equations of motion for steady state saltation over an infinite plane are derived and solved for a simplified model of the grain-surface impact process. Experimentally observed features of the wind velocity profile in saltation are qualitatively reproduced, including a diminution of the sub-saltation layer mean wind speed, as the friction speed increases. In this model the surface impact velocity of the saltating grains remains relatively constant over a wide range of free-stream shear stresses, and the grain mass flux increases with friction speed u_f* less rapidly than u_f³.     

On the assessment of maximum earthquakes in the alps and adjacent areas

Strong tectonic earthquakes within the crust always occur on already existing faults, and they have the property of a shear rupture. Such earthquakes with surface-wave magnitudes M < 7 obviously have a geometric similarity. Because of this similarity and the validity of the Gutenberg and Richter's energy—magnitude relation, the expression M = 2 log₁₀ L + const., with L = focal length, is valid.The expression L_maxL^* for the maximum focal length, is also valid if L^* is the length of the rectilinear extent of the seismic line on which the maximum earthquake occurs. The bounds of L^* may be given by sharp bends and/or by traversing deep faults. Thus the maximum imaginable earthquake on a seismic line with the length L^* has the magnitude M_max = 2 log₁₀ L^* + const.For the investigated region — the Alps and adjacent areas — from the data of recent and historical strong earthquakes, it follows that M_max = 2 log₁₀ L^* + 1.7, if L^* is measured in kilometres. These limiting values lie in the centre-field of the magnitude range for maximum earthquakes, published by Shebalin in 1970. By the aid of this equation it is also possible to assess the upper limiting value of the accompanying maximum scale intensity.     

Grain coarsening in contact metamorphic carbonates: effects of second-phase particles, fluid flow and thermal perturbations

Under contact metamorphic conditions, carbonate rocks in the direct vicinity of the Adamello pluton reflect a temperature‐induced grain coarsening. Despite this large‐scale trend, a considerable grain size scatter occurs on the outcrop‐scale indicating local influence of second‐order effects such as thermal perturbations, fluid flow and second‐phase particles. Second‐phase particles, whose sizes range from nano‐ to the micron‐scale, induce the most pronounced data scatter resulting in grain sizes too small by up to a factor of 10, compared with theoretical grain growth in a pure system. Such values are restricted to relatively impure samples consisting of up to 10 vol.% micron‐scale second‐phase particles, or to samples containing a large number of nano‐scale particles. The obtained data set suggests that the second phases induce a temperature‐controlled reduction on calcite grain growth. The mean calcite grain size can therefore be expressed in the form D = C₂ e^Q*/RT(d_p/f_p)^m*, where C₂ is a constant, Q* is an activation energy, T the temperature and m* the exponent of the ratio d_p/f_p, i.e. of the average size of the second phases divided by their volume fraction. However, more data are needed to obtain reliable values for C₂ and Q*. Besides variations in the average grain size, the presence of second‐phase particles generates crystal size distribution (CSD) shapes characterized by lognormal distributions, which differ from the Gaussian‐type distributions of the pure samples. In contrast, fluid‐enhanced grain growth does not change the shape of the CSDs, but due to enhanced transport properties, the average grain sizes increase by a factor of 2 and the variance of the distribution increases. Stable δ¹⁸O and δ¹³C isotope ratios in fluid‐affected zones only deviate slightly from the host rock values, suggesting low fluid/rock ratios. Grain growth modelling indicates that the fluid‐induced grain size variations can develop within several ka. As inferred from a combination of thermal and grain growth modelling, dykes with widths of up to 1 m have only a restricted influence on grain size deviations smaller than a factor of 1.1. To summarize, considerable grain size variations of up to one order of magnitude can locally result from second‐order effects. Such effects require special attention when comparing experimentally derived grain growth kinetics with field studies.     

Ripple formation in combined transdirectional steady and oscillatory flow

Measurements are described of the geometry of ripples formed on beds of sand exposed to a steady current at right angles to an oscillatory flow. Four different sands were studied. The oscillation was produced by an oscillating tray set into the bed of a steady-flow flume. It was observed that straight-crested ripples formed by oscillatory flow would usually develop a ‘serpentine’ form when the superimposed steady current exceeded a certain limit. For amplitudes of the tray velocity U_∞ less than about 0.38 m s^-1 this limit corresponded to U_∞/ū_*c>31, where ū_*c is the shear velocity measured just upstream of the oscillating tray. It is suggested that the serpentine form is caused by the interaction of vortices carried back and forth between adjacent ripples. On this assumption, the wavelength of the serpentine form would be proportional to the product of period of oscillation and near-bed steady current velocity. The present measurements appear to support this hypothesis although there is also evidence that the wavelength is influenced by preferred spacing patterns between vortices. The measurements also show the ratio of the amplitude of the serpentine form to its wavelength to be approximately constant. Empirical relationships are derived relating ripple geometry to flow and sediment properties. It is observed that the influence of Reynolds number and sediment properties on the geometry is very weak. It is suggested that this is typical of ripples formed with relatively low sediment transport rates. It is also found that, under the present experimental conditions, the ripple spacing in the direction of oscillation is almost independent of the magnitude of the steady current and in close agreement with the wavelengths previously measured in an oscillating water tunnel. This suggests that the additional inertia effects associated with oscillating tray rigs were not sufficient to affect bed geometry under the present test conditions.     

Limitations of dimension and displacement data from single faults and the consequences for data analysis and interpretation

The relationship between the maximum cumulative displacement on a fault (D) and the maximum linear dimension of the fault surface (W) is given by the expression D = cWⁿ, where the value of c is determined by rock properties; proposed values for n range from 1.0 to 2.0. Published datasets of D vs W measurements, together with new data, are presented in a common format. Most datasets are derived from maps and so the measurements of displacement and length do not represent maximum values for each fault. This factor, together with more than an order of magnitude range of c, causes regression on D vs W plots to be unsafe unless the range of W values plotted is ca 5 orders of magnitude. This restriction means that individual datasets must be combined to achieve the required range of fault size. Data analysis shows that the value of n must exceed 1.0 but discrimination between values of 1.5 and 2.0 cannot be made on the basis of data analysis alone. A modified fault growth model in which the increase in dimension of a fault with each slip event is proportional to W^0.5 gives rise to a value for n of 1.5. As this model has a sound mechanical basis 1.5 is the preferred value for n. The value of n influences other aspects of fault geometry, including the displacement profile on a fault surface, the spacing of depth contours on faulted horizons and the displacement populations of single fault surfaces.     

The use of settling velocity in defining the initiation of motion of heavy mineral grains, under unidirectional flow

The results of critical threshold experiments on four commonly occurring heavy minerals are described. The data are presented, in conjunction with comparable quartz data, using the non-dimensional Shields’ Curve and the Movability Number (U*/w_s). The results indicate that critical shear stress for material of high density is overestimated by use of Shields’ Curve, under smooth boundary conditions. Grain settling velocity is found to be a good indicator for the critical shear stress for grains of a wide density range. A physical explanation for the results is proposed.     

Tidally-induced shear stress variability above intertidal mudflats in the macrotidal seine estuary

Tidal currents and the spatial variability of tidally-induced shear stress were studied during a tidal cycle on four intertidal mudflats from the fluvial to the marine part of the Seine estuary. Measurements were carried out during low water discharge (<400 m³ s⁻¹) in neap and spring tide conditions. Turbulent kinetic energy, covariance, and logarithmic profile methods were used and compared for the determination of shear stress. The c_TKE coefficient value of 0.19 cited in the literature was confirmed. Shear stress values were shown to decrease above mudflats from the mouth to the fluvial part of the estuary due to dissipation of the tidal energy, from 1 to 0.2 N m⁻² for spring tides and 0.8 to 0.05 N m⁻² for neap tides. Flood currents dominate tidally-induced shear stress in the marine and lower fluvial estuary during neap and spring tides and in the upper fluvial part during spring tides. Ebb currents control tidally-induced shear stress in the upper fluvial part of the estuary during neap tides. These results revealed a linear relationship between friction velocities and current velocities. Bed roughness length values were calculated from the empirical relationship given by Mitchener and Torfs (1996) for each site; these values are in agreement with the modes of the sediment particle-size distribution. The influence of tidal currents on the mudflat dynamics of the Seine estuary was examined by comparing the tidally-induced bed shear stress and the critical erosion shear stress estimated from bed sediment properties. Bed sediment resuspension induced by tidal currents was shown to occur only in the lower part of the estuary.     

Prediction of solid/liquid distribution coefficients of radiocaesium in soils and sediments. Part three: a quantitative test of a KID predictive equation

An equation is presented for predicting solid/liquid distribution coefficients of radiocaesium on soils and sediments (freshwater and marine). The equation is based on the value of the radiocaesium interception potential of the illitic frayed edge sites of the system and liquid phase composition (K, NH₄ and Na). The predictive potential of the equation is tested for some 130 combinations of soil/sediment and water composition covering a three-order-of-magnitude range in K_D^137_Cs values. On average, experimental K_D^137_Cs values exceed predicted values by a factor of 1.62 ± 0.75.