Paul D. Komar

The Threshold of Sediment Movement Under Oscillatory Water Waves

ABSTRACT As the velocity of the to-and-fro water motion near the bottom under oscillatory waves is increased, there comes a stage when the water exerts a stress on the particles sufficient to cause them to move. This study reviews the analyses and available data on this threshold of sediment motion under wave action. For grain diameters less than about 0.05 cm (medium sands and finer) the threshold is reached while the flow in the boundary layer is still laminar and the threshold is best related by the equation um2/(s-) gD = 0.30 (do/D), where um and do are the near-bottom velocity and orbital diameter of the wave motion, is the density of water, and s and D are respectively the density and diameter of the sediment grains. This relationship is modified after an empirical equation deduced by Bagnold but has a theoretical basis. For grain diameters greater than 0.05 cm (coarse sands and coarser) the threshold occurs after the boundary layer has become turbulent and is best predicted with an empirical curve relating do/D to um/(s - ) g T where T is the wave period. This latter dimensionless number represents the ratio of the acceleration forces to the effective gravity force acting on the grains.

Climate Controls on US West Coast Erosion Processes

Abstract Erosion along the West Coast of the United States is affected by climate controls that include a trend of increasing wave heights during at least the past 25 years that might be related to global warming and the El Niño Southern Oscillation (ENSO) range between El Niños and La Niñas that affects both annual wave conditions and monthly mean water levels that raise tidal elevations. These processes are analyzed for sites from Washington to south-central California, revealing a latitude dependence of the individual processes and how their combinations affect total water levels at the shore, which is important to beach and property erosion. Particularly significant on the coast of the Pacific Northwest (Washington and Oregon) has been the progressive decadal increases in deep-water wave heights and periods, which have increased breaker heights and elevated storm wave runup levels on beaches. Along the entire West Coast, the annual variations in wave conditions above and below any progressive decadal increase are controlled by the North Pacific index (NPI), the atmospheric pressure difference between the Hawaiian High and Aleutian Low, and the ENSO range, as demonstrated by a strong correlation with the multivariate ENSO index (MEI), with the highest wave conditions occurring during El Niños. In addition, the ENSO range is particularly important in controlling mean water levels, causing tides to reach their highest elevations during El Niños, again shown by correlations with MEIs along the entire West Coast. With El Niños producing increased deep-water wave heights, runup levels on beaches, and elevated tides, the total water levels at the shore from the combined processes are significantly higher compared with normal or La Niña years, resulting in episodes of major property erosion along the entire US West Coast.

Comparisons of the hydraulics of water flows in Martian outflow channels with flows of similar scale on earth

Abstract Comparisons are undertaken between the hydraulics of channelized water flows on Mars, large terrestrial rivers, deep-sea turbidity currents, and the catastrophic flow of Lake Missoula floods. Expected bottom shear stresses, velocities and discharges, flow powers, and other parameters are computed for each. Sand transport rates and the times required for channel erosion are estimated for Mangala Channel. These calculations indicate that the turbidity currents and Lake Missoula floods were similar to channelized water flow on Mars in their flow characteristics and in their abilities to erode and transport sediments. Like the Lake Missoula floods, deep-sea turbidity currents are catastrophic in character, being formed by the slumping of large masses of sediment trapped in submarine canyons or deposited on the continental slope. The repeated flows originating from submarine canyons have formed deep-sea channels similar in scale and overall morphology to the Martian outflow channels. The submarine canyon can be viewed as the counterpart of the chaotic terrain or crater which serves as sources for many Martian channels. Like most Martian outflow channels, the deep-sea channels generally lack tributaries or have only minor tributaries, instead consisting of a single pronounced channel extending for several hundred kilometers from its origin at the submarine canyon to deep abyssal depths. The channels vary considerably in dimensions, but most commonly have widths in the range 2 to 15 km with reliefs of 50 to 450 meters, again similar in scale to the Martian channels. Other similarities include sections of anastomosing channels, a general lack of pronounced meandering, and a lack of an apparent “delta” where the transported sediments are deposited. The similarities of channel morphology and flow hydraulics indicate the deep-sea channels and turbidity currents can be useful in furthering our understanding of the Martian outflow channels. Physical processes in the deep-sea occur under a reduced effective gravity because of the overlying water with its buoyancy. The deep-sea channels provide another set of Earth-based channels which can be studied to determine the effects of gravity on such factors as channel meandering and anastomosing characteristics.

Modes of sediment transport in channelized water flows with ramifications to the erosion of the Martian outflow channels

Depending on their grain sizes (settling velocities), sediments are transported in rivers as bed load, in suspension, or as wash load. The coarsest material rolls or bounces along the bottom as bed load whereas finer material is placed into suspension by the water turbulence. The finest sediments are transported as wash load, evenly distributed through the water depth and effectively moving at the same rate as the water. The criteria for quantitatively determining which grain-size ranges are being transported in terrestrial rivers as bed load, suspended load and wash load are applied to an analysis of sediment transport in the large Martian outflow channels, assuming their origin to have been from water flow. Of importance is the balance of the effects of the reduced Martian gravity on the water flow velocity versus the reduction in grain settling velocities. Analyses were performed using grain densities ranging from 2.90 g/cm3 (basalt) to 1.20 g/cm3 (volcanic ash). The results show that the Martian flows could have transported cobbles in suspension and that nearly all sand-size material and finer would have been transported as wash load. Wash-load transport requires little or no net expenditure of the water-flow power, so the sands and finer could have been carried in nearly unlimited quantities. A comparison with terrestrial rivers indicates that concentrations as high as 60–70% by weight of wash-load sediment could have prevailed in the Martian flows, resulting in the very rapid erosion of the channels.

Selective grain entrainment by a current from a bed of mixed sizes; a reanalysis

The selective entrainment of grains by a current from a bed of mixed sizes and densities is important to grain-sorting processes that lead to the formation of placers in sands and to armored beds in gravels. Existing field and laboratory measurements of selective entrainment depart systematically from the standard threshold curves (such as that of Shields) which are based on experiments with nearly uniform grain sizes. Entrainment measurements from beds of mixed sizes form trends which obliquely cross the threshold curves for uniform grains, the crossing point being roughly at the median diameter of the size distribution. Due to this crossover, the coarser size fractions of the distribution require lower-flow stresses for their entrainment than if they formed uniform beds, while the finer-size fractions require higher stresses than uniform beds. With deposits having medians in the range of medium sand through gravel, the larger the individual particle within the mixed sizes, the greater the flow stress required for its entrainment. In this case the smaller grains are preferentially entrained, possibly leading to bed armoring. In contrast, if the median is in the fine-to-medium sand range, the smallest grains in the bed of mixed sizes are the most difficult to entrain due to sheltering by the larger grains; where grain density is also involved, this sorting can lead to the formation of placers. A variety of empirical relationships is considered to quantify the evaluation of selective entrainment from deposits of mixed sizes, but no single formulation is satisfactory for all data sets.

AIRY WAVE THEORY AND BREAKER HEIGHT PREDICTION

The data for the spectra of wind-generated waves measured in a laboratory tank and in a bay are analyzed using the similarity theory of Kitaigorodski, and the one-dimensional spectra of fetch-limited wind waves are determined from the data. The combined field and laboratory data cover such a wide range of dimensionless fetch F (= gF/u ) as F : 10 ~ 10 . The fetch relations for the growthes of spectral peak frequency u)m and of total energy E of the spectrum are derived from the proposed spectra, which are consistent with those derived directly from the measured spectra.A solution of finite amplitude long waves on constant sloping beaches is obtained by solving the equations of the shallow water theory of the lowest order. Non-linearity of this theory is taken into account, using the perturbation method. Bessel functions involved in the solution are approximated with trigonometric functions. The applicable range of this theory is determined from the two limit conditions caused by the hydrostatic pressure assumption and the trigonometric function approximation of Bessel functions. The shoaling of this finite amplitude long waves on constant sloping beaches is discussed. Especially, the effects of the beach slope on the wave height change and the asymmetric wave profile near the breaking point are examined, which can not be explained by the concept of constancy of wave energy flux based on the theory of progressive waves in uniform depth. These theoretical results are presented graphically, and compared with curves of wave shoaling based on finite amplitude wave theories. On the other hand, the experiments are conducted with respect to the transformation of waves progressing on beaches of three kinds of slopes ( 1/30, 1/2.0 and 1/10 ) . The experimental results are compared with the theoretical curves to confirm the validity of the theory.Measurements of drift were made in a wind and wave facility at different elevations below the mean water level. The drift profiles were obtained for reference wind speeds, Ur = 3.1, 5.7 and 9.6 m/sec. The measurement technique involved tracing the movement of small paper discs which were soaked in water to become neutrally buoyant at the elevation of release. A logarithmic drift profile is proposed. The water shear velocity, U*w, predicts a surface stress, TS = pw U*S, in agreement with that obtained from the wind shear velocity, s = Pa U*li where pa and pw refer to air and water densities, respectively.The paper describes a procedure for obtaining field data on the mean concentration of sediments in combination of waves and currents outside the breaker zone, as well as some results of such measurements. It is assumed that the current turbulence alone is responsible for the maintenance of the concentration profile above a thin layer close to the bottom, in which pick-up of sediments due to wave agitation takes place. This assumption gives a good agreement between field data and calculated concentration profiles.A section of beach on the south coast of England has been under surveillance for five years, from March 1966 until March 1971. During this period, two permeable groynes of the Makepeace Wood type were constructed. Beach cross sectional areas and rates of accretion were compared before and after groyne construction. The groynes caused a buildup in beach levels updrift.The results of model tests, carried out to evaluate the stability of submarine slopes under wave action are presented. A Bentonite clay was sedimented in a glass walled tank 6 feet long by 0.5 feet wide by 2.5 feet deep. The sedimentation and consolidation processes were studied and sediment densities were measured at various depths in the profile. Vane shear strength profiles were also measured afvarious average degrees of consolidation. Plastic markers were placed in the sediment adjacent to a glass wall so that the soil movements under both gravity and wave induced slides could be documented by photography. Dimensional similitude is discussed and the model test data are presented in a dimensionless form. All instabilities were observed to be of the infinite slope type. Analysis of the data shows that wave action is instrumental in initiating downslope mass movements in gently to steeply sloping off-shore sediments. General lack of agreement between the model test results and published theoretical analyses was found but there was close similarity in the depths and form of failure under wave action and under gravity stresses alone. The loss of stability under wave action is analyzed on the concept that failure is gravity controlled and the soil strength is reduced to a value commensurate with gravity sliding by the cyclic shearing stresses imposed by progressive waves. A method of evaluating the stability of prototype slopes using a model test correlation and field vane strength measurements is proposed. INTRODUCTION Instabilities in submarine slopes have been observed or have been inferred over a wide range of slope angles from less than half a degree up to about 30°. These subaqueous landslides are believed to have caused rupture of submarine cables and to have generated many of the geomorphological features on the ocean bottom. There are numerous records describing these landslides but very few publications discuss the application of the principles of soil mechanics to the analysis of the stability of submarine slopes. Associate Professor of Civil Engineering, Queens University at Kingston, Canada 2 Soils Engineer, Geocon Ltd., Toronto, Canada 3 Associate Professor of Civil Engineering, Cornell University, Ithaca, N.Y.Several mathematical models have been lately presented which describe the tidal wave propagation within an estuary. The existing models derived from the method for damped co-oscillating tides are based on sinusoidal wave profile. Meanwhile a tidal wave which moves upstream, generally exhibits a progressive deformation which tends to unbalance the length of time between flood and ebb tides. The actual profile is therefore no longer sinusoidal. Our investigation uses the potential method, and takes into account the wave amplitude which is usually neglected compared with the water depth. Finally, the velocity potential is obtained explicitely, using a double iterative method. Tidal elevation, particle velocities and trajectories are given by the same computer programmed algorithm. Our study shows that l) the phenomenon can be clearly visualized on the theoretical curves and 2) the magnitude of this deformation is inversely proportional to the water depth, becoming significant when the ratio f|/h reaches the critical value of 1/10. Damping and geometrical effects are also considered and the theory was applied to the St.Lawrence Estuary. A partial positive reflection of the incoming tidal wave is assumed at the narrow section near Quebec, whereas a complete negative reflection is assumed at the entrance to Lake St.Peter. The calculated and observed wave profiles, velocity distributions, and phase shifts are in good agreement.A numerical model is presented to describe the hydromechanics of lagoons connected to the ocean by relatively narrow inlets. Because special attention is given to the flushing, all second order terms in the hydrodynamic equations are retained. The study is restricted to lagoons with a onedimensional flow pattern and water of uniform density. In designing a numerical solution to the equations, the inlet equations are regarded as implicit boundary conditions to the equations describing the flow in the lagoon proper. The advantages of this approach are: (1) the size of the computational grid in the lagoon can be chosen independently of the relatively small dimensions of the inlets and (2) the flow at branching inlets (an inlet connecting a lagoon to the ocean such that branching of the inlet flow can occur) still can be described by a one-dimensional tidal model. The predictive capability of the numerical model is confirmed by favorable comparison between measured and computed particle paths and net transport for a series of laboratory experiments. In the experiments a canal of uniform width and depth is freely connected to a tidal basin at one end and at the other end is connected to the same basin by a submerged weir.

GRAIN SHAPE EFFECTS ON SETTLING RATES

The departure of a grain from a spherical shape causes a decrease in its settling velocity within a fluid. The more non-spherical the particle the greater the departure from the settling velocity of a spherical grain of the same weight. This study reexamines the various measures of sphericity and their ability to predict the drag coefficient and settling velocity of a non-spherical grain. Experiments were conducted using ellipsoidal pebbles settling in glycerine which has a viscosity some 1,000 times greater than water. The Reynolds numbers range from 0.07-1.5 which is the same range as quartz-density coarse silt through very fine sand settling in water. Therefore the results of the experiments are applicable to common sedimentary materials. The use of pebbles allows for the better determinations of the shape parameters, and eliminates the effects of grain surface roughness and roundness and grain asymmetries that complicate the settling of silt and sand. Analysis of the pebble-settling data indicates that the Corey shape factor provides a much better prediction of the drag coefficient for non-spherical grains than does the sphericity definition of Wadell which is based on the ratio of the surface area of a sphere with the same weight as the pebble to the actual surface area of the pebble. Regression of the data provides an equation which predicts the drag coefficient of the settling particle from its Corey shape factor and the Reynolds number. This drag coefficient relationship is used to obtain a modification of the familiar Stokes settling velocity equation which accounts for non-spherical grain shape effects on the settling rate. The results based on the pebble data are extended to Reynolds numbers up to

SEDIMENT THRESHOLD UNDER OSCILLATORY WAVES

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