The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.

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The Structure of Turbulent Shear Flow

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 ul,,,,, the bottom stress T, and Shields’ relative stress Bt, 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 uloo = 122.6 Do.2B for D 0.2 crn where the velocity uloo measured 100 cm above the sediment bed is given in cmjsec 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.

Threshold of sediment motion under unidirectional currents

Data compiled from eight decades of incipient motion studies were used to calculate dimensionless critical shear stress values of the median grain size, t* c 50 . Calculated t* c 50 values were stratified by initial motion definition, median grain size type (surface, subsurface, or laboratory mixture), relative roughness, and flow regime. A traditional Shields plot constructed from data that represent initial motion of the bed surface material reveals systematic methodological biases of incipient motion definition; t* c 50 values determined from reference bed load transport rates and from visual observation of grain motion define subparallel Shields curves, with the latter generally underlying the former; values derived from competence functions define a separate but poorly developed field, while theoretical values predict a wide range of generally higher stresses that likely represent instantaneous, rather than time-averaged, critical shear stresses. The available data indicate that for high critical boundary Reynolds numbers and low relative roughnesses typical of gravel-bedded rivers, reference-based and visually based studies have t* c50 ranges of 0.052-0.086 and 0.030-0.073, respectively. The apparent lack of a universal t*50 for gravel-bedded rivers warrants great care in choosing defendable t* c50 values for particular applications.

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A systematic analysis of eight decades of incipient motion studies, with special reference to gravel-bedded rivers

An expression for the critical shear stress noncohesive sediment is derived from the balance of forces on individual particles at the surface of a bed. The resulting equation, for a given grain size and density, depends on the near-bed drag force, lift force to drag force ratio, and particle angle of repose. Calculated values of the critical shear stress for uniformly sized sediment correspond closely to those determined from Shields' diagram. The initial motion problem for mixed grain sizes additionally depends on the relative protrusion of the grains into the flow and the particle angle of repose. The latter decreases when the diameter of a moving grain, D, is larger than the length scale of the bed roughness, ks (D/ks > 1), and increases when D/ks < 1, producing a corresponding decrease or increase in critical shear stress. Using the Miller and Byrne experimental relationship between D/ks and particle angle of repose, which is consistent with Shields' definition of initial motion, we obtain results that are in good agreement with the available experimental critical shear stress data for heterogeneous beds.

Calculations of the Critical Shear Stress for Motion of Uniform and Heterogeneous Sediments

In this thesis first a general derivation is given of the 'macro'-equations of mass- and linear-momentum balance that govern the mo'mentum transfer from a Newtonian fluid to rigid particles in a fluid-solid mixture. In particular, attention is paid to a) the attenuation of viscous-momentum transfer from the boundary to the interior of a granular bed subject to a surface flow, b) the drag and lift forces exerted by a turbulent shear flow on particles of the bed surface, and, c) the balance of forces acting on a bed load under uniform-flow conditions. It is shown that filter flow driven by shearing along the boundary of a granular sediment bed exerts a drag force on a layer of only two or three particle diameters within the bed. A drag force on the bulk mass of sediment is only exerted by a pore-pressure gradient. Stability conditions are formulated for a loose granular bed subject to erosive flow, at SHIELDS' grain-movement condition and dUring bed-load transport. 'Macro'-stresses acting along 'wavy' surfaces parallel to the bed are defined for that purpose, and an attenuation factor is introduced for the transmission of turbulent fluid shear from the surface towards the interior of the bed. It is shown that SHIELDS' dimensionless expression for the critical bed shear stress at the threshold of continuous sediment motion, 1/Phi , must reach a constant value for low-shear Reynolds' numbers (Re* < O. 5), as long as there is no cohesion between the particles. It is concluded that the bed load, consisting of particles rolling and saltating over the bed, must reduce the maximum turbulent fluid shear at the bed surface, at sufficiently high bed shear stress, to the critical threshold drag that would lead to the initiation of non-ceasing scour.

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Erosion And Transport Of Bed-Load Sediment

The initial entrainment characteristics of fine bed sand are objectively defined in terms of the measured distributions of critical instantaneous bed shear stress associated with the observed movement of individual surface grains. Critical flow conditions are then predicted by equating the lower extremes in these characteristic critical shear stress distributions to the upper extremes in the distribution of instantaneous bed shear stress produced by the particular type of background flow under consideration. The method is applied to the case of two-dimensional channel flow over a flat bed and yields sufficiently consistent results to suggest an extension to Shields' curve for small grain Reynolds numbers. The detailed experimental observations clearly illustrate the important role played by bed region turbulence in the interaction process between the fluid and the mobile bed grains constituting the deformable boundary.

Initial Instability of Fine Bed Sand

PURPOSE To use bench top techniques to examine the biophysical phenomena affecting the risk of abdominal aortic aneurysm (AAA) rupture relative to the physical properties of the aneurysm sac. METHODS Three latex AAAs with different wall elasticities were tested in a validated pulsatile flow model (PFM). Strain gauges were wired to each AAA model at the neck, inflection point, and at the maximum diameter. In initial studies, the influence of pressurization and the mechanical properties of AAA wall stress were evaluated. In subsequent studies, the latex AAAs were excluded with a tube graft and retested in the PFM. After creation of either a type I or II endoleak of known size and pressure, the systemic/intrasac pressure and the AAA wall stress were measured. RESULTS Each model had a complex wall-stress pattern comprising radial, longitudinal, and shear components. The peak wall stress at any point, in the presence of systemic pressurization or endoleak pressure, only reached 1% of the failure strength. In an AAA with a reinforced wall, the peak stress was significantly greater. Statistical analysis showed that wall strength contributed more significantly to wall stress than increasing pressurization within the AAA sac. CONCLUSIONS AAA wall mechanics contribute more significantly to peak wall stress than pressure variations within the system. In particular, increased stiffness (analogous to collagen deposition) significantly increased peak wall stress, which was located at the inflection point rather than at the maximum diameter. Techniques to measure the AAA wall mechanics and the rate of deterioration may predict AAA rupture in the untreated state or in the presence of an endoleak following endovascular repair.

https://journals.sagepub.com/doi/pdf/10.1177/152660280200900518

Aneurysm Wall Stress and Tendency to Rupture are Features of Physical Wall Properties: An Experimental Study

Intrasac pressure waveforms after endovascular aneurysm repair (EVAR) are a reliable marker of type I endoleaks, but not type II or combined types: an experimental study.

An experimental study is described in which the rate of transport of fine sand over a flat bed was measured as a function of the shear stress exerted on the bed by both laminar and turbulent flows, for a range of water temperatures. The results confirm the great sensitivity of the transport rate to changes in both shear stress and temperature over the test range. The hypothesis is propounded that in certain specified circumstances, the net rate of local bed load transport generated by an arbitrary unsteady flow, can be estimated by integration, using the measured steady laminar flow transport relationships in conjunction with the time history or probability distribution of the fluctuating bed shear stress. The concept has been tested using the measured data with encouraging results. It is suggested that this method of linking the characteristics of the near bed flow field to the local induced rates of sediment transport could be productively applied in a range of studies including the initiation and development of bed sand ripples by the action of various combinations of waves and steady currents.

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Bed load transport of fine sand by laminar and turbulent flow

https://icce-ojs-tamu.tdl.org/icce/index.php/icce/article/download/4232/3913

Anthony J. Grass

Papers

Initial Instability of Fine Bed Sand

Aneurysm Wall Stress and Tendency to Rupture are Features of Physical Wall Properties: An Experimental Study

Intrasac pressure waveforms after endovascular aneurysm repair (EVAR) are a reliable marker of type I endoleaks, but not type II or combined types: an experimental study.

Bed load transport of fine sand by laminar and turbulent flow

The Influence of Currents on Wave Attenuation