Examining the physical components of boundary shear stress for water‐worked gravel deposits

It is argued in this commentary that, in order to understand better the physical mechanisms that generate boundary shear stress over water‐worked gravel beds, flow velocity data should be re‐evaluated by spatial averaging the Reynolds equations to produce time‐ and space‐averaged (double‐averaged) momentum equations. A series of laboratory experiments were conducted in which the flow velocities were measured using a PIV system over two water‐worked gravel deposits. Combined with detailed data on the bed surface topography and vertical porosity, the physical components of shear stress were obtained. This enabled the various momentum transfer mechanisms present above, within and at the interface of a porous, fluvial deposit, to be quantified. This included the examination of the relevant contributions of temporal and spatial fluctuations in velocity and surface drag to the overall momentum transfer. It is demonstrated that double‐averaging represents a logical framework for assessing the fluid forces responsible for sediment entrainment and for investigating intragravel flow and sediment–water interface exchange mechanisms within the roughness layer in water‐worked gravel deposits. By considering the physical components of shear stress and their relative sizes it was possible to provide a physically based explanation for existing observations of enhanced mobility of gravel–sand mixtures and the transfer of solutes into porous, gravel deposits. This analysis reveals the importance of obtaining co‐located, high quality spatial data on the flow field and bed surface topography in order to gain a physical understanding of the mechanisms which generate boundary shear stress. Copyright © 2010 John Wiley & Sons, Ltd.     

Charnock dynamics: a model for the velocity structure in the wave boundary layer of the air–sea interface

We present a unified model of the air–sea boundary layer, which takes account of the air–sea momentum exchange across the sea surface. The recognition of the importance of the velocity shears in the water (which comprise a frictional shear and the Stokes shear due to the wave motion) in determining the sea surface roughness is a distinctive feature of the analysis, which leads to a prediction of the Charnock constant (α) in terms of two independent parameters, namely the wave age and the ratio of the Stokes shear to the Eulerian shear in the water. This expression is used to interpret the large observational variability of the Charnock constant. The 10-m drag coefficient can also be expressed using similar reasoning, and the introduction of a relation in which the ratio of the frictional shear in the water to the frictional shear in the air decreases with the friction velocity yields predictive relations for the variation of the 10-m drag coefficient at very high wind speeds both in the open ocean and in wind–wave tanks. The physical interpretation of this relation is that the production of spray essentially returns momentum from the ocean to the atmosphere, and this process becomes progressively more important as the wind speed increases.     

Shear stress on the base of a lithospheric plate

This paper is a review of the theoretical and observational evidence bearing on the magnitude of the shear stress which acts on the base of a lithospheric plate. Estimates based on the viscosity of the upper mantle do not yield useful limits. Arguments based on the thermal stability of the upper mantle indicate that the basal shear stress is no larger than a few bars. An indirect measurement of the rheology and shear stress can be made by studying the diffusion of stress and displacement following a large decoupling earthquake. When applied to the 1965 Rat Island Earthquake, this method yields a basal shear stress of about 2 bars. These results indicate that for small plates the forces produced by basal shear stress are probably small in comparison with forces acting on plate boundaries. To a first approximation, the smaller plates act as if they were decoupled from the mantle below. These stress estimates lead to a model in which the motion of the smaller lithospheric plates is governed almost entirely by the forces acting on their edges. Forces due to basal shear stress may be comparable to forces acting on the edges of large lithospheric plates. Thus, complete decoupling may not be a good approximation for such plates.     

Influence of the zone of weakness on dip angle and shear heating of subducted slabs

We study the importance of the zones of weakness and the pattern of downgoing flow in steady-state models of subducting lithosphere, which interacts mechanically and thermally with the ambient mantle. The non-linear system of governing equations consists of (i) the momentum equation in stream function formulation and (ii) the steady-state heat transfer equation including conduction and advection of heat and dissipation. A finite element method has been applied to this system. We consider the viscosity to be a non-linear function of both the temperature and the stream function. In steady-state two-dimensional (2D) flow, the stream function isolines follow material trajectories. They are used to follow the top of the subducting slab, which because of its possible increase in water content, is assumed to have a lower viscosity. The zone of weakness has been thus obtained in the self-consistent fashion since the stream function as well as the temperature are the output from our modeling and no a priori assumptions about the shape of the bending lithosphere are taken into account. It was shown that several orders decrease of viscosity in the zone of weakness is required to obtain the dip angle of about 45°. If the decrease of viscosity is not sufficient enough, the subducted slab either sinks almost vertically or does not exhibit a plate-like behavior. We have also demonstrated that shear heating can unrealistically increase at the zone of weakness for fast subductions if decrease of viscosity is underestimated.     

Triggering Mechanisms of Slope Instability and their Relationship to Earthquakes and Tsunamis

— Submarine and shoreline slope failures that accompany large earthquakes and large tsunamis are triggered by several mechanisms. Triggering mechanisms range from direct effects, such as inertial forces from earthquake shaking, to indirect effects, such as rapid drawdown that occurs when an earthquake-generated tsunami first approaches a shoreline. Soil shear strength also plays an important role in earthquake-related slope failures. Earthquakes change the shear strength of the soil by inducing excess pore water pressures. These excess pore water pressures change with time after the earthquake, resulting in changes in shear strength and slope stability with time. This paper reviews earthquake-related triggering mechanisms for submarine and shoreline slope failures. The variation in shear strength with time following an earthquake is examined and it is shown that delayed slope failures after an earthquake can occur as a result of changes in earthquake-induced excess pore water pressures and shear strength with time.     

Turbulent transport of angular momentum and differential rotation

Abstract

With the help of simplifying approximations, we have derived expressions for the non-diffusive fluxes of the angular momentum which are brought about by the action of Coriolis forces on the convective motion. The original turbulence, which is not perturbed by the Coriolis forces, is considered given and weakly anisotropic, the anisotropy having a preferred radial direction. The eddy viscosities are evaluated. Hence, a closed equation for the angular velocity is derived, and then solved for the case of slow rotation. It is shown that the differential rotation is generated most effectively in the case of moderate rotation when the Rossby number is of order unity. At small Rossby numbers, the rotation differentiality is inhibited. A negative eddy viscosity is suggested for the case of rapid rotation. Some implications for the Sun and other astrophysical objects are discussed.     

Shear viscosity of rhyolite-vapor emulsions at magmatic temperatures by concentric cylinder rheometry

The viscosity of natural rhyolitic melt from Lipari, Aeolian Islands and melt-bubble emulsions (30–50 vol% porosity) generated from Lipari rhyolite have been measured in a concentric cylinder rheometer at temperatures and shear rates in the range 925–1150°C and 10⁻³–10^−1.2 s⁻¹, respectively, in order to better understand the dependence of emulsion shear viscosity on temperature and shear rate in natural systems. Bubble-free melt exhibits Newtonian–Arrhenian behavior in the temperature range 950–1150°C with an activation energy of 395±30 kJ/mol; the shear viscosity is given by log η_m=−8.320+20624/T. Suspensions were prepared from natural rhyolite glass to which small amounts of Na₂SO₄ were added as a ‘foaming agent’. Reasonably homogeneous magmatic mixtures with an approximate log-normal distribution of bubbles were generated by this technique. Suspension viscosity varied from 10^6.1 to 10^8.37 Pa s and systematically correlates with temperature and porosity in the shear stress range (10^4.26–10^5.46 Pa) of the experiments. The viscosity of melt-bubble emulsions is described in terms of the relative viscosity, η_r=η_e/η_m where η_e is the emulsion viscosity and η_m is the viscosity of melt of the same composition and temperature. The dependence of relative viscosity on porosity for magmatic emulsions depends on the magnitude of the capillary number Ca≡G/(σr_b⁻¹η_m⁻¹), the ratio of viscous forces acting to deform bubbles to interfacial forces resisting bubble deformation. For inviscid bubbles in magmatic flows three regimes may be identified. For Ca<0.1, bubbles are nearly spherical and relative viscosity is an increasing function of porosity. For dilute systems, η_r=1+φ given by the classical result of Taylor [Proc. R. Soc. London A 138 (1932) 41–48]. For Ca in the range 0.1<Ca<10, emulsions behave as power law fluids and the relative viscosity depends on shear rate (or Ca) as well as porosity. At high Ca (Ca>10) an asymptotic regime is reached in which relative viscosity decreases with increasing porosity and is independent of Ca. Our experiments were carried out for 30<Ca<925 in order to quantify the maximal effect of bubbles in reducing the viscosity of magmatic emulsions relative to single-phase melt at identical conditions of shear rate and temperature. The viscosity of a 50 vol% emulsion is a factor of five smaller than that of melt alone. Rheometric measurements obtained in this study are useful in constraining models of magma transport and volcanic eruption mechanics relevant to transport of volatile-saturated magma in the crust and upper mantle.     

剪切产热不稳定性及其在研究深源地震发生机理上的应用

本文运用稳定性分析的方法,研究在粘弹性介质（Maxwell体）中剪切产热不稳定性的发生条件,并讨论其对于深源地震发生机理的应用.结果表明,在板块向下俯冲的过程中,由粘滞损耗产热将会发生剪切不稳定性,这为解释深源地震发生提供了一个基础.     

剪切产热不稳定性及其在研究深源地震发生机理上的应用

本文运用稳定性分析的方法,研究在粘弹性介质(Maxwell体)中剪切产热不稳定性的发生条件,并讨论其对于深源地震发生机理的应用.结果表明,在板块向下俯冲的过程中,由粘滞损耗产热将会发生剪切不稳定性,这为解释深源地震发生提供了一个基础.     

Nonlinear diffusive instabilities in differentially rotating stars

Abstract

Angular momentum driven instabilities in a stratified differentially rotating star are investigated. In the strong buoyancy limit axisymmetric instabilities of the Goldreich-Schubert type are the most important. A detailed discussion of the linear and small amplitude theories at an arbitrary latitude is given. The bifurcation to finite amplitude steady modes is typically transcritical, and occurs whenever the angular momentum or its gradient is neither parallel not perpendicular to local gravity. Such misalignments enhance the time scale for transport of angular momentum by the Goldreich-Schubert instability. Depending on the turbulent viscosity produced by secondary shear instabilities time scales as short as the Kelvin-Helmholtz time scale are possible.     

磁层顶边界层剪切流引起的MHD波模转化

采用非本征模方法（non modal analysis）研究了磁层顶边界层中剪切流导致的MHD波模转化及其与背景流场的能量交换过程.发现在分别代表磁层顶内、外边界层及过渡区的均匀剪切流场中,初始设定的Alfvén波扰动可部分转化为快、慢磁声波.而且,在不同区域,根据等离子体参数的不同,发生的波模转化过程也不相同.在外边界,Alfvén波主要转化为慢磁声波;在内边界,Alfvén波则主要转化为快磁声波;而在二者之间的过渡区中,Alfvén波可同时转化为两种类型的磁声波.我们还发现,含有较强快波分量的扰动可从磁层顶剪切流场中获得能量而得到线性放大.上述物理过程可能对解释磁鞘至磁层的能量及动量异常输运现象有所帮助.     

Molecular transport in fracture processes

The Asymmetric Continuum Theory based on deformation fields includes the strain rotation as an equally important deformation part as the shear and confining strains; all these fields can be related to their origin in the fracture processes by some displacement motions in a source. Some of these motions may belong to an individual process, some to complex correlated events; in this latter case the displacements related to these strains could be shifted in phase. Moreover, we may expect an appearance of some molecular transport motions; the molecular transport may be helpful for understanding an interaction of the molecular processes and related molecular momentum flux. These correlated events should be mutually related in a source by the release-rebound mechanism. In particular, we consider the point fracture events as associated with a confining load or/and with the shear and rotation processes; we discuss the related effects and their meaning when discussing the fault plane mechanism and emitted waves. It is to be pointed out that such molecular motions are too small to be observed by the existing seismological networks.     

Studies of the formation process of water-in-oil emulsions

This paper summarizes studies to determine the formation process of water-in-oil emulsions and the stability of such emulsions formed in the laboratory and in a large test tank. These studies have confirmed that water-in-oil mixtures can be grouped into four states: stable emulsions, unstable water-in-oil mixtures, mesostable emulsions, and entrained water. These states are differentiated by rheological properties as well as by differences in visual appearance. The viscosity of a stable emulsion at a shear rate of one reciprocal second is about three orders of magnitude greater than that of the starting oil. An unstable emulsion usually has a viscosity no more than about 20 times greater than that of the starting oil. A stable emulsion has a significant elasticity, whereas an unstable emulsion does not. A mesostable emulsion has properties between stable and unstable, but breaks down within a few days of standing. The usual situation is that emulsions are either obviously stable, mesostable, or unstable. Entrained water, water suspended in oil by viscous forces alone, is also evident. Very few emulsions have questionable stability. Analytical techniques were developed to test these observations.

The type of emulsion produced is determined primarily by the properties of the starting oil. The most important of these properties are the asphaltene and resin content and the viscosity of the oil. The composition and property ranges of the starting oil that would be required to form each of the water-in-oil states are discussed in this paper.     

用遗传有限单元法反演川滇下地壳流动对上地壳的拖曳作用

利用震源机制解和地质调查资料,运用伪三维遗传有限单元法反演了中国川滇部分地区（96°E～104°E, 22°N～30°N）受到的边界作用和该地区底部所受的剪切作用力. 对反演方法进行了讨论,获得了稳定的反演结果. 结果显示,该区川滇菱形块体上地壳底部受下地壳南南东向剪切力,与GPS反映的现今地块运动方向大体一致;而研究区域其他地区底部没有受到统一显著的剪切力作用. 结合该地区的研究资料,初步认为青藏高原物质受挤压向东和东南运动过程中,下地壳物质比上地壳更易于流动,从而对川滇菱形块体上地壳有拖曳作用. 从应力场反演的模型位移与GPS实测的现今位移资料也大体吻合,反映结果有合理的物理意义.     

An analysis of the mechanism of flow in ice-covered rivers

The paper presents a mechanism of flow of water in an ice-covered river in the case of movable bottom. The analysis is based upon the principal hydrodynamics equations of turbulent flow in the case of steady uniform motion. It leads to the conclusion of linear distribution of the turbulent shear stress with depth. It allows to obtain the vertical distribution of velocity of flowing water under the assumption that at the boundaries (movable bottom and ice) the viscosity of water is greater than the kinematics viscosity. The relations describing the vertical distribution of velocity of flowing water, as well as the eddy viscosity coefficient under these conditions, are given.     

Ekman circulation and downwelling in narrow lakes

An analytical solution is obtained for the wind-driven steady flow developing under the action of the Coriolis acceleration in a closed basin of elongated shape. Different from the traditional Ekman approach, which determines the velocity distribution along a water column given the free surface shear stress and pressure gradient, here the flow field is solved in the whole cross-section considering the lateral transfer of momentum due to the horizontal eddy viscosity. The solution is derived exploiting a perturbation method, whereby the inverse of the Ekman number is assumed small, and imposing a wind aligned with the main axis of the lake. In the central part of the lake a secondary circulation develops producing downwelling along the right hand side (in the northern hemisphere) and upwelling along the opposite side, whose intensity is modulated by the turbulence anisotropy. The modification of the primary flow is considered as well. The solution, which is also compared with numerical results, is obtained for simplified conditions, but the extension to more general cases is discussed.     

Modeling granular soils liquefaction using coupled lattice Boltzmann method and discrete element method

In this paper, a novel coupled pore-scale model of pore-fluid interacting with discrete particles is presented for modeling liquefaction of saturated granular soil. A microscale idealization of the solid phase is achieved using the discrete element method (DEM) while the fluid phase is modeled at a pore-scale using the lattice Boltzmann method (LBM). The fluid forces applied on the particles are calculated based on the momentum exchange between the fluid and particles. The presented model is based on a first principles formulation in which pore-pressure develops due to actual changes in pore space as particles׳ rearrangement occurs during shaking. The proposed approach is used to model the response of a saturated soil deposit subjected to low and large amplitude seismic excitations. Results of conducted simulations show that at low amplitude shaking, the input motion propagates following the theory of wave propagation in elastic solids. The deposit response to the strong input motion indicates that liquefaction took place and it was due to reduction in void space during shaking that led to buildup in pore-fluid pressure. Soil liquefaction was associated with soil stiffness degradation and significant loss of interparticle contacts. Simulation results also indicate that the level of shaking-induced shear strains and associated volumetric strains play a major role in the onset of liquefaction and the rate of pore-pressure buildup.     

Rheology of the mantle and tectonics of the oceanic lithospheric plates

The modern concepts of the rheology of viscous mantle and brittle lithosphere, as well as the results of the numerical experiments on the processes in a heated layer with a viscosity dependent on pressure, temperature, and shear stress, are reviewed. These dependences are inferred from the laboratory studies of olivine and measurements of postglacial rebound (glacial isostatic adjustment) and geoid anomalies. The numerical solution of classical conservation equations for mass, heat, and momentum shows that thermal convection with a highly viscous rigid lithosphere develops in the layer with the parameters of the mantle with the considered rheology under a temperature difference of 3500 K, without any special additional conditions due to the self-organization of the material. If the viscosity parameters of the lithosphere correspond to dry olivine, the lithosphere remains monolithic (unbroken). At a lower strength (probably due to the effects of water), the lithosphere splits into a set of separate rigid plates divided by the ridges and subduction zones. The plates submerge into the mantle, and their material is involved in the convective circulation. The results of the numerical experiment may serve as direct empirical evidence to validate the basic concepts of the theory of plate tectonics; these experiments also reveal some new features of the mantle convection. The probable structure of the flows in the upper and lower mantle (including the asthenosphere), which shows the primary role of the lithospheric plates, is demonstrated for the first time.     

REGIME MORPHOLOGY OF EQUILIBRIUM ALLUVIAL CHANNELS

IINTRODUCTIONThequestfordeterminingthedesigncharacteristicsofregimechannelshasbeengoingonforalongtime.Peoplehavebeenexcavatingnewormodifyingexistingchannelstousethemforirrigation,watersupply,navigation,floodcontrolandotherpurposes.Recently,archeologistsdiscoveredwhatiscurrentlybelievedtobetheoldestman(madecanalsystem.ItwasfoundintheareawhereMesopotamiausedtoexistanditisdatedbacktoabollt4,000BC.Ifachanne]isnotproperlydesigned,erosionofitsbanksordepositionofsedimentwithinitscross-sectionw…     

On the Nonlinear Dynamics of Rapidly Moving Splashes

Water Resources - The splashes that form on the surface of water bodies under the effect of strong winds have a considerable effect on evaporation, as well as on the exchange by heat and momentum...