The relationship between oil droplet size and upper ocean turbulence

Oil spilled at sea often forms oil droplets in stormy conditions. This paper examines possible mechanisms which generate the oil droplets. When droplet Reynolds numbers are large, the dynamic pressure force of turbulent flows is the cause of droplet breakup. Using dimensional analysis, Hinze (1955, A.I.Ch.E. Journal 1, 289–295) obtained a formula for the maximum size of oil droplets that can survive the pressure force. When droplet Reynolds numbers are small, however, viscous shear associated with small turbulent eddies is the cause of breakup. For the shear mechanism, we obtain estimates of droplet size as a function of energy dissipation rate, the ratio of oil-to-water viscosity and the surface tension coefficient.

The two formulae are applied to oil spills in the ocean. At dissipation rates expected in breaking waves, the pressure force is the dominant breakup mechanism and can generate oil droplets with radii of hundreds of microns. However, when chemical dispersants are used to treat an oil slick and significantly reduce the oil-water interfacial tension, viscous shear is the dominant breakup mechanism and oil droplets with radii of tens of microns can be generated. Viscous shear is also the mechanism for disintegrating water-in-oil emulsions and the size of a typical emulsion blob is estimated to be tens of millimeters.     

The stabilizing effect of viscosity on magnetic wind flows from accretion discs

Magnetically channelled winds are believed to be a feature of most accretion discs. It has been shown that such flows can remove significant amounts of angular momentum from the disc and make a major contribution to driving the inflow. For a suitable range of poloidal magnetic field bending, only a small fraction of the disc mass is lost in the wind flow, so most material reaches the inner region of the disc. However, discs driven purely by such a process are prone to a field-bending instability which can lead to runaway mass loss. It is shown here that a small amount of disc viscosity can quench such an instability and allow steady disc-wind models to be constructed. The effects of perturbations to the coupling between the radial and vertical structures are allowed for, with the thermal balance having particular relevance. Runaway increases in field bending are prevented by increases in the disc temperature and magnetic diffusivity mainly caused by viscous dissipation.     

主应力轴持续旋转条件下饱和松砂的振动孔隙水压力特性

利用新研制的“土工静力-动力液压三轴-扭剪多功能剪切仪”,针对福建标准松砂,在三向非均等固结条件下,进行了能够模拟海洋波浪荷载作用下主应力轴连续旋转的循环耦合剪切试验。通过试验着重探讨了初始主应力方向、振动过程中主应力方向连续变化对不排水条件下砂土的振动孔隙水压力增长特性的影响。实验研究表明:在振动过程中主应力轴连续旋转的条件下,初始主应力方向对砂土的动孔压比与振次比之间关系具有显著的影响,随着初始大主应力与竖向之间夹角的增大,动孔压比的增长速度明显加快,具有较好的规律性;归一化孔压比与广义剪应变之间的关系基本上与初始主应力方向角和振动剪应力幅值无关。     

Experimental and Numerical Investigation of the Flow Hydraulic in Gradual Transition Open Channels

Channel expansions are common in both natural and artificial open channels. With increasing cross-sectional dimensions in an expansion, the flow decelerates. Due to separation of flow and subsequent eddy formation, a significant head loss is occurred along the transition. This study presents the results of experimental investigations on subcritical flow along the expansive transition of rectangular to trapezoidal channels. Also, a numerical simulation was developed using the finite volume method with Reynolds Stress turbulent model. Water surface profiles and velocity distributions of flow through the transition were measured experimentally and compared with the numerical results. Also, hydraulic efficiency of the transition and coefficient of energy head loss were calculated. The results show that with increasing the upstream Froude number, hydraulic efficiency of the transition and coefficient of energy head loss are decreased and increased, respectively. The results also showed the ability of numerical simulation for simulating the flow separation zones and bed shear stress along the transition for different inlet discharges and inflow Froude numbers.     

Cyclic shearing and liquefaction of soil under irregular loading: an incremental model for the dynamic earthquake-induced deformation

The paper presents a mathematical model for the deformation of soil under irregular cyclic loading in the simple-shear conditions. The model includes the possible change in the effective pressure in saturated soil due to the cyclic shearing, the reciprocal influence of the effective pressure on the response of the soil to the shear loading, and the pore pressure dissipation due to the seepage of the pore fluid. The hysteresis curves for the strain–stress relationship are constructed in such a way that they produce both the required backbone curve and the required damping ratio as functions of the strain amplitude. At the same time, the approach enables the constitutive functions involved in the model to be specified in various ways depending on the soil under study. The constitutive functions can be calibrated independently of each other from the conventional cyclic shear tests. The constitutive model is incorporated in the boundary value problem for the dynamic site response analysis of level ground. A numerical solution is presented for the dynamic deformation and liquefaction of soil at the Port Island site during the 1995 Hyogoken-Nambu earthquake.     

Frictional heat generation and seismic radiation in a foam rubber model of earthquakes

Results from a study of stick-slip particle motion at the interface between two stressed foam rubber blocks indicate that normal vibrations and interface separation are an important part of the stick-slip process in foam rubber. The dimension of the dynamic slip pulse is small compared to the dimension of the model (approximately 10 cm vs. 200 cm) consistent with the abrupt-locking slip pulse model ofBrune (1970, 1976), andHeaton (1990). A comparison of frictional heat generation between stable-sliding and stick-slip foam rubber models indicates a linear relation between the temperature increase on the fault surface (for a given distance of slip) and the driving shear force for the stable-sliding model, while for the stick-slip model there is essentially no variation in frictional heat generation with an increase in shear stress. We performed experiments to investigate the ratio of normal motion to shear motion at different levels of normal stress in the stick-slip foam rubber model. Preliminary result indicate that the normal component of the particle motion increases more rapidly with increasing normal stress than the shear component. The phenomenon of interface separation and normal vibrations may thus explain some of the most frustrating problems in earthquake mechanics, e.g., the heat flow paradox, the long-term weakness of major active faults, and anomalousP-wave radiation.     

Direct numerical simulations of interface dynamics to link capillary pressure and total surface energy

The flow of two immiscible fluids through a porous medium depends on the complex interplay between gravity, capillarity, and viscous forces. The interaction between these forces and the geometry of the medium gives rise to a variety of complex flow regimes that are difficult to describe using continuum models. Although a number of pore-scale models have been employed, a careful investigation of the macroscopic effects of pore-scale processes requires methods based on conservation principles in order to reduce the number of modeling assumptions. In this work we perform direct numerical simulations of drainage by solving Navier–Stokes equations in the pore space and employing the Volume Of Fluid (VOF) method to track the evolution of the fluid–fluid interface. After demonstrating that the method is able to deal with large viscosity contrasts and model the transition from stable flow to viscous fingering, we focus on the macroscopic capillary pressure and we compare different definitions of this quantity under quasi-static and dynamic conditions. We show that the difference between the intrinsic phase-average pressures, which is commonly used as definition of Darcy-scale capillary pressure, is subject to several limitations and it is not accurate in presence of viscous effects or trapping. In contrast, a definition based on the variation of the total surface energy provides an accurate estimate of the macroscopic capillary pressure. This definition, which links the capillary pressure to its physical origin, allows a better separation of viscous effects and does not depend on the presence of trapped fluid clusters.     

Modelling the hysteresis in the velocity pattern of slow‐moving earth flows: the role of excess pore pressure

This paper describes the velocity pattern of a slow‐moving earth flow containing a viscous shear band and a more or less rigid landslide body on top. In the case of small groundwater fluctuations, Bingham's law may describe the velocity of these slow‐moving landslides, with velocity as a linear function of excess shear stress. Many authors have stated that in most cases a non‐linear version of Bingham's law best describes the moving pattern of these earth flows. However, such an exponential relationship fails to describe the hysteresis loop of the velocity, which was found by some authors. These authors showed that the velocity of the investigated earth flows proved to be higher during the rising limb of the groundwater than during the falling limb. To explain the hysteris loop in the velocity pattern, this paper considers the role of excess pore pressure in the rheological behaviour of earth flows by means of a mechanistic model. It describes changes in lateral internal stresses due to a change in the velocity of the earth flow, which generates excess pore pressure followed by pore pressure dissipation. Model results are compared with a hysteresis in the velocity pattern, which was measured on the Valette landslide complex (French Alps). Copyright © 2005 John Wiley & Sons, Ltd.     

LABORATORY EXPERIMENTS ON NAVIGATION-INDUCED BED SHEAR STRESSES AND SEDIMENT RESUSPENSION

IINTRODUCTIONDependingonflowandoperatingconditions,navigationtrafficmaycausesignificantresuspensionofdepositedsediment.Jnanumberofsituationsresuspensionofdepositedsedimentcanhavesevereenvironmentalrepercussions.Forinstance,ifthesedimentcontainscontaminants,thecontaminantsmaybereentrainedwiththesediment,taintingthewaterquality(Erdmannetal.,1994).Inothersituations,..evedincreasesintheamountofcleansuspendedsedimentcanbedetrimentalforaquaticplantsandanimals(Garcfaetal.,1998).Inordertoassesst…     

Pore-fluid pressures and frictional heating on a fault surface

This study considers the effects of heat transfer and fluid flow on the thernal, hydrologic, and mechanical response of a fault surface during seismic failure. Numerical modeling techniques are used to account for the coupling of the thermal, fluid-pressure, and stress fields. Results indicate that during an earthquake the failure surface is heated to a tempeature required for the thermal expansion of pore fluids to balance the rate of fluid loss due to flow and the fluid-volume changes due to pore dilatation. Once this condition is established, the pore fluids pressurize and the shear strength decreases rapidly to a value sufficient to maintain the thermal pressurization of pore fluids at near-lithostatic values. If the initial fluid pressure is hydrostatic, the final temperature attained on the failure surface will increase with depth, because a greater pressure increase can occur before a near-lithostatic pressure is reached. The rate at which thermal pressurization proceeds depends primarily on the hydraulic characteristics of the surrounding porous medium, the coefficient of friction on the fault surface, and the slip velocity. If either the permeability exceeds 10^–15 m² or the porous medium compressibility exceeds 10^–8 Pa^–1, then frictional melting may occur on the fault surface before thermal pressurization becomes significant. If the coefficient of friction is less than 10^–1 and if the slip velocity is less than 10^–2 msec^–1, then it is doubtful that either thermal pressurization or frictional melting on the fault surface could cause a reduction in the dynamic shear strength of a fault during an earthquake event.     

Wave-induced setup of the mean surface over a sloping beach

A new theoretical approach for the wave-induced setup over a sloping beach is presented that takes into consideration the explicit variations of the surface waves due to bottom slope and viscosity. In this way, the wave forcing of the mean Lagrangian volume fluxes is calculated without assuming that the local depth is constant. The analysis is valid in the region outside the surf zone and is based on the shallow-water assumption. A novel approach for separating the viscous damping of the waves from the frictional damping of the mean flow is introduced, where the mean Eulerian velocity is applied in the bottom stress for the mean fluxes. In the case where the onshore Lagrangian mean transport is zero, a new formula is derived for the Eulerian mean free surface slope, in which the effects of bottom slope, viscous wave damping and frictional bottom drag on the mean flow are clearly identified. The analysis suggests that viscous damping of the waves and frictional dissipation of the Eulerian near-bed return flow could lead to setup outside the surf zone.     

Thermomechanical balances of ice sheet flows

Abstract

The flow of large natural ice masses under gravity is described by the mass, momentum, and energy balances of an incompressible, homogeneous, heat conducting, non-linearly viscous fluid in which the shear response includes a strongly temperature-dependent rate factor. Dimensionless analysis and co-ordinate stretching reflecting the long aspect ratio show that series expansions in a small parameter which determines the surface slope magnitude are uniformly valid even when temperature variation induces a strongly non-uniform mechanical response. The normalised energy balance shows that both horizontal and vertical advection are significant in thin and thick grounded sheets and in floating shelves, and that viscous dissipation can be significant in basal regions of a grounded sheet, and hence there is strong thermomechanical coupling. Moreover, though a thermal basal boundary layer may arise in a thick sheet, it would only give rise to significantly enhanced temperature and strain-rate gradients in extreme circumstances. The leading order relations for steady plane flow of a grounded sheet are reduced to a parabolic system for the temperature and two velocity components, which incorporates the unknown surface slope in coefficients and boundary conditions. This provides a useful starting point for numerical solution of the thermomechanically coupled problem. A fixed domain mapping is presented as an attractive alternative formulation when the bed topography is close to planar.     

西昌昔格达组黏土岩动力特性试验研究

在大量动三轴试验的基础上,研究了不同固结条件(σ3c=100,200,400 kPa,kc=1.0,1.5,2.0)下西昌昔格达组黏土岩的动应力-动应变关系、动弹性模量、阻尼比及动强度特性。研究结果表明:西昌昔格达组黏土岩在一定条件下的动应力-动应变关系符合幂函数模型。动应力随着固结围压σ3c或固结主压力比kc增大而增大。在相同围压下,达到相同动应变时,偏压固结状态比均压状态所需要的动应力大。当其他条件相同时,动弹性模量随固结压力或固结主压力比增大而增大,随着动应变的增加而减小并趋于稳定。最大动弹性模量Ed0与σ3c/Pa、kc均有良好的幂函数关系,且对不同固结应力状态条件可以归一。阻尼比随动应变增大而增大,但增大幅度随动应变增大而迅速减小,阻尼比随围压或固结主压力比增大而减小,但它们对阻尼比影响较小。不同固结应力状态下(λ/λmax)与(1-Ed/Ed0)有良好的幂函数关系。西昌昔格达组饱和黏土岩动剪应力τd随固结围压σ3c或固结主压力比kc增大而增大,随振动次数增加而减小。τd/σm均随固结围压σ3c增大而减小,随固结压力比kc增大而增大。动剪应力τd与平均压力σm、固结主压力比kc有较好的线性关系。     

反向消磁条件下磁流变脂隔震模拟试验研究

采用电磁线圈及永磁体共同控制磁场,自主设计一种可反向消磁的磁流变脂(MRG)剪切试验装置。利用ANSYS Electronics软件对该试验装置磁场分布进行仿真分析,并制备不同羰基铁粉质量分数的MRG,采用振动台对反向消磁条件下MRG的动态剪切性能开展试验测试,分别研究励磁电流、激振幅值和激励频率对MRG动态性能的影响。结果表明:羰基铁粉质量分数对MRG的动态性能影响显著;MRG的剪切应力随励磁电流的增大先快速增大后趋于平缓,阻尼力则逐渐减小;MRG的耗能能力随位移幅值的增加而增强;随着加载频率的增大,其阻尼力略有增加。     

An earthquake instability model based on faults containing high fluid-pressure compartments

It has been proposed that large strike-slip faults such as the San Andreas contain water in seal-bounded compartments. Arguments based on heat flow and stress orientation suggest that in most of the compartments, the water pressure is so high that the average shear strength of the fault is less than 20 MPa. We propose a variation of this basic model in which most of the shear stress on the fault is supported by a small number of compartments where the pore pressure is relatively low. As a result, the fault gouge in these compartments is compacted and lithified and has a high undisturbed strength. When one of these locked regions fails, the system made up of the neighboring high and low pressure compartments can become unstable. Material in the high fluid pressure compartments is initially underconsolidated since the low effective confining pressure has retarded compaction. As these compartments are deformed, fluid pressure remains nearly unchanged so that they offer little resistance to shear. The low pore pressure compartments, however, are overconsolidated and dilate as they are sheared. Decompression of the pore fluid in these compartments lowers fluid pressure, increasing effective normal stress and shear strength. While this effect tends to stabilize the fault, it can be shown that this dilatancy hardening can be more than offset by displacement weakening of the fault (i.e., the drop from peak to residual strength). If the surrounding rock mass is sufficiently compliant to produce an instability, slip will propagate along the fault until the shear fracture runs into a low-stress region. Frictional heating and the accompanying increase in fluid pressure that are suggested to occur during shearing of the fault zone will act as additional destabilizers. However, significant heating occurs only after a finite amount of slip and therefore is more likely to contribute to the energetics of rupture propagation than to the initiation of the instability.We present results of a one-dimensional dynamic Burridge-Knopoff-type model to demonstrate various aspects of the fluid-assisted fault instability described above. In the numerical model, the fault is represented by a series of blocks and springs, with fault rheology expressed by static and dynamic friction. In addition, the fault surface of each block has associated with it pore pressure, porosity and permeability. All of these variables are allowed to evolve with time, resulting in a wide range of phenomena related to fluid diffusion, dilatancy, compaction and heating. These phenomena include creep events, diffusion-controlled precursors, triggered earthquakes, foreshocks, aftershocks, and multiple earthquakes. While the simulations have limitations inherent to 1-D fault models, they demonstrate that the fluid compartment model can, in principle, provide the rich assortment of phenomena that have been associated with earthquakes.     

Conditional statistics of Reynolds shear stress in flow over 2D dunes in the presence of surface waves

This study presents the analysis of the velocity fluctuations to describe the conditional statistics of Reynolds shear stress in flow over two‐dimensional dunes in the presence of surface waves of varying frequency. The flow velocity measurements over the dunes are made using a 16‐MHz 3D acoustic Doppler velocimeter. The joint probability distributions of the normalized stream‐wise and vertical velocity fluctuations at different vertical locations are calculated in the trough region of a selected dune in quasi‐steady region of the flow. Third‐order moments of the stream‐wise and vertical velocity components over one dune length are also calculated throughout the flow depth for understanding the effect of surface waves on relative contributions to the Reynolds shear stress due to the four quadrant events. The structure of instantaneous Reynolds stresses is analysed using quadrant analysis technique. It has been shown that the contributions of second and fourth quadrant events to the Reynolds shear stress increase with increase in the frequency of surface waves. In fact, the largest contribution to turbulent stresses comes from the second quadrant. The cumulant discard method is applied to describe the statistical properties of the covariance term u′w′. Conditional statistics and conditional sampling are used to compare the experimental and theoretical relative contributions to the Reynolds shear stress from the four quadrant events. Copyright © 2013 John Wiley & Sons, Ltd.     

Pressure and shear stress caused by raindrop impact at the soil surface: Scaling laws depending on the water depth

Raindrop impact is an important process in soil erosion. Through its pressure and shear stress, raindrop impact causes a significant detachment of the soil material, making this material available for transport by sheet flow. Thanks to the accurate Navier–Stokes equations solver Gerris, we simulate the impact of a single raindrop of diameter D, at terminal velocity, on water layers of different thickness h: , , D, 2D, in order to study pressures and shear stresses involved in raindrop erosion. These complex numerical simulations help in understanding precisely the dynamics of the raindrop impact, quantifying in particular the pressure and the shear stress fields. A detailed analysis of these fields is performed and self‐similar structures are identified for the pressure and the shear stress on the soil surface. The evolution of these self‐similar structures are investigated as the aspect ratio h/D varies. We find that the pressure and the shear stress have a specific dependence on the ratio between the drop diameter and the water layer thickness, and that the scaling laws recently proposed in fluid mechanics are also applicable to raindrops, paving the road to obtain effective models of soil erosion by raindrops. In particular, we obtain a scaling law formula for the dependence of the maximum shear stress on the soil on the water depth, a quantity that is crucial for quantifying erosion materials. Copyright © 2016 John Wiley & Sons, Ltd.     

A note on Stokes production of turbulence kinetic energy in the oceanic mixed layer: observations in the Baltic Sea

Shear- and convection-driven turbulence coexists with wind-generated surface gravity waves in the upper ocean. The turbulent Reynolds stresses in the oceanic mixed layer can therefore interact with the shear of the wave-generated Stokes drift velocity to extract energy from the surface waves and inject it into turbulence, thus augmenting the mean shear-driven turbulence. Stokes production of turbulence kinetic energy (TKE) is difficult to measure in the field, since it requires simultaneous measurement of the turbulent stress and the Stokes drift profiles in the water column. However, it is readily inferred using second moment closure models of the oceanic mixed layer provided: (1) wave properties are available, along with the usual water mass properties, and radiative and air–sea fluxes needed to drive the mixed layer model and (2) the model skill can be assessed by comparing the model results against the observed dissipation rates of TKE. Comprehensive measurements made during the Reynolds 2002 campaign in the Baltic Sea have made the estimation of Stokes production possible, and in this paper, we report on the effort and the conclusions reached. Measurements of air–sea exchange parameters and water mass properties during the campaign allowed a mixed layer model to be run and the turbulent stress in the water column to be inferred. Simultaneous wave spectrum measurements enabled Stokes drift profile to be deduced and wave breaking to be included in the model run, and the Stokes production of TKE in the water column estimated. Direct measurements of the TKE dissipation rate from an upward traversing microstructure profiler were used to assure that the model could reproduce the turbulent dissipation rate in the water column. The model results indicate that the Stokes production of TKE in the mixed layer is of the same order of magnitude as the shear production and must therefore be included in mixed layer models.     

Mantle rheology: radial and lateral viscosity variations inferred from microphysical creep laws

Inferences on the rheology of the mantle based on theoretical and experimental rate equations for steady state creep are discussed and compared with results from geophysical models. The radial increase of viscosity by one to three orders of magnitude across the mantle, required by inversion of postglacial rebound and geodynamic data, is confirmed by microphysical models based on the estimation of continuous and discontinuous changes of creep parameters with depth. The upper mantle (viscosity 10²⁰–10²¹ Pa s) is likely to show non-Newtonian rheology (power-law creep) for average grain sizes larger than 0.1 mm as an order of magnitude. Given the variability of both grain size and stress conditions, local regions of linear rheology can be present. The rheology of transition zone and lower mantle (viscosity 10²²–10²⁴ Pa s) cannot be definitely resolved at present. Estimation of creep parameters leads to possible nonlinear or mixed rheology, if grain sizes are not lower than 0.1 mm and flow conditions can be approximated by a constant strain rate of about 10⁻¹⁵ s⁻¹. This conclusion can be modified by different flow conditions (e.g. a decrease in strain rate or constant viscous dissipation). Furthermore, experiments on fine-grained garnetites and perovskite analogues have shown that diffusion creep is predominant at laboratory conditions. However, the pressure dependence of creep in these phases is unknown, and therefore direct extrapolation to lower mantle conditions is necessarily speculative. Lateral variations of viscosity, largest in the upper and lowermost mantle (up to 2–4 orders of magnitude) are predicted by models based on lateral temperature anomalies derived from seismic tomographic models.