General velocity formula of boundary layer above mobile sediment bed induced by asymmetric waves

Sediment movement in the wave boundary layer above a mobile sediment bed is complex.A velocity formula for the boundary layer is proposed for sheet flow induced by asymmetric waves above a mobile sediment bed.The formula consists of a free stream velocity and a defect function which contains a phase-lead,boundary layer thickness and mobile sediment bed.Phase-lag of sediment movement is considered in the formula for the mobile sediment bed.The formula needs six dependent variables about asymmetric wave and sediment characteristics.Asymmetry effects on parameters(orbital amplitude,roughness height,bed shear stress,and boundary layer thickness)are properly considered such that the formula can yield velocity differences among onshore,offshore,acceleration,and deceleration stages.The formula estimates the net boundary layer velocity resulting from the mobile sediment bed and asymmetric boundary layer thickness.In addition,a non-constant phase-lead also contributes to the net boundary layer velocity in asymmetric oscillatory sheet flow.Results of the formula are as good as that of a two-phase numerical model.Sheet flow transport induced by asymmetric waves,and the offshore net sediment transport rate with a large phase-lag under velocity-skewed waves,can be adequately estimated by the formula with a power sediment concentration function.     

中国中原地区随县—安阳剖面深地震测深资料的解释

本文描述随县—安阳剖面深地震测深资料分析解释的初步结果。资料处理结果说明,本地区的莫霍界面埋深约28至36km,其上覆盖层(即地壳)的平均速度约6.24km/s,在新郑和淇县一带该界面埋藏较深。在地表附近沉积层速度约3.50km/s左右,在黄河地区该层厚度最大,约5.5km。而在测线南端的大片地区花岗岩出露地表。该沉积层的下侧是结晶基底,其顶面的首波速度为6.00km/s。在它与莫霍面之间还可分出三层,其相应震相为P₂,P0₃和P0₄,其中P0₃较为稳定,它是地壳内部的反射波震相,平均速度约5.97km/s,深度为18至23km。本文得出了这几层的深度变化剖面图。并发现在新郑与新乡间黄河流经的地区,地壳内速度的横向变化及梯度层的分布情况有其明显特点。从对其他震相的分析,还获得新乡以南沉积层内的速度分布及舞阳附近的断层位置,并表明在本区上地幔内存在高速夹层的可能性。      

Power-law velocity profile in turbulent boundary layers: An integral reynolds-number dependent solution

Geophysical flows of practical interest encompass turbulent boundary layer flows. The velocity profile in turbulent flows is generally described by a log- or a power-law applicable to certain zones of the boundary layer, or by wall-wake law for the entire zone of the boundary layer. In this study, a novel theory is proposed from which the power-law velocity profile is obtained for the turbulent boundary layer flow. The new power-law profile is based on the conservation of mass and the skin friction within the boundary layer. From the proposed theory, analytical expressions for the power-law velocity profile are presented, and their Reynolds-number dependency is highlighted. The velocity profile, skin friction coefficient and boundary layer thickness obtained from the proposed theory are validated by the reliable experimental data for zero-pressure gradient turbulent boundary layers. The expressions for Reynolds shear stress and eddy viscosity distributions across the boundary layer are also obtained and validated by the experimental data.     

Approximate velocity formula over mobile sediment bed induced by velocity-skewed waves and current

A velocity formula is proposed for flow over a mobile sediment bed induced by velocity-skewed waves and current. The formula is obtained by a separation of waves and current velocities and requires seven free variables related to free stream velocity and sediment characteristics. The formula includes two parts:(1) a wave part consisting of the free stream velocity and defect function, which considers phase lead, wave boundary layer thickness, and mobile bed level, and(2) a current part, which ch...     

Experimental investigation of the impacts of coherent flow structures upon turbulence properties in regions of crescentic scour

This study examines the spatial distributions of third‐order moments of velocity fluctuations, the turbulent kinetic energy (TKE) fluxes, and the conditional statistics of Reynolds shear stress across the equilibrium crescentic scour structures generated upstream of short horizontal static cylinders. Detailed velocity data were collected using three‐dimensional (3D) micro‐acoustic Doppler velocimeter (ADV) across and within the equilibrium scour marks. The analysis reveals that the positive and negative values of third‐order moments associated with the level bed surface and the scour holes are directly related to coherent structures. The components of TKE flux are discussed for the near‐bed region of the level bed surface and scour holes in relation to sweep–ejection events. A cumulant‐discard method is applied to the Gram‐Charlier probability distribution of two variables to describe the statistical properties of the term u′w′. The conditional statistics of the Reynolds shear stress show a good agreement with the experimental data. The distribution of the joint probability density function in the near‐bed region changes cyclically along the scour hole depending on the bottom fluid velocity, which implies a change from upward to downward flux of momentum and vice versa. Both the ejection and sweep events at near‐bed points on the level surface are more important than within the scour region; and in contrast, both events are stronger for the scour marks than the level bed surface at the outer layer. Sweeps dominate over ejections for the scour hole induced by smaller diameter and ejections dominate for larger diameter. Copyright © 2013 John Wiley & Sons, Ltd.     

Breakdown of boundary layers: (i) on moving surfaces; (ii) in semi-similar unsteady flow; (iii) in fully unsteady flow

Abstract

The breakdown and separation or reattachment of boundary layers adjoining a mainstream are studied in the three related situations (i)-(iii) of the title. For (i) the classical steady boundary layer generally admits a logarithmic singularity in the displacement when breakdown occurs on a downstream-moving surface whereas the corresponding singularity for an upstream-moving surface can be logarithmic or of minus-one-sixth form. Conversely, the breakdown can be delayed to the onset of zero mainstream flow, in which case the displacement singularity is again logarithmic. In certain flows these singularities prove to be removable locally, yielding a breakaway separation or reattachment and including the first known successes of a classical strategy in describing large-scale separation. Other flows, by contrast, require an interactive strategy. Again, even on a fixed surface a breakdown different from Goldstein's can be produced if there is a moving section of surface further upstream. The application to (ii), semi-similar unsteady boundary layers, e.g. near an impulsively started wedge-like trailing edge, then follows readily and predicts analogous forms of singularity. The corresponding singularity in displacement predicted for fully unsteady classical boundary layers, (iii), occurs within a finite time and, like (i) (usually) and (ii), a three-tiered breakdown is involved at first. Subsequently interaction comes into play. Comparisons with numerical and/or earlier work are noted. In all three situations (i)-(iii), although the dynamics involved near breakdown, separation or reattachment are predominantly inviscid, the presence of small viscosity is of significance in enforcing smoothness of the local velocity profiles.     

Numerical simulation of internal solitary wave—induced reverse flow and associated vortices in a shallow,two-layer fluid benthic boundary layer

The wave-induced velocity and pressure fields beneath a large amplitude internal solitary wave of depression propagating over a smooth, flat, horizontal, and rigid boundary in a shallow two-layer fluid are computed numerically. A numerical ocean model is utilised, the set-up of which is designed and tuned to replicate the previously published experimental results of Carr and Davies (Phys Fluids 18(1):016,601–1–016,601–10, 2006). Excellent agreement is found between the two data sets and, in particular, the numerical simulation replicates the finding of a reverse flow along the bed aft of the wave. The numerically computed velocity and pressure gradients confirm that the occurrence of the reverse flow is a consequence of boundary layer separation in the adverse pressure gradient region. In addition, vortices associated with the reverse flow are seen to form near the bed.     

Bed load transport by bed form migration

A theoretically-based methodology is presented for the determination of bed load transport from high-resolution measurements of bed surface elevations for steady-state or developing dunes. The methodology is based on the general form of the Exner equation for sediment continuity and requires information on the distribution of sediment volume concentration as well as the migration velocity of bed layers. In order to determine layer speeds, a new method based on cross-correlation analysis of elevation slices is proposed. The methodology is tested using artificially-created data as well as data from a physical model and from a flume study of developing bed forms. The analyses show the applicability of the method to determine bed load transport without the need to introduce assumptions about the form of the migrating surface. It is shown that predicted transport rates match measured or theoretical transport rates for steadily moving bed forms of an arbitrary shape. The method can also be used to predict transport rates over deforming bed forms, with the reasons for potential deviations between predicted and measured or theoretical transport rates for deforming bed forms identified and discussed. It is further shown that a simplified bulk-surface approach, that is relatively straightforward to apply and in which it is assumed that bed-layer velocity is constant with depth, gives results that are comparable to analyses based on determined bed-layer velocity variation with depth.     

Comparison of a simple planetary boundary layer model with measurements of a turbulent boundary layer under pack ice

A simple analytical theory which describes the motion in a turbulent planetary boundary layer near a rough sea bed by using a two-layer eddy viscosity model is presented. The vertical structure of the current in the boundary layer is presented, and comparisons are made with data fromMcPhee and Smith (1976, Journal of Physical Oceanography,6, 696–711) obtained from measurements of the turbulent boundary layer under drifting Arctic ice.     

Wave-induced steady streaming,mass transport and net sediment transport in rough turbulent ocean bottom boundary layers

The interaction between two important mechanisms which causes streaming has been investigated by numerical simulations of the seabed boundary layer beneath both sinusoidal waves and Stokes second order waves, as well as horizontally uniform bottom boundary layers with asymmetric forcing. These two mechanisms are streaming caused by turbulence asymmetry in successive wave half-cycles (beneath asymmetric forcing), and streaming caused by the presence of a vertical wave velocity within the seabed boundary layer as earlier explained by Longuet-Higgins. The effect of wave asymmetry, wave length to water depth ratio, and bottom roughness have been investigated for realistic physical situations. The streaming induced sediment dynamics near the ocean bottom has been investigated; both the resulting suspended load and bedload are presented. Finally, the mass transport (wave-averaged Lagrangian velocity) has been studied for a range of wave conditions. The streaming velocities beneath sinusoidal waves (Longuet-Higgins streaming) is always in the direction of wave propagation, while the streaming velocities in horizontally uniform boundary layers with asymmetric forcing are always negative. Thus the effect of asymmetry in second order Stokes waves is either to reduce the streaming velocity in the direction of wave propagation, or, for long waves relative to the water depth, to induce a streaming velocity against the direction of wave propagation. It appears that the Longuet-Higgins streaming decreases as the wave length increases for a given water depth, and the effect of wave asymmetry can dominate, leading to a steady streaming against the wave propagation. Furthermore, the asymmetry of second order Stokes waves reduces the mass transport (wave-averaged Lagrangian velocity) as compared with sinusoidal waves. The boundary layer streaming leads to a wave-averaged transport of suspended sediments and bedload in the direction of wave propagation.     

Under-ice seiches

A closed, ice-covered water body containing water with homogeneous density distribution is considered. No-slip conditions are specified for flow velocity at the lower ice boundary and on the bed. Two variants of boundary conditions are considered on the side boundary: the boundary is either a solid vertical wall with a finite liquid depth or the liquid wedges out to zero depth values. Ice either is attached fast to the shore or is separated from it by an open-water zone. A basic fourth order equation is derived for the amplitude of ice oscillations. The introduction of friction results in the appearance of reduced depth. Eigenvalue problem is considered for evaluating seiche periods. For the case when the liquid wedges out at the shore, the basic equation becomes singular at water body boundaries. A lake with a longitudinal depth profile, which can be approximated by a parabola, is considered. The solution is found by the method of matched asymptotic expansions. In the inner domain, beyond the boundary layers, the equation is reduced to Legendre equation, which yields a new relationship for the spectrum of seiche oscillations both in the presence of ice and in an open lake with varying depth. Boundary layers appear at the margins of the lake, where the liquid wedges out; a solution is found for these layers.     

Layer-stripping reverse-time migration1

We present a layer-stripping method of migration for irregularly layered media in which first-order velocity discontinuities separate regions of constant or smoothly varying velocity. We use the reverse-time method to migrate seismic data layer by layer, from the surface downwards. As part of the migration of a given layer, the bottom boundary of the layer is defined based on power in the migrated signal, and a seismic section is collected along it. This new section serves as the boundary condition for migration in the next layer. This procedure is repeated for each layer, with the final image formed from the individual layer images. Layer-stripping migration consists of three steps: (1) layer definition, (2) wavefield extrapolation and imaging, and (3) boundary determination. The migration scheme when used with reverse-time extrapolation is similar to datuming with an imaging condition. The reverse-time method uses an explicit fourth-order time, tenth-order space, finite-difference approximation to the scalar wave equation. The advantages of layer-stripping reverse-time migration are: (1) it preserves the benefits of the reverse-time method by handling strong velocity contrasts between layers and steeply dipping structures; (2) it reduces computer memory and saves computation time in high-velocity layers, and (3) it allows interpretational control of the image. Post-stack layer-stripping reverse-time migration is illustrated with a synthetic CMP data example. Prestack migration is illustrated with a synthetic data set and with a marine seismic reflection profile across the Santa Maria Basin and the Hosgri Fault in central California.     

Refraction of elastic waves into a medium of lower velocity — Pseudospherical waves

Summary An irregular wave group (here called pseudospherical), the existence of which is connected with the velocity boundary at which the velocity decreases discontinuously, is investigated. A schlieren modelling device was chosen for a model investigation of this wave since it permits the investigation of wave fields inside the measured models. The model consisted of two layers of transparent gels, the source lay in the layer of higher velocity. The measurements have shown that an irregular wave in the layer of lower velocity exists only in a certain region along the boundary; its wave front has a spherical form and its intensity decreases rapidly with increasing distance of the source from the boundary. The wave always comes only after the regular refracted wave which conforms with the ray theory. These properties correspond to the properties of a wave first described byOtt [1]³) andBrekhovskikh [2]. In the conclusion of the present paper the possibilities of recording pseudospherical waves in seismology are outlined.     

On the use of horizontal acoustic Doppler profilers for continuous bed shear stress monitoring

Continuous monitoring of bed shear stress in large river systems may serve to better estimate alluvial sediment transport to the coastal ocean.Here we explore the possibility of using a horizontally deployed acoustic Doppler current profiler(ADCP) to monitor bed shear stress,applying a prescribed boundary layer model,previously used for discharge estimation.The model parameters include the local roughness length and a dip correction factor to account for sidewall effects.Both these parameters depend on river stage and on the position in the cross-section, and were estimated from shipborne ADCP data.We applied the calibrated boundary layer model to obtain bed shear stress estimates over the measuring range of the HADCP.To validate the results,co-located coupled ADCPs were used to infer bed shear stress,both from Reynolds stress profiles and from mean velocity profiles. From HADCP data collected over a period of 1.5 years,a time series of width profiles of bed shear stress was obtained for a tidal reach of the Mahakam River,East Kalimantan,Indonesia.A smaller dataset covering 25 hours was used for comparison with results from the coupled ADCPs.The bed shear stress estimates derived from Reynolds stress profiles appeared to be strongly affected by local effects causing upflow and downflow,which are not included in the boundary layer model used to derive bed shear stress with the horizontal ADCP.Bed shear stresses from the coupled ADCP are representative of a much more localized flow,while those derived with the horizontal ADCP resemble the net effect of the flow over larger scales.Bed shear stresses obtained from mean velocity profiles from the coupled ADCPs show a good agreement between the two methods,and highlight the robustness of the method to uncertainty in the estimates of the roughness length.     

Fine upper crustal structure of Jiashi strong earthquake swarm region in Xinjiang inferred from high resolution seismic refraction profile data

Introduction Jiashi-Artux area in southwest Xinjiang is one of the most active earthquake provinces at pre-sent in Chinese mainland. In the last century, about 3/4 strong earthquakes in Chinese mainland hit this area, and especially from January 21 to April 16 in 1997, 7 earthquakes with the magnituderanging from 6.0 to 6.9 occurred in a very small area of 9 km×18 km near Jiashi (ZHU et al, 1998). It has never taken place before in Chinese mainland that a series of strong earthquakes shoo…     

青藏高原岩石圈多层构造应力场

青藏高原构造应力场可按岩石圈下层、多震层和浅层地壳区分为三层。除了震源机制解方法和井孔原地测量方法可分别用于推测多震层和浅层的应力状况外,还可根据下层塑性流动网络,采用平分网络共轭角的方法估计下层的应力方向。对比岩石圈下层与上层(多震层)的构造应力场,其结果表明: 由于板块边缘驱动力主要通过下层的网络状流动实现其远程传递,故在总体作用趋势上,上层的应力方向受控于下层;又由于高原靠近喜马拉雅驱动边界,部分驱动力直接沿上层传递,致使局部地区上、下层应力方向相差显著。     

Laboratory measurements of vortex-induced sediment pickup rates

In the present study,vortices were generated in open channel flow with a cross-flow cylinder installed horizontally near the bed.Sediment pickup rates were then measured over the channel bed downstream the cylinder using a sediment lift.The experimental data show that the pickup rate increases exponentially in the presence of vortices.Two different relationships can be clearly observed between the pickup rate and the maximum root-mean-square (rms) value of the streamwise velocity fluctuation,one for the cylinder-obstructed flow and the other for the unobstructed flow.The results imply that the vortex-induced sediment pickup cannot be explained based on the traditional boundary layer theory.     

BED SHEAR IN EVOLVING SCOUR AT A CYLINDER:A THEORETICAL APPROACH

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