Mechanisms of bottom boundary fluxes in a numerical model of the Shetland shelf

Across-slope bottom boundary layer (BBL) fluxes on the shelf-edge connect this region to deeper waters. Two proposed ways in which across-slope BBL fluxes can occur, in regions that have a slope current aligned to the bathymetry, are the frictional veering of bottom currents termed the ‘Ekman drain’ and through local wind-forced downwelling (wind-driven surface Ekman flow with an associated bottom flow). We investigate the variability, magnitude and spatial scale of BBL fluxes on the Shetland shelf, which has a prominent slope current, using a high-resolution (～2 km) configuration of the MITgcm model. Fluxes are analysed in the BBL at the shelf break near the 200 m isobath and are found to have a seasonal variability with high/low volume transport in winter/summer respectively. By using a multivariate regression approach, we find that the locally wind-driven Ekman transport plays no explicit role in explaining daily bottom fluxes. We can better explain the variability of the across-slope BBL flux as a linear function of the speed and across-slope component of the interior flow, corresponding to an Ekman plus mean-flow flux. We estimate that the mean-flow is a greater contributor than the Ekman flux to the BBL flux. The spatial heterogeneity of the BBL fluxes can be attributed to the mean-flow, which has a much shorter decorrelation length compared to the Ekman flux. We conclude that both the speed and direction of the interior current determines the daily BBL flux. The wind does not explicitly contribute through local downwelling, but may influence the interior current and therefore implicitly the BBL fluxes on longer timescales.     

Effect of bottom slope on the nonlinear triad interactions in shallow water

This paper aims at investigating the effect of bottom slope to the nonlinear triad interactions for irregular waves propagating in shallow water. The physical experiments are conducted in a wave flume with respect to the transformation of waves propagating on three bottom slopes (β?=?1/15, 1/30, and 1/45). Irregular waves with different type of breaking that are mechanically generated based on JONSWAP spectra are used for the test. The obviously different variations of spectra measured on each bottom reveal a crucial role of slope effect in the energy transfer between harmonics. The wavelet-based bispectrum were used to examine the bottom slope effect on the nonlinear triad interactions. Results show that the different bottom slopes which waves are propagated on will cause a significant discrepancy of triad interactions. Then, the discussions on the summed bicoherence which denote the distribution of phase coupling on each frequency further clarify the effect of bottom slope. Furthermore, the summed of the real and imaginary parts of bispectrum which could reflect the intensity of frequency components participating in the wave skewness and asymmetry were also investigated. Results indicate that the value of these parameters will increase as the bottom slope gets steeper.     

Array measurements of the bottom boundary layer and the internal wave field on the continental slope

Abstract

An array of current meters was placed on the continental slope and rise for two months in the autumn of 1970. The bottom boundary layer was penetrated on the slope. On the smallest array scale, of the order of 1 kilometer, the array functioned as a directional internal wave antenna. Moving shoreward, the current spectra show strong suppression of the inertial peak and strong enhancement of the semidiurnal tide. The measured wave number spectra show that the tidal energy is almost completely baroclinic, and probably being generated in the region where the slope becomes “critical” for the tidal period. If this area is typical of worldwide conditions, a substantial fraction of the dissipation of surface tides takes place on the continental slopes by conversion to baroclinic waves. The bottom boundary layer has been modeled by an extension of the work of Ellison (1956) to a sloping boundary in a fluid of positive stability. An equivalent constant eddy coefficient has the value 3 cm²/sec as determined from the measurements.     

Flow modelling in gravel‐bed rivers: rethinking the bottom boundary condition

A key problem in computational fluid dynamics (CFD) modelling of gravel‐bed rivers is the representation of multi‐scale roughness, which spans the range from grain size, through bedforms, to channel topography. These different elements of roughness do not clearly map onto a model mesh and use of simple grain‐scale roughness parameters may create numerical problems. This paper presents CFD simulations for three cases: a plane bed of fine gravel, a plane bed of fine gravel including large, widely‐spaced pebble clusters, and a plane gravel bed with smaller, more frequent, protruding elements. The plane bed of fine gravel is modelled using the conventional wall function approach. The plane bed of fine gravel including large, widely‐spaced pebble clusters is modelled using the wall function coupled with an explicit high‐resolution topographic representation of the pebble clusters. In these cases, the three‐dimensional Reynolds‐averaged continuity and Navier–Stokes equations are solved using the standard k ? ε turbulence model, and model performance is assessed by comparing predicted results with experimental data. For gravel‐bed rivers in the field, it is generally impractical to map the bed topography in sufficient detail to enable the use of an explicit high‐resolution topography. Accordingly, an alternative model based on double‐averaging is developed. Here, the flow calculations are performed by solving the three‐dimensional double‐averaged continuity and Navier‐Stokes equations with the spatially‐averaged 〈k ? ε〉 turbulence model. For the plane bed of fine gravel including large, widely‐spaced pebble clusters, the model performance is assessed by comparing the spatially‐averaged velocity with the experimental data. The case of a plane gravel bed with smaller, more frequent, protruding elements is represented by a series of idealized hypothetical cases. Here, the spatially‐averaged velocity and eddy viscosity are used to investigate the applicability of the model, compared with using the explicit high‐resolution topography. The results show the ability of the model to capture the spatially‐averaged flow field and, thus, illustrate its potential for representing flow processes in natural gravel‐bed rivers. Finally, practical data requirements for implementing such a model for a field example are given. Copyright © 2011 John Wiley & Sons, Ltd.     

The role of eddies on pathways,transports, and entrainment in dense water flows along a slope

Ocean Dynamics - The flow of dense water along slopes has been investigated in several numerical investigations based on the Dynamics of Overflow Mixing and Entrainment (DOME) setup. In the present...     

Barotropic instability of a boundary jet on a sloping bottom

Abstract

The stability of a shear flow on a sloping bottom in a homogeneous, rotating system was investigated by means of a laboratory experiment.

The basic flow was driven near a vertical wall of a circular container by a ring-shaped plate that contacted with a free surface of the working fluid and rotated relative to the fluid container. The velocity profile was asymmetric in the radial direction and had only one inflection point. The velocity profile was well expressed by a linear theory for the vertical shear layer.

The effect of the circular geometry was checked by comparing experimental results obtained in two fluid systems in which only the sign of the curvature was opposite and it was confirmed that circular geometry was not essential for the shear flow on the sloping bottom in this experiment.

It was found that the sloping bottom stabilizes the basic flow only when the drift direction of the topographic Rossby wave is opposite to that of the basic flow. The viscous dissipation in both the Ekman layer and the interior region was also important in determining the critical Rossby number.

The eddy fields caused by the instability can be classified into two types: One is the stationary eddy field in which a row of eddies moves along the basic flow without changing form. The other is the flow pattern in which eddies have finite life times and their configuration is not well organized. When the sloping bottom does not stabilize the basic flow, the former flow pattern is realized, otherwise the latter flow pattern appears.

The wave numbers of the eddies in the regular flow pattern were observed as a function of the Rossby number. The relation did not fit to linear preferred modes predicted by an eigenvalue problem.     

基于UPML边界条件的交替方向隐式有限差分法GPR全波场数值模拟

交替方向隐式差分(ADI-FDTD)法突破了Courand-Friedrich-Levy(CFL)条件的约束,具有无条件稳定的特点;而单轴各向异性完全匹配层(UPML)边界条件具有宽频带吸收特性,不需要对电场和磁场进行分裂,迭代公式简单,便于编程的特点.综合两者优势,本文提出了基于UPML边界条件的ADI-FDTD探地雷达数值模拟算法,通过对3个二维Maxwell方程进行离散化,推导了GPR波的ADI-FDTD及其UPML边界条件的两个子时间步的迭代差分公式,并分别给出了详细计算步骤.在此基础上,开发了相应的模拟程序,应用该程序对两个GPR模型进行了正演模拟,得到了两个正演模型的wiggle图、扫描图与全波场快照.通过分析这些雷达剖面图与波场快照,可以了解雷达波形在空间中的传播过程及变化规律,有助于雷达资料更可靠、更准确的解释.模拟结果表明,基于UPML边界条件的ADI-FDTD算法可取较大的时间步长,消除了截断边界处的强反射,能对简单与复杂GPR模型进行快速、高效模拟.     

A comparison between experimental and numerical investigations of the motion of the water surface in a model surge tank

This paper describes an investigation into the motion of the water surface in a simple model surge tank, and the relevant factors governing its behaviour. The oscillation of the free water surface is an unsteady flow problem, which is amenable to a mathematical solution using a finite difference step-by-step integration procedure. For comparison, two such methods are presented: (i) a simple initial value method and (ii) a predictor-corrector technique. Computer programs have been developed linked to a graph plotter to give a visual presentation of the numerical solutions together with the experimental results of the damped oscillation of the water surface in the model surge tank.     

Model simulations of dense bottom currents in the Western Baltic Sea

Only recently, medium intensity inflow events into the Baltic Sea have gained more awareness because of their potential to ventilate intermediate layers in the Southern Baltic Sea basins. With the present high-resolution model study of the Western Baltic Sea a first attempt is made to obtain model based realistic estimates of turbulent mixing in this area where dense bottom currents resulting from medium intensity inflow events are weakened by turbulent entrainment. The numerical model simulation which is carried out using the General Estuarine Transport Model (GETM) during nine months in 2003 and 2004 is first validated by means of three automatic stations at the Drogden and Darss Sills and in the Arkona Sea. In order to obtain good agreement between observations and model results, the 0.5×0.5$0.5\times 0.5$ nautical mile bathymetry had to be adjusted in order to account for the fact that even at that scale many relevant topographic features are not resolved. Current velocity, salinity and turbulence observations during a medium intensity inflow event through the Øresund are then compared to the model results. Given the general problems of point to point comparisons between observations and model simulations, the agreement is fairly good with the characteristic features of the inflow event well represented by the model simulations. Two different bulk measures for mixing activity are then introduced, the vertically integrated decay of salinity variance, which is equal to the production of micro-scale salinity variance, and the vertically integrated turbulent salt flux, which is related to an increase of potential energy due to vertical mixing of stably stratified flow. Both measures give qualitatively similar results and identify the Drogden and Darss Sills as well as the Bornholm Channel as mixing hot spots. Further regions of strong mixing are the dense bottom current pathways from these sills into the Arkona Sea, areas around Kriegers Flak (a shoal in the western Arkona Sea) and north–west of the island of Rügen.     

Effect of water depth and the bottom boundary layer upon internal wave generation over abrupt topography

The role of water depth and bottom boundary layer turbulence upon lee-wave generation in sill regions is examined. Their effect upon vertical mixing is also considered. Calculations are performed using a non-hydrostatic model in cross-section form with a specified tidal forcing. Initial calculations in deeper water and a sill height such that the sill top is well removed from the surrounding bed region showed that downstream lee-wave generation and associated mixing increased as bottom friction coefficient k increased. This was associated with an increase in current shear across the sill. However, for a given k, increasing vertical eddy viscosity A _v reduced vertical shear in the across sill velocity, leading to a reduction in lee-wave amplitude and associated mixing. Subsequent calculations using shallower water showed that for a given k and A _v, lee-wave generation was reduced due to the shallower water depth and changes in the bottom boundary layer. However, in this case (unlike in the deepwater case), there is an appreciable bottom current. This gives rise to bottom mixing which in shallow water extends to mid-depth and enhances the mid-water mixing that is found on the lee side of the sill. Final calculations with deeper water but small sill height showed that lee waves could propagate over the sill, thereby reducing their contribution to mixing. In this case, bottom mixing was the major source of mixing which was mainly confined to the near bed region, with little mid-water mixing.     

Retrospective assessment of bottom sediment condition in the Vygozero Reservoir

The results of long-term observations of the chemical composition of bottom sediments in the Vygozero Reservoir are presented. They revealed the main regularities in variation of the composition, sediment properties, and the present condition of bottom sediments. As shown, changes in the environmental conditions in the area of Vygozero influenced the processes of sedimentogenesis in the water body.     

On the Leontovich boundary condition in geoelectromagnetism

The paper is dedicated to the 70th anniversary of the formulation of the Leontovich impedance boundary condition. This boundary condition is applied in geophysics for sounding of the lithosphere and diagnostics of the magnetosphere by electromagnetic waves. The use of the Leontovich condition is shown to open new possibilities for investigating the anharmonicity of MHD oscillations of the magnetosphere. The differential impedance equation, which is derived with the aid of the Leontovich boundary condition, can prove useful in the investigation of the electroconductivity of the lithosphere by the method of inductive sounding. It is shown within the framework of a simple model that the method of the Leontovich parabolic equation makes it possible to find a correction to the Leontovich boundary condition caused by the fact that, in general, the relation between the horizontal components of an electromagnetic field is not local. It is shown that the anharmonicity of MHD oscillations of the magnetosphere coupled with the nonlocality of the boundary condition on the Earth’s surface can lead to an apparent nonlinearity of the surface impedance calculated in accordance with the classical technique of magnetotelluric sounding.     

An experimental study of the effects of the upper boundary condition on the thermal convection in a rotating,differentially heated cylindrical annulus of water

Abstract

The effects of the upper boundary condition on the regime diagram and certain characteristics of the convection within a rotating, differentially heated cylindrical anulus of water were studied in the laboratory. It was found that the regime diagram was not substantially affected by the upper boundary condition. However, the thermal amplitude of the baroclinic waves, as a function of parameter space, and, as expected from previous work, the angular drift velocity of those waves were found to be strongly affected by the upper boundary condition. When the upper surface was free, the amplitude changes were explosive and highly non-linear (as discovered earlier by Kaiser, 1970). When the upper surface was rigid, they were smooth and quite linear. The baroclinic wave patterns drifted round the annulus at rates which were in direct response to the imposed “thermal wind”. However, (as previously observed by Koschmieder, 1972), when the upper surface was rigid they drifted approximately ten times more slowly than when it was free.     

Effects of bottom slope, flocculation and hindered settling on the coupled dynamics of currents and suspended sediment in highly turbid estuaries, a simple model

This study aims at gaining basic understanding about two specific phenomena that are observed in the highly turbid estuaries tidal Ouse, Yangtze and Ems, i.e. (1) the accumulation of suspended matter in the deeper parts of the estuaries and (2) the relatively high values of turbidity near the surface in the area of the turbidity maximum. A semi-analytical model is analysed to verify the hypothesis that these phenomena result from bottom slope-induced turbidity currents and from hindered settling, respectively. The model governs the dynamics of residual flow, driven by fresh water discharge, salinity gradients and turbidity gradients. It further uses the condition of morphodynamic equilibrium (no divergence of net sediment transport) to compute the residual sediment concentration. New aspects are that depth variations on flow and mixing processes, as well as flocculation and hindered settling of sediment, are explicitly accounted for. Tides act as a source of mixing and erosion of sediment only, thus processes like tidal pumping are not considered. Model results show that the estuarine turbidity maximum (ETM) shifts in the down-slope direction, compared to the case of a constant depth. Slope-induced turbidity currents, which are directed down-slope near the bottom and up-slope near the surface, are responsible for this shift, thereby confirming the first part of the hypothesis above. The down-slope shift of the ETM is reduced by currents resulting from gradients in depth-dependent mixing, which counteract turbidity currents, but which are always weaker. Including flocculation and hindered settling yields increased surface sediment concentrations in the area of the turbidity maximum, compared to the situation of a constant settling velocity, thereby supporting the second part of the hypothesis. Sensitivity experiments reveal that the conclusions are not sensitive to the values of the model parameters.     

Antarctic bottom water fluctuations in the Vema Channel: Effects of velocity changes on particle alignment and size

The anisotropy of magnetic susceptibility (AMS) and mean particle size in the silt fraction have been measured in surface sediments and down selected cores from the Vema Channel. Results show that a function (F_s) which represents magnetic grain long axis alignment is highly correlated with variation in mean size of the silt fraction. An increase in alignment is caused by an increase in bottom water velocity which corresponds to an increase in mean particle size. Best alignments and coarsest particle sizes are found in the axis of the Vema Channel. In contrast, poor particle alignment and fine silt mean characteristics the shallower region east of the channel axis, consistent with lower current velocities.Core CH 115-61 was collected near the Level of Least Motion at the transition between northward-flowing Antarctic Bottom Water (AABW) and southward-flowing North Atlantic Deep Water. A positive relationship exists between silt size and AMS in the core. Fluctuations in particle alignment and mean silt size indicate three or four periods of increased velocity during the past 150,000 years.Geographic orientation of the maximum AMS axes in cores CH 115-60 and -61 was accomplished using the declination of remanent magnetism and an axial dipole as the reference azimuth. The data show that the larger magnetic grains in these sediments are aligned normal to the bathymetric trend of the channel which suggests that these grains are aligned by traction transport. The result indicates that AABW in the Vema Channel has flowed along an azimuth of approximately N30°E for the past 150,000 years.     

铁路重力式桥墩墩底局部加密纵筋高度研究

为研究墩底加密纵筋高度对铁路重力式桥墩抗震性能的影响,提出加密纵筋高度的确定原则,推导纵筋加密高度计算公式.设计5个不同加密纵筋类型的桥墩,通过数值分析研究桥墩的滞回曲线和骨架曲线,对比分析墩底加密纵筋后桥墩的抗震性能.研究结果表明:墩底局部加密纵向钢筋可有效提高桥墩的承载能力;桥墩抗震设计验算时截面配筋率可取墩底纵筋加密后的截面配筋率;数值分析结果验证纵筋加密高度计算公式的合理性.研究成果可为铁路重力式桥墩抗震设计提供有价值的参考.     

Variability of dense water formation in the Ross Sea

This paper presents results from a model study of the interannual variability of high salinity shelf water (HSSW) properties in the Ross Sea. Salinity and potential temperature of HSSW formed in the western Ross Sea show oscillatory behaviour at periods of 5–6 and 9 years superimposed on long-term fluctuations. While the shorter oscillations are induced by wind variability, variability on the scale of decades appears to be related to air temperature fluctuations. At least part of the strong decrease of HSSW salinities deduced from observations for the period 1963–2000 is shown to be an aliasing artefact due to an undersampling of the periodic signal. While sea ice formation is responsible for the yearly salinity increase that triggers the formation of HSSW, interannual variability of net freezing rates hardly affects changes in the properties of the resulting water mass. Instead, results from model experiments indicate that the interannual variability of dense water characteristics is predominantly controlled by variations in the shelf inflow through a sub-surface salinity and a deep temperature signal. The origin of the variability of inflow characteristics to the Ross Sea continental shelf can be traced into the Amundsen and Bellingshausen Seas. The temperature anomalies are induced at the continental shelf break in the western Bellingshausen Sea by fluctuations of the meridional transport of circumpolar deep water with the eastern cell of the Ross Gyre. In the Amundsen Sea, upwelling due to a persistently cyclonic wind field carries the signal into the surface mixed layer, leading to fluctuations of the vertical heat flux, anomalies of brine release near the sea ice edge, and consequently to a sub-surface salinity anomaly. With the westward flowing coastal current, both the sub-surface salinity and deep temperature signals are advected onto the Ross Sea continental shelf. Convection carries the signal of salinity variability into the deep ocean, where it interacts with modified circumpolar deep water upwelled onto the continental shelf as the second source water mass of HSSW. Sea ice formation on the Ross Sea continental shelf thus drives the vertical propagation of the signal rather than determining the signal itself.     

A numerical model of the wave boundary layer

A numerical model of deep, uniform, oscillatory, rough-turbulent boundary-layer flow is described. The model is based upon the governing horizontal momentum equation and a closure scheme involving the turbulent-energy equation and various turbulence-scaling laws. Finite difference solutions of these equations are obtained for a range of values of the ‘relative roughness’ (A₀/k_s), whereA₀ is the excursion amplitude of the water particles in the free-stream flow andk_s is the ‘equivalent bed roughness’. Typical vertical profiles of horizontal velocity, turbulence energy and eddy viscosity, and time-series of the bed shear stress are presented. The model results are then used to determine the wave drag coefficient, boundary-layer thickness and phase lead of the bed shear stress over the free-stream velocity, each as a function ofA₀/k_s. These results are shown to be in generally good agreement with previous experimental and theoretical results. Finally, the model is used to test for the existence of a universal velocity distribution for uniform oscillatory (sinusoidal) rough-turbulent flow. The ‘law of the wall’ and the ‘defect law’ proposed by Jonsson (1980, Ocean Engineering, 7, 109–152) are well supported by the model, and the existence of a logarithmic ‘velocity overlap layer’ in which both of these laws are valid is demonstrated forA_o/k_s30.