The effects of large and small-scale topography upon internal waves and implications for tidally induced mixing in sill regions

A free surface non-hydrostatic model in a cross-sectional form, namely, two-dimensional, in the vertical is used to examine the role of larger-scale topography, namely, sill width, and smaller scale topography, namely, ripples on the sill upon internal wave generation and mixing in sill regions. The present work is set in the context of earlier work and the wider literature in order to emphasise the problems of simulating mixing in hydrographic models. Highlights from previous calculations and references to the literature for detail, together with new results presented here with smooth and “ripple” topography, are used to show that an idealised cross-sectional model can reproduce the dominant features found in observations at the Loch Etive sill. Calculations show that on both the short and long time scales, the presence of small-scale “ripple” topography influence the mixing and associated Richardson number distribution in the sill region. Subsequent calculations in which the position and form of the small-scale sill topography is varied show for the first time that it is the small-scale topography near the sill crest that is particularly important in enhancing mid-water mixing on the lee side of the sill. Both short-term and longer-term calculations with a reduced sill width and associated time series show that as the sill width is reduced, the non-linear response of the system increases. In addition, Richardson number plots show that the region of critical Richardson number, and hence enhanced mixing, increases with time and a reduction in sill width. Calculations in which buoyancy frequency N varies through the vertical show that buoyancy frequency close to the top of the sill is primarily controlling mixing rather than its mean value. Hence, a Froude number based on sill depth and local N is the critical parameter rather than one based on total depth and mean N.     

Effect of coastal boundary resolution and mixing upon internal wave generation and propagation in coastal regions

A non-linear two-dimensional vertically stratified cross-sectional model of a constant depth basin without rotation is used to investigate the influence of vertical and horizontal diffusion upon the wind-driven circulation in the basin and the associated temperature field. The influence of horizontal grid resolution, in particular the application of an irregular grid with high resolution in the coastal boundary layer is examined. The calculations show that the initial response to a wind impulse is downwelling at the downwind end of the basin with upwelling and convective mixing at the opposite end. Results from a two-layer analytical model show that the initial response is the excitation of an infinite number of internal seiche modes in order to represent the initial response which is confined to a narrow near coastal region. As time progresses, at the downwind end of the basin a density front propagates away from the boundary, with the intensity of its horizontal gradient and associated vertical velocity determined by both horizontal and vertical viscosity values. Calculations demonstrate the importance of high horizontal grid resolution in resolving this density gradient together with an accurate density advection scheme. The application of an irregular grid in the horizontal with high grid resolution in the nearshore region enables the initial response to be accurately reproduced although physically unrealistic short waves appear as the frontal region propagates onto the coarser grid. Parameterization of horizontal viscosity using a Smagorinsky-type formulation acts as a selective grid size-dependent filter, and removes the short-wave problem although enhanced smoothing can occur if the scaling coefficient in the formulation is too large. Calculations clearly show the advantages of using an irregular grid but also the importance of using a grid size-dependent filter to avoid numerical problems.     

On the influence of stratification and tidal forcing upon mixing in sill regions

A cross-sectional non-hydrostatic model with idealized topography was used to examine the processes influencing tidal mixing in the region of sills. Initial calculations with appropriate parameters for the sill at the entrance to Loch Etive showed that the model could reproduce the main features of the observed mixing in the region. In particular, the hydraulic jump in the sill region was reproduced, as was an intense mid-water jet that was observed to separate from the lee side of the sill. Shear instabilities associated with the jet appeared to be a source of mixing within the thermocline. In addition, internal lee waves were generated on the lee side of the sill, with the observed amplification because of trapping during the flood stage. Their magnitude and hence the mixing increased with increasing Froude number (F _r). In the case of vertically varying buoyancy frequency, its value near the sill top determined the F _r number, with its value below influencing internal waves magnitude at depth. At high F _r values particularly with strong currents, short waves and overturning occurred.     

Tidal mixing in sill regions: influence of sill depth and aspect ratio

A non-hydrostatic model in cross-sectional form with an idealized sill is used to examine the influence of sill depth (h _s) and aspect ratio upon internal motion. The model is forced with a barotropic tide and internal waves and mixing occurs at the sill. Calculations using a wide sill and quantifying the response using power spectra show that for a given tidal forcing namely Froude number F _r as the sill depth (h _s) increases the lee wave response and vertical mixing decrease. This is because of a reduction in across sill velocity U _s due to increased depth. Calculations show that the sill Froude number F _s based on sill depth and across sill velocity is one parameter that controls the response at the sill. At low F _s (namely F _s ≪ 1) in the wide sill case, there is little lee wave production, and the response is in terms of internal tides. At high F _s, calculations with a narrow sill show that for a given F _s value, the lee wave response and internal mixing increase with increasing aspect ratio. Calculations using a narrow sill with constant U _s show that for small values of h _s, a near surface mixed layer can occur on the downstream side of the sill. For large values of h _s, a thick well-mixed bottom boundary layer occurs due to turbulence produced by the lee waves at the seabed. For intermediate values of h _s, “internal mixing” dominates the solution and controls across thermocline mixing.     

Non-hydrostatic and non-linear contributions to the internal wave energy flux in sill regions

A three-dimensional non-linear, non-hydrostatic model in cross-sectional form is used to determine the factors influencing the relative importance of the linear, non-hydrostatic and non-linear contributions to the internal wave energy flux in sill regions due to tidal forcing. The importance of the free surface elevation term is also considered. Idealised topography representing the sill at the entrance to Loch Etive, the site of a recent measurement programme, is used. Calculations show that the non-linear terms in the energy flux become increasingly important as the sill Froude Number (F _s) increases and the sill aspect ratio is increased. The vertical profile of the stratification, in particular its value close to the sill crest where internal waves are generated, has a significant influence on unsteady lee wave and mixed tidal–lee wave generation and the non-linear contribution to the energy flux. Calculations show that as F _s increases, the energy flux due to the non-linear and non-hydrostatic terms increases more rapidly than the linear term. The importance of the non-linear terms in the energy flux also increases as the sill aspect ratio is increased. Increasing the buoyancy frequency reduces the contribution of the non-hydrostatic and non-linear terms to the total energy flux. Also, as the buoyancy frequency is increased, this reduces unsteady lee wave and mixed tidal–lee wave generation. In essence, these calculations show that the energy flux due to the non-hydrostatic and non-linear terms is appreciable in sill regions.     

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.     

On the importance of non-hydrostatic processes in determining tidally induced mixing in sill regions

The importance of using a non-hydrostatic model to compute tidally induced mixing and flow in the region of a sill is examined using idealized topography representing the sill at the entrance to Loch Etive. This site is chosen since detailed measurements were recently made there. Calculations are performed with and without the inclusion of non-hydrostatic dynamics using a vertical slice model for a range of sill widths corresponding to typical sill regions. Initial non-hydrostatic calculations showed that the model could reproduce the observed flow characteristics in the region. However, when calculations were performed using the model in hydrostatic form, the significant artificial convective mixing that occurred in order to remove density inversions led to excessively high vertical mixing. This influenced the computed temperature field and the intensity of the current jet that separated from the sill on its lee side. In addition it affected the magnitude and spatial characteristics of the lee waves generated on the lee side of the sill. Calculations with a range of sill widths, showed that as the sill width decreased the difference between the solution computed with the non-hydrostatic and hydrostatic model increased.     

Influence of open boundary conditions and sill height upon seiche motion in a gulf

A cross-sectional model of an idealised constant depth gulf with a sill at its entrance, connected to a deep ocean, is used to examine the barotropic and baroclinic response of the region to wind forcing. The role of the oceanic boundary condition is also considered. Calculations show that in the case of a tall sill, where the pycnocline intersects the sill, the baroclinic response of the gulf is similar to that of a lake, and internal waves cannot radiate energy out of the gulf. The barotropic response shows free surface oscillations, with nodes located close to the centre of the oceanic basin and entrance to the gulf, with associated barotropic resonant periods. As the sill height is reduced, baroclinic wave energy is radiated from the gulf into the ocean, and the form of the baroclinic response changes from a standing wave (tall sill) as in a lake to a progressive wave (no sill). The location of sea surface elevation nodes and resonant periods changes as the sill height is reduced. Calculations of the barotropic resonant periods with and without stratification could not determine if they were influenced by the presence of stratification, although published analytical theory suggests that they should be able to when energy is lost from the gulf by internal wave radiation. This inability to detect changes in barotropic resonant period due to stratification effects is due to the small change in resonant frequency produced by baroclinic effects, as shown by analytical results, and the broad peak nature of the computed resonant frequency. In the case of a closed offshore boundary (an offshore island), there is a stronger and narrower energy peak at the resonant frequency than when a barotropic radiation condition is applied. However, the influence of stratification upon the resonant frequency could not be accurately determined. Although the offshore boundary was well removed from the gulf to such an extent that any baroclinic waves reflected from it could not reach the gulf within the integration period, it did, however, slightly influence the gulf baroclinic response due to its influence on the barotropic response.     

On the effect of subinertial phenomena on the internal lee waves generation in the Strait of Gibraltar

The generation of internal lee waves (ILW) in the Strait of Gibraltar takes place in the main sill where the tidal flow interacts with a submarine obstacle. The tidal flow is perturbed by subinertial phenomena of different nature summarized in the subinertial currents that can inhibit the ILW generation. The authors present an attempt to randomize the problem by the introduction of a Gaussian noise in the Taylor–Goldstein equation. The random number sets are generated from the statistical distribution of the previously isolated random part of the subinertial currents from experimental data taken in the area during the Gibraltar Experiment 94–96. The effect of the noise is translated into a continuous spreading of the spectrum around the solution of the noise-free problem. A stability analysis is carried out in order to determine the single neutral modes of oscillations and the phase space is divided onto regions of stability and instability as a function of the inflowing subinertial current. The methodology and results could be useful for the design and timing of oceanographic surveys in straits where the ILWs occur.     

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.     

Secondary flow deflection in the lee of transverse dunes with implications for dune morphodynamics and migration

Measurements of lee‐side airflow response from an extensive array of meteorological instruments combined with smoke and flow streamer visualization is used to examine the development and morphodynamic significance of the lee‐side separation vortex over closely spaced transverse dune ridges. A differential deflection mechanism is presented that explains the three‐dimensional pattern of lee‐side airflow structure for a variety of incident flow angles. These flow patterns produce reversed, along‐dune, and deflected surface flow vectors in the lee that are inferred to result in net ‘lateral diversion’ of sand transport over one dune wavelength for incident angles as small as 10° from crest‐transverse (i.e. 80° from the crest line). This lateral displacement increases markedly with incident flow angle when expressed as the absolute value of the total deflection in degrees. Reversed and multi‐directional flow occurs for incident angles between 90° and 50°. These results document the three‐dimensional nature of flow and sand transport over transverse dunes and provide empirical evidence for an oblique migration model. Copyright © 2013 John Wiley & Sons, Ltd.     

Some observations of internal wave current fluctuations at the shelf-edge and their implications for sediment transport

Observations of internal wave current fluctuations at a site on the European continental shelf are described. These have revealed current ‘pulses’ of regular tidal (M₂) phase which may be associated with internal tides generated at the shelf-edge. Current ‘pulses’ have been observed with amplitudes of 30 to 40 cm s^?1 superimposed on peak spring tidal currents of the order 60 to 70 cm s^?1. The measurements have shown that these fluctuations extended throughout the bottom mixed layer to within at least 2 m of the sea bed where they may play an important role in modifying sediment transport rates.     

Determining magma flow in sills,dykes and laccoliths and their implications for sill emplacement mechanisms

Three-dimensional seismic data from the Faeroe-Shetland Basin provides detailed information on the relationships between sills, dykes, laccoliths and contemporaneous volcanic activity. The data shows that sills are predominantly concave upwards, being complete or partial versions of radially or bilaterally symmetrical forms that possess flat inner saucers connected to a flat outer rim by a steeply inclined sheet. Such morphologies are only partially modified by pre-existing faults. Sills can be sourced from dykes or the steep climbing portions of deeper sills. Both sills and dykes can provide magma to overlying volcanic fissures and sills can be shown to feed shallow laccoliths. Magma flow patterns, as revealed by opacity rendering, suggest that sills propagate upwards and outwards away from the magma feeder. As an individual sill can consist of several leaves emplaced at different stratigraphic levels, and as a sill or dyke can provide magma to volcanic fissures, other sills and laccoliths, the data suggests that neutral buoyancy concepts may not provide a complete explanation for the mechanism and level of sill emplacement. Instead, the data suggests that the presence of lithological contrasts, particularly ductile horizons such as overpressured shales may permit sill formation at any level below the neutrally buoyant level. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. Ken Thomson–deceased, April 2007     

拟静力试验中摩擦力的影响及去除方法

土木工程拟静力试验中经常会使用到加载与反力装置,当作动器施加荷载时,作动器与反力装置之间会产生摩擦力。摩擦力会对试验结果产生影响,特别是对拟动力和混合试验需要位移在线更新的试验影响更大。然而,关于摩擦力对抗震试验影响的研究鲜有报道且去除摩擦力的方法较少。为此,本文通过理论分析研究了摩擦力对抗震试验各参数的影响,并发展了从测量数据中去除摩擦力的方法,减小摩擦力对拟静力试验的影响。     

地球介质自组织性对地震波走时和振幅的影响

本文采用随机介质描述地球内部大尺度背景场上存在的小尺度不均匀性和自组织结构;文中没有采用传统的层状网格结构,提出了块状结构来描述复杂的二维自组织结构的方法,分别以高斯型、指数型和von Karman型等自相关函数描述各向同性和各向异性非均匀分布自组织特征;采用射线追踪分析了不同分布特征自组织结构对地震波运动学和动力学特征参数的影响;结果表明,由于地球内部介质的自组织性存在,地震波射线轨迹可能发生明显的畸变; 不同偏移距处,地震反射振幅减弱或增强; 自组织结构从高斯型到von Karman型,在小尺度上表现更大的非均匀性,因此走时和振幅表征依次更强的平均效应.     

ELF wave generation in the ionosphere using pulse modulated HF heating: initial tests of a technique for increasing ELF wave generation efficiency

This paper describes the results of a preliminary study to determine the effective heating and cooling time constants of ionospheric currents in a simulated modulated HF heating, ‘beam painting’ configuration. It has been found that even and odd harmonics of the fundamental ELF wave used to amplitude modulate the HF heater are sourced from different regions of the ionosphere which support significantly different heating and cooling time constants. The fundamental frequency and its odd harmonics are sourced in a region of the ionosphere where the heating and cooling time constants are about equal. The even harmonics on the other hand are sourced from regions of the ionosphere characterised by ratios of cooling to heating time constant greater than ten. It is thought that the even harmonics are sourced in the lower ionosphere (around 65 km) where the currents are much smaller than at the higher altitudes around 78 km where the currents at the fundamental frequency and odd harmonics maximise.     

The frictional behavior of lizardite and antigorite serpentinites: Experiments,constitutive models,and implications for natural faults

Laboratory studies of the frictional behavior of rocks can provide important information about the strength and sliding stability of natural faults. We have conducted friction experiments on antigorite and lizardite serpentinites, rocks common to both continental and oceanic crustal faults. We conducted both velocity-step tests and timed-hold tests on bare surfaces and gouge layers of serpentinite at room temperature. We find that the coefficient of friction of lizardite serpentinite is quite low (0.15–0.35) and could explain the apparent low stresses observed on crustal transform faults, while that of antigorite serpentinite is comparable to other crustal rocks (0.50–0.85). The frictional behavior of both types of serpentinite is well described by a two-mechanism model combining state-variable-dominated behavior at high slip velocities and flow-dominated behavior at low velocities. The two-mechanism model is supported by data from velocity-step tests and timed-hold tests. The low velocity behavior of serpentinite is strongly rate strengthening and should result in stable fault creep on natural faults containing either antigorite or lizardite serpentinite.     

层结海洋中小振幅内行进波的演变和破碎

采用高精度的拟谱方法,数值模拟了层结海洋中小振幅内行进波的演变和破碎过程.在演变过程中,导致内波破碎的PSI不稳定机制在共振相互作用中逐渐占据主导地位,能量从初级波向低频、高波数运动缓慢传递并形成一次级波包,随即破碎发生.破碎后产生的层化湍流引起的强烈混合以及湍流间歇性可从总能量和涡度峰度随时间的变化趋势看出.我们分析了层化湍流的一些统计特性,包括动能和有效位能沿垂向波数ky的功率谱.结果表明,动能和有效位能谱都存在一个谱段满足k-3y律,且分别可表示为0.1N4k-3y和0.2N4k-3y(N为Brunt-Visl频率),通常称其为浮力子区.另外,我们分析了Cox数(湍流扩散系数与分子扩散系数之比),在层化湍流维持在一定强度时,计算结果和由海洋内区观测(远离内波强生成源和复杂地形)所推测的结论较为吻合.     

川滇及周边地区地壳横波衰减的成像研究

利用由149个台站记录的中国地震年报、四川和云南区域地震台网观测报告的5897个近震的27530条横波振幅与周期资料,反演得到川滇地区及周边的地壳衰减Q0值（频率为1 Hz时的Q值）空间分布图像、台站的场地响应以及由于介质衰减不同造成的震级偏差.结果表明,川滇及周边地区的地壳横波衰减Q0值在200～600范围内变化,平均值为400,横向变化显著.在川西-滇西北-保山地区、云贵交界-昆明-思茅地区以及海原-祁连、汾渭和东昆仑等活动块体边界带的Q0值明显较低,这些地区地震和构造活动相对活跃;而构造相对稳定的四川盆地、马尔康块体、桂西滇东断块以及鄂尔多斯、秦岭-大别等地区的Q0值则明显较高.此外,川滇地区大多数台站的场地响应都在1附近,仅有少数增益或衰减较大,达到2倍左右,且其分布无明显规律性.该区观测报告给出的大多数地震震级偏差不大于0.3,但也有少数震级偏差达0.4,其分布与介质品质因子Q0值分布相关,说明震级测定可能受地壳介质衰减横向变化的影响.     

川滇及周边地区地壳横波衰减的成像研究

利用由149个台站记录的中国地震年报、四川和云南区域地震台网观测报告的5897个近震的27530条横波振幅与周期资料，反演得到川滇地区及周边的地壳衰减Q0值（频率为1 Hz时的Q值）空间分布图像、台站的场地响应以及由于介质衰减不同造成的震级偏差.结果表明，川滇及周边地区的地壳横波衰减Q0值在200～600范围内变化，平均值为400，横向变化显著.在川西-滇西北-保山地区、云贵交界-昆明-思茅地区以及海原-祁连、汾渭和东昆仑等活动块体边界带的Q0值明显较低，这些地区地震和构造活动相对活跃；而构造相对稳定的四川盆地、马尔康块体、桂西滇东断块以及鄂尔多斯、秦岭-大别等地区的Q0值则明显较高.此外，川滇地区大多数台站的场地响应都在1附近，仅有少数增益或衰减较大，达到2倍左右，且其分布无明显规律性.该区观测报告给出的大多数地震震级偏差不大于03，但也有少数震级偏差达04，其分布与介质品质因子Q0值分布相关，说明震级测定可能受地壳介质衰减横向变化的影响.