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.     

Turbulence in the presence of internal waves in the bottom boundary layer of the California inner shelf

Turbulence measurements were collected in the bottom boundary layer of the California inner shelf near Point Sal, CA, for 2 months during summer 2015. The water column at Point Sal is stratified by temperature, and internal bores propagate through the region regularly. We collected velocity, temperature, and turbulence data on the inner shelf at a 30-m deep site. We estimated the turbulent shear production (P), turbulent dissipation rate (ε), and vertical diffusive transport (T), to investigate the near-bed local turbulent kinetic energy (TKE) budget. We observed that the local TKE budget showed an approximate balance (P?≈?ε) during the observational period, and that buoyancy generally did not affect the TKE balance. On a finer resolution timescale, we explored the balance between dissipation and models for production and observed that internal waves did not affect the balance in TKE at this depth.     

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.     

S wave attenuation based on Stokes boundary layer

Biot theory was based on two ideas: the coupling factor to quantify the kinetic energy of fluid and Darcy permeability to quantify the dissipation function. As Biot theory did not well predict attenuation of ultrasonic S wave, we modify the theory to better characterize the S wave attenuation. The range of the coupling factor is at first estimated in view of fluid mechanics. Application of the original theory to water-saturated Boise sandstone and brine-saturated Berea sandstone shows that the model prediction significantly underestimates the S wave attenuation ultrasonically measured. For this reason, we replace Darcy permeability with variable permeability to improve the fluid momentum equation. The new model yields predictions of phase velocity and the quality factor both close to the ultrasonic measurements. The reason why the improved model is superior to Biot theory is that variable permeability is based on the Stokes boundary layer at the fluid–solid interface, thus accurately quantifying the viscous stress between the two phases. Finally, the length scale of the viscous stress is calculated in the mesoscopic sense.     

The boundary layer of the residence time field

The residence time of a tracer in a control domain is usually computed by releasing tracer parcels and registering the time when each of these tracer parcels cross the boundary of the control domain. In this Lagrangian procedure, the particles are discarded or omitted as soon as they leave the control domain. In a Eulerian approach, the same approach can be implemented by integrating forward in time the advection–diffusion equation for a tracer. So far, the conditions to be applied at the boundary of the control domain were uncertain. We show here that it is necessary to prescribe that the tracer concentration vanishes at the boundary of the control domain to ensure the compatibility between the Lagrangian and Eulerian approaches. When we use the Constituent oriented Age and Residence time Theory (CART), this amounts to solving the differential equation for the residence time with boundary conditions forcing the residence time to vanish at the open boundaries of the control domain. Such boundary conditions are likely to induce the development of boundary layers (at outflow boundaries for the tracer concentration and at inflow boundaries for the residence time). The thickness of these boundary layers is of the order of the ratio of the diffusivity to the velocity. They can however be partly smoothed by tidal and other oscillating flows.     

Vertical structure of the stable boundary layer detected by RASS-SODAR and in-situ measurements in SABLES 2006 field campaign

Data from the SABLES 2006 field campaign are used in order to analyse some of the main processes present along the nocturnal periods: surface-based inversions, low level jets, katabatic winds, wave-like motions, pressure perturbations, etc. These processes have an important influence on the vertical structure (both thermal and dynamical) of the atmospheric boundary layer, and can be better described with the synergetic combination of RASS-SODAR data and in-situ measurements (such as sonic anemometer data and high-resolution pressure series from microbarometers). It is shown how the different air masses and their evolution are easily identified when pressure and RASS-SODAR wind and temperature data are presented together. Likewise, periodic pressure fluctuations observed in the surface array of microbarometers reveal the existence of gravity wave motions whose propagation is better understood after locating the wave ducting layers with the help of RASS-SODAR average wind ant temperature profiles.     

Effects of the bottom boundary condition in numerical investigations of dense water cascading on a slope

The flow of dense water along continental slopes is considered. There is a large literature on the topic based on observations and laboratory experiments. In addition, there are many analytical and numerical studies of dense water flows. In particular, there is a sequence of numerical investigations using the dynamics of overflow mixing and entrainment (DOME) setup. In these papers, the sensitivity of the solutions to numerical parameters such as grid size and numerical viscosity coefficients and to the choices of methods and models is investigated. In earlier DOME studies, three different bottom boundary conditions and a range of vertical grid sizes are applied. In other parts of the literature on numerical studies of oceanic gravity currents, there are statements that appear to contradict choices made on bottom boundary conditions in some of the DOME papers. In the present study, we therefore address the effects of the bottom boundary condition and vertical resolution in numerical investigations of dense water cascading on a slope. The main finding of the present paper is that it is feasible to capture the bottom Ekman layer dynamics adequately and cost efficiently by using a terrain-following model system using a quadratic drag law with a drag coefficient computed to give near-bottom velocity profiles in agreement with the logarithmic law of the wall. Many studies of dense water flows are performed with a quadratic bottom drag law and a constant drag coefficient. It is shown that when using this bottom boundary condition, Ekman drainage will not be adequately represented. In other studies of gravity flow, a no-slip bottom boundary condition is applied. With no-slip and a very fine resolution near the seabed, the solutions are essentially equal to the solutions obtained with a quadratic drag law and a drag coefficient computed to produce velocity profiles matching the logarithmic law of the wall. However, with coarser resolution near the seabed, there may be a substantial artificial blocking effect when using no-slip.     

A continental channel wave,guided by the intermediate layer in the crust

Summary A study has been made of a new channel wave, denotedLi, using a total of 83 observations from the seismic records of Swedish stations, mainly from earthquakes at normal depth.Li resembles theLg waves in several respects: it propagates only through continental structures, it has a similar particle motion, i.e. mainly transverse horizontal, and only slightly larger period. ButLi has a higher velocity, 3.79±0.07 km/sec, and it is believed to propagate in the intermediate layer in the crust in a way similar to the propagation of theLg waves in the granitic layer.Li is identical withS ^* in records of near-by earthquakes in the same way asLg2 is identical withSg. Li usually exhibits no clear dispersion.

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Zusammenfassung Es wurden Untersuchungen angestellt über eine neue Kanalwelle, welcher die BezeichnungLi gegeben wurde, wobei insgesamt 83 Erdbebenregistrierungen von schwedischen Stationen Verwendung fanden. Hauptsächlich waren es Erdbeben mit normaler Herdtiefe. DieLi-Wellen haben in verschiedener Hinsicht Ähnlichkeit mit denLg-Wellen: Sie pflanzen sich nur im Bereich kontinentaler Struktur fort und sie haben eine ähnliche Partikelbewegung, d.h. hauptsächlich horizontaltransversal.Li hat eine nur unwesentlich höhere Periode als dieLg-Wellen. AberLi hat eine wesentlich höhere Geschwindigkeit, 3.79±0.07 km/sec, und es ist anzunehmen, dass sie sich in der Basaltschicht der Kruste in ähnlicher Weise fortpflanzt wieLg in der Granitschicht.Li ist identisch mitS ^* in Aufzeichnungen von Nahbeben, so wieLg2 identisch mitSg ist.Li weist gewöhnlich keine deutliche Dispersion auf.

     

Destabilization of a 650 km chemical boundary layer and its bearing on the evolution of the continental crust

A mechanism for the production of a chemical change in the mantle, from primordial silicate compositions above the 650 km discontinuity to differentiated compositions below, is reviewed. Some consequences of this are the stabilization of two layer convection with a temperature contrast between the anhydrous mantle solidus and the geotherm which, at 650 km depth, is lower than any other location in the mantle. With thermal contributions from the concentration of the heat producing elements U, Th and K below the 650 km mantle boundary layer and the higher geotherms in the past, widespread or catastrophic melting may have taken place at this location. An episodic breach of this boundary layer by extensive heat and mass transport may have periodically destroyed any simple two-layer convection geometry in the mantle. Such episodic injections of mass and energy into the upper mantle from below may have been the mechanism responsible for episodes of enhanced surface tectonism and thermal activity which appear to be recorded in apparent polar wandering paths and radiometric ages of continental rocks.     

Numerical study on wave propagation over a fluid-mud layer with different bottom conditions

Wave decay over a muddy seabed has been widely reported. In previous studies, the fluid-mud layer is usually treated as a homogeneous layer with a certain thickness lying on the rigid bottom. However, the muddy seabed beneath a fluid-mud layer is usually movable in practice. This study aims to find out the influence of the movable seabed beneath a fluid-mud layer. For this purpose, a numerical model for wave propagation over a multilayered muddy seabed is developed, in which water is treated as a Newtonian fluid, and the rheology of mud is described by a visco-elastic–plastic model. The laboratory experiments of Sakakiyama and Bijker (J Waterw Port Coast Ocean Eng 115(5):614–633, 1989) are chosen to validate the numerical model. The model is then employed to investigate the movement of a fluid-mud layer with different conditions of the underlying mud layer and its influence on wave decay. It is found that the underlying mud layer plays a very important role in the wave–mud interaction and greatly affects the wave decay rate.     

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.     

The variability of the large-amplitude internal wave field on the Australian North West Shelf

Observations are presented of large-amplitude internal waves (LAIWs) generated by the steepening of the internal tide on the Australian North West Shelf (NWS) over a 4-month period extending from strongly stratified summer conditions to weakly stratified winter conditions. The observations are from a site in water depth of 124 m where current and temperature measurements were made from a fixed vertical mooring and a benthic L-shaped spatial array. The observations show the LAIWs at this site to be characterized by strong seasonal variability, with energetic LAIWs of depression being dominant during summer and weaker LAIWs of elevation being dominant during the winter months as the stratification weakens, the upper mixed layer deepens, and the thermocline is close to the bottom. Waves were also seen to propagate from a range of directions towards the observation site. Modeling using the Regional Ocean Modeling System (ROMS v2.1) revealed that internal tide generation in the area occurred at water depths of between 400 and 600 m along an arc of approximately 120 km in length, some 70 km to the northwest of our experimental site. The results demonstrate both the 3D nature as well as the seasonal variation of the LAIW field.     

Along-shelf evolution and sea levels across the continental slope

If wind-stress or a horizontal oceanic density gradient acts over an ocean basin with an adjacent continental shelf and slope, sea-surface slopes and currents are set up along the shelf and slope with a return flow in the ocean. The currents evolve from zero at blocked ends of the shelf and basin. Such evolution is essentially barotropic (even for baroclinic forcing) and is relevant to all flow adjustments after longshore changes of depth profile or forcing. The distance over which this evolution takes place is investigated analytically for simple geometries, and numerically for a range of shelf, slope and ocean widths, shelf/ocean depth ratios, frictional decay rates and oscillatory frequencies. A close correspondence is found with the decay distance (group velocity x decay time) for a lowest mode continental shelf wave, often exceeding 1000 km. This correspondence is used to interpret some published model calculations of shelf and slope currents or return flows resulting from wind-stress or alongshore pressure gradients.Where a slope current is evolving, coastal sea levels do not follow oceanic levels. Implications for coastal/oceanic level differences are discussed. Oceanic sea-level features of shorter scale than the above 1000 km (say) do not penetrate fully to the coast. However, coastal sea levels averaged around small islands without broad shelves well represent surrounding oceanic levels.     

海底边界层异常(地震海洋学)反射地震特征的地球物理分析

通过对南海北部与西部大量反射地震剖面海水层部分进行再处理,与以往地震海洋学主要关注海水层内部的反射结构不同,本文重点对海底附近水体的各种复杂反射地震特征进行分类、分析与总结.与传统对海底边界层的定义不同,我们将海底边界附近的水体称之为海底边界层.本文利用传统地震相分析方法,分析海底边界层各种复杂反射地震结构的几何形态、内部反射结构、连续性、振幅以及视频率特征,结合过去相关的地震海洋学研究成果、海底边界层理论与其它各种海底附近作用/过程,不仅对中尺度涡旋、内孤立波和背风波在地震剖面上的反射地震特征进行了归类与分析,并推断最新发现的一些反射地震特征可能揭示的各种海洋作用/过程,例如不同的地震相特征可能反映了海底湍流边界层,海底沉积物再悬浮,天然气渗漏羽状流和麻坑内部异常上升流相关海底界面作用过程.结果分析表明,地震海洋学方法不仅能够对海洋内波、涡旋等物理海洋现象进行研究,同时也能够对海底附近各种复杂海洋作用/过程进行成像,从而拓展了地震海洋学的研究领域,一定程度上也能为过去不能有效对海底边界面发生的各种冷泉热液活动、生物和沉积等作用过程进行现场观测提供新的探测方法和研究视角.     

Turbulent measurements in the stable atmospheric boundary layer during SHEBA: ten years after

This paper surveys results of the comprehensive turbulent measurements in the stable boundary layer (SBL) made over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) in the Beaufort Gyre from October 1997 through September 1998. Turbulent fluxes and mean meteorological data were continuously measured and reported hourly at five levels on a 20-m main SHEBA tower. Eleven months of measurements during SHEBA cover a wide range of stability conditions, from the weakly unstable regime to very stable stratification, and allow studying the SBL in detail. A brief overview of the SBL regimes, the flux-profile relationships, the turbulent Prandtl number, and other parameters obtained during SHEBA is given. The traditional Monin—Obukhov approach, z-less scaling, and gradient-based scaling are evaluated and discussed based on the data from SHEBA.     

Perfectly matched layer boundary conditions for frequency-domain acoustic wave simulation in the mesh-free discretization

Mesh-free discretization, flexibly distributing nodes without computationally expensive meshing process, is able to deal with staircase problem, oversampling and undersampling problems and saves plenty of nodes through distributing nodes suitably with respect to irregular boundaries and model parameters. However, the time-domain mesh-free discretization usually exhibits poorer stability than that in regular grid discretization. In order to reach unconditional stability and easy implementation in parallel computing, we develop the frequency-domain finite-difference method in a mesh-free discretization, incorporated with two perfectly matched layer boundary conditions. Furthermore, to maintain the flexibility of mesh-free discretization, the nodes are still irregularly distributed in the absorbing zone, which complicates the situation of artificial boundary reflections. In this paper, we implement frequency-domain acoustic wave modelling in a mesh-free system. First, we present the perfectly matched layer boundary condition to suppress spurious reflections. Moreover, we develop the complex frequency shifted–perfectly matched layer boundary condition to improve the attenuation of grazing waves. In addition, we employ the radial-basis-function-generated finite difference method in the mesh-free discretization to calculate spatial derivatives. The numerical experiment on a rectangle homogeneous model shows the effectiveness of the perfectly matched layer boundary condition and the complex frequency shifted–perfectly matched layer boundary condition, and the latter one is better than the former one when absorbing large angle incident waves. The experiment on the Marmousi model suggests that the complex frequency shifted–perfectly matched layer boundary condition works well for complicated models.     

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.     

Localisation of a wave source by point measurements of its field

Summary As a solution of an inverse problem consisting of finding the position of a wave source in a linear medium by measuring its field components at several points we propose a method which would replace the inverse by a direct method. This enables us to perform an effective numerical realization.

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