Influence of bottom frictional effects in sill regions upon lee wave generation and implications for internal mixing

A cross-sectional nonhydrostatic model using idealized sill topography is used to examine the influence of bottom friction upon unsteady lee wave generation and flow in the region of a sill. The implications of changes in shear and lee wave intensity in terms of local mixing are also considered. Motion is induced by a barotropic tidal flow which produces a hydraulic transition, associated with which are convective overturning cells, wave breaking, and unsteady lee waves that give rise to mixing on the lee side of the sill. Calculations show that, as bottom friction is increased, current profiles on the shallow sill crest develop a highly sheared bottom boundary layer. This enhanced current shear changes the downwelling of isotherms downstream of the sill with an associated increase in the hydraulic transition, wave breaking, and convective mixing in the upper part of the water column. Both short and longer time calculations with wide and narrow sills for a number of sill depths and buoyancy frequencies confirm that increasing bottom friction modifies the flow and unsteady lee wave distribution on the downstream side of a sill. Associated with this increase in bottom friction coefficient, there is increased mixing in the upper part of the water column with an associated decrease in the vertical temperature gradient. However, this increase in mixing and decrease in temperature gradient in the upper part of the water column is very different from the conventional change in near-bed temperature gradient produced by increased bottom mixing that occurs in shallow sea regions as the bottom drag coefficient is increased.     

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.     

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.     

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.     

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.     

Evolution of internal solitary waves on the slope-shelf topography in the northern South China Sea

Ocean Dynamics - Based on a non-hydrostatic two-dimensional and high-resolution model, evolution of internal solitary waves (ISWs) on the typical slope-shelf topography in the northern South China...     

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.     

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.     

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     

Geomagnetic field variations induced by internal and surface waves in the four-layer model of the marine environment

The layered model of the marine environment, including the atmosphere, two seawater layers with different conductivity and density, and the bottom rock layer, has been considered. The geomagnetic field variations, generated by internal and surface waves with different frequency and propagation direction, have been found in the scope of this model. The effect of magnetic permeability and electric conductivity of bottom rocks on induced magnetic field has been taken into account. The transfer functions and spectral densities of these variations have been analytically determined and numerically estimated.     

The effects of alongshore variation in bottom topography on a boundary current—(topographically induced upwelling)

A theory which describes the constant f-plane flow of a steady inviscid baroclinic boundary current over a continental margin with a bathymetry that varies slowly in the alongshore but rapidly in the offshore directions is developed in the parameter regime (L_D/L)² ≤ Ro 1, where L_D is the internal deformation radius, L the horizontal length scale, and Ro the Rossby number. To lowest order in the Rossby number the flow is along isobaths with speed q_o = V_u(h,z)|Vh|/α, where V_u(h,z) is the upstream speed, α the upstream bottom slope at depth h, and Vh the bottom slope downstream at depth h. The lowest order flow produces a variation in the vertical component of relative vorticity along the isobath as the magnitude and direction of Vh vary in the downstream direction. The variation of vorticity requires a vertical as well as a cross-isobath flow at first order in the Rossby number. The first order vertical velocity is computed from the vorticity equation in terms of upstream conditions and downstream variations of the bathymetry. The density, pressure, and cross-isobath flow at first order in the Rossby number are then calculated. It is shown that in the cyclonic region of current (d/dh(V_u/α) > 0), if the isobaths diverge in the downstream direction ((∂/∂s)|Vh| < 0), then upwelling and onshore flow occur. The theory is applied to the northeastern Florida shelf to explain bottom temperature observations.     

地震海洋学方法在海洋混合参数提取中的研究与应用——以南海内波和地中海涡旋为例

混合是海洋中普遍存在的一种海水运动形式,对多个海洋学分支的研究具有重要的影响.随着物理海洋学的研究重心从大尺度向中小尺度现象过渡,近年来混合问题的研究重心也逐渐转向了中小尺度现象.内波与中尺度涡都是非常重要的中小尺度物理海洋学现象,对海洋能量在不同尺度中的级联发挥着重要的作用.本文基于地震海洋学研究了海洋混合参数的提取方法,并以南海内波和地中海涡旋为例进行了计算和分析.结果显示,南海内波在200~600 m深度范围内所引起的混合可达10-2.79 m2·s-1左右,比大洋的统计结果10-5 m2·s-1高出两个数量级以上.而地中海涡旋所引起的湍流混合率可达10-3.44m2·s-1左右,与大洋统计结果相比高出1.5个数量级左右,并且地中海涡旋下边界的混合要强于上边界,这一特征与前人的研究一致,另外涡旋上边界之上以及侧边界的外侧也具有非常高的混合率.     

Propagation of seismic waves in a viscoelastic medium and the effect of topography

In this paper we have simulated the propagation of seismic waves in viscoelastic medium and calculated the effect of irregular surface topography by using finite element method. Several types of elastic and viscoelastic medium models, such as block structure, vidges and/or valley with and without a soft layer underneath have been studied. The distribution of maximum amplitude of displacement and acceleration on surface has been calculated in the case of vertically incident SH and P waves from the basement. The possible application in earthquake engineering is also discussed. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 442–449, 1991.     

Critical movement of large rocks in currents and waves

Cobbles, boulders, and rocks often are used in a bed protection layer near a structure to protect the underlying sand bed against erosion by combined current and waves. The design of a bed protection layer consisting of loose rocks (rubble mound) requires knowledge of the stability and movement (as bed load) of very coarse materials. If some movement (or damage) is acceptable, the rock diameter can be designed to be smaller. This paper addresses the stability and movement of very coarse materials (cobbles, boulders, and rocks) based on the concept of the critical Shields mobility number. It is shown that the bed load transport of large cobbles, boulders, and rocks can be described by the equations of Meyer-Peter and Mueller (MPM) and Cheng. Both are valid for relatively small Shields mobility numbers. New and general equations for the design of a bed protection layer (including some permissible damage) in conditions with a current with or without waves are proposed based on the Shields mobility parameter and the bed load transport equation of Cheng. Laboratory and field data of critical velocities for pebbles, cobbles, boulders, and rocks have been analyzed and compared to the computed results of the proposed equations. Practical applications are given to demonstrate the general applicability of the proposed equations.     

The radioactive abnormality characteristics of typical regions in Ordos Basin and its geological implications

There are many results of single mineral enrichment characteristic, such as oil, gas, coal and uranium, but little is known about the synergistic research of these important minerals and the study of uranium enrichment features in the deep basin. So, the study on the paragenesis regularity and coexisting relation of many minerals in the basin will promote the integrated forecast and cooperative exploitation of the basin. Based on the plentiful logging data and geological data, this paper studies the distributing feature of higher Gamma abnormality. The analysis on 33 core samples’ test results indicates that the increasing of Gamma abnormality is due to the increasing of the uranium element, and the enrichment of uranium is a result of the activation and conglomeration of uranium. On the basis of the recognization of radioactive abnormality and the study about the reality of oil,gas,coal or uranium coexisting in a basin and its mechanism, the paper shows that there is a certain mutual promotion in oil, gas, coal and uranium in the basin, which provides an important theory basis for cooperative exploitation of energy resources.     

The radioactive abnormality characteristics of typical regions in Ordos Basin and its geological implications

There are many results of single mineral enrichment characteristic, such as oil, gas, coal and uranium, but little is known about the synergistic research of these important minerals and the study of uranium enrichment features in the deep basin. So, the study on the paragenesis regularity and coexisting relation of many minerals in the basin will promote the integrated forecast and cooperative exploitation of the basin. Based on the plentiful logging data and geological data, this paper studies the distributing feature of higher Gamma abnormality. The analysis on 33 core samples' test results indicates that the increasing of Gamma abnormality is due to the increasing of the uranium element, and the enrichment of uranium is a result of the activation and conglomeration of uranium. On the basis of the recognization of radioactive abnormality and the study about the reality of oil,gas,coal or uranium coexisting in a basin and its mechanism, the paper shows that there is a certain mutual promotion in oil, gas, coal and uranium in the basin, which provides an important theory basis for cooperative exploitation of energy resources.     

Electromagnetic waves in the auroral and subauroral regions of the topside ionosphere

The density and temperature of the plasma electron component and wave emission intensity in the topside ionosphere were measured by the INTERCOSMOS-19 satellite. In the subauroral ionosphere, a decrease in the plasma density correlates with an increase in the plasma electron component temperature. In this case, the additional increase in the electron component temperature was measured in regions with increased plasma density gradients during the substorm recovery phase. In a linear approximation, the electromagnetic wave growth increments are small on electron fluxes precipitating in the auroral zone. It has been indicated that Bernstein electromagnetic waves propagating in the subauroral topside ionosphere can intensify in regions with increased plasma density gradients on electron fluxes orthogonal to the geomagnetic field, which are formed when plasma is heated by decaying electrostatic oscillations of the plasma electron component. This can be one of the most important factors responsible for the intensification of auroral kilometric radiation.