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

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

日本东北M_W9.0地震海啸在港池及邻近区域诱发的涡流危险性计算与评估分析

海啸造成的灾害与损失并非都与淹没有关,特别是港口中海啸诱导的强流会对船只及海事设施产生重要的影响及损害.由于海啸流观测数据稀缺及海啸诱导涡流机制的不确定性,过去60年海啸科学主要集中于对海啸波特征及淹没过程的研究与分析,海啸流模拟及验证工作开展较少,导致对海啸流基本特征及其造成灾害现象的曲解.开展海啸诱导的涡流研究及预警服务显得尤为重要及紧迫.考虑快速海啸预警需要,综合对比海啸诱导涡流的物理框架及模型方法,探索兼顾效率与计算精度的海啸流模拟方法是本文的核心工作及出发点.通过分析浅层湍流相干结构(TCS)产生的主要物理耗散机制,确定了考虑2D水平耗散机制的非线性浅水方程可用于海啸涡流的模拟分析.基于高精、高分辨率有限体积模型Geoclaw建立了三个精细化的港口海啸流模型,模型分辨率为5m.利用基于海啸浮标反演的海啸源模型作为初始条件,模拟分析了日本东北地震海啸在远场的海啸波流特征.海啸波流特征模拟结果与观测吻合较好,结果可信.对比发现:波驱动的自由表面流,小的位相或波幅误差就会导致大的流速误差,流的模拟和预报相对波幅来说更具挑战性.研究了海啸波流能量在港池中的分布特征,得到:港池入口及防波堤两端常被强流控制,具有极高的危险性;相对于波幅的空间变化,海啸流具有更强的空间敏感性;所建立的高分辨率海啸模型模拟再现了日本海啸在近场的涡旋结构,给出了与观测基本一致的涡流特征.最后,引入海啸流危险等级标准,分析了港口海啸流危险性等级分布、船只疏散的安全深度及回港的时间周期.针对港口、海湾同时考虑海啸波流特征的海啸预警与评估对于港口应急管理者科学决策具有重要意义.     

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.     

Inshore/offshore gradients of imposex and organotin contamination in Nassarius reticulatus (L.) along the Portuguese coast

Imposex and organotin (OT) tissue contamination of the netted whelk Nassarius reticulatus (L.) were assessed in the continental shelves around the main estuaries of the central coast of Portugal (Lisbon: Tagus estuary; Setúbal: Sado estuary) and the main coastal lagoon in the Southern of Portugal (Faro: Ria Formosa). Pollution levels were higher in areas of more intense boat traffic and shipyard activities and imposex showed a clear decreasing gradient from the estuaries to the offshore, in relation to a similar gradient of tissue contamination by tributyltin. Remarkably, imposex was extensively spread over the adjacent continental shelves of Tagus and Sado estuaries. The current work shows that TBT pollution is undoubtedly a matter of concern not only for the above estuaries where harbours are implanted but also for the adjacent continental shelves, regardless the massive dilution of contaminants that may occur in these deeper areas.     

Gravity-driven sediment transport on continental shelves: A status report

Recent field observations from several shelf environments show that gravity-driven transport within negatively buoyant layers is an important mode of fine sediment transport across continental shelves. Specifically, Dick Sternberg, along with his students and colleagues, stimulated a paradigm shift by reporting strong evidence from the Amazon and Eel shelves that hyperpycnal layers do not require autosuspension for sustenance but can be initiated by sediment flux convergence and supported by wave and current-induced suspension within relatively thin near-bed layers. As these layers move downslope under the influence of gravity, they may deposit sediment in response to decreases in bottom orbital velocities, near-bed current velocity, and/or bed slope. Direct or indirect evidence for wave or current supported sediment gravity flows has recently been reported off other high-load rivers including the Atchafalaya, Fly, Ganges–Brahmaputra, Klamath, Mad, Mississippi, Po, Rhone, Waiapu, Waipaoa, Yangtze, and Yellow among others. Growing evidence from observational and modeling studies suggests that flux convergence followed by wave and current supported gravity driven transport is a primary cause of across-shelf transport and emplacement of flood deposits on many muddy shelves and may be a major contributor to and control on the large-scale formation and morphology of subaqueous deltas and shelf clinoforms. Recent and ongoing studies on this subject are synthesized in this paper and recommendations are offered for further study.     

Was there a wind-driven Tethys circumglobal current in the Late Cretaceous?

The problem of the existence of a Tethys circumglobal current (TCC) in the Late Cretaceous continental geometry (Campanian) is addressed. Within an ocean model which is expected to strongly overestimate the wind-driven TCC volume transport, a relatively weak TCC is found for the reconstructed Campanian paleogeography used. As a measure of the strength of the TCC, a circumglobal flow index is introduced. This index is based on volume fluxes through meridional sections within the equatorial part of the domain. The impact of changes in the paleogeography on the TCC is considered by computing steady flows for different shapes of Eurasia. The results on the extent of Eurasia such that a strong TCC appears provide support that no strong wind-driven TCC has existed during the Campanian.     

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.     

Relative role of subinertial and superinertial modes in the coastal long wave response forced by the landfall of a tropical cyclone

A set of numerical experiments has been performed in order to analyze the long-wave response of the coastal ocean to a translating mesoscale atmospheric cyclone approaching the coastline at a normal angle. An idealized two-slope shelf topography is chosen. The model is forced by a radially symmetric atmospheric pressure perturbation with a corresponding gradient wind field. The cyclone's translation speed, radius, and the continental shelf width are considered as parameters whose impact on the long wave period, modal structure, and amplitude is studied. Subinertial continental shelf waves (CSW) dominate the response under typical forcing conditions and on the narrower shelves. They propagate in the downstream (in the sense of Kelvin wave propagation) direction. Superinertial edge wave modes have higher free surface amplitudes and faster phase speeds than the CSW modes. While potentially more dangerous, edge waves are not as common as subinertial shelf waves because their generation requires a wide, gently sloping shelf and a storm system translating at a relatively high (∼10 m s⁻¹ or faster) speed. A relatively smaller size of an atmospheric cyclone also favors edge wave generation. Edge waves with the highest amplitude (up to 60% of the forced storm surge) propagate upstream. They are produced by a storm system with an Eulerian time scale equal to the period of a zero-mode edge wave with the wavelength of the storm spatial scale. Large amplitude edge waves were generated during Hurricane Wilma's landfall (2005) on the West Florida shelf with particularly severe flooding occurring upstream of the landfall site.     

Multi-block lattice Boltzmann simulations of solute transport in shallow water flows

We report a two-dimensional multi-block lattice Boltzmann model for solute transport in shallow water flows, which is developed based on the advection–diffusion equation for mass transport and the shallow water equations for the flows. A weighting factor is included in the centered scheme for improved accuracy. The model is firstly verified by simulating three benchmark tests: wind-driven circulation in a dish-shaped lake, jet-forced flow in a circular basin, and flow formed by two parallel streams containing different uniform concentrations at the same constant velocity; and then it is applied to a practical wind-induced flow, Baiyangdian Lake, which is characterized by irregular geometries and complex bathymetries. The numerical results have shown that the model is able to produce accurate and detailed results for both water flows and solute transport, which is attractive, especially for flows in narrow zones of practical terrains and certain areas with largely varying pollutant concentrations.     

A numerical study of island wake generated by an elliptical tidal flow

An idealized numerical study of the influence of a tidal flow around an island has been undertaken with ROMS. The study focusses on coastal island wakes which are mainly controlled by elliptical tidal current flows on shallow shelves. This model is typical of some isolated continental shelf islands. The model is forced by a semi-diurnal barotropic inertia gravity wave imposed on the four open boundaries of a rectangular domain and its propagation results in an elliptical tidal flow within the domain in which the circular island lies. The influence of the surrounding island bathymetry and of the ellipse shape has been studied both in two and three dimensions. In the island vicinity, the residual circulation patterns over a tidal period show alongshore flow divergence along the major axis and convergence along the minor axis. A thin tidal ellipse (i.e. with a large ratio between major and minor axes) leads to strong eddy activity periods in the lee of the island during the flood and ebb phases, with eddy dissipation phases in between. By contrast, an almost round ellipse (axis ratio nearly 1) leads to vorticity filaments which continuously progress around the island without eddy shedding. The presence of a topographic slope in the vicinity of the island strengthens the eddy activity. This study suggests that the tidal current rotation favors the development of the eddy rotating in the same direction and weakens the development of the second eddy. In three dimensions with a surrounding bathymetry, an intense upwelling occurs in a large area in the lee of the island and the vertical velocities are stronger with thinner ellipses. With a flat bottom the vertical motions are almost fully generated by convergence and divergence of the secondary flow. With a varying bottom topography, the vertical motions come from a combination of this mechanism with convergence and divergence of the depth averaged flow.     

Linear mechanism by which internal gravity waves are generated and intensified in the ionosphere when interacting with an inhomogeneous zonal wind: 2. Internal gravity wave generation and intensification during the linear evolution stage

The linear mechanism by which internal gravity waves (IGWs) are generated and subsequently intensified in a stably stratified dissipative ionosphere in the presence of an inhomogeneous zonal wind (shear flow) has been studied. In the case of shear flows, the operators of linear problems are nonself-adjoint and the corresponding eigenfunctions are nonorthogonal; a canonical approach can hardly be used to study such motions. It is more adequate to apply the so-called nonmodal calculation. Dynamic equations and equations of energy transfer of IGW disturbances in the ionosphere with a shear flow have been obtained based on a nonmodal approach. Exact analytical solutions for the constructed dynamic equations have been found. The growth rate of the IGW shear instability has been determined. It has been established that IGW disturbances are intensified in an algebraically power manner rather than exponentially in the course of time. The effectiveness of the linear mechanism by which IGWs are intensified when interacting with an inhomogeneous zonal wind is analyzed. It has been indicated that IGWs effectively obtain the shear flow energy during the linear evolution stage and substantially increase (by an order of magnitude) their amplitude and energy. The frequency and the wave vector of generated IGW modes depend on time; therefore, a wide spectrum of wavelike disturbances, depending on the linear, rather than nonlinear, turbulent effects, is formed in the ionosphere with a shear flow. Thereby, a new degree of freedom appears, and the turbulent state of atmospheric—ionospheric layers can be formed on IGW disturbances.     

Internal solitary wave-induced flow over a corrugated bed

A combined numerical and experimental study of the propagation of an internal solitary wave (ISW) over a corrugated bed is presented, in which the amplitude and the wavelength of the corrugated bed, together with the wave amplitude and wave speed of the ISW, have been varied parametrically. Both ISWs of elevation and depression have been considered. The wave-induced currents over the corrugated bed cause flow separation at the apex of the corrugations and a sequence of lee vortices forms as a result. These vortices develop fully after the main wave has passed over the topographic feature, resulting in deformation of the overlying pycnocline and, in some instances, significant vertical mixing. It is found that the intensity of the vortex formation is dependent on both the amplitude and wavelength of the bottom topography. In the case of an ISW of depression, the generation of vertically (upward)-propagating vortices is seen to result in entrainment of fluid from a bottom boundary jet (Carr and Davies, Phys Fluids 18:016601, 2006), while, in the elevation case, a second mechanism is present to induce significant turbulent mixing in the water column. It occurs when the bottom corrugations reach into, or are very near, the pycnocline at rest. Large waves of elevation that are stable on approach to the corrugations exhibit evidence of a spatio-temporally developing shear instability as they interact with the bottom corrugation. The shear instability takes the form of billows that have a vertical extent that can reach 50% of the wave amplitude.     

Fine grain sediment transport and deposition in the Patos Lagoon–Cassino beach sedimentary system

Extensive mud deposits superimposed on the predominantly sandy inner continental shelf adjacent to the Patos Lagoon estuary, indicates that the Lagoon is a potential source of fine sediments to the coastal sedimentary system. The lagoon is large and shallow, and the water movement is mainly controlled by wind-driven set-up and set-down. The mean river inflow is around 2000 m³ s⁻¹, although peak flow rates exceeding 20,000 m³ s⁻¹ have been observed during El Niño periods. Though the tidal elevations are small, tidal velocities in the lagoon's inlet can be significant due to the large extension of the backwaters. Moreover, significant exchange flows can be generated between the estuary and coastal area due to barotropic pressure gradients established as a function of wind and freshwater discharge. The predominant net flow is seawards, but opposite near-bed flows due to pronounced vertical salinity stratification can also be observed. The coastal area is characterized by small tidal effects, large scale ocean circulation, wind-induced residual flows and wave-driven currents, where the waves originate from swell or are locally generated.     

Failure of Marine Deposits and their Redistribution by Sediment Gravity Flows

— SedFlux simulates the fill of sedimentary basins, and can be used to examine the location and attributes of sediment failure on continental margins and the runout of their associated sediment gravity flows. Numerical experiments show how the evolving boundary conditions of sea-level fluctuations, floods, storms, tectonic and other relevant processes control the rate and size of slope instabilities. By tracking deposit properties (pore pressures, grain size, bulk density, porosity), a finite-slope factor-of-safety analysis of marine deposits examines failure potential. A decider routine is used to determine whether the failed material will travel down slope as turbidity current or a debris flow. Examples provided insight into: (i) why fjords dominated by turbidity current deposition often contain debris flow deposits; (ii) how glaciated margins prograde seaward through shallow failures of low yield strength material; and, (iii) how large-scale basin subsidence can control the onset of canyon formation across continental slopes.     

Observations of the spring–neap modulation of the gravitational circulation in a partially mixed estuary

The long-term variability of the non-tidal circulation in Southampton Water, a partially mixed estuary, was investigated using 71-day acoustic Doppler current profiler (ADCP) time series. The data show evidence that the spring–neap tidal variability of the turbulent mixing modulates the strength of the non-tidal residual circulation, with subtidal neap tide surface flows reaching 0.12 m s^–1 compared to <0.05 m s^–1 at spring tides. The amplitude of the neap-tide events in this non-tidal circulation is shown to be related to a critical value of the tidal currents, illustrating the strong dependence on tidal mixing. The results suggest that the dominant mechanism for generating these neap-tide circulation events is the baroclinic forcing of the horizontal density gradient, rather than barotropic forcing associated with ebb-induced periodic stratification. While tidal turbulence is thought to be the dominant control on this gravitational circulation, there is evidence of the additional effect of wind-driven mixing, including the effects of wind fetch and possibly wave development with along-estuary winds being more efficient at mixing the estuary than across-estuary winds. Rapid changes in atmospheric pressure also coincided with fluctuations in the gravitational circulation. The observed subtidal flows are shown to be capable of rapidly flushing buoyant material out of the estuary and into the coastal sea at neap tides.Responsible Editor: Iris Grabemann     

A discontinuous finite element baroclinic marine model on unstructured prismatic meshes

We describe the space discretization of a three-dimensional baroclinic finite element model, based upon a discontinuous Galerkin method, while the companion paper (Comblen et al. 2010a) describes the discretization in time. We solve the hydrostatic Boussinesq equations governing marine flows on a mesh made up of triangles extruded from the surface toward the seabed to obtain prismatic three-dimensional elements. Diffusion is implemented using the symmetric interior penalty method. The tracer equation is consistent with the continuity equation. A Lax–Friedrichs flux is used to take into account internal wave propagation. By way of illustration, a flow exhibiting internal waves in the lee of an isolated seamount on the sphere is simulated. This enables us to show the advantages of using an unstructured mesh, where the resolution is higher in areas where the flow varies rapidly in space, the mesh being coarser far from the region of interest. The solution exhibits the expected wave structure. Linear and quadratic shape functions are used, and the extension to higher-order discretization is straightforward.     

A reappraisal of shear wave splitting parameters from Italian active volcanic areas through a semiautomatic algorithm

Shear wave splitting parameters represent a useful tool to detail the stress changes occurring in volcanic environments before impending eruptions. In the present paper, we display the parameter estimates obtained through implementation of a semiautomatic algorithm applied to all useful datasets of the following Italian active volcanic areas: Mt. Vesuvius, Campi Flegrei, and Mt. Etna. Most of these datasets have been the object of several studies (Bianco et al., Annali di Geofisica, XXXXIX 2:429–443, 1996, J Volcanol Geotherm Res 82:199–218, 1998a, Geophys Res Lett 25(10):1545–1548, 1998b, Phys Chem Earth 24:977–983, 1999, J Volcanol Geotherm Res 133:229–246, 2004, Geophys J Int 167(2):959–967, 2006; Del Pezzo et al., Bull Seismol Soc Am 94(2):439–452, 2004). Applying the semiautomatic algorithm, we confirmed the results obtained in previous studies, so we do not discuss in much detail each of our findings but give a general overview of the anisotropic features of the investigated Italian volcanoes. In order to make a comparison among the different volcanic areas, we present our results in terms of the main direction of the fast polarization (φ) and percentage of shear wave anisotropy (ξ).     

Field study on flow structures within aquatic vegetation under combined currents and small-scale waves

Field measurements were conducted to study the influence of aquatic vegetation on flow structures in floodplains under combined currents and wind-driven waves. Wave and turbulent velocities were decomposed from the time series of instantaneous velocity and analysed separately. In the present study, the wind waves were small, leading to the ratios of wave excursion (E_w) to stem spacing (S) for all cases tested here were less than 0.5. This caused the vertical distributions of time-averaged velocity (U_horiz) and turbulent kinetic energy (TKE) impacted by vegetation similar with the vegetated flow structures under pure current conditions. For emergent vegetation, U_horiz and TKE distributed uniformly through the entire water column or increased slightly from bed to water surface. Similar distributions were present in the lower part of submerged vegetation. In the upper part of submerged vegetation, U_horiz and TKE increased rapidly toward water surface and TKE reached its maximum near the top of vegetation. The measured wave orbital velocity (U_w) fitted linear wave theory well through the entire water depth for both the emergent and submerged cases, so that with small E_w/S the wave velocity was not attenuated within vegetation and U_w within canopy can be predicted by the linear wave theory under combined currents and waves. However, wind-driven waves made the turbulence generated near the top of canopy penetrate a deeper depth into vegetation than predictions under pure current conditions.     

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

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