Topographic steering of dense overflows: Laboratory experiments with V-shaped ridges and canyons

Topographic corrugations such as canyons and ridges cross-cutting the path of a dense plume may effectively steer all or part of the plume downslope. Here, topographically steered flows are investigated experimentally, as laminar, dense gravity currents are observed to impinge on and flow along sloping, V-shaped canyons and ridges. Ridges, as well as canyons, were observed to steer the dense water downslope. A dynamical regime, in which the along-slope transport is balanced by a return flow in the Ekman layer to maintain a geostrophically balanced downslope flow along the corrugation, has been proposed. Results from a previously published analytical model describing such flows are compared with the laboratory experiments. The response of the flow to variations in four governing parameters (slope, rotation, volume flux and reduced gravity) is generally described well by the model and results agree qualitatively, although theory slightly underestimates the dense layer thickness. Vertical velocity profiles resolving the Ekman spiral were obtained using a laser Doppler velocimeter and they showed the secondary, transverse circulation superimposed on the primary, downslope flow. A particle flowing down the canyon/along the ridge can be expected to follow a helix-like path, and dye released within the dense layer showed this. The experiments support the analytical model and the dynamical regime proposed for topographically steered flows. The gravity current split in two when the transport capacity of the corrugation was exceeded; one part continued along the slope and the other flowed downslope along the corrugation.     

台风影响下长江口羽流的响应与淡水输运机制

河口区域冲淡水锋面及物质输运会对台风产生快速而复杂的响应,并产生显著的生态效应及沉积过程,且不同类型的台风会对水动力及物质输运产生不同影响。本文以长江河口为研究区域,利用盐度锋面附近的浮标站点观测数据,发现在登陆型超强台风“利奇马”的影响下,旋转流特征消失,站点全水深出现持续近两天的北向流;而在转向型强台风“巴威”的影响下,出现持续约三天的全水深南向流。应用覆盖长江口及邻近海域的有限体积海洋模型（FVCOM）对两次台风过程进行模拟,实验对比台风过境前后流场、盐度场并且计算淡水通量,发现台风过境时通过破坏夏季典型的向海扩张的表层平流型羽流结构,从而促进盐度垂向混合,导致大量淡水堆积在靠岸一侧,加强了沿岸的淡水输运,进而形成底部捕获型羽流。对于登陆型台风“利奇马”的影响,淡水输运主要沿苏北海岸向北,而在转向型台风“巴威”偏北风的影响下,淡水则显著沿岸向浙闽海域流动。这两种台风过后,表层淡水开始向海扩展,垂向盐度分层再一次呈现,在2～3天内完全恢复为表层平流型羽流结构。     

Megaplume bubble process visualization by 3D multibeam sonar mapping

MultiBeam echosounder data were collected during a surface-ship survey of the 22/4b well site in the North Sea in September 2011 using a Teledyne-Reson 7125. Modern multibeam echosounders are instrumental in providing detection and accurate localization of weak to strong bubble plumes. Two survey profiles effectively insonified the bubble plumes rising from the main crater at the well site, providing snapshot data of bubble plume processes. Additionally, three profiles insonified bubble plumes rising from, in, and to the south of a secondary crater, 1.2 km southeast of the main crater. Data processing included a simple algorithm that muted mislocated echoes from incomplete sidelobe suppression. The data processing produced a Cartesian volume of echo intensity from the water column and seabed.Plume geometry was analyzed to investigate a number of important large-scale plume processes, including plume bubble detrainment due to currents and stratification, downwelling flows, sea surface interaction, plume heterogeneity, and other fluid transport processes. The data showed strong upwelling flows, with bubble vertical motions generally much faster than currents. One important finding was that megaplumes create intrusions above the general thermocline, in part because their extensive upwelling flow lifts the thermocline locally. As a result, the intrusion layer deposits dissolved gases in the upper wave-mixed layer of the water column where it is not isolated from the atmosphere, unlike dissolved gases in the lower water column.The analysis shows that high fidelity multibeam echosounder data can provide a wealth of remote sensing information on bubble plume characteristics and processes, with important applications, including blowout monitoring and response, better understanding of megaplumes such as used in lake destratification, and improved characterization of natural seep emission processes.     

Effects of topography on lofting gravity flows: Implications for the deposition of deep-water massive sands

Hyperpycnal flows are generated in the marine environment by sediment-laden fresh water discharge into the ocean. They frequently form at river mouths and are also generated in proximal ice-melting settings and are thought to be responsible for transporting a large proportion of suspended river sediment onto and off the continental shelf. Hyperpycnal flows are an example of gravity currents that display reversing buoyancy. This phenomenon is generated by the fresh water interstitial fluid being less dense than that of the ambient seawater. Thus after sufficient particles are sedimented the flow can become positively buoyant and loft, forming a rising plume. Here we present results from physical scale-modelling experiments of lofting gravity currents upon interaction with topography. Topography, in the form of a vertical obstacle, triggered a localised lofting zone on its upstream side. This lofting zone was maintained in a fixed position until the bulk density of the flow had reduced enough to allow lofting along its entire length. The obstructed lofting zone is associated with a sharp increase in deposit thickness. By inference these experimentally established lofting dynamics are applied to improve understanding of the potential for hyperpycnal flows to deposit deep-water massive sands. This study provides a depositional mechanism by which large volumes of sand can be deposited in the absence of traction and the fines removed, leaving thick deposits of structureless sand with a low percentage of mud. This conceptual model for the first time provides a framework by which the geometries of certain deep-water massive sands may be predicted within specific depositional and basinal settings. This is crucial to our understanding of massive sand deposits in modern and ancient turbiditic systems and in the commercial evaluation of hydrocarbon potential of such sedimentary successions.     

Derivation of internal solitary wave amplitude in the South China Sea deep basin from satellite images

In the present study, theories based on the Korteweg–de Vries equation are extended to the Benjamin–Ono equation to allow the determination of internal solitary wave (ISW) amplitude from satellite images. The free surface flow induced by an ISW is derived for deep water. As a coherent structure, the amplitude of the ISW has a unique relation to the convergence/divergence of surface flow, such that the flow convergence/divergence will increase/decrease the backscattering cross section and generate bright/dark bands in satellite images. The distance between bright and dark bands can be related to the amplitude of ISW. To validate the theory, a multi-ship measurement made on 9–11 May 2005 during the spring tide period is used. A systematic approach to determine the thickness and density of the upper and lower layers is also included so that the free surface flow can be determined with a relatively high accuracy.     

The behavior of a two-dimensional dual forced plume

The behavior of two plumes ejected into a thin water tank is investigated experimentally. As the time elapses, the plume axes deflect towards each other. Time evolution of this two-dimensional, dual forced plume is found to be similar to that of a two-dimensional, single plume ejected near a vertical wall. The symmetric plane of the two plumes in the former case plays the role of the vertical wall. The time required for the dual plume to attain a quasi-steady state is shorter than that for the single plume. The deflection angles of the plume axes are smaller for the dual plume, and the plume water remains near the free water surface in a quasi-steady state. Water circulation in a triangular region surrounded by the free water surface, the side of the plume and the symmetric plane (or the vertical wall for the single plume case) may account for this difference; the circulation is much more pronounced in the single plume case.     

Comparative Study of Different SPH Schemes on Simulating Violent Water Wave Impact Flows

Free surface flows are of significant interest in Computational Fluid Dynamics（CFD）. However, violent water wave impact simulation especially when free surface breaks or impacts on solid wall can be a big challenge for many CFD techniques. Smoothed Particle Hydrodynamics（SPH） has been reported as a robust and reliable method for simulating violent free surface flows. Weakly compressible SPH（WCSPH） uses an equation of state with a large sound speed, and the results of the WCSPH can induce a noisy pressure field and spurious oscillation of pressure in time history for wave impact problem simulation. As a remedy, the truly incompressible SPH（ISPH） technique was introduced, which uses a pressure Poisson equation to calculate the pressure. Although the pressure distribution in the whole field obtained by ISPH is smooth, the stability of the techniques is still an open discussion. In this paper, a new free surface identification scheme and solid boundary handling method are introduced to improve the accuracy of ISPH. This modified ISPH is used to study dam breaking flow and violent tank sloshing flows. On the comparative study of WCSPH and ISPH, the accuracy and efficiency are assessed and the results are compared with the experimental data.     

A higher-efficient three-dimensional numerical model for small amplitude free surface flows

A higher-efficient three-dimensional non-hydrostatic model is developed to simulate small amplitude free surface flows based on a staggered unstructured grid. In this model, a fractional step algorithm is adopted to solve the Navier-Stokes equations in two major steps. A top-layer pressure method is proposed to minimize the number of vertical layers and subsequently the computational cost. Three classical examples of small amplitude free surface flows are used to demonstrate the capability and efficiency of the model. The satisfactory results demonstrated the capability and efficiency of modelling a range of small amplitude free surface flows with only a small number of vertical layers.     

Circular plumes in Lake Pontchartrain estuary under wind straining

Circular shaped density plumes of low turbidity, low fecal indicator (Escherichia coli and enterococci) concentrations, and high salinity have been observed near the Industrial Canal in Lake Pontchartrain, north of the City of New Orleans. A conceptual model in polar coordinates and a numerical model are developed, together with data analysis, to illustrate the dense plume. It is demonstrated that the northward expansion of the plume occurs under northerly winds. The northward expansion of the plume occurs under northerly winds that drive downwind flow at the surface and upwind radial flow at the bottom. Northerly wind-induced straining, similar to tidal straining, promotes vertical stratification. As a result, the water becomes stratified near a thin bottom layer (<1 m), within which density currents are facilitated. The stability of the stratified plume suppresses wind-induced turbulent mixing inside the plume. The bottom water outside of the plume is more effectively stirred by the wind, the result being that the suspended sediment concentration outside of the plume area is much higher than inside. This contrast in mixing makes the plume visible from the surface by satellites even though the stratification is at the bottom. Laterally, wind stress produces a torque (vorticity) in areas of non-uniform depth such that upwind flow is developed in deep water and downwind flow in shallow water. The continuity requirement produces an upwind flow along the axis of the Industrial Canal (IC). The upwind flow is balanced by the downwind flow over the shallower peripheral areas along the coast.     

Viscosity and nonlinearity effects on the forces and waves generated by a floating twin hull under heave oscillation

Nonlinear hydrodynamics of a twin rectangular hull under heave oscillation is analyzed using numerical methods. Two-dimensional nonlinear time-domain solutions to both inviscid and viscous problems are obtained and the results are compared with linear, inviscid frequency-domain results obtained in [26] to quantify nonlinear and viscous effects. Finite-difference methods based on boundary-fitted coordinates are used for solving the governing equations in the time domain [2]. A primitive-variables based projection method [6] is used for the viscous analysis and a mixed Eulerian–Lagrangian formulation [11] for inviscid analysis. The algorithms are validated and the order of accuracy determined by comparing the results obtained from the present algorithm with the experimental results of Vugt [22] for a heaving rectangle in the free surface. The present study on the twin-hull hydrodynamics shows that at large and non-resonant regular frequencies, and small amplitude of body oscillation, the fluid viscosity does not significantly affect the wave motion and the radiation forces. At low frequencies however the viscosity effect is found to be significant even for small amplitude of body oscillation. In particular, the hydrodynamic force obtained from the nonlinear viscous analysis is found to be closer to the linear inviscid force than the nonlinear inviscid force to the linear inviscid force, the reason for which is attributed to the wave dampening effect of viscosity. Since the wave lengths generated at smaller frequencies of oscillation are longer and therefore the waves could have a more significant effect on the dynamic pressure on the bottom of the hulls which contribute to the heave force, the correlation between the heave force and the wave elevation is found to be larger at smaller frequencies. Because of nonlinearity, the wave radiation and wave damping force remained nonzero even at and around the resonant frequencies – with the resonant frequencies as determined in [26] using linear potential flow theory. As to be expected, the nonlinear effect on the wave force is found to be significant at all frequencies for large amplitude of oscillation compared to the hull draft. The effect of viscosity on the force, by flow separation, is also found to be significant for large amplitude of body oscillation.     

Prediction of hydrodynamic loading on a mini TLP with free surface effects

This paper describes the extension of a fluid-flow simulations method to capture the free surface evolution around a full-scale Tension Leg Platform (TLP). The focus is on the prediction of the resulting hydrodynamic loading on the various elements of the TLP in turbulent flow conditions and, in particular, on quantifying the effects of the free surface distortion on this loading. The basic method uses finite-volume techniques to discretize the differential equations governing conservation of mass and momentum in three dimensions. The time-averaged forms of the equations are used, and the effects of turbulence are accounted for by using a two-equation, eddy-viscosity closure. The method is extended here via the incorporation of surface-tracking algorithm on a moving grid to predict the free-surface shape. The algorithm was checked against experimental measurements from two benchmark flows: the flow over a submerged semi-circular cylinder and the flow around a floating parabolic hull. Predictions of forces on a model TLP were then obtained both with and without allowing for the deformation of the free surface. The results suggest that the free surface effects on the hydrodynamic loads are small for the values of Froude number typically encountered in offshore engineering practice.     

三维自由面流动模拟中GPU并行计算技术

MPS(Moving Particle Semi-implicit)法能够有效地处理溃坝、晃荡等自由面大变形流动问题。在三维MPS方法中,粒子数量的急剧增加会导致其计算效率的降低并限制其在大规模流动问题中的应用。基于自主开发的MPS求解器MLParticleSJTU,本文对求解过程中耗时最多的邻居粒子搜寻和泊松方程求解两个模块采用了GPU并行加速,详细探讨了CPU+GPU策略。以三维晃荡和三维溃坝这两种典型的自由面大变形流动为例,比较了CPU+GPU相对于MLParticle-SJTU串行求解时的加速情况,结果表明CPU+GPU在邻居粒子和泊松方程这两个模块中的加速比最高能达到十倍左右。此外,采用CPU+GPU并行能够较准确地模拟溃坝、晃荡等自由面大变形问题。     

Large eddy simulation of breaking waves

A numerical model is used to simulate wave breaking, the large scale water motions and turbulence induced by the breaking process. The model consists of a free surface model using the surface markers method combined with a three-dimensional model that solves the flow equations. The turbulence is described by large eddy simulation where the larger turbulent features are simulated by solving the flow equations, and the small scale turbulence that is not resolved by the flow model is represented by a sub-grid model. A simple Smagorinsky sub-grid model has been used for the present simulations. The incoming waves are specified by a flux boundary condition. The waves are approaching in the shore-normal direction and are breaking on a plane, constant slope beach. The first few wave periods are simulated by a two-dimensional model in the vertical plane normal to the beach line. The model describes the steepening and the overturning of the wave. At a given instant, the model domain is extended to three dimensions, and the two-dimensional flow field develops spontaneously three-dimensional flow features with turbulent eddies. After a few wave periods, stationary (periodic) conditions are achieved. The surface is still specified to be uniform in the transverse (alongshore) direction, and it is only the flow field that is three-dimensional.The turbulent structures are investigated under different breaker types, spilling, weak plungers and strong plungers. The model is able to reproduce complicated flow phenomena such as obliquely descending eddies. The turbulent kinetic energy is found by averaging over the transverse direction. In spilling breakers, the turbulence is generated in a series of eddies in the shear layer under the surface roller. After the passage of the roller the turbulence spreads downwards. In the strong plunging breaker, the turbulence originates to a large degree from the topologically generated vorticity. The turbulence generated at the plunge point is almost immediately distributed over the entire water depth by large organised vortices. Away from the bed, the length scale of the turbulence (the characteristic size of the eddies resolved by the model) is similar in the horizontal and the vertical direction. It is found to be of the order one half of the water depth.     

The advection effect of planetary vorticity on sea level slope in a western boundary current

Western boundary currents, such as the Gulf Stream, are often modeled as flows in near cross‐stream geostrophic balance with paths that are straight or nearly straight. The effect of planetary vorticity advection on the downstream sea‐level slope in these rectilinear flows is re‐examined and found negligible. Instead, the re‐examination reveals a much greater effect of the ageostrophic component of the horizontal divergence in determining the downstream slope. Overlooked in previous studies is the geostrophic component of the horizontal divergence because of a hidden assumption of parallel flow. To avoid this pitfall, we employ a natural coordinate system to follow precisely the downstream direction. Further, we differentiate between weak geostrophic flows with small accelerations and flows in cross‐stream geostrophic balance where downstream acceleration might be appreciable. Two Rossby numbers are employed: a small cross‐stream number (≤0.01) to describe the near cross‐stream balance, and a large downstream number (≤0.1) to describe the large downstream accelerations that are found in western boundary flows. Finally, by means of a scale analysis we show that over the whole range of possible Rossby numbers, the advection effect of planetary vorticity on downstream sea level slope is negligible compared to the effect of the ageostrophic component of the horizontal divergence. Some new data on the nearshore gradient of the Reynolds stress are also included.     

波浪与大孔隙多孔介质相互作用的耦合数学模型

建立了波浪与大孔隙多孔介质相互作用的耦合数学模型,波浪域的控制方程为雷诺时均方程和k-ε紊流模型。对于计算域的入射波采用推板式造波,它可以是线性波、椭圆余弦波和孤立波。采用PLIC-VOF法追踪波浪自由表面。对于多孔介质内的孔隙流场采用非线性Forchheimer方程,两区域共享连续方程,最后导出的波浪域与孔隙流域的压力修正方程具有完全相同的形式,利用这个方程能够同时而不是分别求解波浪场和孔隙流场,避免了在内部边界上给定匹配条件,实现了波浪场与孔隙流场的同步耦合。波浪与粗颗粒海床、平底床面上抛石潜堤及斜坡上抛石潜堤相互作用的验证计算结果表明该模型可用于研究波浪与大孔隙多孔介质相互作用的问题。     

Explicit wave-averaged primitive equations using a generalized Lagrangian mean

The generalized Langrangian mean theory provides exact equations for general wave–turbulence–mean flow interactions in three dimensions. For practical applications, these equations must be closed by specifying the wave forcing terms. Here an approximate closure is obtained under the hypotheses of small surface slope, weak horizontal gradients of the water depth and mean current, and weak curvature of the mean current profile. These assumptions yield analytical expressions for the mean momentum and pressure forcing terms that can be expressed in terms of the wave spectrum. A vertical change of coordinate is then applied to obtain glm2z-RANS equations with non-divergent mass transport in cartesian coordinates. To lowest order, agreement is found with Eulerian mean theories, and the present approximation provides an explicit extension of known wave-averaged equations to short-scale variations of the wave field, and vertically varying currents only limited to weak or localized profile curvatures. Further, the underlying exact equations provide a natural framework for extensions to finite wave amplitudes and any realistic situation. The accuracy of the approximations is discussed using comparisons with exact numerical solutions for linear waves over arbitrary bottom slopes, for which the equations are still exact when properly accounting for partial standing waves. For finite amplitude waves it is found that the approximate solutions are probably accurate for ocean mixed layer modelling and shoaling waves, provided that an adequate turbulent closure is designed. However, for surf zone applications the approximations are expected to give only qualitative results due to the large influence of wave nonlinearity on the vertical profiles of wave forcing terms.     

Water and fine sediment dynamics in transient river plumes in a small, reef-fringed bay, Guam

Fouha Bay is a 400-m-long funnel-shaped, 10-m-deep, coral-fringed embayment on the southwest coast of Guam. It drains a small catchment area (5 km²) of steeply sloping, highly erodible lateritic soils. River floods are short-lived and the sediment load is very large, with suspended sediment concentration (SSC) exceeding 1000 mg l⁻¹. The resulting river plume is about 1 m thick and is pulsing in a series of 1–2 h-long events, with outflow velocity peaking at 0.05 m s⁻¹. Turbulent entrainment results in an oceanic inflow at depth into the bay. As soon as river flow stops, the plume floats passively and takes 5 days to be flushed out of Fouha Bay. The suspended fine sediment flocculates in 5 min and aggregates on ambient transparent exopolymer particles to form muddy marine snow flocs. In calm weather, about 75% of the riverine mud settles out of the river plume into the underlying oceanic water where it forms a transient nepheloid layer. This mud ultimately settles and is trapped in Fouha Bay. Under typhoon-driven, swell waves, the surface plume is at least 7 m thick and bottom entrainment of mud results in SSC exceeding 1000 mg l⁻¹ for several days. It is suggested that successful management of fringing coral reefs adjacent to volcanic islands may not be possible without proper land use management in the surrounding catchment.     

Wedge entry into initially calm water

This paper presents results of calculations based on the Cauchy's theorem method of Vinje and Brevig¹ for the two-dimensional entry of wedges of various angles into initially calm water. The problem has a long history which is briefly reviewed in the introduction, and significant progress has been made with both linear theories (valid for low entry speed) and with theories which treat the free surface conditions exactly but with the assumptions of zero gravity and constant speed of entry. This simplifies the problem to one which is self-similar in dimensionless space variables ξ = x/vt and η = y/vt and this has a number of consequences. For wedges with half-angles up to about 45° and with high entry speeds, the numerical approach, which includes gravity, validates these assumptions and the agreement between both free surface displacements and pressure distributions on the wetted wedge surface is excellent except in the region of the jet of fluid which rises up the side of the wedge. Because the potential flow initial value problem is singular at the intersection of the free surface and wedge surface, exact numerical resolution of the jet is not possible. Nevertheless, the rest of the fluid motion is insensitive to the treatment of the jet, which itself may be calculated quite realistically. Of particular interest (but little practical relevance) is the pressure on the upper part of the wedge surface (in the jet region) which according to self-similar theories is very small but positive, but which is calculated to be small but negative by the numerical scheme. This effect, which is enhanced when gravity is included, is insensitive to the numerical resolution of the jet and suggests that the jet may separate from the wedge surface, the new intersection point being where the pressure vanishes on the wedge surface. A modified numerical scheme allows this to happen and the results are in qualitative agreement with the experiments by Greenhow and Lin.²

The numerical method presented here is extremely versatile and a number of other effects may be explored. Examples of transient motion, non-constant speed of entry, oblique entry and complete penetration of the surface so that a cavity is formed behind the wedge are presented.     

Numerical simulation of oscillatory flows over a rippled bed by immersed boundary method

In this paper, a well-developed numerical model based on the immersed boundary (IB) method is used to study oscillatory flows over a bed with large-amplitude ripples in a systematic manner. The work shows that the complex flow over the rippled bed can be numerically dealt with in Cartesian coordinate by the IB method and that the IB method is able to provide main features of the flows near the ripples. An accurate simulation of vortices generation as a result of flow separation at the rippled bed is obtained. It is found that the oscillatory flows start to separate during the flow deceleration when the Keulegan–Carpenter (KC) number is small. The steady streaming for various ripple steepness is simulated and the criterion for separating the single and double structure streaming is also discussed. Moreover, a new type of steady streaming which consists of a pair of embedded recirculations in the vicinity of the ripple trough is obtained for relatively steep ripples in this work. The numerical results, including the steady streaming in particular, may be helpful to improve the understanding of the sediment transport and the seabed evolution with natural ripples under sea waves.     

Dynamics of the Mackenzie River plume on the inner Beaufort shelf during an open water period in summer

The oceanographic conditions of the Mackenzie River plume in the Arctic Ocean were examined during a 12-day period in August 2007. Field observations in the river channel and the delta region (2–6 m depth), ship-based observations on the shelf and satellite observations of sea surface temperatures indicate that movements of plume density fronts cause changes in water temperatures of over 10  C over a few days. We used a 1D model to compare the strength of stratification versus surface wind stress, and a 3D numerical model to simulate the plume motions under forcing from the river flows, local wind and water level variations from tides and wind-driven surge. The results indicate that the coastal region is stratified with a ∼2 m thick surface plume even in water depths of 3–4 m, resulting in strong vertical variation of horizontal currents. Moderate easterly winds of 5–10 m/s are sufficient to induce offshore transport of the surface plume and onshore transport of the deeper shelf water, leading to large fluctuations in temperature and salinity in the coastal region. This study examined a period of offshore transport and mean water level set-down, and indicates the rapid response of the plume to wind over the shallow delta.