Mixing dynamics of turbidity currents interacting with complex seafloor topography

Direct Numerical Simulations are employed to investigate the mixing dynamics of turbidity currents interacting with seamounts of various heights. The mixing properties are found to be governed by the competing effects of turbulence amplification and enhanced dissipation due to the three-dimensional topography. In addition, particle settling is seen to play an important role as well, as it affects the local density stratification, and hence the stability, of the current. The interplay of these different mechanisms results in the non-monotonic dependence of the mixing behavior on the height of the seamount. Regions of dilute lock fluid concentration generally mix more intensely as a result of the seafloor topography, while concentrated lock fluid remains relatively unaffected. For long times, the strongest mixing occurs for intermediate bump heights. Particle settling is seen to cause turbidity currents to mix more intensely with the ambient than gravity currents.     

Structure of a dense release produced by varying initial conditions

Buoyancy driven flows such as gravity currents, present in nature and human made applications, are conveyors of particles or dissolved substances for long distances with clear implications for the environment. This transport depends on the triggering conditions of the current. Gravity currents are experimentally simulated under varying initial conditions by combining three different initial buoyancies and five volumes of dense fluid released. The horizontal and vertical structures of the gravity currents are analysed and it is shown that the variation on the initial configuration is conditioning for these. Vertical transport through the gravity current is influenced at the bottom by the solid wall over which the current flows, and at the upper interface by the contact with the ambient water. The relative contribution of shear stress at the bottom and at the upper interfaces are estimated and analysed in terms of the initial triggering conditions of the current; these two compete with the buoyancy, the driver of the current, determining mixing and entrainment. By using a proper parametrization, which accounts for both initial volume of release and location of the observation position relative to the lock, a relation between the resistance at the bottom and at the upper interfaces with the initial conditions of release (i.e. the lock-length) has been found; this is found to be independent of the initial density in the lock. The present study shows that the variation of the initial conditions have consequences on (1) the configuration of the currents and on (2) the hydrodynamics of the currents, including mass and momentum exchanges, which are in addition mutually dependent.     

On gravity currents confined by porous boundaries in containers of general cross-sections

Environmental Fluid Mechanics - We consider an inertial (large Reynolds number) gravity current (GC) released from a lock of length $$x_0$$ and height $$h_0$$ into an ambient fluid of height...     

Front velocity and structure of bottom gravity currents with a low volume of release propagating in a porous medium

The paper reports results of large eddy simulations of lock exchange compositional gravity currents with a low volume of release advancing in a horizontal, long channel. The channel contains an array of spanwise-oriented square cylinders. The cylinders are uniformly distributed within the whole channel. The flow past the individual cylinders is resolved by the numerical simulation. The paper discusses how the structure and evolution of the current change with the main geometrical parameters of the flow (e.g., solid volume fraction, ratio between the initial height of the region containing lock fluid and the channel depth, ratio between the initial length and height of the region containing lock fluid) and the Reynolds number. Though in all cases with a sufficiently large solid volume fraction the current transitions to a drag-dominated regime, the value of the power law coefficient, α, describing the front position’s variation with time (x _f  ~ t ^α , where t is the time measured from the removal of the lock gate) is different between full depth cases and partial depth cases. The paper also discusses how large eddy simulation (LES) results compare with findings based on shallow-water equations. In particular, LES results show that the values of α are not always equal to values predicted by shallow water theory for the limiting cases where the current height is comparable, or much smaller, than the channel depth.     

初论地表粗糙度

粗糙度是流体力学引进的一个重要参数,是现代地球表面各种物质流运动研究中不可或缺的一个重要概念。它在定床流动中曾获得巨大的成功,但在动床及所谓零位移较大的粗糙面上,表现出其局限性。文章在系统阐述了空气动力学意义上粗糙度概念的由来及其物理意义;在总结某些学科领域中粗糙度的应用成果基础上,发现对于定床,地表粗糙具有地表阻力系数特性,它比地表物体群落平均高度小一个量级;而对于动床,粗糙度则更具有阻力系数的特性,它与超出临界摩阻之值成正比;至于植被地表的粗糙度则近似于定床,但它要从零平面位移高度算起。因此,地表粗糙度概念的进一步完善应从地表阻力系数和实验研究入手,并加强自然界和室内实验室的观测和实验以获得相应系数的变化规律,最终解决粗糙度本身和流体力学相关的理论和实践问题。     

Visualization of the internal flow properties and the material exchange interface in an entraining viscous Newtonian gravity current

In order to simulate a simple entraining geophysical flow, a viscous Newtonian gravity current is released from a reservoir by a dam-break and flows along a rigid horizontal bed until it meets a layer of entrainable material of finite depth, identical to the current. The goal is to examine the entrainment mechanisms by observing the interaction between the incoming flow and the loose bed. The sole parameter varied is the initial volume of the gravity current, thus altering its height and velocity. The gravity current plunges or spills into the entrainable bed and the velocity of the flow front becomes linear with time. The bed material is directly affected: motion is generated in the fluid far downstream of, and in that lying beneath the encroaching front. Shear bands are identified, separating horizontal flow downstream from flow with a strong vertical component close to the step. Downstream of the step the flow is horizontal and stratified, with no slip on the bottom boundary and very low shear near the surface. Between these two regions may lie transitional zones with linear velocity profiles, separated by horizontal bands of high shear; the number of transitional zones in the cross-section varies with the initial volume of the dam-break.     

Lock-exchange gravity currents over rough bottoms

In nature, density driven currents often flow over or within a bottom roughness: a sea breeze encountering tall buildings, a shallow flow encountering aquatic vegetation, or a dense oceanic current flowing over a rough bottom. Laboratory experiments investigating the mechanisms by which bottom roughness enhances or inhibits entrainment and dilution in a lock-exchange dense gravity current have been conducted. The bottom roughness has been idealized by an array of vertical, rigid cylinders. Both spacing (sparse vs. dense configuration) and height of the roughness elements compared with the height of the current have been varied. Two-dimensional density fields have been obtained. Experimental results suggest that enhancement of the entrainment/dilution of the current can occur due to two different mechanisms. For a sparse configuration, the dense current propagates between the cylinders and the entrainment is enhanced by the vortices generated in the wake of the cylindrical obstacles. For a dense configuration, the dense current rides on top of the cylinders and the dilution is enhanced by the onset of convective instability between the dense current above the cylinders and the ambient lighter water between the cylinders. For low values of the ratio of the cylinder to lock height \(\lambda \) the dense current behavior approaches that of a current over a smooth bottom, while the largest deviations from the smooth bottom case are observed for large values of \(\lambda \).     

Shoaling internal waves may reduce gravity current transport

Gravity currents descending along slopes have typically been studied in quiescent environments, despite the fact that in many geophysical settings there is significant externally driven motion. Here we investigate how the head of a gravity current is influenced by interfacial internal waves at the pycnocline of a two-layer ambient water column. Our experimental measurements show that larger amplitude internal waves, interacting with the gravity current, reduce both the mass transport by the gravity current and its thickness. These results suggest that the ambient internal wave field should be considered when estimating transport by gravity currents in geophysical settings with strong internal waves, such as lakes and the coastal ocean.     

Effect of initial excess density and discharge on constant flux gravity currents propagating on a slope

The effect of the upstream conditions on propagation of gravity current over a slope is investigated using three-dimensional numerical simulations. The current produced by constant buoyancy flux, is simulated using a large eddy simulation solver. The dense saline solution used at the inlet is the driving force of the flow. Higher replenishment of the current is possible either by a high inflow discharge or high initial fractional density excess. In the simulations, it is observed that these two parameters affect the flow in different ways. Results show that the front speed of the descending current is proportional to the cube root of buoyancy flux, $(g_o^{\prime } Q)^{1/3}$ , which agrees with the previous experimental and numerical observations. The height of the tail of the current grows linearly in the streamwise direction. Formation of a strong shear layer at the boundary of mixed upper layer and dense lower layer is observed within the body and the tail of the current. Over the tail of the current far enough from the inlet, the vertical velocity and density profiles are compared to the ones from an experimental study. Distance from the bed to the point of maximum velocity increases with an increase in inflow discharge, while it remains practically unchanged with increasing initial fractional excess density in the simulations. Even though the velocity profiles are in good agreement, some discrepancies are observed in fractional excess density profiles among experimental and numerical results. Possible reasons for these discrepancies are discussed. Generally, gravity current type of flows could be expressed in layer-integrated formulation of governing equations. However, layer integration introduces several constants, commonly known as shape factors, to the equations of motion. The values of these shape factors are calculated based on simulation results and compared to the values from experiments and to the favorably used ‘top hat’ assumption.     

Blockage of saline intrusions in restricted,two-layer exchange flows across a submerged sill obstruction

Results are presented from a series of large-scale experiments investigating the internal and near-bed dynamics of bi-directional stratified flows with a net-barotropic component across a submerged, trapezoidal, sill obstruction. High-resolution velocity and density profiles are obtained in the vicinity of the obstruction to observe internal-flow dynamics under a range of parametric forcing conditions (i.e. variable saline and fresh water volume fluxes; density differences; sill obstruction submergence depths). Detailed synoptic velocity fields are measured across the sill crest using 2D particle image velocimetry, while the density structure of the two-layer exchange flows is measured using micro-conductivity probes at several sill locations. These measurements are designed to aid qualitative and quantitative interpretation of the internal-flow processes associated with the lower saline intrusion layer blockage conditions, and indicate that the primary mechanism for this blockage is mass exchange from the saline intrusion layer due to significant interfacial mixing and entrainment under dominant, net-barotropic, flow conditions in the upper freshwater layer. This interfacial mixing is quantified by considering both the isopycnal separation of vertically-sorted density profiles across the sill, as well as calculation of corresponding Thorpe overturning length scales. Analysis of the synoptic velocity fields and density profiles also indicates that the net exchange flow conditions remain subcritical (G < 1) across the sill for all parametric conditions tested. An analytical two-layer exchange flow model is then developed to include frictional and entrainment effects, both of which are needed to account for turbulent stresses and saline entrainment into the upper freshwater layer. The experimental results are used to validate two key model parameters: (1) the internal-flow head loss associated with boundary friction and interfacial shear; and (2) the mass exchange from the lower saline layer into the upper fresh layer due to entrainment.     

A two-dimensional inviscid model of the gravity-current head by Lagrangian block simulation

A two-dimensional inviscid model of the gravity-current head produced by the release of a relatively small volume of dense fluid from behind a tall lock gate is constructed by Lagrangian block simulation. Three numerical experiments are conducted for the lock’s height-to-length aspect ratios H/L _o  = 8, 4 and 2. The front speeds obtained by the simulations agree with the laboratory observation for a similar range of aspect ratios. The floor velocity in the wake behind these heads is found to be greater than their front speed. The high floor velocity is caused by the impingement of the coherent wake vortex on the floor. It is a condition that permits these gravity-current heads to maintain their structural integrity so that the fine sediments can travel with the head over long distances on the ocean floor. The structural coherence of the current head depends on the lock aspect ratio. The gravity-current head produced by the release from the lock with the highest aspect ratio of H/L _o  = 8 is most coherent and relatively has the greatest floor velocity and the least trailing current behind the head.     

Gravity currents with double stratification: a numerical and analytical investigation

We consider high-Reynolds-number Boussinesq gravity current and intrusion systems in which both the ambient and the propagating “current” are linearly stratified. The main focus is on a current of fixed volume released from a rectangular lock; the height ratio of the fluids $H$ , the stratification parameter of the ambient $S$ , and the internal stratification parameter of the current, $\sigma $ , are quite general. We perform two-dimensional Navier–Stokes simulation and compare the results with those of a previously-published one-layer shallow-water model. The results provide insights into the behavior of the system and enhance the confidence in the approximate model while also revealing its limitations. The qualitative predictions of the model are confirmed, in particular: (1) there is an initial “slumping” stage of propagation with constant speed $u_N$ , after which $u_N$ decays with time; (2) for fixed $H$ and $S$ , the increase of $\sigma $ causes a slower propagation of the current; (3) for some combinations of the parameters $H,S, \sigma $ the fluid released from the lock lacks initially (or runs out quickly of) buoyancy “driving power” in the horizontal direction, and does not propagate like a gravity current. There is also a fair quantitative agreement between the predictions of the model and the simulations concerning the spread of the current.     

A review of gravity currents formed by submerged single-port discharges in inland and coastal waters

In this paper, the authors review the current state of the science on the dynamics of gravity currents generated by positively and negatively buoyant jet discharges from submerged round outfalls (i.e., a point source) in inland and coastal waters. Specifically, this article focuses on describing gravity currents occurring at both the bottom boundary and the free surface of the receiving fluid. The manmade discharge operations generating both types of gravity currents and their significance to sustainability of the surrounding hydro-environment are first described. The authors then summarize the flow regimes characteristics of these discharges before becoming gravity currents and how those flow regimes influence the dynamics of the gravity currents. The gravity current dynamics in the calm receiving waters are then analyzed. This analysis is followed by an analysis of the influence of the hydrodynamic forces (e.g., currents, turbulence, waves) on the dynamics of gravity currents. Finally, the authors review quantitative modeling approaches for different forms of gravity current, and identify the current knowledge gaps and research needs.     

Gravity currents in two-layer stratified media

An analytical, experimental and numerical study of boundary gravity currents propagating through a two-layer stratified ambient of finite vertical extent is presented. Gravity currents are supposed to originate from a lock-release apparatus; the (heavy) gravity current fluid is assumed to span the entire channel depth, H, at the initial instant. Our theoretical discussion considers slumping, supercritical gravity currents, i.e. those that generate an interfacial disturbance whose speed of propagation matches the front speed, and follows from the classical analysis of Benjamin (J Fluid Mech 31:209?C248, 1968). In contrast to previous investigations, we argue that the interfacial disturbance must be parameterized so that its amplitude can be straightforwardly determined from the ambient layer depths. Our parameterization is based on sensible physical arguments; its accuracy is confirmed by comparison against experimental and numerical data. More generally, measured front speeds show positive agreement with analogue model predictions, which remain strictly single-valued. From experimental and numerical observations of supercritical gravity currents, it is noted that this front speed is essentially independent of the interfacial thickness, ??, even in the limiting case where ?? = H so that the environment is comprised of a uniformly stratified ambient with no readily discernible upper or lower ambient layer. Conversely, when the gravity current is subcritical, there is a mild increase of front speed with ??. Our experiments also consider the horizontal distance, X, at which the front begins to decelerate. The variation of X with the interface thickness and the depths and densities of the ambient layers is discussed. For subcritical gravity currents, X may be as small as three lock lengths whereas with supercritical gravity currents, the gravity current may travel long distances at constant speed, particularly as the lower layer depth diminishes.     

Parameterization of the roughness length over the sea in forced and free convection

In the condition of free convection, the Charnock relation is inadequate. In this paper we extend the Charnock relation to include the effect of free convection on the roughness length. As a result, the singularity in the Monin–Obukhov similarity theory can be avoided. This paper shows two approaches to derive the roughness length formula in the forced and free convections. The first approach is based on the mixing length theory and the use of the observational data of the vertical velocity variance. We introduce a new vertical velocity scale based on the vertical velocity variance; this velocity variance is well behaved in the atmospheric boundary layer and easy to obtain from field experiments. The second approach is based on the theoretical framework of Sykes et al. (Q R Met Soc, 119: 409–421). From that framework, we develop a theory to obtain the roughness length formula. The results of these two approaches are in agreement with each other. In the past, a multiplication factor associated with free convection was considered to be a constant. This paper shows that this multiplication factor is, in fact, also dependent on the depth of the mixing height. In previous studies, experimental works were often conducted without taking into account the depth of the mixing height. Not taking into account the mixing height in the estimation of the roughness length in free convection would result in an inaccurate estimate of the roughness length and hence the drag coefficient. An erratum to this article can be found at     

Experimental and numerical investigation of density current over macro-roughness

The dynamics of density current over a bottom covered by macro-roughness elements were investigated by laboratory experiments and a computational model using large eddy simulations. The macro-roughness considered had significant size in comparison with the scale of density current. Five different roughness conditions were considered, namely flat bottom (for reference), half spheres, fine gravels, medium gravels, and large gravels. These bottom conditions had variations in roughness element size, shape, angularity, and spatial configuration. The density current was a lock-exchange type with a density difference of 1% between the two fluids initially separated by a gate in the middle. In the computational model, the roughness was captured using two different methods depending on the size of the roughness elements. For the large roughness elements, i.e., the half spheres and the medium and large gravels, an immersed boundary method was used to resolve the surface of each gravel, which was obtained through 3D laser scanning. The realistic and physically correct placement of these scanned objects in the simulation domain was achieved using a computer tool which can detect the collision of rigid bodies and simulate their dynamics. For the fine gravels, a rough wall function was used. The computational model was validated with the data measured in the experiments, including front position and velocity, and point velocity measurement within the current. The results show that density currents over macro-roughness have distinct behavior from those over a smooth boundary. The characteristics (size, angularity, and pavement pattern) of the macro-roughness play a key role in the current development. Macro-roughness significantly retards the front propagation and enhances entrainment.     

Experimental study of a positive surge. Part 1: basic flow patterns and wave attenuation

A positive surge results from a sudden change in flow that increases the depth. It is the unsteady flow analogy of the stationary hydraulic jump and a geophysical application is the tidal bore. Positive surges are commonly studied using the method of characteristics and the Saint-Venant equations. The article presents the results from new experimental investigations conducted in a large rectangular channel. Detailed unsteady velocity measurements were performed with a high temporal resolution using acoustic Doppler velocimetry and non-intrusive free-surface measurement devices. Several experiments were conducted with the same initial discharge (Q = 0.060 m³/s) and six different gate openings after closure resulting in both non-breaking undular and breaking bores. The analysis of undular surges revealed wave amplitude attenuation with increasing distance of surge propagation were in agreement with Ippen and Kulin theory. Also, undular wave period and wave length data were relatively close to the values predicted by the wave dispersion theory for gravity waves in intermediate water depths.     

Concept and application of anaerobic suspended granular sludge bed （SGSB） reactor for wastewater treatment

Bed expansion serves an important function in the design and operation of an upflow anaerobic reactor. An analysis of the flow pattern of expanded granular sludge bed （EGSB） reactors shows that most EGSB reactors do not behave as expanded bed reactors, as is widely perceived. Rather, these reactors behave as fluidized bed reactors based on the classic chemical reactor theory. In this paper, four bed expansion modes, divided as static bed, expanded bed, suspended bed, and fluidized bed, for bioreactors are proposed. A high-rate anaerobic suspended granular sludge bed （SGSB） reactor was then developed. The SGSB reactor is an upflow anaerobic reactor, and its expansion degree can be easily controlled within a range to maintain the suspended status of the sludge bed by controlling upfiow velocity. The results of the full-scale reactor confirmed that the use of SGSB reactors is advantageous. The full-scale SGSB reactor runs stably and achieves high COD removal efficiency （about 90%） at high loading rates （average 40 kg-COD·m^-3·d^-1, maximum to 52 kg·COD·m^-3 ·d^-1） based on the SGSB theory, and its expansion degree is between 22% and 37%.     

Fixed-bed adsorption of Malachite Green onto binary solid mixture of adsorbents: seashells and eggshells

In this work, continuous removal of Malachite Green from aqueous solution by adsorption was investigated using a laboratory scale fixed-bed column packed with binary solid mixture of seashell powder (SSP) and eggshell powder (ESP). The effects of initial dye concentration, feed flow rate, bed height, and the SSP?:?ESP ratio in the binary solid mixture on the breakthrough characteristics were studied. The breakthrough time decreased with increase in the flow rate and the initial dye concentration. The breakthrough time also varied greatly with change in bed height. The breakthrough time increased from 17.2?h to 34.5?h with increase in bed height from 6?cm to 12?cm. The breakthrough time was significantly affected by the change in the SSP?:?ESP ratio in the binary mixture. The breakthrough time decreased with increase in the SSP ratio in the binary mixture. In order to determine the column kinetic parameters, three different column kinetic models, namely Adams–Bohart, Bed Depth Service Time (BDST), and Yoon–Nelson models were fitted to the dynamic flow experimental data. The BDST model showed good agreement with the experimental results at all the process parameters studied. Results suggest that this novel approach of simultaneous utilization of adsorbents can be adopted for the treatment of dye-bearing effluents.     

Turbulence investigation in the roughness sub-layer of a near wall flow

The turbulence behaviour along a wall roughened by pyramidal elements was analysed in the region extending from the apex of the roughness elements up to the external limit of the roughness sub-layer. The data used for the analysis were obtained by particle image velocimetry technique. The rough wall turbulent boundary layer flow is characterized by a relatively low Reynolds number. All the results on the rough wall were compared with data referring to the canonical flow on a smooth wall turbulent boundary layer. Mean values and turbulence quantities for the two flows collapse when approaching the external limit of the roughness sublayer. The quadrant analysis of the Reynolds shear stress, in the region near the surface, shows that the contribution of the sweep motions is about equivalent for the two flows (except for wall distances lower than 40 viscous units). The contribution of the ejection motions appears to be more important over the smooth wall than over the rough wall with increasing differences approaching the wall. The probability density functions of the streamwise fluctuating velocity field for the rough wall case appear to be positively skewed in the zone very close to the pyramid apex, in contrast with the behavior observed for the smooth wall case at corresponding distances from the wall. The integral and Taylor scales for the rough wall case appear to be strongly reduced by the presence of the roughness, while the Kolmogorov microscale shows higher values.