The effects of large and small-scale topography upon internal waves and implications for tidally induced mixing in sill regions

A free surface non-hydrostatic model in a cross-sectional form, namely, two-dimensional, in the vertical is used to examine the role of larger-scale topography, namely, sill width, and smaller scale topography, namely, ripples on the sill upon internal wave generation and mixing in sill regions. The present work is set in the context of earlier work and the wider literature in order to emphasise the problems of simulating mixing in hydrographic models. Highlights from previous calculations and references to the literature for detail, together with new results presented here with smooth and “ripple” topography, are used to show that an idealised cross-sectional model can reproduce the dominant features found in observations at the Loch Etive sill. Calculations show that on both the short and long time scales, the presence of small-scale “ripple” topography influence the mixing and associated Richardson number distribution in the sill region. Subsequent calculations in which the position and form of the small-scale sill topography is varied show for the first time that it is the small-scale topography near the sill crest that is particularly important in enhancing mid-water mixing on the lee side of the sill. Both short-term and longer-term calculations with a reduced sill width and associated time series show that as the sill width is reduced, the non-linear response of the system increases. In addition, Richardson number plots show that the region of critical Richardson number, and hence enhanced mixing, increases with time and a reduction in sill width. Calculations in which buoyancy frequency N varies through the vertical show that buoyancy frequency close to the top of the sill is primarily controlling mixing rather than its mean value. Hence, a Froude number based on sill depth and local N is the critical parameter rather than one based on total depth and mean N.     

Recent pH and CO2 profiles at Lakes Nyos and Monoun, Cameroon: implications for the degassing strategy and its numerical simulation

In situ pH profiles are reported for the first time for Lakes Nyos and Monoun. The pH profiles were converted to CO₂ profiles using HCO₃⁻ profiles calculated from conductivity data. Recent observations (1993–1996) at Lake Nyos indicates that CO₂ still accumulates below 180 m depth at a rate of 125 Mmol year⁻¹. At Lake Monoun, the majority of CO₂ is present below a depth of 60 m, only 25 m below the saturation depth. Consequently, a potential danger of gas explosion is high at both lakes, and artificial degassing of the lakes should be performed as soon as possible. A system for industrial degassing of the lakes is proposed. The system, based on the self-sustained gas lift principle, consists of multiple pipes (14 cm in diameter) with different intake depths; 12 pipes for Lake Nyos (four each at 185, 195 and 205 m) and three pipes for Lake Monoun (at 70, 80 and 90 m). The stepped degassing at different depths is intended to keep the maximum stability of the lakes. The proposed degassing operation was simulated using the code for both lakes. In 5 years, approximately 50% of currently dissolved CO₂ in Lake Nyos and 90% in Lake Monoun will be removed. The expected changes in the thermal and chemical structures of the lakes as degassing proceeds will be most easily monitored with a carefully calibrated CTD equipped with a pH sensor. The simulation indicates that the discharged degassed water will sink to a level of neutral buoyancy, i.e. to a maximum of 70 m at Lake Nyos and 35 m at Lake Monoun. There would be no possibility of triggering a gas explosion by this plunge of discharged water because the water present there would have already been replaced by water at lower CO₂ concentration, during the degassing from shallower pipes.     

OBSERVATIONS ON ESTUARINE FLUID MUD ENTRAINMENT

I. INTRODUCTIONPrediction of mud bed erosion by forcing due to tidal currents usually requires a numerical solution of the advection--dispersion equation for sediment mass transport. Key role is of course played inthis by the bottom boundary conditions defining erosion and deposition fluxes. The issue of erosion isbriefly considered here. noting that it is customary to calculate the rate of erosion as a function of thebed shear stress in excess of the erosion shear strength of the bed (Me…     

Dispersal and air entrainment in unconfined dilute pyroclastic density currents

Unconfined scaled laboratory experiments show that 3D structures control the behavior of dilute pyroclastic density currents (PDCs) during and after liftoff. Experiments comprise heated and ambient temperature 20 μm talc powder turbulently suspended in air to form density currents within an unobstructed 8.5?×?6?×?2.6-m chamber. Comparisons of Richardson, thermal Richardson, Froude, Stokes, and settling numbers and buoyant thermal to kinetic energy densities show good agreement between experimental currents and dilute PDCs. The experimental Reynolds numbers are lower than those of PDCs, but the experiments are fully turbulent; thus, the large-scale dynamics are similar between the two systems. High-frequency, simultaneous observation in three orthogonal planes shows that the currents behave very differently than previous 2D (i.e., confined) currents. Specifically, whereas ambient temperature currents show radial dispersal patterns, buoyancy reversal, and liftoff of heated currents focuses dispersal along narrow axes beneath the rising plumes. The aspect ratios, defined as the current length divided by a characteristic width, are typically 2.5–3.5 in heated currents and 1.5–2.5 in ambient temperature currents, reflecting differences in dispersal between the two types of currents. Mechanisms of air entrainment differ greatly between the two currents: entrainment occurs primarily behind the heads and through the upper margins of ambient temperature currents, but heated currents entrain air through their lateral margins. That lateral entrainment is much more efficient than the vertical entrainment, >0.5 compared to ～0.1, where entrainment is defined as the ratio of cross-stream to streamwise velocity. These experiments suggest that generation of coignimbrite plumes should focus PDCs along narrow transport axes, resulting in elongate rather than radial deposits.     

Development and sensitivity analysis of a model for assessing stratification and safety of Lake Nyos during artificial degassing

To prevent the recurrence of a disastrous eruption of carbon dioxide (CO₂) from Lake Nyos, a degassing plan has been set up for the lake. Since there are concerns that the degassing of the lake may reduce the stability of the density stratification, there is an urgent need for a simulation tool to predict the evolution of the lake stratification in different scenarios. This paper describes the development of a numerical model to predict the CO₂ and dissolved solids concentrations, and the temperature structure as well as the stability of the water column of Lake Nyos. The model is tested with profiles of CO₂ concentrations and temperature taken in the years 1986 to 1996. It reproduces well the general mixing patterns observed in the lake. However, the intensity of the mixing tends to be overestimated in the epilimnion and underestimated in the monimolimnion. The overestimation of the mixing depth in the epilimnion is caused either by the parameterization of the k-epsilon model, or by the uncertainty in the calculation of the surface heat fluxes. The simulated mixing depth is highly sensitive to the surface heat fluxes, and errors in the mixing depth propagate from one year to the following. A precise simulation of the mixolimnion deepening therefore requires high accuracy in the meteorological forcing and the parameterization of the heat fluxes. Neither the meteorological data nor the formulae for the calculation of the heat fluxes are available with the necessary precision. Consequently, it will be indispensable to consider different forcing scenarios in the safety analysis in order to obtain robust boundary conditions for safe degassing. The input of temperature and CO₂ to the lake bottom can be adequately simulated for the years 1986 to 1996 with a constant sublacustrine source of 18 l s^–1 with a CO₂ concentration of 0.395 mol l^–1 and a temperature of 26 °C. The results of this study indicate that the model needs to be calibrated with more detailed field data before using it for its final purpose: the prediction of the stability and the safety of Lake Nyos during the degassing process.Responsible Editor: Hans Burchard     

Energetics of gas-driven limnic and volcanic eruptions

This paper lays the foundation for the rigorous treatment of the energetics of gas exsolution from a gas-containing liquid, which powers gas-driven volcanic and limnic eruptions. Various exsolution processes (reversible or irreversible, slow or rapid) are discussed, and the maximum amount of kinetic energy derivable from a reversible gas exsolution process is obtained. The concept of dynamic irreversibility is proposed for discussing the kinetic energy available from irreversible gas exsolution processes. The changes of thermodynamic properties during gas exsolution processes are derived. Density–pressure relations for gas–liquid mixtures are presented, including empirical relations for irreversible gas exsolution. The energetics of gas-driven eruptions through both fluid and rigid media, including the role of buoyancy and the role of magma chamber expansion work, are investigated. For reversible processes, the energetics can be used to discuss the dynamics of gas-driven eruptions, leading to maximum erupting velocities and maximum eruptible fractions. For irreversible processes, empirical relations and parameters must be employed. The exit velocities of the Lake Nyos eruption and the 18 May 1980 eruption of Mount St. Helens are modeled by incorporating possible irreversibility.     

Richardson number profiles in laboratory experiments applied to shallow seas

Abstract

A unified analysis is given of the critical conditions for the onset of stratification due to either a vertical or a horizontal buoyancy flux, with tidal or wind stirring.

The critical conditions for the onset of stratification with a horizontal buoyancy flux are found to be of the form of ratios of the tidal slope, or wind setup, to the equivalent surface slope due to the lateral density gradient. These ratios, which are easily determined from sea data, indicate that the profiles of critical flux Richardson Number, averaged over the stirring cycle, are similar to those inferred from the laboratory experiments of Hopfinger and Linden (1982) in which there is zero mean shear turbulence with a stabilising buoyancy flux, and also that the efficiency for the conversion of kinetic energy to potential energy for tidal stirring is similar to that for wind stirring.

The observed much greater efficiency for wind stirring, compared with tidal stirring with a vertical buoyancy flux, is also consistent with the existence of flux Richardson Number profiles in the sea similar to those occurring in the corresponding laboratory experiments. Using the solution of the turbulent kinetic energy equation for the water column, the relative importance of the production of turbulent kinetic energy, and its diffusion by turbulence are assessed, and the critical conditions for the onset of stratification with a vertical buoyancy flux are shown to reduce the classical Simpson—Hunter form.     

U-series dating of Lake Nyos maar basalts,Cameroon (West Africa): Implications for potential hazards on the Lake Nyos dam

From previously published ¹⁴C and K–Ar data, the age of formation of Lake Nyos maar in Cameroon is still in dispute. Lake Nyos exploded in 1986, releasing CO₂ that killed 1750 people and over 3000 cattle. Here we report results of the first measurements of major elements, trace elements and U-series disequilibria in ten basanites/trachy-basalts and two olivine tholeiites from Lake Nyos. It is the first time tholeiites are described in Lake Nyos. But for the tholeiites which are in ²³⁸U–²³⁰Th equilibrium, all the other samples possess ²³⁸U–²³⁰Th disequilibrium with 15 to 28% enrichment of ²³⁰Th over ²³⁸U. The (²²⁶Ra/²³⁰Th) activity ratios of these samples indicate small (2 to 4%) but significant ²²⁶Ra excesses. U–Th systematics and evidence from oxygen isotopes of the basalts and Lake Nyos granitic quartz separates show that the U-series disequilibria in these samples are source-based and not due to crustal contamination or post-eruptive alteration. Enrichment of ²³⁰Th is strong prima facie evidence that Lake Nyos is younger than 350 ka. The ²³⁰Th–²²⁶Ra age of Nyos samples calculated with the (²²⁶Ra/²³⁰Th) ratio for zero-age Mt. Cameroon samples is 3.7 ± 0.5 ka, although this is a lower limit as the actual age is estimated to be older than 5 ka, based on the measured mean ²³⁰Th/²³⁸U activity ratio. The general stability of the Lake Nyos pyroclastic dam is a cause for concern, but judging from its ²³⁰Th–²²⁶Ra formation age, we do not think that in the absence of a big rock fall or landslide into the lake, a big earthquake or volcanic eruption close to the lake, collapse of the dam from erosion alone is as imminent and alarming as has been suggested.     

On the dynamics of 3-D single thermal plumes at various Prandtl numbers and Rayleigh numbers

Three-dimensional (3-D) numerical simulations of single turbulent thermal plumes in the Boussinesq approximation are used to understand more deeply the interaction of a plume with itself and its environment. In order to do so, we varied the Rayleigh and Prandtl numbers from Ra?～?10⁵ to Ra?～?10⁸ and from Pr?～?0.025 to Pr?～?70. We found that thermal dissipation takes place mostly on the border of the plume. Moreover, the rate of energy dissipation per unit mass ε _T has a critical point around Pr?～?0.7. The reason is that at Pr greater than ～0.7, buoyancy dominates inertia and thermal advection dominates wave formation whereas this trend is reversed at Pr less than ～0.7. We also found that for large enough Prandtl number (Pr?～?70), the velocity field is mostly poloidal although this result was known for Rayleigh–Bénard convection (see Schmalzl et al. [On the validity of two-dimensional numerical approaches to time-dependent thermal convection. Europhys. Lett. 2004, 67, 390--396]). On the other hand, at small Prandtl numbers, the plume has a large helicity at large scale and a non-negligible toroidal part. Finally, as observed recently in details in weakly compressible turbulent thermal plume at Pr?=?0.7 (see Plourde et al. [Direct numerical simulations of a rapidly expanding thermal plume: structure and entrainment interaction. J. Fluid Mech. 2008, 604, 99--123]), we also noticed a two-time cycle in which there is entrainment of some of the external fluid to the plume, this process being most pronounced at the base of the plume. We explain this as a consequence of calculated Richardson number being unity at Pr?=?0.7 when buoyancy balance inertia.     

Small scale turbulent diffusion determined with underwater flow visualization

Dye plumes were generated at three depths in the seasonal thermocline between 7 and 11 m, 22 km south of Key West on 21 August 1980 and photographed at about 10 second intervals with an underwater camera system. Eleven pairs of consecutive pictures are analyzed to determine the mean current vertical shear and the width of the plumes by positioning reference points relative to the rod attached to the camera system. The relative distances of reference points are calibrated with the stereophotogrammetric method for one pair. The eddy diffusivity is calculated by use of a model of turbulent diffusion developed byTaylor (1921). Its values range from 5 to 25 cm²s^–1 for the plume widths ranging from 33 to 132 cm. The Richardson number is calculated for each pair of pictures with the vertical density gradient estimated from temperature profiles. Its values are higher than the critical value of 0.25 except for one case. The diffusivity was higher by orders of magnitude than the molecular one and indicates the presence of turbulence together with billow like features of the plumes in spite of high Richardson numbers. This suggests that the billow turbulence might be caused by effects of surface gravity waves and not by the Kelvin-Helmholtz instability.     

MYJ和YSU方案对WRF边界层气象要素模拟的影响

研究新一代中尺度气象模式WRF中两种大气边界层方案(MYJ,YSU)对沈阳冬季大气边界层结构模拟的影响,重点分析温度层结、低层风场、边界层高度等对污染物扩散有重要影响的气象要素.和观测数据的比对表明WRF基本能够模拟出温度风速的日变化特征,但模拟风速偏大.YSU方案由于模拟的边界层顶卷挟和边界层内混合作用较强,夜间接地逆温强度低于MYJ方案,逆温维持时间比MYJ方案短4小时,同时模拟边界层高度也高于MYJ方案,有利于污染物垂直扩散.边界层高度的3种计算方法中,湍流动能方法计算的边界层高度最高,Richardson数方法次之,位温方法得到的高度最低.Richardson数方法对临界值的选取较敏感.     

Circulation induced by subglacial discharge in glacial fjords: Results from idealized numerical simulations

The flow caused by the discharge of freshwater underneath a glacier into an idealized fjord is simulated with a 2D non-hydrostatic model. As the freshwater leaves horizontally the subglacial opening into a fjord of uniformly denser water it spreads along the bottom as a jet, until buoyancy forces it to rise. During the initial rising phase, the plume meanders into complex flow patterns while mixing with the surrounding fluid until it reaches the surface and then spreads horizontally as a surface seaward flowing plume of brackish water. The process induces an estuarine-like circulation. Once steady-state is reached, the flow consists of an almost undiluted buoyant plume rising straight along the face of the glacier that turns into a horizontal surface layer thickening as it flows seaward. Over the range of parameters examined, the estuarine circulation is dynamically unstable with gradient Richardson number at the sheared interface having values of <1/4. The surface velocity and dilution factors are strongly and non-linearly related to the Froude number. It is the buoyancy flux that primarily controls the resulting circulation with the momentum flux playing a secondary role.     

The influences of composition-sand temperature-dependent rheology in thermal-chemical convection on entrainment of the D″-layer

The entrainment dynamics in the D″-layer are influenced by multitudinous factors, such as thermal and compositional buoyancy, and temperature- and composition-dependent viscosity. Here, we are focusing on the effect of compositionally dependent viscosity on the mixing dynamics of the D″-layer, arising from the less viscous but denser D″-material. The marker method, with one million markers, is used for portraying the fine scale features of the compositional components, D″-layer and lower-mantle. The D″-layer has a higher density but a lower viscosity than the ambient lower-mantle, as suggested by melting point systematics. Results from a two-dimensional finite-difference numerical model including the extended Boussinesq approximation with dissipation number Di=0.3, show that a D″-layer, less viscous than the ambient mantle by 1.5 orders of magnitude, cannot efficiently mix with the lower-mantle, even though the buoyancy parameter is as low as R_ρ=0.6. However, very small-scale schlieren structures of D″-layer material are entrained into the lower-mantle. These small-scale lower-mantle heterogeneities have been imaged with one-dimensional wavelets in order to delineate quantitatively the multiscale features. They may offer an explanation for small-scale seismic heterogeneity inferred by seismic scattering in the lower-mantle.     

Constraints on the age of Lake Nyos, Cameroon

The upper 40 m of Lake Nyos are retained by a weak natural dam which, if it were to fail, would not only devastate the area hit by the 1986 gas disaster but would also cause a serious flood to surge down the Katsina Ala into Nigeria. The age of the pyroclastic cone, of which the dam is the last remnant, is therefore of great practical importance to the people of the area. If the pyroclastic cone is only a few hundred years old, as some have suggested, then it is eroding away quickly and the dam must surely fail in the very near future. If, on the other hand, it is many thousands of years old, then there is less immediate cause for concern.The age of the pyroclastic cone can be constrained in three ways:(1) Two samples of basalt, one from the dam itself and one from a lava flow which post-dates the pyroclastic cone, have both yielded K–Ar ages in excess of 100,000 years.(2) Photographic evidence indicates that there has been no detectable change (>2 m) to the width of the dam since 1958. This constrains the average erosion rate and suggests that the pyroclastic cone is at least 4000 years old.(3) Cores from sediment deposited after the level of a small lake to the northeast of Lake Nyos was raised by a debris slide from the pyroclastic cone, contain no volcanic ash. A sample from the base of this sequence has yielded a radiocarbon age of 2700 years.The Lake Nyos dam must therefore be, at the very least, a few thousand years old and although its general stability must give serious cause for concern there is no reason to suspect that the rate at which it is currently eroding away is of itself sufficient to pose an immediate threat.     

太湖鱼类放流增殖的有效数量和合理结构

根据2006-2007年太湖生物资源调查,估算出太湖浮游植物、浮游动物、底栖动物和水生植物总渔产潜力约为78494 t.太湖实施以渔改水的生物调控措施,应加大鲢、鳙放流数量和放流规格,在提高鱼产量的同时对抑制太湖蓝藻水华能起到积极作用;推算每年放流鳙约1000×104尾,鲢约300×104尾,规格为20尾/kg为宜.草鱼、团头鲂、青鱼、鲤等要在保护太湖水草和底栖动物资源和生物多样性前提下适当放流,每年宜放流草鱼150×104尾,团头鲂165×104尾,青鱼8×104 ～ 10×104尾,鲤夏花2500×104尾.而对调控鱼类结构小型化、单一化具有重要作用的肉食性鱼类翘嘴铂建议加大放流量,年放流量可扩大至500×104尾左右,在调控的同时提高湖泊渔业附加值.     

Temperature, density and buoyancy fluxes in “black smoker” plumes, and the criterion for buoyancy reversal

Measurements of the temperature and composition of effluent from vents on the sea floor can be used to deduce the in-situ density of this fluid, which is required for calculations of flow in the chimneys and through their porous walls. This density is, however, not directly relevant when calculating the buoyancy flux in the plume above a smoker. It is the asymptotic buoyancy flux, following extensive dilution with seawater, which is required when estimating the height of rise of plumes in a stably stratified ocean, and when calculating the criterion for reversal of buoyancy due to non-linear mixing effects. The results of mixing calculations show that the effluent from hydrothermal vents on the sea floor will exhibit reversing buoyancy if the ejected fluid has a temperature of 300°C and a salinity greater than 8 wt.% NaCl. If the temperature of the effluent is 200°C the salinity required for reversing buoyancy falls to 5.5 wt.% NaCl. Measurements of temperature and salinities of sea-floor hydrothermal fluid suggest that fluids with the characteristics required to form reversing plumes are ejected at the sea floor. The possibility that reversing plumes may be found has important implications for the formation of massive sulfide deposits.     

Simulation of vertical position of buoyancy regulating Microcystis aeruginosa in a shallow eutrophic lake

Vertical distributions of the cyanobacterium Microcystis aeruginosa are examined in a shallow lake in relation to mixing and thermal stratification over three days. A model of buoyancy regulation by Microcystis aeruginosa, applicable for turbulent environments, is coupled with a one-dimensional hydrodynamic model. The coupled model is applied to Thomsons Lake in Western Australia to examine the relationship between buoyancy regulation and the daily stratification/destratification cycle. The vertical distribution of Microcystis aeruginosa in Thomsons Lake depends on the carbohydrate ballast dynamics and the colony size. When thermal stratification occurs, all the simulations show a similar general pattern of diurnal vertical migration of the Microcystis aeruginosa colonies. The colonies accumulate at the surface during the night and in the morning the colonies lose buoyancy, which leads to a reduction by ~ \sim 50% in colony concentration in the top 0.2--0.3 m of the water column. Afternoon winds redistribute the population over the entire water column. When the lake is fully mixed, the vertical migration pattern of the Microcystis aeruginosa colonies may be affected, depending on the colony size and the intensity of the mixing.     

Mixing efficiency in stably-stratified decaying turbulence

Abstract

The behavior of the flux Richardson number R _f, as a function of the overall Richardson number Ri ₀, was investigated for a stably stratified, grid-generated, turbulent flow evolving in a closed-loop water channel. The turbulent dissipation rate ε, the buoyancy or vertical mass flux p wbar; and the rms density fluctuation ρ′ were obtained from simultaneous single-point measurements of the horizontal and vertical velocity components and density fluctuations. From these, R _f and Ri ₀ were calculated at each point in the spatially evolving flow. The resulting curves of R _f vs. Ri ₀ exhibit the full range of behavior found in the very different case studied by Linden (1980). The length scale arguments of Gibson (1980) and Stillinger et al. (1983b) provide an underlying mechanism which successfully accounts for the shape of the R _f vs. Ri ₀ curve.     

Modelling hydrodynamics in Yachiyo Lake using a non‐hydrostatic general circulation model with spatially and temporally varying meteorological conditions

In this study, a three‐dimensional (3D) non‐hydrostatic circulation model was applied to study the thermal structure, its evolution and water circulation of Yachiyo Lake in Hiroshima, Japan. The simulations were conducted for 1 month during July 2006. The meteorological forcing variables such as wind stress, surface atmospheric pressure and heat flux transfer through the lake surface were provided by an atmospheric mesoscale model run. The vertical mixing process of the lake was calculated using the Mellor‐Yamada turbulence model. The 1‐month numerical simulation revealed the wind‐induced currents of the lake, two gyres in the mid‐layer, and depth‐averaged monthly mean currents. Further numerical experiments studying the mechanism of the two gyres in the lake showed the important role of topography in gyre formation. The thermal structure of the lake and its evolution both in space and in time as predicted by the model showed very good agreement with the observed values and characteristics of Yachiyo Lake. The internal gravity waves, which are crucial for mixing in the stratified lake, are depicted by the vertical fluctuation of isotherms. Using the non‐dimensional gradient Richardson number, Yachiyo Lake was determined to be stable under strong stratification during the study period, and therefore very sensitive to wind stress. Copyright © 2009 John Wiley & Sons, Ltd.