Modelling Gravitational Instabilities: Slab Break–off and Rayleigh–Taylor Diapirism

A non-standard new code to solve multiphase viscous thermo–mechanical problems applied to geophysics is presented. Two numerical methodologies employed in the code are described: A level set technique to track the position of the materials and an enrichment of the solution to allow the strain rate to be discontinuous across the interface. These techniques have low computational cost and can be used in standard desktop PCs. Examples of phase tracking with level set are presented in two and three dimensions to study slab detachment in subduction processes and Rayleigh–Taylor instabilities, respectively. The modelling of slab detachment processes includes realistic rheology with viscosity depending on temperature, pressure and strain rate; shear and adiabatic heating mechanisms; density including mineral phase changes and varying thermal conductivity. Detachment models show a first prolonged period of thermal diffusion until a fast necking of the subducting slab results in the break–off. The influence of several numerical and physical parameters on the detachment process is analyzed: The shear heating exerts a major influence accelerating the detachment process, reducing the onset time to one half and lubricating the sinking of the detached slab. The adiabatic heating term acts as a thermal stabilizer. If the mantle temperature follows an adiabatic gradient, neglecting this heating term must be included, otherwise all temperature contrasts are overestimated. As expected, the phase change at 410 km depth (olivine–spinel transition) facilitates the detachment process due to the increase in negative buoyancy. Finally, simple plume simulations are used to show how the presented numerical methodologies can be extended to three dimensions.     

Effects of molecular ions on the Rayleigh–Taylor instability in the night-time equatorial ionosphere

In view of composition measurements in the night-time equatorial ionosphere, the role of molecular ions on the collisional Rayleigh–Taylor instability is examined using a linear perturbation analysis and a growth rate expression in the presence of double-ion species is obtained. The expression reveals that the growth rate depends on the number densities of both the ion species. This is in contrast to a single ionic constituent wherein the growth rate is independent of number density. The numerical calculation under realistic conditions reveals that the growth rate of the instability reduces with the introduction of the second dominant ion species and never exceeds the growth rate corresponding to a single ionic constituent. Further, the growth of the plasma instability is feasible even when the scale length of the second dominant ion is negative.     

Fate of persistent organic pollutants in the water column: does turbulent mixing matter?

The effect of vertical turbulent mixing on the dynamics of persistent organic pollutants has long been overlooked and its role is still hardly understood. Here we present the first comprehensive analysis of the role of turbulent diffusion on the distribution of those contaminants and its interplay with sinking fluxes. To this end, a 1D dynamic coupled hydrodynamic-contaminant model has been developed and applied to a Mediterranean continental shelf environment. The hydrodynamic sub-model is adapted from COHERENS, the contaminant sub-model is an improvement from the BIODEP model and considers the contaminant in 3 phases: dissolved-colloidal-particulate. The simulation highlights the role of turbulence in determining the POP distribution and variability in the water column. In short, turbulent flux of contaminants strengthens the upward diffusion of sediment entrained contaminants and determines the extent to which inputs from the atmosphere mix into the water column. It acts in parallel with degradation and sinking fluxes, the combined effect yielding a surface enriched - depth depleted - benthic layer enriched region distribution, which presents similarities to reported experimental measures.     

大气重力波触发的Rayleigh－Taylor不稳定性的时空演变

对大气重力波触发的赤道电离层Ｒａｙｌｅｉｇｈ－Ｔａｙｌｏｒ不稳定性的时空演变进行了数值模拟．结果表明，重力波能在Ｆ区底部触发Ｒａｙｌｅｉｇｈ－Ｔａｙｌｏｒ不稳定性，这种等离子体不稳定扰动穿过Ｆ峰，到达Ｆ区顶部，形成等离子体泡结构．等离子体泡出现向西倾斜和分岔等特征．当夜Ｆ区较高时，产生等离子体泡的时间仅１９００ｓ．数值模拟结果证实了重力波触发．Ｒａｙｌｅｉｇｈ－Ｔａｙｌｏｒ不稳定性的理论，解释了大量电离层观测现象．     

Seawater–freshwater mixing and resulting calcite dissolution: an example from a coastal alluvial aquifer in eastern South Korea

Abstract

In order to evaluate groundwater quality and geochemical reactions arising from mixing between seawater and dilute groundwater, we performed a hydrochemical investigation of alluvial groundwater in a limestone-rich coastal area of eastern South Korea. Two sites were chosen for comparison: an upstream site and a downstream site. Data of major ion chemistry and ratios of oxygen–hydrogen isotopes (δ¹⁸O, δD) revealed different major sources of groundwater salinity: recharge by sea-spray-affected precipitation in the upstream site, and seawater intrusion and diffusion zone fluctuation in the downstream site. The results of geochemical modelling showed that Ca²⁺ enrichment in the downstream area is caused by calcite dissolution enhanced by the ionic strength increase, as a result of seawater–groundwater mixing under open system conditions with a constant P_CO2 value (about 10^?1.5 atm). The results show that, for coastal alluvial groundwater residing on limestone, significant hydrochemical change (especially increased hardness) due to calcite dissolution enhanced by seawater mixing should be taken into account for better groundwater management. This process can be effectively evaluated using geochemical modelling.

Editor D. Koutsoyiannis; Associate editor Y. Guttman

Citation Chae, G.-T., Yun, S.-T., Yun, S.-M., Kim, K.-H., and So, C.-S., 2012. Seawater–freshwater mixing and resulting calcite dissolution: an example from a coastal alluvial aquifer in eastern South Korea. Hydrological Sciences Journal, 57 (8),1–12.     

Tsunami–tide interactions: A Cook Inlet case study

First, we investigated some aspects of tsunami–tide interactions based on idealized numerical experiments. Theoretically, by changing total ocean depth, tidal elevations influence the speed and magnitude of tsunami waves in shallow regions with dominating tidal signals. We tested this assumption by employing a simple 1-D model that describes propagation of tidal waves in a channel with gradually increasing depth and the interaction of the tidal waves with tsunamis generated at the channel's open boundary. Important conclusions from these studies are that computed elevations by simulating the tsunami and the tide together differ significantly from linear superposing of the sea surface heights obtained when simulating the tide and the tsunami separately, and that maximum tsunami–tide interaction depends on tidal amplitude and phase. The major cause of this tsunami–tide interaction is tidally induced ocean depth that changes the conditions of tsunami propagation, amplification, and dissipation. Interactions occur by means of momentum advection, bottom friction, and variable water flux due to changing total depth and velocity. We found the major cause of tsunami–tide interactions to be changing depth. Secondly, we investigate tsunami–tide interactions in Cook Inlet, Alaska, employing a high-resolution 2-D numerical model. Cook Inlet has high tides and a history of strong tsunamis and is a potential candidate for tsunami impacts in the future. In agreement with previous findings, we find that the impacts of tsunamis depend on basin bathymetries and coastline configurations, and they can, in particular, depend on tsunami–tide interactions. In regions with strong tides and tsunamis, these interactions can result in either intensification or damping of cumulative tsunami and tide impacts, depending on mean basin depth, which is regulated by tides. Thus, it is not possible to predict the effect of tsunami–tide interaction in regions with strong tides without making preliminary investigations of the area. One approach to reduce uncertainties in tsunami impact in regions with high tides is to simulate tsunamis together with tidal forcing.     

Numerical simulation of surf–swash zone motions and turbulent flow

A two-dimensional numerical model was presented for the simulation of wave breaking, runup and turbulence in the surf and swash zones. The main components of the model are the Reynolds-Averaged Navier–Stokes equations describing the average motion of a turbulent flow, a k–ε turbulence closure model describing the transformation and dissipation processes of turbulence and a volume of fluid technique for tracking the free surface motion. Nearshore wave evolution on a sloping bed, the velocity field and other wave characteristics were investigated. First, the results of the model were compared with experimental results for different surf zone hydrodynamic conditions. Spilling and plunging breakers were simulated and the numerical model investigated for different wave parameters. The turbulence field was also considered and the spatial and time-dependent variations of turbulence parameters were discussed. In the next stage of the study, numerical results were compared with two sets of experimental data in the swash zone. Generally, there is good agreement except for turbulence predictions near the breaking point where the model does not represent well the physical processes. On the other hand, turbulence predictions were found to be excellent for the swash zone. The model provides a precise and efficient tool for the simulation of the flow field and wave transformations in the nearshore, especially in the swash zone. The numerical model can simulate the surface elevation of the vertical shoreline excursion on sloping beaches, while swash–swash interactions within the swash zone are accounted for.     

Complexity analysis of precipitation using the Lempel–Ziv algorithm and a multi-scaling approach: a case study in Jilin province,China

Precipitation is an important part of the hydrologic cycle, and its complexity is closely related to surface runoff and changing groundwater dynamics, which in turn influences the accuracy of precipitation forecasts. In this study, we used the Lempel–Ziv algorithm (LZA) and a multi-scaling approach to assess precipitation complexity for 1958–2011 by analyzing time series data from 28 gauging stations located throughout Jilin province, China. The spatial distribution of normalized precipitation complexity was measured by LZA, a symbolic dynamics algorithm, and by a multi-scaling approach, which is described by fractals. In addition, the advantages and limitations of these two methods were investigated. The results indicate that both methods are applicable and consistent for calculating precipitation complexity, and that the degree of relief is a primary factor controlling precipitation complexity in the mountainous area; in the plain terrain, however, the prominent influencing factor is climate.     

A case study of the mesoscale dynamics in the North-Western Mediterranean Sea: a combined data–model approach

The Northern current is the main circulation feature of the North-Western Mediterranean Sea. While the large-scale to mesoscale variability of the northern current (NC) is well known and widely documented for the Ligurian region, off Nice or along the Gulf of Lions shelf, few is known about the current instabilities and its associated mesoscale dynamics in the intermediate area, off Toulon. Here, we took advantage of an oceanographic cruise of opportunity, the start of a HF radar monitoring programme in the Toulon area and the availability of regular satellite sea surface temperature and chlorophyll a data, to evaluate the realism of a NEMO-based regional high-resolution model and the added value brought by HF radar. The combined analysis of a 1/64° configuration, named GLAZUR64, and of all data sets revealed the occurrence of an anticyclonic coastal trapped eddy, generated inside a NC meander and passing the Toulon area during the field campaign. We show that this anticyclonic eddy is advected downstream along the French Riviera up to the study region and disturbs the Northern current flow. This study aims to show the importance of combining observations and modelling when dealing with mesoscale processes, as well as the importance of high-resolution modelling.     

Do mixing models with different input requirement yield similar streamflow source contributions? Case study: A tropical montane catchment

Hydrogeochemical based mixing models have been successfully used to investigate the composition and source identification of streamflow. The applicability of these models is limited due to the high costs associated with data collection and the hydrogeochemical analysis of water samples. Fortunately, a variety of mixing models exist, requiting different amount of data as input, and in data scarce regions it is likely that preference will be given to models with the lowest requirement of input data. An unanswered question is if models with high or low input requirement are equally accurate. To this end, the performance of two mixing models with different input requirement, the mixing model analysis (MMA) and the end-member mixing analysis (EMMA), were verified on a tropical montane headwater catchment (21.7 km²) in the Ecuadorian Andes. Nineteen hydrogeochemical tracers were measured on water samples collected weekly during 3 years in streamflow and eight potential water sources or end-members (precipitation, lake water, soil water from different horizons and springs). Results based on 6 conservative tracers, revealed that EMMA (using all tracers) and MMA (using pair-combinations out of the 6 conservative ones), identified the same end-members: rainfall, soil water and spring water., as well as, similar contribution fractions to streamflow from rainfall 21.9% and 21.4%, soil water 52.7% and 52.3%, and spring water 26.1% and 28.7%, respectively. Our findings show that a hydrogeochemical mixing model requiring a few tracers can provide similar outcomes than models demanding more tracers as input data. This underlines the value of a preliminary detailed hydrogeochemical characterization as basis to derive the most cost-efficient monitoring strategy.     

Space–time forecasting using soft geostatistics: a case study in forecasting municipal water demand for Phoenix, Arizona

Managing environmental and social systems in the face of uncertainty requires the best possible forecasts of future conditions. We use space–time variability in historical data and projections of future population density to improve forecasting of residential water demand in the City of Phoenix, Arizona. Our future water estimates are derived using the first and second order statistical moments between a dependent variable, water use, and an independent variable, population density. The independent variable is projected at future points, and remains uncertain. We use adjusted statistical moments that cover projection errors in the independent variable, and propose a methodology to generate information-rich future estimates. These updated estimates are processed in Bayesian Maximum Entropy (BME), which produces maps of estimated water use to the year 2030. Integrating the uncertain estimates into the space–time forecasting process improves forecasting accuracy up to 43.9% over other space–time mapping methods that do not assimilate the uncertain estimates. Further validation studies reveal that BME is more accurate than co-kriging that integrates the error-free independent variable, but shows similar accuracy to kriging with measurement error that processes the uncertain estimates. Our proposed forecasting method benefits from the uncertain estimates of the future, provides up-to-date forecasts of water use, and can be adapted to other socio-economic and environmental applications.     

Fluid–particle interaction in turbulent open channel flow with fully-resolved mobile beds

The paper presents Direct Numerical Simulations of an open channel flow laden with spherical particles at a bulk Reynolds number of 2941. The transport of thousands of mobile particles is simulated propagating over a rough bed which consists of immobile particles of the same size in hexagonal ordering. An Immersed Boundary Method is used for the numerical representation of the particles. With 22 points per diameter even the viscous scales of the flow are resolved at this Reynolds number. The reference run contains just as many fixed as mobile particles with a relative density slightly above the nominal threshold of incipient motion. Further runs were conducted with decreased mass loading and decreased Shields number together with a simulation containing only immobile particles. The variation of the parameters defining the mobile sediment yields a strong modification of particle–fluid as well as particle–particle interactions yielding different structures in space and time. This is assessed by means of appropriate statistical quantities addressing the continuous and the disperse phase. The results are in qualitative agreement with experimental observations at higher Reynolds number.     

Helicity–vorticity turbulent pumping of magnetic fields in the solar convection zone

We study the effect of turbulent drift of a large-scale magnetic field that results from the interaction of helical convective motions and differential rotation in the solar convection zone. The principal direction of the drift corresponds to the direction of the large-scale vorticity vector. Thus, the effect produces a latitudinal transport of the large-scale magnetic field in the convective zone wherever the angular velocity has a strong radial gradient. The direction of the drift depends on the sign of helicity and it is defined by the Parker–Yoshimura rule. The analytic calculations are done within the framework of mean-field magnetohydrodynamics using the minimal τ-approximation. We estimate the magnitude of the drift velocity and find that it can be a few m/s near the base of the solar convection zone. The implications of this effect for the solar dynamo are illustrated on the basis of an axisymmetric mean-field dynamo model with a subsurface shear layer. The model shows that near the bottom of the convection zone the helicity–vorticity pumping results mostly from the kinetic helicity contributions. We find that the magnetic helicity contributions to the pumping effect are dominant at the subsurface shear layer. There the magnitude of the drift velocity is found to be a few cm/s. We find that the helicity–vorticity pumping effect can have an influence on the features of the sunspot time–latitude diagram, producing a fast drift of the sunspot activity maximum at the rise phase of the cycle and a slow drift at the decay phase of the cycle.     

Analysis of natural tracers and genetic runoff components in mixing models: Case study of small basins in Primor’e

An algorithm has been proposed for the diagnostics of the number of runoff genetic components and reliable chemical tracers in mixing models. The algorithm is applied to the analysis of data of hydrological—hydrochemical monitoring obtained during experimental studies on small watersheds in Elovyi Creek basin. The number of stable genetic runoff components and the list of tracers can vary from year to year depending on the state of moistening on the watershed.     

Flood–ebb and spring–neap variations of mixing,stratification and circulation in Chesapeake Bay

A three-dimensional hydrodynamic model is used to investigate intra-tidal and spring–neap variations of turbulent mixing, stratification and residual circulation in the Chesapeake Bay estuary. Vertical profiles of salinity, velocity and eddy diffusivity show a marked asymmetry between the flood and ebb tides. Tidal mixing in the bottom boundary layer is stronger and penetrates higher on flood than on ebb. This flood–ebb asymmetry results in a north–south asymmetry in turbulent mixing because tidal currents vary out of phase between the lower and upper regions of Chesapeake Bay. The asymmetric tidal mixing causes significant variation of salinity distribution over the flood–ebb tidal cycle but insignificant changes in the residual circulation. Due to the modulation of tidal currents over the spring–neap cycle, turbulent mixing and vertical stratification show large fortnightly and monthly fluctuations. The stratification is not a linear function of the tidal-current amplitude. Strong stratification is only established during those neap tides when low turbulence intensity persists for several days. Residual circulation also shows large variations over the spring–neap cycle. The tidally averaged residual currents are about 50% stronger during the neap tides than during the spring tides.     

Air–water two-phase flow modeling of turbulent surf and swash zone wave motions

Wave breaking and wave runup/rundown have a major influence on nearshore hydrodynamics, morphodynamics and beach evolution. In the case of wave breaking, there is significant mixing of air and water at the wave crest, along with relatively high kinetic energy, so prediction of the free surface is complicated. Most hydrodynamic studies of surf and swash zone are derived from single-phase flow, in which the role of air is ignored. Two-phase flow modeling, consisting of both phases of water and air, may be a good alternative numerical modeling approach for simulating nearshore hydrodynamics and, consequently, sediment transport. A two-phase flow tool can compute more realistically the shape of the free surface, while the effects of air are accounted for. This paper used models based on two-dimensional, two-phase Reynolds-averaged Navier–Stokes equations, the volume-of-fluid surface capturing technique and different turbulence closure models, i.e., k–ε, k–ω and re-normalized group (RNG). Our numerical results were compared with the available experimental data. Comparison of the employed method with a model not utilizing a two-phase flow modeling demonstrates that including the air phase leads to improvement in simulation of wave characteristics, especially in the vicinity of the breaking point. The numerical results revealed that the RNG turbulence model yielded better predictions of nearshore zone hydrodynamics, although the k–ε model also gave satisfactory predictions. The model provides new insights for the wave, turbulence and means flow structure in the surf and swash zones.