Importance of subgrid-scale parameterization in numerical simulations of lake circulation

Two subgrid-scale modeling techniques––Smagorinsky’s postulation for the horizontal eddy viscosity and the Mellor–Yamada level-2 model for the vertical eddy viscosity––are applied as turbulence closure conditions to numerical simulations of resolved-scale baroclinic lake circulations. The use of the total variation diminishing (TVD) technique in the numerical treatment of the advection terms in the governing equations depresses numerical diffusion to an acceptably low level and makes stable numerical performances possible with small eddy viscosities resulting from the turbulence closure parameterizations. The results show that, with regard to the effect of an external wind stress, the vertical turbulent mixing is mainly restricted to the topmost epilimnion with the order of magnitude for the vertical eddy viscosity of 10⁻³ m² s⁻¹, whilst the horizontal turbulent mixing may reach a somewhat deeper zone with an order of magnitude for the horizontal eddy viscosity of 0.1–1 m² s⁻¹. Their spatial and temporal variations and influences on numerical results are significant. A comparison with prescribed constant eddy viscosities clearly shows the importance of subgrid-scale closures on resolved-scale flows in the lake circulation simulation. A predetermination of the eddy viscosities is inappropriate and should be abandoned. Their values must be determined by suitable subgrid-scale closure techniques.     

An integral equation for the homogeneous Neumann condition1

Modelling the theoretical response of several important geophysical systems involves the solution of Poisson's equation with homogeneous Neumann boundary conditions (i.e. a zero normal gradient) imposed over either open or closed surfaces. A simple integral equation solution to this problem is derived from first principles. It is applicable to both types of surface and in this respect represents an improvement on existing integral equation techniques. However, the present surface integral equation displays a strong singularity of order 1/R³ which requires an appropriate interpretation for its implementation. A comparison of some numerical results with analytical data taken from the literature demonstrates that the proposed integral equation technique is suitably robust, accurate and efficient for practical application in geophysical interpretation.     

Correction to: Inertial instability and phase error in Euler forward predictorcorrector time integration schemes: Improvement of modeling Great Lakes thermal structure and circulation using FVCOM

This study investigates the inertial stability properties and phase error of numerical time integration schemes in several widely-used ocean and atmospheric models. These schemes include the most widely used centered differencing (i.e., leapfrog scheme or the 3-time step scheme at n-1, n, n+1) and 2-time step (n, n+1) 1^st-order Euler forward schemes, as well as 2^nd-stage and 3^rd- and 4^th-stage Euler predictor-corrector (PC) schemes. Previous work has proved that the leapfrog scheme is neutrally stable with respect to the Coriolis force, with perfect inertial motion preservation, an amplification factor (AF) equal to unity, and a minor overestimation of the phase speed. The 1^st-order Euler forward scheme, on the other hand, is known to be unconditionally inertially unstable since its AF is always greater than unity. In this study, it is shown that 3^rd- and 4^th-order predictor-corrector schemes 1) are inertially stable with weak damping if the Coriolis terms are equally split to n+1 (new value) and n (old value); and 2) introduce an artificial computational mode. The inevitable phase error associated with the Coriolis parameter is analyzed in depth for all numerical schemes. Some schemes (leapfrog and 2^nd-stage PC schemes) overestimate the phase speed, while the others (1^st-order Euler forward, 3^rd- and 4^th-stage PC schemes) underestimate it. To preserve phase speed as best as possible in a numerical model, alternating a scheme that overestimates the phase speed with a scheme that underestimates the phase speed is recommended. Considering all properties investigated, the leapfrog scheme is still highly recommended for a time integration scheme. As an example, a comparison between a leapfrog scheme and a 1^st-order Euler forward scheme is presented to show that the leapfrog scheme reproduces much better vertical thermal stratification and circulation in the weakly-stratified Great Lakes.

     

Imaging hyporheic zone solute transport using electrical resistivity

Traditional characterization of hyporheic processes relies upon modelling observed in‐stream and subsurface breakthrough curves to estimate hyporheic zone size and infer exchange rates. Solute data integrate upstream behaviour and lack spatial coverage, limiting our ability to accurately quantify spatially heterogeneous exchange dynamics. Here, we demonstrate the application of near‐surface electrical resistivity imaging (ERI) methods, coupled with experiments using an electrically conductive stream tracer (dissolved NaCl), to provide in situ imaging of spatial and temporal dynamics of hyporheic exchange. Tracer‐labelled water in the stream enters the hyporheic zone, reducing electrical resistivity in the subsurface (to which subsurface ERI is sensitive). Comparison of background measurements with those recording tracer presence provides distributed characterization of hyporheic area (in this application, ∼0·5 m²). Results demonstrate the first application of ERI for two‐dimensional imaging of stream‐aquifer exchange and hyporheic extent. Future application of this technique will greatly enhance our ability to quantify processes controlling solute transport and fate in hyporheic zones, and provide data necessary to inform more complete numerical models. Copyright © 2010 John Wiley & Sons, Ltd.     

Application of non‐linear multiple tuned mass dampers to suppress man‐induced vibrations of a pedestrian bridge

This paper presents an application of multiple tuned mass dampers (MTMDs) with non‐linear damping devices to suppress man‐induced vibrations of a 34m long pedestrian bridge. The damping force generated by each of these damping devices is simply a drag force from liquid acting on an immersed section. The quadratic non‐linear property of these devices was directly determined from free vibration tests of a simple laboratory set‐up. Dynamic models of the bridge and pedestrian loads were constructed for numerical investigation based on field measurement data. The control effectiveness of non‐linear MTMDs was examined along with its sensitivity against estimation errors in the bridge's natural frequency and magnitude of pedestrian load. The numerical results indicated that the optimum non‐linear MTMD system was as effective and robust as its linear counterpart. Then, a six‐unit non‐linear MTMD system was designed, constructed, and installed on the bridge. Field measurements after the installation confirmed the effectiveness of non‐linear MTMDs, and the measurement results were in good agreement with numerical predictions. After the installation, the average damping ratio of the bridge was raised from 0.005 to 0.036 and the maximum bridge accelerations measured during walking tests were reduced from about 0.80–1.30 ms^?2 to 0.27–0.40 ms^?2, which were within an acceptable range. Copyright © 2003 John Wiley & Sons, Ltd.     

Evaluating the source and seasonality of submarine groundwater discharge using a radon-222 pore water transport model

Pore water radon (²²²Rn) distributions from Indian River Lagoon, Florida, are characterized by three zones: a lower zone where pore water ²²²Rn and sediment-bound radium (²²⁶Ra) are in equilibrium and concentration gradients are vertical; a middle zone where ²²²Rn is in excess of sediment-bound ²²⁶Ra and concentration gradients are concave-downward; and an upper zone where ²²²Rn concentration gradients are nearly vertical. These ²²²Rn data are simulated in a one-dimensional numerical model including advection, diffusion, and non-local exchange to estimate magnitudes of submarine groundwater discharge components (fresh or marine). The numerical model estimates three parameters, fresh groundwater seepage velocity, irrigation intensity, and irrigation attenuation, using two Monte Carlo (MC) simulations that (1) ensure the minimization algorithm converges on a global minimum of the merit function and the parameter estimates are consistent within this global minimum, and (2) provide 90% confidence intervals on the parameter estimates using the measured ²²²Rn activity variance. Model estimates of seepage velocities and discharge agree with previous estimates obtained from numerical groundwater flow models and seepage meter measurements and show the fresh water component decreases offshore and varies seasonally by a factor of nine or less. Comparison between the discharge estimates and precipitation patterns suggests a mean residence time in unsaturated and saturated zones on the order of 5 to 7 months. Irrigation rates generally decrease offshore for all sampling periods. The mean irrigation rate is approximately three times greater than the mean seepage velocity although the ranges of irrigation rates and seepage velocities are the same. Possible mechanisms for irrigation include density-driven convection, wave pumping, and bio-irrigation. Simulation of both advection and irrigation allows the separation of submarine groundwater discharge into fresh groundwater and (re)circulated lagoon water.     

Soil-structure interaction using BEM–FEM coupling through ANSYS software package

The main aim of this work is to develop, verify and apply in simulation study an efficient hybrid approach to study seismic response of a soil-structure system taking into account all the important components as: (1) the line time-harmonic source with its specific geophysical properties; (2) the inhomogeneity and heterogeneity of the wave path from the source to the local geological region; (3) the geotechnical properties of the near-field local geological profile and finally (4) the properties of the engineering structure itself. Plane strain state is considered. The hybrid computational tool is based on the boundary element method (BEM¹) for modeling the infinite far-field geological media and finite element method (FEM²) for treating the dynamic behavior of the structure and the near-field finite soil geological region. Each of the two techniques is applied in that part of the whole model where it works more efficiently. The hybrid numerical scheme is realized via the sub-structure approach, direct BEM¹, conventional FEM² and insertion of the BEM¹ model of the seismically active far-field geological media as a macro-finite element (MFE³) in the FEM² commercial program ANSYS. The accuracy and verification study of the proposed method is presented by solution of numerical test examples simulating different seismic scenarios. The obtained results show clearly that the hybrid model is able to demonstrate the sensitivity of the synthetic signals to the source properties, to the heterogeneous character of the wave path, to the relief peculiarities of the local layered geological deposit and to the specific properties of the engineering structure.     

Evaluation of the fourth-order tesseroid formula and new combination approach to precisely determine gravitational potential

Calculating topographic gravitational potential (GP) is a time-consuming process in terms of efficiency. Prism, mass-point, mass-line, and tesseroid formulas are generally used to calculate the topographic GP effect. In this study, we reformulate the higher-order formula of the tesseroid by Taylor series expansion and then evaluate the fourth-order formula by numerical tests. Different simulation computations show that the fourth-order formula is reliable. Using the conventional approach in numerical calculations, the approximation errors in the areas of the north and south poles are extremely large. Thus, in this study we propose an approach combining the precise numerical formula and tesseroid formulas, which can satisfactorily solve the calculation problem when the computation point is located in the polar areas or areas very near the surface. Furthermore, we suggest a “best matching choice” of new combination approach to calculate the GP precisely by conducting various experiments. Given the computation point at different positions, we may use different strategies. In the low latitude, we use a precise numerical formula, the fourth-order tesseroid formula, the second-order tesseroid formula, and the zero-order formula, in the 1° range (from the computation point), 1° to 15° range, 15° to 40° range, and the range outside 40°, respectively. The accuracy can reach 2 × 10^?5 m² s^?2. For the high latitude, we use the precise numerical formula, fourth-order tesseroid, second-order tesseroid, and zero-order tesseroid formulas in the ranges of 0° to 1°, 1° to 10°, 10° to 30°, and the zones outside 30°, respectively. However, if an accuracy level of 2 × 10^?5 m² s^?2 is required, the zero-order tesseroid formulas should not be used and the second-order tesseroid formula should be used in the region outside 15° for the low latitude and in the region outside 10° for the high latitude.     

Geoid Determination through Ellipsoidal Stokes Boundary-Value Problem

Martinec and Grafarend (1997) have shown how the construction of Green's function in the Stokes boundary-value problem with gravity data distributed on an ellipsoid of revolution is approached in the O(e ₀ ² )-approximation. They have also expressed the ellipsoidal Stokes function describing the effect of ellipticity of the boundary as a finite sum of elementary functions. We present an effective method of avoiding the singularity of spherical and the ellipsoidal Stokes functions, and also an analytical expression for the ellipsoidal Stokes integral around the computational point suitable for numerical solution. We give the numerical results of solving the ellipsoidal Stokes boundary-value problem and their difference with respect to the spherical Stoke boundary-value problem.     

Numerical simulation of a mesolow over a Gulf Stream filament

A three-dimensional mesoscale numerical model is used to investigate mesoscale circulation over a Gulf Stream filament. Two numerical experiments are performed with different initial uniform ambient wind speeds (U=0.1 m s^–1, 3.5 m s^–1 and 7 m s^–1) for a typical winter day. It is found that for both low and moderate winds, a closed mesoscale circulation forms over the Gulf Stream filament. When the Gulf Stream filament was removed, the model did not predict a mesoscale circulation. The modeled circulation over the filament is in agreement with the observations, suggesting that the atmospheric circulations over the filaments may be an important mechanism in the U.S. East Coast cyclogenesis.     

Estimating groundwater residence time and recharge patterns in a saline coastal aquifer

A detailed study using environmental tracers such as chloride (Cl^?) and tritium (³H), deuterium (²H) and oxygen (¹⁸O) isotopes was performed in an alluvial coastal aquifer in two contrasting environments (urban and agricultural). These environmental tracers combined with a high‐resolution multi‐level sampling approach were used to estimate groundwater residence time and recharge patterns and to validate the hydrogeochemical conceptual model already proposed in previous studies. δ¹⁸O and δ²H combined with Cl^? data proved that the hypersaline groundwater present in the deepest part of the aquifer was sourced from the underlying hypersaline aquitard via an upward flux. Both chemical and isotopic data were employed to calibrate a density‐dependent numerical model based on SEAWAT 4.0, where ³H and Cl^? were helped quantifying solutes transport within the modelled aquifer. Model results highlighted the differences on estimated recharge in the two contrasting environments, with the urban one exhibiting concentrated recharge because of preferential infiltration associated to the storm water drains network, while scarce local recharge characterized the agriculture setting. In the urban field site, is still possible to recognize at 9 m b.g.l. the input of the atmospheric anthropogenic ³H generated by testing of thermonuclear weapons, while in the agricultural field site, the ³H peak has been washed out at 6 m b.g.l. because the groundwater circulation is restricted only to the upper fresh part of the aquifer, drained by the reclamation system. The presented approach that combined high‐resolution field monitoring, environmental tracers and numerical modelling, resulted effective in validating the conceptual model of the aquifer salinization. Copyright © 2016 John Wiley & Sons, Ltd.     

Horizontal patterns of water temperature and salinity in an estuarine tidal channel: Ria de Aveiro

This work presents results from two complementary and interconnected approaches to study water temperature and salinity patterns in an estuarine tidal channel. This channel is one of the four main branches of the Ria de Aveiro, a shallow lagoon located in the Northwest coast of the Iberian Peninsula. Longitudinal and cross-sectional fields of water temperature and salinity were determined by spatial interpolation of field measurements. A numerical model (Mohid) was used in a 2D depth-integrated mode in order to compute water temperature and salinity patterns. The main purpose of this work was to determine the horizontal patterns of water temperature and salinity in the study area, evaluating the effects of the main forcing factors. The field results were depth-integrated and compared to numerical model results. These results obtained using extreme tidal and river runoff forcing, are also presented. The field results reveal that, when the river flow is weak, the tidal intrusion is the main forcing mechanism, generating saline and thermal fronts which migrate with the neap/spring tidal cycle. When the river flow increases, the influence of the freshwater extends almost as far as the mouth of the lagoon and vertical stratification is established. Results of numerical modelling reveal that the implemented model reproduces quite well the observed horizontal patterns. The model was also used to study the hydrology of the study area under extreme forcing conditions. When the model is forced with a low river flow (1 m³ s⁻¹) the results confirm that the hydrology is tidally dominated. When the model is forced with a high river flow (1,000 m³ s⁻¹) the hydrology is dominated by freshwater, as would be expected in such an area.     

Sulfate Land Application Enhances Biodegradation in a Petroleum Hydrocarbon Smear Zone

Delivery of sulfate to petroleum hydrocarbons (PHCs) source zones and groundwater plumes is desirable to enhance biodegradation rates when treatment has become limited due to depletion of sulfate. Sulfate land application involves spreading sulfate salts on ground surface and allowing their dissolution and infiltration of sulfate into subsurface. The objectives of this pilot-scale investigation were to capture the vertical transport of sulfate beneath an application area, confirm that sulfate reduction was occurring, and explore how the added sulfate affected biodegradation of benzene and toluene. Approximately 4000 kg of gypsum was spread over a 30 m × 30 m study area above a smear zone located approximately 2 m below-ground surface. Precipitation was augmented by two irrigation events. Groundwater samples, collected over 1058 days from multilevel wells and a conventional long-screened monitoring well, were analyzed for benzene, toluene, ethylbenzene, and xylenes (BTEX), sulfate, bromide, dissolved inorganic carbon (DIC) and methane. Compound-specific isotope analyses (CSIA) for benzene and toluene, and isotope analyses of ¹³C-DIC and ³⁴S-SO₄²⁻ were performed. Following application, an increase in sulfate concentration was noted in the smear zone. ³⁴S-SO₄²⁻ enrichment and ¹³C-DIC depletion indicated that sulfate reduction and mineralization of PHCs were enhanced. CSIA results provided unequivocal evidence of anaerobic biodegradation of benzene and toluene. After 1058 days when sulfate was depleted, methane concentrations were about three times greater than baseline conditions suggesting syntrophic benefit of the delivered sulfate. Observations from this investigation support the viability of sulfate land application to enhance biodegradation rates in shallow PHC smear zones.     

THE INDUCTIVE RESPONSE OF A HORIZONTAL CONDUCTING CYLINDER BURIED IN A UNIFORM EARTH FOR A UNIFORM INDUCING FIELD*

The inductive response of a conducting horizontal cylinder embedded in a uniform earth is studied using numerical results obtained for an analytical solution for the problem of a conducting cylinder buried in a homogeneous earth for the case of a uniform inducing field. A check of the validity of the numerical results is made by a comparison with analogue model measurements for a number of cases. Numerical results for a range of cylinder radii (a = 1–10 km), depths of burial (d= 0–4 km), conductivity contrasts (σ₂= 10^?2-10 Sm^?1), and source frequencies (f= 10^?1-10^?4 Hz) of interest in the interpretation of magnetotelluric field measurements are presented. The results indicate that for a uniform inducing field the conductivity and depth of burial of a horizontal cylindrical inhomogeneity are best determined through a measurement of the amplitudes H_y, H_z and E_x and the phases φ_y and Ψ_x.     

Explicit Modeling of Radon-222 in HydroGeoSphere During Steady State and Dynamic Transient Storage

Transient storage zones (TSZs) are located at the interface of rivers and their abutting aquifers and play an important role in hydrological and biogeochemical functioning of rivers. The natural radioactive tracer ²²²Rn is a particularly well-suited tracer for studying TSZ water exchange and age. Although ²²²Rn measurement techniques have developed rapidly, there has been less progress in modeling ²²²Rn activities. Here, we combine field measurements with the numerical model HydroGeoSphere (HGS) to simulate ²²²Rn emanation, decay and transport during steady state (riffle-pool sequence) and transient (bank storage) conditions. Comparing the HGS mean water ages with the conventional ²²²Rn apparent ages during steady state showed a systemic underestimation of apparent age with increasing dispersion and especially where large concentration gradients exist within the subsurface. A large underestimation of apparent water age was also observed at the advective front during bank storage where regional high ²²²Rn groundwater mixes with newly infiltrated surface water. The explicit modeling of radiogenic tracers such as ²²²Rn offers a physical interpretation of this data as well as a useful way to test simplified apparent age models.     

Gravity field determination using boundary element methods

The Boundary Element Method (BEM), a numerical technique for solving boundary integral equations, is introduced to determine the earth's gravity field. After a short survey on its main principles, we apply this method to the fixed gravimetric boundary value problem (BVP), i.e. the determination of the earth's gravitational potential from measurements of the intensity of the gravity field in points on the earth's surface. We show how to linearize this nonlinear BVP using an implicit function theorem and how to transform the linearized BVP into a boundary integral equation using the single layer representation. A Galerkin method is used to transform the boundary integral equation using the single layer representation. A Galerkin method is used to transform the boundary integral equation into a linear system of equations. We discuss the major problems of this approach for setting up and solving the linear system. The BVP is numerically solved for a bounded part of the earth's surface using a high resolution reference gravity model, measured gravity values of high density, and a 50 50 m² digital terrain model to describe the earth's surface. We obtain a gravity field resolution of 1 1 km² with an accuracy of the order 10^–3 to 10^–4 in about 1 CPU-hour on a Siemens/Fujitsu SIMD vector pipeline machine using highly sophisticated numerical integration techniques and fast equation solvers. We conclude that BEM is a powerful numerical tool for solving boundary value problems and may be an alternative to classical geodetic techniques.     

Field isotope investigations and numerical simulation of lake hydrodynamics

A three‐dimensional, numerical free‐surface‐flow simulation model is developed to investigate hydrodynamics of a lake and the predictive capabilities of the numerical model are validated by comparing them with field results obtained from Lake Naini, Uttar Pradesh, using environmental isotope (δ¹⁸O, δD and ³H) techniques. This has been carried out in order to understand the hydrodynamics of a lake (i.e. circulations, mixing and transport of water within the lake). Copyright © 2002 John Wiley & Sons, Ltd.     

Uncertainties in mean discharges from two large South American rivers due to rating curve variability

Abstract

The aim of this study was to assess the effect of land application of sewage sludge on phosphorus (P) losses during intense rainfall. Three rainfall simulations (40 mm h^?1 of 30 min duration) were conducted on a field amended with sewage sludge. The overland flow water (OFW) was monitored and sampled every minute. The suspended solid, the dissolved and total phosphorus (respectively SS, TP and DP) concentrations were analysed. The forms of particulate bound P (PP) were investigated. Several results stem from this experiment: (a) sludge application induced a large increase in the DP content of the OFW; the concentrations obtained (0.15–0.57 mg l^?1) were shown to result from desorption processes from the SS; and (b) in contrast, sludge application affected neither the SS content nor the TP concentration of OFW (9.5 g mg l^?1 P, consisting of PP for 95%). However, sludge preserved the structure of soil surface and led to a 45% decrease in runoff rate (150 m³ ha^?1 collected on the test surface compared to 290 m³ ha^?1 on a reference). This indirectly reduced TP losses (2.7 kg ha^?1 on the reference surface compared to 1.4 kg ha^?1 on the test surface).     

Maximally-efficient-generation approach in the dynamo theory

Abstract

We propose a method of derivation of global asymptotic solutions of the hydromagnetic dynamo problem at large magnetic Reynolds number. The procedure reduces to matching the local asymptotic forms for the magnetic field generated near individual extrema of generation strength. The basis of the proposed method, named here the Maximally-Efficient-Generation Approach (MEGA), is the assertion that properties of global asymptotic solutions of the kinematic dynamo are determined by the distribution of the generation strength near its leading extrema and by the number and distribution of the extrema.

The general method is illustrated by the global asymptotic solution of the α²-dynamo problem in a slab. The nature of oscillatory solutions revealed earlier in numerical simulations and the reasons for the dominance of even magnetic modes in slab geometry are clarified.

Applicability of the asymptotic solutions at moderate values of the asymptotic parameter is also discussed. We confirm this applicability using comparisons with complementary asymptotic expansions and numerical simulations. In particular, this justifies application of the MEGA solutions to estimation of the generation threshold.