A reduced 3D hydrodynamic model of a shallow,long, and weakly curved stream

A reduced three-dimensional mathematical model of a free-flow stream in nondeformable channels (a model of a long shallow flow), proposed earlier, has been studied analytically and numerically. The reduced model has been verified by direct numerical simulation of the flow by full hydrodynamic models in COMSOL finite-element software complex for laminar and turbulent flows of a viscous fluid. The obtained results show that the proposed reduced model of a shallow weakly curved stream flow adequately describes its hydrodynamics, so it can be used in systems of complex simulation of the ecology of water objects and the use of water resources.     

山体遮挡对滇池风生流的影响初探

用二维风生流数值模型模拟滇池湖流运动。滇池在主导风向西南风作用下,假定湖面风场是均匀的,数值模拟的湖流流态与实测湖流结果相差很大。而考虑山体遮挡影响,根据实测湖流期间现有的风情资料,在湖面上构造一非均匀风场,数值模拟结果与实测值基本一致。山体遮挡对滇池风生流的影响是不容忽视的。建议进一步进行湖流和湖面风向、风速监测,并建立过山气流数学模型,深入研究山体遮挡对湖泊风生流的影响。     

Geohydrological conditions of the Deccan Trap flow around Saugor (M.P.), India

The geological formations that occur around Sagar consist of Upper Rewa quartzitic sandstones of Vindhvan age and nine Deccan Trap flows with three main inter-trappean bands. Most of the villages around Sagar depend upon the flow No. 5 for their water supplies. This flow forms valleys which may occur either in between the Vindhyan hills or Vindhyan hills and Trap hills, or Trap hills. To evaluate the geo-hydrological conditions of this flow under different topographic and stratigraphic controls, detailed geologic, water-shed and water table maps were prepared and analysed, after taking into consideration rain fall data for a period of sixty years. The villages selected for studies include the farm-lands of Richonda which occur in between the Vindhyan hills and Kudari, which occurs in between the Trap and Vindhyan hills. Villages like Patkui and Bhainsa, occurring on either side of the surface water divide of the same flow, are also taken into consideration. Water table maps for these villages were prepared once before the onset of rains and the second time immediately after the rains, on a scale of 16″ to a mile at 1 foot contour intervals. From such studies made on this flow, the following conclusions have been arrived at:

1. Where a flow occurs in adjacent Deccan Trap valleys separated by a long continuous Vindhyan ridge, the Vindhyan ridge may act as an underground barrier, separating the ground water body of the flow into two distinct units, and the upper unit may give rise to springs on that valley side of the Vindhyan having the lower elevation.
2. Where the Vindhyan ridge loses its height and disappears below the flow, the adjacent separate water bodies of this flow merge into a single water body. The portion of the Vindhyan ridge that occurs below the ground still continues to act as barrier for the water bodies of the lower flows.
3. Where the flow occurs over a large area, but at places is overlaid by younger flows, giving rise to hills with distinct water-shed characteristics, the water body of the flow is generally continuous on either side of the hills, immediately after the rains. This, however, gets disrupted into separate water bodies during summer months and it is found to recede in the slope direction; nevertheless, the trend of recession is controlled locally by the levels at which the porous zone of a flow occurs.
4. Where the continuity of the flow is disrupted due to denudation, producing valleys, the continuity of the water table of that flow is also interrupted.
5. On either side of a distinct surface water divide of a flow, the ground water bodies occur as separate units in the flow.

     

Gravity currents down canyons: effects of rotation

The flow of dense water in a V-shaped laboratory-scale canyon is investigated by using a non-hydrostatic numerical ocean model with focus on the effects of rotation. By using a high-resolution model, a more detailed analysis of plumes investigated in the laboratory (Deep-Sea Res I 55:1021–1034 2008) for laminar flow is facilitated. The inflow rates are also increased to investigate plume structure for higher Reynolds numbers. With rotation, the plumes will lean to the side of the canyon, and there will be cross-canyon geostrophic currents and Ekman transports. In the present study, it is found that the cross-canyon velocities are approximately 5 % of the down-canyon velocities over the main body of the plume for the rotational case. With rotation, the flow of dense water through the body of the plume and into the plume head is reduced. The plume head becomes less developed, and the speed of advance of the head is reduced. Fluid parcels near the top of the plume will to a larger extent be left behind the faster flowing dense core of the plume in a rotating system. Near the top of the plume, the cross-canyon velocities change direction. Inside the plume, the cross-flow is up the side of the canyon, and above the interface to the ambient there is a compensating cross-flow down the side of the canyon. This means that parcels of fluid around the interface become separated. Parcels of fluid around the interface with small down-canyon velocity components and relative large cross-canyon components will follow a long helix-like path down the canyon. It is found that the entrainment coefficients often are larger in the rotational experiments than in corresponding experiments without rotation. The effects of rotation and higher inflow rates on the areal patterns of entrainment velocities are demonstrated. In particular, there are bands of higher entrainment velocities along the lateral edges of the plumes in the rotational cases.     

Modelling of hydrodynamics and cohesive sediment transport in Tanshui River estuarine system,Taiwan

A laterally averaged two-dimensional numerical model is used to simulate hydrodynamics and cohesive sediment transport in the Tanshui River estuarine system. The model handles tributaries as well as the main stem of the estuarine system. Observed time series of salinity data and tidally averaged salinity distributions have been compared with model results to calibrate the turbulent diffusion coefficients. The overall model verification is achieved with comparisons of residual currents and salinity distribution. The model reproduces the prototype water surface elevation, currents and salinity distributions. Comparisons of the suspended cohesive sediment concentrations calculated by the numerical model and the field data at various stations show good agreement. The validated model is applied to investigate the tidally averaged salinity distributions, residual circulation and suspended sediment concentration under low flow conditions in the Tanshui River estuarine system. The model results show that the limit of salt intrusion in the mainstem estuary is located at Hsin-Hai bridge in Tahan Stream, 26 km from the River mouth under Q75 flow. The null point is located at the head of salt intrusion, using 1 ppt isohaline as an indicator. The tidally averaged sediment concentration distribution exhibits a local maximum around the null point.     

Pattern of induced currents in a conducting sphere in an oscillating uniform field and their contribution to the measured signal

Summary Expressions are obtained for the currents induced in a conducting sphere placed in an oscillating uniform field. The induced currents are plane circular loops around the axis of symmetry with respect to the external field. Current profiles are presented at three latitudinal planes inside the sphere for three parametric values of that are of importance in prospecting. Magnetic fields created by these currents loops at a point on the axis of the sphere are calculated. This study reveals some interesting results like the existence of zones contributing positively and negatively to the signal measured outside the sphere and behaviour of these zones with parameter.     

Quantifying the effect of rheology on lava-flow margins using fractal geometry

This study aims at quantifying the effect of rheology on plan-view shapes of lava flows using fractal geometry. Plan-view shapes of lava flows are important because they reflect the processes governing flow emplacement and may provide insight into lava-flow rheology and dynamics. In our earlier investigation (Bruno et al. 1992), we reported that flow margins of basalts are fractal, having a characteristic shape regardless of scale. We also found we could use fractal dimension (D, a parameter which quantifies flow-margin convolution) to distinguish between the two endmember types of basalts: a a (D: 1.05–1.09) and pahoehoe (D: 1.13–1.23). In this work, we confirm those earlier results for basalts based on a larger database and over a wider range of scale (0.125 m–2.4 km). Additionally, we analyze ten silicic flows (SiO₂: 52–74%) over a similar scale range (10 m–4.5 km). We note that silicic flows tend to exhibit scale-dependent, or non-fractal, behavior. We attribute this breakdown of fractal behavior at increased silica contents to the suppression of small-scale features in the flow margin, due to the higher viscosities and yield strengths of silicic flows. These results suggest we can use the fractal properties of flow margins as a remote-sensing tool to distinguish flow types. Our evaluation of the nonlinear aspects of flow dynamics indicates a tendency toward fractal behavior for basaltic lavas whose flow is controlled by internal fluid dynamic processes. For silicic flows, or basaltic flows whose flow is controlled by steep slopes, our evaluation indicates non-fractal behavior, consistent with our observations.     

Topographically generated steady currents in barotropic turbulence

Abstract

Steady currents develop in oceanic turbulence above topography even in the absence of steady forcing. Mesoscale steady currents are correlated with mesoscale topography with anticyclonic eddies above topographic bumps, and large scale westward flows develop when β is non-zero. The relationship between those two kinds of steady currents, as well as their dependence on various parameters, is studied using a barotropic quasi-geostrophic channel model. The percentage of steady energy is found to depend on the forcing, friction and topography in a non-monotonic fashion. For example, the percentage of steady currents grows with the energy level in the linear regime (low energies) and decreases when the energy level increases in the nonlinear regime (high energies). Mesoscale steady currents are the energy source for the steady westward flow U, and therefore U is the maximum when large scale and mesoscale currents are of the same order of magnitude. This happens when the ratio S of the large scale slope βH/f ₀ and the mesoscale rms topographic slope α is of order one. U decreases for both small and large values of S.     

On the Difficulty of Detecting Streaming Potentials Generated at Depth

— In order to investigate how a streaming potential coefficient measured in the laboratory, at a typical scale of 10 cm, can be incorporated into a field model, with a typical scale of 1 to 10 km, we measured the electric field induced by water flows forced at 150 m depth through a 10-m wide granite fractured zone. The water flows were obtained by pumping cyclically 10 m of water from a borehole that cut the fractured zone at depth, and contemporaneously reinjecting it into another borehole located 50 m away. After one day a steady-state fluid flow regime was reached, with pumping cycles lasting 45 minutes, indicating a hydraulic conductivity of 10^?5 m s^?1 and a specific storage coefficient of 3.25×10^?6 m^?1. The expected self-potential at the surface was an anomaly with two maxima of opposite sign and 2μV amplitude each, both located 160 m away from the middle of the borehole heads, the signal being divided by two 500 m away from the middle of the borehole heads (in agreement with Wurmstich and Morgan, 1994). Instead, we observed an electrical signal of 8 mV midway between the borehole heads, and smaller than 5 mV, 33 m away from the borehole heads. The discrepancy observed between the data and the model can be explained by fluid flow leakages that occurred close to the water-table head, represented about 20% of the total water flow, and activated smaller but closer electric sources. This experiment thus illustrates the practical difficulty of detecting streaming potentials generated at depth. It shows in particular that in fractured zones, and hence in the vicinity of a major active fault small water flows located distantly from an energetic targeted source, but close to some of the electrodes of the network, can sometimes drastically distort the shape of the expected anomaly. Models of possible electrical earthquake precursors therefore turn out to be more speculative than expected.     

A numerical study of rotating annulus flows using a modified Galerkin method

Summary Physical phenomena fundamental to rotating, baroclinically driven flows are studied with reference to results of numerical simulation of rotating annulus flows, using a modified Galerkin Model. Both local and global effects of sources, sinks, and transports of heat and momentum are discussed. A convenient energy exchange diagram reveals detailed information that is used to analyze nonlinear equilibration and amplitude vacillation of quasi-geostrophic baroclinic eddies. Transient inertial oscillations, sidewall boundary layers, and internal boundary layers are also discussed.A detailed study of symmetric flows is made, eleven of which are tested numerically for stability with respect to three-dimensional disturbances of a given zonal wave number. Two of the four unstable cases are integrated to a numerical steady state with finite-amplitude, quasi-geostrophic baroclinic waves. With the rigid-lid geometry assumed, the average zonal velocity is zero, resulting in zero phase velocity of the waves. The structure of the thermal wave is nearly coherent in the vertical. These numerical results are consistent with laboratory observations.The eddy flow is quasi-geostrophic except in horizontal boundary layers, where the flow is driven toward low pressure. A small cross-isotherm advection is sufficient to maintain the temperature wave against diffusion and vertical advection. The eddy flow adjusts spontaneously toward the form of the fastest growing or slowest decaying disturbance representable by the truncated space resolution. The eddy flow feeds energy into the mean zonal flow in barotropic-type interactions reflected mainly by the familiar tilted trough. During equilibration, the eddy flow alters the mean zonal flow in such a way that eddy energy sources are reduced relative to energy sinks. However, this adjustment is small compared to the change of total flow, which reflects a relatively large change of eddy amplitude. This suggests that small errors in the mean zonal flow representation can lead to relatively large errors in total flow representation.In most flows studied the kinetic energy dissipation is concentrated in thin boundary layers. In spite of this thinness, the basically laminar character of these dissipative boundary layers allows accurate and economical numerical simulation through the use of characteristic functions, which is a natural refinernent of the basic Galerkin method used. (In this prototype study, only moderately characteristic functions are used, thus sacrificing numerical economy while simplifying the programming.) Similarly, the generation of potential energy, which is transformed into the kinetic energy of the flow, is accurately simulated. In most cases studied, this generation is also concentrated in thin boundary layers where thermal energy is extracted from cold fluid and added to warm fluid.Contribution number 76 of the Geophysical Fluid Dynamics Institute, Florida State University, USA.     

Pore scale modeling of immiscible and miscible fluid flows using smoothed particle hydrodynamics

A numerical model based on smoothed particle hydrodynamics (SPH) was developed and used to simulate immiscible and miscible fluid flows in porous media and to study effects of pore scale heterogeneity and anisotropy on such flows.     

Sediment-induced buoyancy destruction and drag reduction in estuaries

This paper presents an analysis of drag reduction by buoyancy destruction in sediment-laden open channel flow. We start from the log-linear profile proposed by Barenblatt (Prikladnaja Matematika i Mekhanika, 17:261–274, 1953), extended with a second length scale to account for free surface effects. Upon analytical integration over the water depth, an expression for sediment-induced drag reduction is found in terms of an effective Chézy number, water depth, bulk Richardson number, and Rouse number. This relation contains one empirical/experimental coefficient, which was obtained from a large series of numerical experiments with a 1DV point model. Upon calibration of this model against field and laboratory observations, we tuned the turbulent Prandtl–Schmidt number and found an optimal value of σ _T?=?2, consistent to observations by Cellino and Graf (ASCE, J Hydraulic Engineering, 125:456–462, 1999). All numerical results could be correlated with the simple relation \( C_{\text{eff}} = C_0 + 4\sqrt {g} hRi_{*} \beta \), which is valid for fine sediment suspensions under conditions typical in open channel flow.     

Spatial variations of flow structure over estuarine hollows

Observations of the flow field over an elongated hollow (bathymetric depression) in the lower Chesapeake Bay showed tidally asymmetric distributions. Current speed increased over the landward side of the hole during flood tides and decreased in the deepest part of the hollow during ebb tides. A simple conceptual analysis indicated that the presence of a horizontal density gradient can generate the asymmetric spatial variations of flow structure depending on the sign of the horizontal density gradient. When water density decreases downstream, the velocity increases over the downstream edge of the hollow. Conversely when water density increases downstream, the flow decreases over the hollow more than a case without a horizontal density gradient. The conceptual analysis is confirmed by numerical experiments of simplified hollows in steady open channel flows and of an idealized tidal estuary. These hollows also alter the local current field of tidally averaged estuarine exchange flows. The residual depth-averaged currents over a hollow show a two-cell circulation when Coriolis forcing is neglected and an asymmetric two-cell circulation, with a stronger cyclonic eddy, when Coriolis forcing is included.     

Numerical resolution of well-balanced shallow water equations with complex source terms

This paper presents a well-balanced numerical scheme for simulating frictional shallow flows over complex domains involving wetting and drying. The proposed scheme solves, in a finite volume Godunov-type framework, a set of pre-balanced shallow water equations derived by considering pressure balancing. Non-negative reconstruction of Riemann states and compatible discretization of slope source term produce stable and well-balanced solutions to shallow flow hydrodynamics over complex topography. The friction source term is discretized using a splitting implicit scheme. Limiting value of the friction force is derived to ensure stability. This new numerical scheme is validated against four theoretical benchmark tests and then applied to reproduce a laboratory dam break over a domain with irregular bed profile.     

Geomagnetotail dynamics: Different types of equilibriums and transitions between them

Two time scales are distinguished in the geomagnetotail dynamics. The small scale (T ₁) corresponds to disturbances propagating in the tail lobes, which have a relatively strong magnetic field and low plasma density. The larger scale (T ₂) corresponds to plasma motions in the plasma sheet and has a relatively weak magnetic field and a relatively higher density. A disturbance, which is initiated by a localized burst of magnetic reconnection and appears in the geomagnetotail on the time scale T ₁, generates the upset of equilibrium in the plasma sheet zones with intermediate spatial dimensions (about R _E). The theoretical considerations and numerical simulation indicate that the relaxation process, which subsequently proceeds on the larger time scale (T ₂), results in the appearance of extremely thin embedded current sheets and in the generation of fast plasma flows. This process gives an effective mechanism by which the magnetic energy stored in the geomagnetotail is transformed into the plasma flow kinetic energy. Such fast flows can also generate eddy plasma motions on smaller spatial scales. On the one hand, fast MHD components of this process carry a disturbance in other plasma sheet zones, where new magnetic reconnection bursts can originate at a large distance from the zone of an initial nonlinear disturbance. As a result, new recurrent processes of relaxation originate on the T ₂ time scale. Alternation originating in such a way is apparently the characteristic feature of eddy disturbances actually observed in the plasma sheet.     

Subtidal variability of transverse flow off a cape

Time series of velocity profiles at two Chesapeake Bay entrance sites were used to characterize the subtidal variability of transverse flows off a cape. A shallow sampling site was located near Cape Henry over 6 m of water and separated from a deep site, 20 m deep, by a distance of 4 km. The velocity profiles showed that wind-induced subtidal variations in general masked curvature effects (centrifugal accelerations) that may produce secondary circulation associated with tidal flow around a cape. Such secondary circulation, consisting of flow away from the cape at surface and toward the cape at depth, was observed only during periods of weak winds. Most of the time, transverse flows were unidirectional throughout the water column and moved in opposite directions at the two sites examined. This caused convergence of transverse flow between the two sites under the influence of northerly winds and divergence of transverse flow with southwesterly winds. In addition to unidirectional and curvature-induced secondary flows, other modes of subtidal variability consisted of (1) two-layered responses with surface flow toward the cape, and (2) three-layered responses. These two- and three-layered structures were observed more frequently at the deep site, where greater stratification is expected, than at the shallow site.Responsible Editor: Iris Grabemann     

Contemporary hydrodynamics and morphological change of a microtidal estuary: a numerical modelling study

Contemporary hydrodynamics and morphological change are examined in a shallow microtidal estuary, located on a wave-dominated coast (Port Stephens, NSW, Australia). Process-based numerical modelling is undertaken by combining modules for hydrodynamics, waves, sediment transport and bathymetry updates. Model results suggest that the complex estuarine bathymetry and geometry give rise to spatial variations in the tidal currents and a marked asymmetry between ebb and flood flows. Sediment transport paths correspond with tidal asymmetry patterns. The SE storms significantly enhance the quantities of sediment transport, while locally generated waves by the westerly strong winds also are capable of causing sediment entrainment and contribute to the delta morphological change. The wave/wind-induced currents are not uniform with flow over shoals driven in the same direction as waves/winds while a reverse flow occurring in the adjacent channel. The conceptual sediment transport model developed in this study shows flood-directed transport occurs on the flood ramp while ebb-directed net transport occurs in the tidal channels and at the estuary entrance. Accretion of the intertidal sand shoals and deepening of tidal channels, as revealed by the model, suggest that sediment-infilling becomes advanced, which may lead to an ebb-dominated estuary. It is likely that a switch from flood- to ebb-dominance occurs during the estuary evolution, and the present-day estuary acts as a sediment source rather than sediment sink to the coastal system. This is conflictive to the expectation drawn from the estuarine morphology; however, it is consistent with previous research suggesting that, in an infilling estuary, an increase in build-up of intertidal flats/shoals can eventually shift an estuary towards ebb dominance. Thus, field data are needed to validate the result presented here, and further study is required to investigate a variety of estuaries in the Australian area.     

An extended stability criterion for density-driven flows in homogeneous porous media

Stability of density-driven flows is a challenging problem with current applications in major areas like energy exploration, water pollution, nuclear and oil industries. The mathematical model for such flows is a system of coupled non linear partial differential equations. To study the physical stability of the system, we consider steady-state flow and perturb the solution of the full system of equations (without Boussinesq approximation) and investigate how it evolves in time: if the solution does not grow indefinitely, the system is called stable. The perturbations are treated as being the result of sub-scale interactions between the velocity field and the solute mass. Making use of a two-scale expansion of the solution, we derived extended stability criteria that include the effects of density, viscosity and flow velocity in flow configurations aligned parallel as well as orthogonal to gravity forces. Numerical simulations with the numerical simulator d³f$d^{3}f$ are presented to test the theoretical stability criteria.     

Mixing at the interface between fresh and salt waters in 3D steady flow with application to a pumping well in a coastal aquifer

We consider 3D steady flow of fresh water over a salt water body in a confined aquifer of constant thickness D, with application to a pumping well in a coastal aquifer. With neglect of mixing, a sharp interface separates the two fluid bodies and an existing analytical solution, based on the Dupuit assumption, is adopted. The aim is to solve for the mixing between the fresh and salt waters for α_T/D  1 (α_T transverse dispersivity), as field studies indicate that α_T = O(10⁻³ − 10⁻² m). The mixing zone around the interface is narrow and solutions by existing codes experience numerical difficulties. The problem is solved by the boundary layer (BL) approximation, extending a method, applied previously to two-dimensional flows. The BL equations of variable-density flow are solved by using the Von Karman integral method, to determine the BL thickness and the rate of entrainment of salt water along the interface. Application to the pumping well problem yields the salinity of the pumped water, as function of the parameters of the problem (well discharge, seaward discharge, well distance from the coast and density difference).     

The nematode/copepod ratio and its use in pollution ecology

The nematode/copepod ratio is critically examined with a view to adding some precision to its proposed use in pollution ecology. At two unpolluted intertidal sites, differing markedly in sediment grade, the metabolic requirements of copepods are shown to be equivalent to the requirements of that fraction of the nematode population which feeds in the same way. The partitioning of this total energy requirement among individuals depends on the distribution of individual metabolic body sizes and the relative rates of metabolism. The distribution of body sizes is constrained by the sediment granulometry, which affects nematodes and copepods differently. These considerations enable precise predictions of the nematode/copepod ratios expected in unpolluted situations, against which observed ratios can be compared.