Stochastic Analysis of the Variability of Groundwater Flow Fields in Heterogeneous Confined Aquifers of Variable Thickness

2021 ◽  
Author(s):  
Ching-Min Chang ◽  
Chuen-Fa Ni ◽  
We-Ci Li ◽  
Chi-Ping Lin ◽  
I-Hsian Lee
Keyword(s):  
Hydraulic Conductivity ◽  
Closed Form ◽  
Variable Thickness ◽  
Stochastic Theory ◽  
Flow Fields ◽  
Perturbation Approach ◽  
Mean Flow ◽  
Spatial Covariance ◽  
Confined Aquifers ◽  
Specific Discharge

Abstract The problem of flow through heterogeneous confined aquifers of variable thickness is analyzed from a stochastic point of view. The analysis is carried out on the basis of the integrated equations of the depth-averaged hydraulic head and integrated specific discharge, which are developed by integrating the continuity equation and equation for the specific discharge over the thickness, respectively. A spectrally based perturbation approach is used to arrive at the general results for the statistics of the flow fields in the Fourier domain, such as the variance of the depth-averaged head, and the mean and variance of integrated discharge. However, the closed-form expressions are obtained under the condition of steady unidirectional mean flow in the horizontal plane. In developing stochastic solutions, the input hydraulic conductivity parameter is viewed as a spatial random field characterized by the theoretical spatial covariance function. The evaluation of the closed-form solutions focuses on the influence of the controlling parameters, namely as a geometrical parameter defining the variation of the aquifer thickness and the correlation scale of log hydraulic conductivity, on the variability of the fluid fields. The application of the present stochastic theory to predict the total specific discharge under uncertainty using the field data is also provided.

Data Analysis Methods for Stereo PIV of a High Aspect Ratio Flexible Cylinder

2007 ◽  
Author(s):  
D. Furey ◽  
P. Atsavapranee ◽  
K. Cipolla
Keyword(s):  
Boundary Layer ◽  
Data Analysis ◽  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Particle Image Velocimetry Data ◽  
Flow Fields ◽  
Mean Flow ◽  
Boundary Flow ◽  
The Mean ◽  
Cylinder Flow

Stereo Particle Image velocimetry data was collected over high aspect ratio flexible cylinders (L/a = 1.5 to 3 × 105) to evaluate the axial development of the turbulent boundary layer where the boundary layer thickness becomes significantly larger than the cylinder diameter (δ/a>>1). The flexible cylinders are approximately neutrally buoyant and have an initial length of 152 m and radii of 0.45 mm and 1.25 mm. The cylinders were towed at speeds ranging from 3.8 to 15.4 m/sec in the David Taylor Model Basin. The analysis of the SPIV data required a several step procedure to evaluate the cylinder boundary flow. First, the characterization of the flow field from the towing strut is required. This evaluation provides the residual mean velocities and turbulence levels caused by the towing hardware at each speed and axial location. These values, called tare values, are necessary for comparing to the cylinder flow results. Second, the cylinder flow fields are averaged together and the averaged tare fields are subtracted out to remove strut-induced ambient flow effects. Prior to averaging, the cylinder flow fields are shifted to collocate the cylinder within the field. Since the boundary layer develops slowly, all planes of data occurring within each 10 meter increment of the cylinder length are averaged together to produce the mean boundary layer flow. Corresponding fields from multiple runs executed using the same experimental parameters are also averaged. This flow is analyzed to evaluate the level of axisymmetry in the data and determine if small changes in cylinder angle affect the mean flow development. With axisymmetry verified, the boundary flow is further averaged azimuthally around the cylinder to produce mean boundary layer profiles. Finally, the fluctuating velocity levels are evaluated for the flow with the cylinder and compared to the fluctuating velocity levels in the tare data. This paper will first discuss the data analysis techniques for the tare data and the averaging methods implemented. Second, the data analysis considerations will be presented for the cylinder data and the averaging and cylinder tracking techniques. These results are used to extract relevant boundary layer parameters including δ, δ* and θ. Combining these results with wall shear and momentum thickness values extracted from averaged cylinder drag data, the boundary layer can be well characterized.

scholarly journals A full wave description for thin wire structures with TLST and perturbation theory

2018 ◽  
Vol 16 ◽  
pp. 123-133
Author(s):  
Fabian Ossevorth ◽  
Ralf T. Jacobs ◽  
Hans Georg Krauthäuser
Keyword(s):  
Perturbation Theory ◽  
Closed Form ◽  
Current Distribution ◽  
Perturbation Approach ◽  
Mixed Potential ◽  
Thin Wire ◽  
Method Of Moment ◽  
Initial Current ◽  
Full Wave ◽  
Good Agreement

Abstract. A full wave description of a thin wire structure, that includes mutual interactions and radiation, can be obtained in closed form with the so-called Transmission Line Super Theory or a refined variant of this method that utilises perturbation theory. In either procedure, a set of mixed potential integral equations is solved for the currents that propagate along a wire. With the perturbation approach, no iteration is required to approximate the initial current distribution on the wire. This procedure will be applied to solve multi-wire problems. The theory will be derived and computed results will be shown to be in good agreement with method of moment computations.

Turbulent open-channel flows over mobile granular low-tortuosity beds: velocity distribution and friction factor

2020 ◽  
Author(s):  
Rui M L Ferreira ◽  
Rigden Y Tenzin ◽  
Ana M Ricardo
Keyword(s):  
Hydraulic Conductivity ◽  
Friction Factor ◽  
Open Channel ◽  
High Conductivity ◽  
Channel Flows ◽  
Rough Boundary ◽  
Roughness Parameters ◽  
Mean Flow ◽  
Open Channel Flows ◽  
Log Law

<p>Open channel flows over granular mobile beds are affected by the nature and intensity of hyporheic/surface mass and momentum exchanges. Near-bed surface mean flow and turbulence find an equilibrium with the flow in the hyporheic region and with the type and amount of granular material transported in equilibrium conditions. The processes involved in these adaptive process are not well known. This work addresses this knowledge gap and it is aimed at describing the effect of the hydraulic conductivity on the friction factor and on the parameters of the log-law that is thought to constitute a valid model for the turbulent flow in the overlapping region of fully developed hydraulically rough boundary layers over mobile cohesionless beds. To fulfil the objectives, experimental tests performed in high conductivity beds (mono-sized glass sphere beads) are compared with the existing database of low conductivity beds of Ferreira et al. (2012), keeping constant the range of values of porosity, Shields parameters and roughness Reynolds numbers. The hydraulic conductivity is varied by changing the tortuosity (and the dimensions of the pore paths) and not the porosity.</p><p>A new database of instantaneous velocities was acquired with Particle Image Velocimetry (PIV) and processed to gather time-averaged velocities and space-time (double-averaged) quantities, namely velocities, Reynolds stresses and form-induced stresses. The hydraulic conductivity was measured for both types of bed.</p><p>The parameters of log-law obtained from high conductivity are compared with low conductivity of existing database, for mobile and immobile bed conditions. The main finding can be summarized as follows.</p><p>i. Hydraulic conductivity does not affect the location of the zero plane of the log-law, the thickness of the region above the crests where the flow is determined by roughness.</p><p>ii. Increasing the hydraulic conductivity does not appear to decrease the value of bed roughness parameters such as the roughness heigh.</p><p>iii. Higher hydraulic conductivity is associated to a structural change: the same near-bed velocity can be achieved with lower shear stress in the inner region. A lower friction factor, (<em>u</em><sub>*</sub>/<em>U</em>)<sup>2</sup>, is thus registered.</p><p>iv. Flows over high conductivity beds appear drag-reducing even if roughness parameters do not change appreciably.</p><p> </p><p>This research was partially supported by Portuguese and European funds, within the COMPETE 2020 and PORL-FEDER programs, through project PTDC/CTA-OHR/29360/2017 RiverCure</p>

Evolution of solitary marginal disturbances in baroclinic frontal geostrophic dynamics with dissipation and time-varying background flow

2007 ◽  
Vol 463 (2083) ◽  
pp. 1749-1769 ◽  
Author(s):  
Mattea R Turnbull ◽  
Gordon E Swaters
Keyword(s):  
Lower Layer ◽  
Baroclinic Instability ◽  
Variable Coefficients ◽  
Time Variability ◽  
Perturbation Approach ◽  
Dynamical Regime ◽  
Time Varying ◽  
Mean Flow ◽  
Background Flow ◽  
Frontal Geostrophic Dynamics

A two-layer frontal geostrophic flow corresponds to a dynamical regime that describes the low-frequency evolution of baroclinic ocean currents with large amplitude deflections of the interface between the layers on length-scales longer than the internal deformation radius within the context of a thin upper layer overlying a dynamically active lower layer. The finite-amplitude evolution of solitary disturbances in baroclinic frontal geostrophic dynamics in the presence of time-varying background flow and dissipation is shown to be governed by a two-equation extension of the unstable nonlinear Schrödinger (UNS) equation with variable coefficients and forcing. The soliton solution of the unperturbed UNS equation corresponds to a saturated isolated coherent anomaly in the baroclinic instability of surface-intensified oceanographic fronts and currents. The adiabatic evolution of the propagating soliton and the uniformly valid first-order perturbation fields are determined using a direct perturbation approach together with phase-averaged conservation relations when both dissipation and time variability are present. It is shown that the soliton amplitude parameter decays exponentially due to the presence of the dissipation but is unaffected by the time variability in the background flow. On the other hand, the soliton translation velocity is unaffected by the dissipation and evolves only in response to the time variability in the background flow. The adiabatic solution for the induced mean flow exhibits a dissipation-generated ‘shelf region’ in the far field behind the soliton, which is removed by solving the initial-value problem.

The Simulation of Airframe Noise Applying Euler-Perturbation and Acoustic Analogy Approaches

2005 ◽  
Vol 4 (1-2) ◽  
pp. 69-91 ◽  
Author(s):  
R. Ewert ◽  
J.W. Delfs ◽  
M. Lummer
Keyword(s):  
Mach Number ◽  
Scaling Laws ◽  
Perturbation Approach ◽  
Far Field ◽  
Acoustic Analogy ◽  
Mean Flow ◽  
Trailing Edge ◽  
Airframe Noise ◽  
Trailing Edge Noise ◽  
The Mean

The capability of three different perturbation approaches to tackle airframe noise problems is studied. The three approaches represent different levels of complexity and are applied to trailing edge noise problems. In the Euler-perturbation approach the linearized Euler equations without sources are used as governing acoustic equations. The sound generation and propagation is studied for several trailing edge shapes (blunt, sharp, and round trailing edges) by injecting upstream of the trailing edge test vortices into the mean-flow field. The efficiency to generate noise is determined for the trailing edge shapes by comparing the different generated sound intensities due to an initial standard vortex. Mach number scaling laws are determined varying the mean-flow Mach number. In the second simulation approach an extended acoustic analogy based on acoustic perturbation equations (APEs) is applied to simulate trailing edge noise of a flat plate. The acoustic source terms are computed from a synthetic turbulent velocity model. Furthermore, the far field is computed via additional Kirchhoff extrapolation. In the third approach the sources of the extended acoustic analogy are computed from a Large Eddy Simulation (LES) of the compressible flow problem. The directivities due to a modeled and a LES based source, respectively, compare qualitatively well in the near field. In the far field the asymptotic directivities from the Kirchhoff extrapolation agree very well with the analytical solution of Howe. Furthermore, the sound pressure spectra can be shown to have similar shape and magnitude for the last two approaches.

Statistical Tests of Taylor’s Hypothesis: An Application to Precipitation Fields

2009 ◽  
Vol 10 (1) ◽  
pp. 254-265 ◽  
Author(s):  
Bo Li ◽  
Aditya Murthi ◽  
Kenneth P. Bowman ◽  
Gerald R. North ◽  
Marc G. Genton ◽  
...  
Keyword(s):  
Correlation Analysis ◽  
Time Scale ◽  
Statistical Tests ◽  
Spatial Scales ◽  
Statistical Significance ◽  
Time Lag ◽  
Mean Flow ◽  
Spatial Covariance ◽  
Simple Correlation ◽  
Taylor’S Hypothesis

Abstract The Taylor hypothesis (TH) as applied to rainfall is a proposition about the space–time covariance structure of the rainfall field. Specifically, it supposes that if a spatiotemporal precipitation field with a stationary covariance Cov(r, τ) in both space r and time τ moves with a constant velocity v, then the temporal covariance at time lag τ is equal to the spatial covariance at space lag r = vτ that is, Cov(0, τ) = Cov(vτ, 0). Qualitatively this means that the field evolves slowly in time relative to the advective time scale, which is often referred to as the frozen field hypothesis. Of specific interest is whether there is a cutoff or decorrelation time scale for which the TH holds for a given mean flow velocity v. In this study, the validity of the TH is tested for precipitation fields using high-resolution gridded Next Generation Weather Radar (NEXRAD) reflectivity data produced by the WSI Corporation by employing two different statistical approaches. The first method is based on rigorous hypothesis testing, while the second is based on a simple correlation analysis, which neglects possible dependencies between the correlation estimates. Radar reflectivity values are used from the southeastern United States with an approximate horizontal resolution of 4 km × 4 km and a temporal resolution of 15 min. During the 4-day period from 2 to 5 May 2002, substantial precipitation occurs in the region of interest, and the motion of the precipitation systems is approximately uniform. The results of both statistical methods suggest that the TH might hold for the shortest space and time scales resolved by the data (4 km and 15 min) but that it does not hold for longer periods or larger spatial scales. Also, the simple correlation analysis tends to overestimate the statistical significance through failing to account for correlations between the covariance estimates.

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