Search USGS⌕ Search

Geology topics

Roy A. Walters

Publications and source records attributed to Roy A. Walters.

11 recordsLinked to original sources
USGS2010

Accuracy of an estuarine hydrodynamic model using smooth elements

A finite element model which uses triangular, isoparametric elements with quadratic basis functions for the two velocity components and linear basis functions for water surface elevation is used in the computation of shallow water wave motions. Specifically addressed are two common uncertainties in this class of two-dimensional hydrodynamic models: the treatment of the boundary conditions at open boundaries and the treatment of lateral boundary conditions. The accuracy of the models is tested with a set of numerical experiments in rectangular and curvilinear channels with constant and variable depth. The results indicate that errors in velocity at the open boundary can be significant when boundary conditions for water surface elevation are specified. Methods are suggested for minimizing these errors. The results also show that continuity is better maintained within the spatial domain of interest when ‘smooth’ curve-sided elements are used at shoreline boundaries than when piecewise linear boundaries are used. Finally, a method for network development is described which is based upon a continuity criterion to gauge accuracy. A finite element network for San Francisco Bay, California, is used as an example.

California↗
USGS2010

Simulation of solute transport in a mountain pool-and-riffle stream: A transient storage model

The physical characteristics of mountain streams differ from the uniform and conceptually well- defined open channels for which the analysis of solute transport has been oriented in the past and is now well understood. These physical conditions significantly influence solute transport behavior, as demonstrated by a transient storage model simulation of solute transport in a very small (0.0125 m 3 s −1 ) mountain pool-and-riffle stream. The application is to a carefully controlled and intensively monitored chloride injection experiment. The data from the experiment are not explained by the standard convection-dispersion mechanisms alone. A transient storage model, which couples dead zones with the one-dimensional convection-dispersion equation, simulates the general characteristics of the solute transport behavior and a set of simulation parameters were determined that yield an adequate fit to the data. However, considerable uncertainty remains in determining physically realistic values of these parameters. The values of the simulation parameters used are compared to values used by other authors for other streams. The comparison supports, at least qualitatively, the determined parameter values.

Water Resources Research↗
USGS1989

A comparison of two finite element models of tidal hydrodynamics using a North Sea data set

Using the region of the English Channel and the southern bight of the North Sea, we systematically compare the results of two independent finite element models of tidal hydrodynamics. The model intercomparison provides a means for increasing our understanding of the relevant physical processes in the region in question as well as a means for the evaluation of certain algorithmic procedures of the two models.

Advances in Water Resources↗
USGS1989

Effects of runoff changes and sea level rise on salinity in the Delaware River estuary

The objective of this study is to investigate changes in the spatial distribution of salt in the Delaware Estuary resulting from climate induced changes in freshwater inflows and in the position of mean sea level. The approach adopted for this study is composed of two parts: An analysis of existing physical data in order to derive a basic understanding of the salt dynamics, and numerical simulation of future conditions based upon this analysis.

Conference Paper↗
USGS1987

A model for tides and currents in the English Channel and southern North Sea

The amplitude and phase of 11 tidal constituents for the English Channel and southern North Sea are calculated using a frequency domain, finite element model. The governing equations - the shallow water equations - are modifed such that sea level is calculated using an elliptic equation of the Helmholz type followed by a back-calculation of velocity using the primitive momentum equations. Triangular elements with linear basis functions are used. The modified form of the governing equations provides stable solutions with little numerical noise. In this field-scale test problem, the model was able to produce the details of the structure of 11 tidal constituents including O1, K1, M2, S2, N2, K2, M4, MS4, MN4, M6, and 2MS6.

Conference Paper↗
USGS1986

Phytoplankton spatial distribution in south San Francisco Bay: mesoscale and small-scale variability

Horizontal transects of surface salinity and in-vivo fluorescence indicate the existence of three distinct spatial regimes in South San Francisco Bay. A mid-Bay region of low phytoplankton biomass with little small-scale variance is bounded to the north and south by water masses having higher in-vivo fluorescence and enhanced small-scale variability. Autocorrelation analyses demonstrate that the length scale of phytoplankton patchiness is longest in the mid-Bay region. The persistent discontinuities of in-vivo fluorescence and salinity are associated with topographic features—a large shoal to the north and a constriction to the south. The three spatial regimes are consistent with measured zooplankton distributions, existing current meter data, estimated longitudinal transports, and numerical simulations of residual circulations that show one (and perhaps two) large-scale gyre(s) bounded by the northern shoal and southern constriction. Topographic features are the most important physical factors controlling mesoscale (~ 10 km) variability of phytoplankton in South San Francisco Bay. We speculate that vertical current shear and salinity stratification (and their effects upon turbulence and diffusion) control small-scale patchiness, but quantitative estimates are needed to determine the influence of large-scale (and local) phytoplankton growth and loss processes.

Book chapter↗
USGS1984

Finite element solution methods for circulation in estuaries

In this paper, the shallow water equations are used to approximate the depth-mean circulation in estuaries. The time scales of the motions can be conveniently divided into three ranges: 1) low-frequency (residual) variations with periods of two days or longer, 2) tidal-frequency variations, and 3) high-frequency variations with periods of an hour or shorter. The emphasis here will be on the tidal-period variations that are characterized by line spectra and thus allow a harmonic decomposition of the governing equations.

Book chapter↗
USGS1983

Analysis of spurious oscillation modes for the shallow water and Navier-Stokes equations

The origin and nature of spurious oscillation modes that appear in mixed finite element methods are examined. In particular, the shallow water equations are considered and a modal analysis for the one-dimensional problem is developed. From the resulting dispersion relations we find that the spurious modes in elevation are associated with zero frequency and large wave number (wavelengths of the order of the nodal spacing) and consequently are zero-velocity modes. The spurious modal behavior is the result of the finite spatial discretization. By means of an artificial compressibility and limiting argument we are able to resolve the similar problem for the Navier-Stokes equations. The relationship of this simpler analysis to alternative consistency arguments is explained. This modal approach provides an explanation of the phenomenon in question and permits us to deduce the cause of the very complex behavior of spurious modes observed in numerical experiments with the shallow water equations and Navier-Stokes equations. Furthermore, this analysis is not limited to finite element formulations, but is also applicable to finite difference formulations.

Computers and Fluids↗
USGS1982

Low-frequency variations in sea level and currents in south San Francisco Bay

In order to examine physical process in the subtidal time range, sea-level and current meter data for south San Francisco Bay (South Bay) were filtered using a low-pass digital filter to remove tidal period variations. and then subjected to an empirical orthogonal function analysis. For the sea-level data, there is one dominant empirical mode that is correlated with nonlocal coastal forcing. A small amount of the variance is associated with local wind setup. For the current meter data, there are two dominant empirical modes that correlate with local wind forcing and tidal forcing over the spring-neap cycle. In general, South Bay is dominated by coastal forcing on sea level during all seasons, and dominated by wind and tidal forcing on the residual currants during the summer.

California↗
USGS1979

A two-dimensional hydrodynamic model of a tidal estuary

A finite element model is described which is used in the computation of tidal currents in an estuary. This numerical model is patterned after an existing algorithm and has been carefully tested in rectangular and curve-sided channels with constant and variable depth. One of the common uncertainties in this class of two-dimensional hydrodynamic models is the treatment of the lateral boundary conditions. Special attention is paid specifically to addressing this problem. To maintain continuity within the domain of interest, ‘smooth’ curve-sided elements must be used at all shoreline boundaries. The present model uses triangular, isoparametric elements with quadratic basis functions for the two velocity components and a linear basis function for water surface elevation. An implicit time integration is used and the model is unconditionally stable. The resultant governing equations are nonlinear owing to the advective and the bottom friction terms and are solved iteratively at each time step by the Newton-Raphson method. Model test runs have been made in the southern portion of San Francisco Bay, California (South Bay) as well as in the Bay west of Carquinez Strait. Owing to the complex bathymetry, the hydrodynamic characteristics of the Bay system are dictated by the generally shallow basins which contain deep, relict river channels. Great care must be exercised to ensure that the conservation equations remain locally as well as globally accurate. Simulations have been made over several representative tidal cycles using this finite element model, and the results compare favourably with existing data. In particular, the standing wave in South Bay and the progressive wave in the northern reach are well represented.

California↗