Development of a three-dimensional time-dependent flow field model

A three-dimensional, time-dependent mathematical model to represent Mobile Bay was developed. Computer programs were developed which numerically solve the appropriate conservation equations for predicting bay and estuary flow fields. The model is useful for analyzing the dispersion of sea water into fresh water and the transport of sediment, and for relating field and physical model data

A three-dimensional, time-dependent model of Mobile Bay

A three-dimensional, time-variant mathematical model for momentum and mass transport in estuaries was developed and its solution implemented on a digital computer. The mathematical model is based on state and conservation equations applied to turbulent flow of a two-component, incompressible fluid having a free surface. Thus, bouyancy effects caused by density differences between the fresh and salt water, inertia from thare river and tidal currents, and differences in hydrostatic head are taken into account. The conservation equations, which are partial differential equations, are solved numerically by an explicit, one-step finite difference scheme and the solutions displayed numerically and graphically. To test the validity of the model, a specific estuary for which scaled model and experimental field data are available, Mobile Bay, was simulated. Comparisons of velocity, salinity and water level data show that the model is valid and a viable means of simulating the hydrodynamics and mass transport in non-idealized estuaries

A dependent nominal type theory

Nominal abstract syntax is an approach to representing names and binding pioneered by Gabbay and Pitts. So far nominal techniques have mostly been studied using classical logic or model theory, not type theory. Nominal extensions to simple, dependent and ML-like polymorphic languages have been studied, but decidability and normalization results have only been established for simple nominal type theories. We present a LF-style dependent type theory extended with name-abstraction types, prove soundness and decidability of beta-eta-equivalence checking, discuss adequacy and canonical forms via an example, and discuss extensions such as dependently-typed recursion and induction principles

Mode-coupling theory for multiple-time correlation functions of tagged particle densities and dynamical filters designed for glassy systems

The theoretical framework for higher-order correlation functions involving multiple times and multiple points in a classical, many-body system developed by Van Zon and Schofield [Phys. Rev. E 65, 011106 (2002)] is extended here to include tagged particle densities. Such densities have found an intriguing application as proposed measures of dynamical heterogeneities in structural glasses. The theoretical formalism is based upon projection operator techniques which are used to isolate the slow time evolution of dynamical variables by expanding the slowly-evolving component of arbitrary variables in an infinite basis composed of the products of slow variables of the system. The resulting formally exact mode-coupling expressions for multiple-point and multiple-time correlation functions are made tractable by applying the so-called N-ordering method. This theory is used to derive for moderate densities the leading mode coupling expressions for indicators of relaxation type and domain relaxation, which use dynamical filters that lead to multiple-time correlations of a tagged particle density. The mode coupling expressions for higher order correlation functions are also succesfully tested against simulations of a hard sphere fluid at relatively low density.Comment: 15 pages, 2 figure

Numerical modeling of thermal bar and stratification pattern in Lake Ontario using the EFDC model

Thermal bar is an important phenomenon in large, temperate lakes like Lake Ontario. Spring thermal bar formation reduces horizontal mixing, which in turn, inhibits the exchange of nutrients. Evolution of the spring thermal bar through Lake Ontario is simulated using the 3D hydrodynamic model Environmental Fluid Dynamics Code (EFDC). The model is forced with the hourly meteorological data from weather stations around the lake, flow data for Niagara and St. Lawrence rivers, and lake bathymetry. The simulation is performed from April to July, 2011; on a 2-km grid. The numerical model has been calibrated by specifying: appropriate initial temperature and solar radiation attenuation coefficients. The existing evaporation algorithm in EFDC is updated to modified mass transfer approach to ensure correct simulation of evaporation rate and latent heatflux. Reasonable values for mixing coefficients are specified based on sensitivity analyses. The model simulates overall surface temperature profiles well (RMSEs between 1-2°C). The vertical temperature profiles during the lake mixed phase are captured well (RMSEs < 0.5°C), indicating that the model sufficiently replicates the thermal bar evolution process. An update of vertical mixing coefficients is under investigation to improve the summer thermal stratification pattern. Keywords: Hydrodynamics, Thermal BAR, Lake Ontario, GIS

Heterogeneous processes: Laboratory, field, and modeling studies

The efficiencies of chemical families such as ClO(x) and NO(x) for altering the total abundance and distribution of stratospheric ozone are controlled by a partitioning between reactive (active) and nonreactive (reservoir) compounds within each family. Gas phase thermodynamics, photochemistry, and kinetics would dictate, for example, that only about 1 percent of the chlorine resident in the lower stratosphere would be in the form of active Cl or ClO, the remainder existing in the reservoir compounds HCl and ClONO2. The consistency of this picture was recently challenged by the recognition that important chemical transformations take place on polar regions: the Airborne Antarctic Ozone Experiment (AAOE) and the Airborne Arctic Stratospheric Expedition (AASA). Following the discovery of the Antarctic ozone hole, Solomon et al. suggested that the heterogeneous chemical reaction: ClONO2(g)+HCl(s) yields Cl2(g)+HNO3(s) could play a key role in converting chlorine from inactive forms into a species (Cl2) that would rapidly dissociate in sunlight to liberate atomic chlorine and initiate ozone depletion. The symbols (s) and (g) denote solid phase, or adsorbed onto a solid surface, and gas phase, respectively, and represent the approach by which such a reaction is modeled rather than the microscopic details of the reaction. The reaction was expected to be most important at altitudes where PSC's were most prevalent (10 to 25 km), thereby extending the altitude range over which chlorine compounds can efficiently destroy ozone from the 35 to 45 km region (where concentrations of active chlorine are usually highest) to lower altitudes where the ozone concentration is at its peak. This chapter will briefly review the current state of knowledge of heterogeneous processes in the stratosphere, emphasizing those results obtained since the World Meteorological Organization (WMO) conference. Sections are included on laboratory investigations of heterogeneous reactions, the characteristics and climatology of PSC's, stratospheric sulfate aerosols, and evidence of heterogeneous chemical processing