Mathematical hydraulics of surface irrigation

The general hydrodynamic equations for a spatially varied unsteady flow in a prismatic open channel having an arbitrary cross-sectional shape can be derived from the equations of continuity and momentum. The assumptions based on the general concept of hydrodynamics and the theory of shallow water is introduced. The mathematical models in the surface irrigation can be formulated by these equations of motion with the appropriate initial and boundary conditions prescribed at the singularity point (the origin in the x, t-plane) and at x = 0. Therefore, the flow in the surface irrigation must be described by solving the boundary-value problem for the velocity and the depth of flow. In the two-dimensional flow, the discontinuity at the origin in the x, t-plane is overcome by imposing a critical velocity and correspondingly, a critical depth at the initial state. Without considering all the channel slope, friction, and infiltration terms, the mathematical model becomes the model for a “centered simple wave,” in which an exact solution, the Ritter solution, in the dam-breaking problem is already well-known. The Ritter solution satisfies the boundary condition at x = 0, where the discharge is always constant. However, even though an additional term, the channel slope, is considered, the modified Ritter solution no longer satisfies the same boundary condition. No exact solution seems possible with the present knowledge of mathematical techniques. The theory of characteristics is presented and the method of finite-difference based on this basic theory with the fixed-theme interval is introduced for the basic equations of motion in the surface irrigation. The trajectory of the wavefront is usually defined as a locus of zero celerity (c = 0) and forming an envelope of two different families of characteristics. Such an extremely complicated situation at the wavefront results in the possible failure of the present technique by simply using the finite-difference method unless some additional judicious assumptions at the wavefront, some type of the boundary-layer technique must be developed. This is the present status of the finite-difference method in the surface irrigation. The more simplified approximation by the kinematic-wave method is presented, based on an additional assumption analogous to the Dupit-Forchheimer theory in the groundwater flow. The method possesses a potential applicability in the surface irrigation. Inasmuch as no results are yet available, this study will be limited to a description of what is hoped to be accomplished and how it will be done

Urban Storm Runoff Inlet Hydrograph Study, Volume 5, Soil-Cover-Moisture Complex: Analysis of Parametric Infiltration Models for Highway Sideslopes

The main objective of this study is to develop an accurate design method for computing inlet hydrographs of surface runoff, with average recurrence intervals of 10, 25, and 50 years, from typical urban highway by flood routing technique. The boundary-value problem of one-dimensional infiltration resulting from rainfall is formulated and solved numerically on a digital computer. The numerical solutions of this idealized mathematical model is used as a basic testing tool in the subsequent analysis of various parametric infiltration models including the Green-Ampt, Kostiakov, Philip, Horton, and Holtan equations. The time of ponding is shown to be the most important parameter in a parametric infiltration model and can be expressed in terms of other parameters in the model as well as the rainfall intensity. The values of all the model parameters in the model as well as the rainfall intensity. The values of all the model parameters are determined to be fairly constant for a soil having the same initial and upper boundary (soil surface) conditions. Use of the Green-Ampt, Kostiakov, and Philip type models for the prediction of the infiltration rate before and after ponding is proved to be satisfactory. For engineering practice, the standard infiltration-capacity curves for soil-cover-moisture complexes representing urban highway sideslopes are empirically developed based on the unique selection of the Soil Conservation Service runoff curve number. Validity of typical standard curves so developed were experimentally examined in the Utah Water Research Laboratory stormflow experiment facility

Urban Storm Runoff Inlet Hydrograph Study Volume 2; Laboratory Studies of the Resistance Coefficient for Sheet Flow over Natural Turf Surfaces

The main objective of this study is to develop an accurate design method for computing inlet hydrogaphs of surface runoff, with average recurrence intervals of 10, 25, and 50 years, from typical urban highway by flood routing technique. Resistance to sheet flows over natural turf surfaces is experimentally investigated. The formuation of a functional relationship between the resistence coefficient and controlling parameters for shallow flows over various turf surfaces is essential to the mathematical modeling of surface runoff from urban highway sideslopes covered with different species of turf. An analysis of results obtained from laboratory experiments from laminar flow on Kentucky Blue grass and Bermuda grass reveals that a relationship exists between the Darcy-Weisback friction coefficient, Reynolds number, and bed slope. Time did not premit tests to be performed on all species of turf other than Kentucky Blue grass and Bermuda grass which can be sodded. However, a general trend of the resistance relationship for shallow flows over such dense turf surfaces as affected by raindrop impact and roughness is qualitatively determined

Urban Storm Runoff Inlet Hydrograph Study Volume 4; Synthetic Storms for Design of Urban Highway Drainage Facilities.

The main objective of this study is to develop an accurate design method for computing inlet hydrographs of surface runoff, with average recurrence intervals of 10, 25, and 50 years, from typical urban highway by flood routing technique. Knowledge of the time distribution of rainfall in heavy storms constitutes a basis for the design of an urban storm sewer system. A unified time-coordinate system and the rainfall intensity-duration-frequency relationships are used to develop the generalized synthetic (design) hyetograph equations for all types of storms. The hyetograph equations are further normalized for identifying the dimensionless parameters that play predominant roles in the formulation of a design storm pattern. The method of least squares and an optimization technique are applied to the evaluation of the storm parameters through the use of the rainfall intensity-duration-frequency maps in the U.S. Weather Bureau Technical Paper No. 40. It is found that the parameter evaluation method can greatly be simplified by establishing relationships among the storm parameters. However, ana analysis of available actual hyetographs failed to establish any relationships between the storm skewness and the other storm parameters

Slow Mass Transport and Statistical Evolution of An Atomic Gas Across the Superfluid-Mott Insulator Transition

We study transport dynamics of ultracold cesium atoms in a two-dimensional optical lattice across the superfluid-Mott insulator transition based on in situ imaging. Inducing the phase transition with a lattice ramping routine expected to be locally adiabatic, we observe a global mass redistribution which requires a very long time to equilibrate, more than 100 times longer than the microscopic time scales for on-site interaction and tunneling. When the sample enters the Mott insulator regime, mass transport significantly slows down. By employing fast recombination pulses to analyze the occupancy distribution, we observe similarly slow-evolving dynamics, and a lower effective temperature at the center of the sample

Process Studies and Modeling of Self-Cleaning Capacity of Mountain Creeks for Recreation Planning and Management

Reaeration process studies were conducted on a mountain creek and a large laboratory flume. The method of evaluating the dispersion coefficient, mean velocity, and reaeration coefficient for both creek and flume consisted of finding these values for a deoxygenated portion of the flow containing a conservative tracer (dye). The deoxygenated slug is measured as it moved downstream and the three values are best fit in the analytical solution of the longitudinal dispersion equation which dynamically describes the flow of the dispersing slug in the stream. The best fit was accomplished by using the method of least squares of the differences between the dissolved oxygen and dye concentration calculated from the dispersion equation and those obtained from the actual measurements is minimized. A reaeration coefficient prediction model of general form was developed. The model is composed of two dimensionless parameters which were identified from the normalized dissolved-oxygen balance equation. A simplified model which has two model parameters was also developed. Both model parameters were evaluated specifically for the mountain creek and laboratory flume. A comparison of this simplified model with existing models revealed that most existing models are incomplete in form. It was found that inclusion of the dispersion coefficient in the reaeration coefficient model improved the prediction accuracy. The information obtained from this study would aid in determining the oxygen balance of mountain creeks which is essential to the resource management of mountain watersheds

Urban Storm Runoff Inlet Hydrograph Study Volume 3: Hydrologic Data for Two Urban Highway Watersheds in the Salt Lake City Area, Utah

The main objective of this study is to develop an accurate design method for computing inlet hydrographs of surface runoff, with average recurrence intervals of 10, 25, and 50 years, from typical urban highway by flood routing technique. Hydrologic data such as the rainfall intensity, runoff flow rate, air temperature, wind velocity, and soil moisture content were collected during rainfall seasons in 1972 and 1973 on two urban highway watersheds in the Salt Lake City area, Utah. These data were used in the verification of a mathematical model simulating the surface runoff from such highway watersheds. The difficulties and inherent problems associated with field data collection from urban highway cross-section are discussed and possible remedies recommended. Hyetographs and the corresponding hydrographs of major storms which occurred in 1972 and 1973 at both sites are presented. Watershed infiltration capacities of sideslopes at both sites are empirically evaluated

In situ observation of self-patterned defect formation in atomic superfluids -- from ring dark solitons to vortex dipole necklaces

Unveiling non-equilibrium dynamics of solitonic and topological defect structures in a multidimensional nonlinear medium is a current frontier across diverse fields. One of the quintessential objects is a ring dark soliton (RDS), whose dynamics are expected to display remarkable interplay between symmetry and self-patterned topological defect formation from a transverse (snake) instability but has thus far evaded full experimental observations. Here, we report an experimental realization of RDS generation in a two-dimensional atomic superfluid trapped in a circular box. By quenching the confining box potential, we observe spontaneous soliton emission from the edge and its peculiar signature in radial motion. As an RDS evolves, we observe spontaneous transverse modulations at discrete azimuthal angles, which clearly result in a patterned formation of a circular vortex dipole array. Through collisions of the vortex dipoles with the box trap, we observe vortex unbinding, vortex pinning to the edge, and emission of rarefaction pulses. Our box-quench protocol opens a new way to study multidimensional dark solitons, structured formation of topological defects, and potentially the dynamics of ordered quantum vortex matter