This thesis deals with the squat of a moving ship; that is, the downward displacement and angle of trim caused by its forward motion. The thesis is divided into two parts, in which the ship is considered to be moving in water of constant depth and non-constant depth respectively. In both parts, results are given for ships in channels and in open water. Since squat is essentially a Bernoulli effect, viscosity is neglected throughout most of the work, which results in a boundary value problem involving Laplace's equation. Only qualitative statements about the effect of viscosity are made. For a ship moving in water of constant depth, we first consider a one-dimensional theory for narrow channels. This is described for both linearized flow, where the disturbance due to the ship is small, and nonlinear flow, where the disturbance due to the ship is large. For nonlinear flow we develop an iterative method for determining the nonlinear sinkage and trim. Conditions for the existence of steady flow are determined, which take into account the squat of the ship. We then turn to the problem of ships moving in open water, where one-dimensional theory is no longer applicable. A well-known slender-body shallow-water theory is modified to remove the singularity which occurs when the ship's speed is equal to the shallow-water wave speed. This is done by including the effect of dispersion, in a manner similar to the derivation of the Korteweg-deVries equation. A finite-depth theory is also used to model the flow near the critical speed. For a ship moving in water of non-uniform depth, a linearized one-dimensional theory is derived which is applicable to unsteady flow. This is applied to simple bottom topographies, using analytic as well as numerical methods. A corresponding slender-body shallow-water theory for variable depth is also developed, which is valid for ships in channels or open water. Numerical results are given for a step depth change, and an analytic solution to the problem is discussed. / Thesis (Ph.D.)--Applied Mathematics, 2000.

This thesis deals with the squat of a moving ship; that is, the downward displacement and angle of trim caused by its forward motion. The thesis is divided into two parts, in which the ship is considered to be moving in water of constant depth and non-constant depth respectively. In both parts, results are given for ships in channels and in open water. Since squat is essentially a Bernoulli effect, viscosity is neglected throughout most of the work, which results in a boundary value problem involving Laplace's equation. Only qualitative statements about the effect of viscosity are made. For a ship moving in water of constant depth, we first consider a one-dimensional theory for narrow channels. This is described for both linearized flow, where the disturbance due to the ship is small, and nonlinear flow, where the disturbance due to the ship is large. For nonlinear flow we develop an iterative method for determining the nonlinear sinkage and trim. Conditions for the existence of steady flow are determined, which take into account the squat of the ship. We then turn to the problem of ships moving in open water, where one-dimensional theory is no longer applicable. A well-known slender-body shallow-water theory is modified to remove the singularity which occurs when the ship's speed is equal to the shallow-water wave speed. This is done by including the effect of dispersion, in a manner similar to the derivation of the Korteweg-deVries equation. A finite-depth theory is also used to model the flow near the critical speed. For a ship moving in water of non-uniform depth, a linearized one-dimensional theory is derived which is applicable to unsteady flow. This is applied to simple bottom topographies, using analytic as well as numerical methods. A corresponding slender-body shallow-water theory for variable depth is also developed, which is valid for ships in channels or open water. Numerical results are given for a step depth change, and an analytic solution to the problem is discussed. / Thesis (Ph.D.)--Applied Mathematics, 2000.

This thesis deals with the squat of a moving ship; that is, the downward displacement and angle of trim caused by its forward motion. The thesis is divided into two parts, in which the ship is considered to be moving in water of constant depth and non-constant depth respectively. In both parts, results are given for ships in channels and in open water. Since squat is essentially a Bernoulli effect, viscosity is neglected throughout most of the work, which results in a boundary value problem involving Laplace's equation. Only qualitative statements about the effect of viscosity are made. For a ship moving in water of constant depth, we first consider a one-dimensional theory for narrow channels. This is described for both linearized flow, where the disturbance due to the ship is small, and nonlinear flow, where the disturbance due to the ship is large. For nonlinear flow we develop an iterative method for determining the nonlinear sinkage and trim. Conditions for the existence of steady flow are determined, which take into account the squat of the ship. We then turn to the problem of ships moving in open water, where one-dimensional theory is no longer applicable. A well-known slender-body shallow-water theory is modified to remove the singularity which occurs when the ship's speed is equal to the shallow-water wave speed. This is done by including the effect of dispersion, in a manner similar to the derivation of the Korteweg-deVries equation. A finite-depth theory is also used to model the flow near the critical speed. For a ship moving in water of non-uniform depth, a linearized one-dimensional theory is derived which is applicable to unsteady flow. This is applied to simple bottom topographies, using analytic as well as numerical methods. A corresponding slender-body shallow-water theory for variable depth is also developed, which is valid for ships in channels or open water. Numerical results are given for a step depth change, and an analytic solution to the problem is discussed. / Thesis (Ph.D.)--Applied Mathematics, 2000.

This thesis deals with the squat of a moving ship; that is, the downward displacement and angle of trim caused by its forward motion. The thesis is divided into two parts, in which the ship is considered to be moving in water of constant depth and non-constant depth respectively. In both parts, results are given for ships in channels and in open water. Since squat is essentially a Bernoulli effect, viscosity is neglected throughout most of the work, which results in a boundary value problem involving Laplace's equation. Only qualitative statements about the effect of viscosity are made. For a ship moving in water of constant depth, we first consider a one-dimensional theory for narrow channels. This is described for both linearized flow, where the disturbance due to the ship is small, and nonlinear flow, where the disturbance due to the ship is large. For nonlinear flow we develop an iterative method for determining the nonlinear sinkage and trim. Conditions for the existence of steady flow are determined, which take into account the squat of the ship. We then turn to the problem of ships moving in open water, where one-dimensional theory is no longer applicable. A well-known slender-body shallow-water theory is modified to remove the singularity which occurs when the ship's speed is equal to the shallow-water wave speed. This is done by including the effect of dispersion, in a manner similar to the derivation of the Korteweg-deVries equation. A finite-depth theory is also used to model the flow near the critical speed. For a ship moving in water of non-uniform depth, a linearized one-dimensional theory is derived which is applicable to unsteady flow. This is applied to simple bottom topographies, using analytic as well as numerical methods. A corresponding slender-body shallow-water theory for variable depth is also developed, which is valid for ships in channels or open water. Numerical results are given for a step depth change, and an analytic solution to the problem is discussed. / Thesis (Ph.D.)--Applied Mathematics, 2000.

This thesis deals with the squat of a moving ship; that is, the downward displacement and angle of trim caused by its forward motion. The thesis is divided into two parts, in which the ship is considered to be moving in water of constant depth and non-constant depth respectively. In both parts, results are given for ships in channels and in open water. Since squat is essentially a Bernoulli effect, viscosity is neglected throughout most of the work, which results in a boundary value problem involving Laplace's equation. Only qualitative statements about the effect of viscosity are made. For a ship moving in water of constant depth, we first consider a one-dimensional theory for narrow channels. This is described for both linearized flow, where the disturbance due to the ship is small, and nonlinear flow, where the disturbance due to the ship is large. For nonlinear flow we develop an iterative method for determining the nonlinear sinkage and trim. Conditions for the existence of steady flow are determined, which take into account the squat of the ship. We then turn to the problem of ships moving in open water, where one-dimensional theory is no longer applicable. A well-known slender-body shallow-water theory is modified to remove the singularity which occurs when the ship's speed is equal to the shallow-water wave speed. This is done by including the effect of dispersion, in a manner similar to the derivation of the Korteweg-deVries equation. A finite-depth theory is also used to model the flow near the critical speed. For a ship moving in water of non-uniform depth, a linearized one-dimensional theory is derived which is applicable to unsteady flow. This is applied to simple bottom topographies, using analytic as well as numerical methods. A corresponding slender-body shallow-water theory for variable depth is also developed, which is valid for ships in channels or open water. Numerical results are given for a step depth change, and an analytic solution to the problem is discussed. / Thesis (Ph.D.)--Applied Mathematics, 2000.

Factors related to operations of a well that impact drilling uncertainties in the shallow water region of the Gulf of Mexico (GOM) can be directly linked to the site specific issues; such as water depth and local geological depositional environments. Earlier risk assessment tools and general engineering practice guidelines for the determination of the conductor casing design were based more on traditional practices rather than sound engineering practices. This study focuses on the rudimentary geological and engineering concepts to develop a methodology for the conductor setting depth criteria in the shallow water region of the GOM.

No description available.

Conventional morphodynamic models are typically based on a coupled system of hydrodynamic equations, a bed-update equation, and a sediment-transport equation. However, the sediment-transport equation is almost invariably empirical, with numerous options available in the literature. Bed morphological evolution predicted by a conventional model can be very sensitive to the choice of sediment-transport formula. This thesis presents a physics-based model, where the shallow water-sediment-mixture flow is idealised as being divided into two layers of variable (in time and space) densities: the lower layer concerned with bedload transport, and the upper layer representing sediment in suspension. The model is referred to as a Quasi-2-Layer (Q2L) model in order to distinguish it from typical 2-Layer models representing stratified flow by two layers of different but constant and uniform densities. The present model, which does not require the selection of a particular empirical formula for sediment transport rates, is satisfactorily validated against widely used empirical expressions for bedload and total transport rates. Analytical solutions to the model are derived for steady uniform flow over an erodible bed. Case studies show that the Q2L model, in contrast to conventional morphodynamic approaches, yields more realistic results by inherently including the influence of the bed slope on the sediment transport. This conclusion is validated against experimental data from a steep sloping duct. An analytical study using the Q2L model investigates the influence of bed-slope on bedload transport; the resulting expressions are in turn used to modify empirical sediment transport formulae (derived for horizontal beds) in order to render them applicable to arbitrary stream-wise slopes. The Q2L model provides an alternative approach to studying sediment-transport phenomena, whose adequate analysis cannot be undertaken following coniv ventional approaches without further increasing their degree of empiricism. The Q2L model can also lead to the enhancement of conventional morphodynamic models. For coarse sediments and/or relatively low flow velocities, bedload transport is usually responsible for most sediment transport. Bedload transport consists of a combination of particles rolling, sliding and saltating (hopping) along the bed. Hence, saltation models provide considerable insight into near-bed sediment transport. This thesis also presents an analysis of the statistics and mechanics of a saltating particle model. For this purpose, a mathematically simple, computationally efficient, stochastic Lagrangian model has been derived. This model is validated satisfactorily against previously published experimental data on saltation. The model is then employed to derive two criteria aimed at ensuring that statistically convergent results are achieved when similar saltation models are employed. According to the first criterion, 103 hops should be simulated, whilst 104 hops ought to be considered according to the second criterion. This finding is relevant given that previous studies report results after only a few hundred, or less, particle hops have been simulated. The model also investigates sensitivity to the lift force formula, the friction coefficient, and the collision line level. A method is proposed by which to estimate the bedload sediment concentration and transport rate from particle saltation characteristics. This method yields very satisfactory results when compared against widely used empirical expressions for bedload transport, especially when contrasted against previously published saltation-based expressions.

An adaptive mesh refinement algorithm for shallow water equations is presented. The algorithm uses upwind scheme that is Godunov type and which approximately solves the Riemann problem using Roe's technique. A highly accurate solution is achieved by using the adaptive mesh refinement technique of Berger and Oliger for mesh refinement algorithm. The numerical method is second-order accurate and approximately max-min preserving by using van Leer limited-slope technique. One-dimensional nesting algorithm has been implemented successfully. Numerical results on a test problem verify the second order accuracy of the algorithm. The nested grid results yield the equivalent solution to that of the corresponding fine grid solution.

Significant effort has been made to quantify and predict roll damping of vessels in the past. Similarly, efforts have been made to provide effective methods for calculating the roll gyradius of vessels. Both the damping and the gyradius of a vessel are traditionally quantified through the use of a sally test. Experience with the USS Midway showed that shallow water has significant effect on the rolling period and thus the experimentally determined roll gyradius. To date, little effort has been directed to the problem of the effect of shallow water on roll damping and roll period except when trying to match model and full scale experimental data. No clear guidelines exist for the boundary between deep and shallow water or the amount of overprediction of roll period that is likely for a given water depth. In order to provide greater understanding of the effects of shallow water on roll period and roll damping, this thesis performed experiments in varying scale water depths for 5 models: 4 box barges and a model of the USS Essex. The following conclusions were reached: As water depth to draft ratio, d/T, approaches 1 the roll period can increase as much as 14%. The boundary between deep and shallow water is a water depth somewhere between 4 and 7 times the vessel draft depending on the particulars of the vessel's hull form. Vessels with a larger beam to draft ratio will experience shallow water effects in relatively deeper water, that is to say the depth to draft ratio will be greater at the upper limit of deep water. Additionally, vessels with a higher beam to draft ratio will experience larger shallow water effects for a given depth to draft ratio. Finally, for vessels of very fine hull forms, the boundary between deep and shallow water will occur a relatively shallower depths, in other terms, the boundary will occur at a lower depth to draft ratio. / Master of Science