A model for tidal motion and level in the Tay Estuary

1987 ◽  
Vol 92 (3-4) ◽  
pp. 257-273
Author(s):  
D. J. Gunn ◽  
O. Yenigun
Keyword(s):  
Boundary Conditions ◽  
Integral Method ◽  
Equations Of Motion ◽  
Hydrodynamic Resistance ◽  
Two Dimensional ◽  
Final Solution ◽  
The Road ◽  
Tidal Motion ◽  
Outer Estuary ◽  
Tay Estuary

SynopsisA new mathematical model has been constructed for tidal motion and level in the Tay Estuary. The model is based upon the two-dimensional vertically integrated equations of motion and gives two-dimensional vector velocities and levels from the rail bridge to the Bar, about 5 km east of Buddon Ness. The extent of the model outside the mouth of the Tay is 3 km north of Buddon Ness and 7 km south. The equations of motion are expressed in the form of central differences in space and solved explicitly in time using the Local Integral Method. The emergence and submergence of drying zones in the estuary are calculated during the tidal cycle. A representation of the hydrodynamic resistance of the road bridge was included in the model.The boundary conditions for the model were based upon estimates of river flows at the western entrance and tidal levels at the eastern, northern and southern boundaries. Boundary conditions at the eastern end of the model presented considerable complexities because of the presence of an amphidromic system to the south of the Norwegian coast. The final solution adopted was to choose tidal levels along the easterly boundaries to give velocities in the outer estuary that agreed with available tidal atlases of the region.Velocities and levels at intervals of 250 m for the period of a tide show the prevalent shoaling conditions over the estuary combined during certain periods with conditions of high velocity, giving very difficult approaches to the River Tay.

Partial validation of a numerical model for tidal motion in the Tay Estuary

1987 ◽  
Vol 92 (3-4) ◽  
pp. 275-283
Author(s):  
D. J. Gunn ◽  
J. McManus ◽  
O. Yenigun
Keyword(s):  
Mathematical Model ◽  
Numerical Model ◽  
Boundary Conditions ◽  
North Sea ◽  
Integral Method ◽  
The Road ◽  
Tidal Motion ◽  
The North ◽  
Open Sea ◽  
The North Sea

SynopsisIn a mathematical model of the Tay (Gunn & Yenigun 1987) based upon the Local Integral Method (Gunn & Yenigun 1985), tidal levels at the seaward boundaries and velocities at landward boundaries are used in setting boundary conditions, so that validation studies are mainly based upon changes in internal tidal levels, and comparison between computed and measured velocities within the modelled region. The comparisons of tidal levels within this estuary over a 5.0 m tide showed agreement with overall values from Buddon Ness to the rail bridge, but within the overall agreement there were significant differences in the immediate vicinity of the road bridge. Velocities predicted within the estuary have been compared with measurements provided by a number of surveys in the period from 1972-78. The agreement between experiment and prediction was good in the central and western regions of the model, but the comparison between measurement and prediction was less good near the eastern boundaries. The principal reason for poorer agreement in the east was the difficulty in setting boundary conditions at the open sea extremes of the model. The most satisfactory way of improving the model near the open sea boundaries would be to link the model for the Tay with a model for velocity and level in the North Sea.

Dynamic Characteristics of Large Repetitive Framelike Structures

1984 ◽  
Vol 51 (3) ◽  
pp. 510-518 ◽  
Author(s):  
Adnan H. Nayfeh ◽  
Michael S. Hartle
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Dynamic Characteristics ◽  
Building Block ◽  
Equations Of Motion ◽  
Single Element ◽  
Two Dimensional ◽  
Energy Equivalent ◽  
Theoretical Predictions ◽  
Block Approach

Using a building block approach and starting with a single element, expressions for the energy of various two-dimensional frametype gridwork configurations are derived. These are then used to develop energy equivalent continua for the grid-works. Equations of motion and associated boundary conditions are obtained for the continua. Some dynamic characteristics of these continua are investigated and compared with corresponding results obtained from finite element codes and also with some available theoretical predictions.

Symbolic computation to estimate two-sided boundary conditions in two-dimensional conduction problems

10.2514/3.920 ◽  
1997 ◽  
Vol 11 ◽  
pp. 472-476
Author(s):  
Henry H. Kerr ◽  
F. C. Frank ◽  
Jae-Woo Lee ◽  
W. H. Mason ◽  
Ching-Yu Yang
Keyword(s):  
Boundary Conditions ◽  
Symbolic Computation ◽  
Two Dimensional

Model of vortex flow of charge in a vessel with turbine impeller

1987 ◽  
Vol 52 (8) ◽  
pp. 1888-1904
Author(s):  
Miloslav Hošťálek ◽  
Ivan Fořt
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Theoretical Data ◽  
Eddy Diffusion ◽  
Quantitative Agreement ◽  
Creeping Flow ◽  
Model Parameters ◽  
Mean Flow ◽  
Two Dimensional Flow ◽  
Vorticity Transport

A theoretical model is described of the mean two-dimensional flow of homogeneous charge in a flat-bottomed cylindrical tank with radial baffles and six-blade turbine disc impeller. The model starts from the concept of vorticity transport in the bulk of vortex liquid flow through the mechanism of eddy diffusion characterized by a constant value of turbulent (eddy) viscosity. The result of solution of the equation which is analogous to the Stokes simplification of equations of motion for creeping flow is the description of field of the stream function and of the axial and radial velocity components of mean flow in the whole charge. The results of modelling are compared with the experimental and theoretical data published by different authors, a good qualitative and quantitative agreement being stated. Advantage of the model proposed is a very simple schematization of the system volume necessary to introduce the boundary conditions (only the parts above the impeller plane of symmetry and below it are distinguished), the explicit character of the model with respect to the model parameters (model lucidity, low demands on the capacity of computer), and, in the end, the possibility to modify the given model by changing boundary conditions even for another agitating set-up with radially-axial character of flow.

scholarly journals Singular BPS boundary conditions in $$ \mathcal{N} $$ = (2, 2) supersymmetric gauge theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Tadashi Okazaki ◽  
Douglas J. Smith
Keyword(s):  
String Theory ◽  
Boundary Conditions ◽  
Gauge Theories ◽  
Holomorphic Curve ◽  
Two Dimensional ◽  
Supersymmetric Gauge Theories ◽  
Special Lagrangian ◽  
Supersymmetric Gauge ◽  
M Theory

Abstract We derive general BPS boundary conditions in two-dimensional $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories. We analyze the solutions of these boundary conditions, and in particular those that allow the bulk fields to have poles at the boundary. We also present the brane configurations for the half- and quarter-BPS boundary conditions of the $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories in terms of branes in Type IIA string theory. We find that both A-type and B-type brane configurations are lifted to M-theory as a system of M2-branes ending on an M5-brane wrapped on a product of a holomorphic curve in ℂ2 with a special Lagrangian 3-cycle in ℂ3.

Two-dimensional leaps in near-critical flow over isolated orography

2005 ◽  
Vol 461 (2064) ◽  
pp. 3747-3763 ◽  
Author(s):  
E.R Johnson ◽  
G.G Vilenski
Keyword(s):  
Unsteady Flow ◽  
Equations Of Motion ◽  
Fold Increase ◽  
Flow Speed ◽  
Two Dimensional ◽  
Subcritical Flow ◽  
One Dimensional ◽  
Petviashvili Equation ◽  
Lee Wave ◽  
Supercritical Flows

This paper describes steady two-dimensional disturbances forced on the interface of a two-layer fluid by flow over an isolated obstacle. The oncoming flow speed is close to the linear longwave speed and the layer densities, layer depths and obstacle height are chosen so that the equations of motion reduce to the forced two-dimensional Korteweg–de Vries equation with cubic nonlinearity, i.e. the forced extended Kadomtsev–Petviashvili equation. The distinctive feature noted here is the appearance in the far lee-wave wake behind obstacles in subcritical flow of a ‘table-top’ wave extending almost one-dimensionally for many obstacles widths across the flow. Numerical integrations show that the most important parameter determining whether this wave appears is the departure from criticality, with the wave appearing in slightly subcritical flows but being destroyed by two-dimensional effects behind even quite long ridges in even moderately subcritical flow. The wave appears after the flow has passed through a transition from subcritical to supercritical over the obstacle and its leading and trailing edges resemble dissipationless leaps standing in supercritical flow. Two-dimensional steady supercritical flows are related to one-dimensional unsteady flows with time in the unsteady flow associated with a slow cross-stream variable in the two-dimensional flows. Thus the wide cross-stream extent of the table-top wave appears to derive from the combination of its occurrence in a supercritical region embedded in the subcritical flow and the propagation without change of form of table-top waves in one-dimensional unsteady flow. The table-top wave here is associated with a resonant steepening of the transition above the obstacle and a consequent twelve-fold increase in drag. Remarkably, the table-top wave is generated equally strongly and extends laterally equally as far behind an axisymmetric obstacle as behind a ridge and so leads to subcritical flows differing significantly from linear predictions.

scholarly journals A methodology for hygrothermal modelling of imperfect masonry interfaces

2021 ◽  
pp. 174425912198938
Author(s):  
Michael Gutland ◽  
Scott Bucking ◽  
Mario Santana Quintero
Keyword(s):  
Boundary Conditions ◽  
Material Properties ◽  
Structural Integrity ◽  
Bulk Material ◽  
Weather Conditions ◽  
Masonry Wall ◽  
Two Dimensional ◽  
Liquid Transport ◽  
Imperfect Contact ◽  
Moisture Contents

Hygrothermal models are important tools for assessing the risk of moisture-related decay mechanisms which can compromise structural integrity, loss of architectural features and material. There are several sources of uncertainty when modelling masonry, related to material properties, boundary conditions, quality of construction and two-dimensional interactions between mortar and unit. This paper examines the uncertainty at the mortar-unit interface with imperfections such as hairline cracks or imperfect contact conditions. These imperfections will alter the rate of liquid transport into and out of the wall and impede the liquid transport between mortar and masonry unit. This means that the effective liquid transport of the wall system will be different then if only properties of the bulk material were modelled. A detailed methodology for modelling this interface as a fracture is presented including definition of material properties for the fracture. The modelling methodology considers the combined effect of both the interface resistance across the mortar-unit interface and increase liquid transport in parallel to the interface, and is generalisable to various combinations of materials, geometries and fracture apertures. Two-dimensional DELPHIN models of a clay brick/cement-mortar masonry wall were created to simulate this interaction. The models were exposed to different boundary conditions to simulate wetting, drying and natural cyclic weather conditions. The results of these simulations were compared to a baseline model where the fracture model was not included. The presence of fractures increased the rate of absorption in the wetting phase and an increased rate of desorption in the drying phase. Under cyclic conditions, the result was higher peak moisture contents after rain events compared to baseline and lower moisture contents after long periods of drying. This demonstrated that detailed modelling of imperfections at the mortar-unit interface can have a definitive influence on results and conclusions from hygrothermal simulations.

scholarly journals Phase transitions in GLSMs and defects

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ilka Brunner ◽  
Fabian Klos ◽  
Daniel Roggenkamp
Keyword(s):  
Phase Transitions ◽  
Boundary Conditions ◽  
Sigma Models ◽  
Domain Walls ◽  
Two Dimensional ◽  
Linear Sigma Models

Abstract In this paper, we construct defects (domain walls) that connect different phases of two-dimensional gauged linear sigma models (GLSMs), as well as defects that embed those phases into the GLSMs. Via their action on boundary conditions these defects give rise to functors between the D-brane categories, which respectively describe the transport of D-branes between different phases, and embed the D-brane categories of the phases into the category of D-branes of the GLSMs.

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