Analytical solution for the propagation of finite crested long waves over a sloping beach

Download

10447693.pdf

Date

2022-2-10

Author

Yağmur, Ahmed Sabri

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

396
views

137
downloads

The analytical solution of shallow water-wave equations, both linear and nonlinear, is widely used to provide an insightful understanding of the coastal effect of long waves. These solutions are generally carried out for two-dimensional (1 space + 1 time) propagation, even though there are a limited number of analytical solutions for the three-dimensional (2 space + 1 time) propagation. Three-dimensional propagation of long waves over a sloping beach is considered here. The analytical solution is obtained using the linear shallow water-wave theory resulting in double indefinite integrals. The solution is evaluated using various numerical methods, and results are discussed.

Subject Keywords

analytical solution, shallow water, long waves, finite crest, tsunami

URI

https://hdl.handle.net/11511/96239

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Analytical modeling of nonlinear evolution of long waves Aydın, Baran; Kanoğlu, Utku (2015-06-22) We present an initial-boundary value problem formulation for the solution of the nonlinear shallow-water wave (NSW) equations. We transform the nonlinear equations into a linear problem by using the Carrier-Greenspan transformation. Then, we obtain the solution through the separation of variables method rather than integral transform techniques, which is the usual practice (Carrier et al., J Fluid Mech 2003; Kanoglu, J Fluid Mech 2004). This formulation allows the use of any physically realistic initial wav...
Analytical solutions for evolution and runup of longwaves over a sloping beach Ceylan, Nihal; Kanoğlu, Utku; Department of Engineering Sciences (2019) The initial value problem of the linear evolution and runup of long waves on a plane beach is analyzed analytically. The shallow water-wave equations are solved by integral transform and eigenvalue expansion methodologies. The results from linear solutions are compared with the solution of the nonlinear shallow water-wave equations confirming the runup invariance, i.e. nonlinear and linear theories produce same maximum runup. Then, existing analytical nonlinear solution for shoreline motion is implemented f...
New Analytical Solution for Nonlinear Shallow Water-Wave Equations AYDIN, BARAN; Kanoğlu, Utku (2017-08-01) We solve the nonlinear shallow water-wave equations over a linearly sloping beach as an initial-boundary value problem under general initial conditions, i.e., an initial wave profile with and without initial velocity. The methodology presented here is extremely simple and allows a solution in terms of eigenfunction expansion, avoiding integral transform techniques, which sometimes result in singular integrals. We estimate parameters, such as the temporal variations of the shoreline position and the depth-av...
STOCHASTIC-ANALYSIS OF UNSATURATED FLOW - ONE-DIMENSIONAL MONTE-CARLO SIMULATIONS AND COMPARISONS WITH SPECTRAL PERTURBATION ANALYSIS AND FIELD OBSERVATIONS Ünlü, Kahraman; BIGGAR, JW (1990-09-01) A numerical experiment was designed to study the stochastic behavior of one‐dimensional transient unsaturated flow in a Monte Carlo setting. Soil hydraulic properties, log‐saturated hydraulic conductivity ln Ks, pore size distribution parameter α, and the specific water capacity C are assumed to be statistically homogeneous random fields described by exponential correlation functions with identical correlation lengths. Fifty realizations of each soil hydraulic property, with statistical properties obtained ...
Long wave runup on piecewise linear topographies Kanoğlu, Utku (1998-11-10) We study long-wave evolution and runup on piecewise linear one- and two-dimensional bathymetries analytically and experimentally with the objective of understanding certain coastal effects of tidal waves. We develop a general solution method for determining the amplification factor of different ocean topographies consisting of linearly varying and constant-depth segments to study how spectral distributions evolve over bathymetry, and apply our results to study the evolution of solitary waves. We find asympt...

Citation Formats

A. S. Yağmur, “Analytical solution for the propagation of finite crested long waves over a sloping beach,” M.S. - Master of Science, Middle East Technical University, 2022.