Analytical solutions for evolution and runup of longwaves over a sloping beach

Ceylan, Nihal
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 for the waveforms given for near-shore earthquakes producing results exactly compared with existing ones, but with a much simpler algebra.


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...
Analytical solution for the propagation of finite crested long waves over a sloping beach
Yağmur, Ahmed Sabri; Kanoğlu, Utku; Department of Aerospace Engineering (2022-2-10)
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 u...
Analytical solutions of shallow-water wave equations
Aydın, Baran; Kanoğlu, Utku; Department of Engineering Sciences (2011)
Analytical solutions for the linear and nonlinear shallow-water wave equations are developed for evolution and runup of tsunamis –long waves– over one- and two-dimensional bathymetries. In one-dimensional case, the nonlinear equations are solved for a plane beach using the hodograph transformation with eigenfunction expansion or integral transform methods under different initial conditions, i.e., earthquake-generated waves, wind set-down relaxation, and landslide-generated waves. In two-dimensional case, th...
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...
Nonlinear evolution and runup–rundown of long waves over a sloping beach
Kanoğlu, Utku (Cambridge University Press (CUP), 2004-8-25)
The initial value problem of the nonlinear evolution, shoreline motion and flow velocities of long waves climbing sloping beaches is solved analytically for different initial waveforms. A major difficulty in earlier work utilizing hodograph-type transformation when solving either boundary value or initial value problems has been the specification of equivalent boundary or initial condition in the transformed space. Here, in solving the initial value problem, the transformation is linearized in space at t = ...
Citation Formats
N. Ceylan, “Analytical solutions for evolution and runup of longwaves over a sloping beach,” Thesis (M.S.) -- Graduate School of Natural and Applied Sciences. Engineering Sciences., Middle East Technical University, 2019.