The initial value problem solution of the nonlinear shallow water–wave equations developed by Kânoğlu (2004) is applied to the benchmark problem — tsunami runup onto a plane beach — and results are compared. Comparisons with the benchmark solution produce identical results.


Numerical simulation of non-reacting turbulent flows over a constant temperature solid surface in regression
Karaeren, Cenker; Albayrak, Kahraman; Department of Mechanical Engineering (2007)
In this study, an attempt is made to obtain convergent and stable solutions of the K-E turbulence model equations for non-reacting turbulent flows over an isothermal solid surface in regression. A physics based mathematical model is used to describe the flow and temperature field over the moving surface. The flow is assumed to be two-dimensional, unsteady, incompressible with boundary layer approximations. Parabolized form of the standard K-E equations is adopted to simulate turbulence in the flow. Regressi...
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...
Initial value problem solution of nonlinear shallow water-wave equations
Kanoğlu, Utku (2006-10-06)
The initial value problem solution of the nonlinear shallow water-wave equations is developed under initial waveforms with and without velocity. We present a solution method based on a hodograph-type transformation to reduce the nonlinear shallow water-wave equations into a second-order linear partial differential equation and we solve its initial value problem. The proposed solution method overcomes earlier limitation of small waveheights when the initial velocity is nonzero, and the definition of the init...
Nonlinear mixing length model for prediction of secondary currents in uniform channel flows
Aydın, İsmail (American Society of Civil Engineers (ASCE), 2009-01-29)
A nonlinear turbulence model for numerical solution of uniform channel flow is presented. Turbulent stresses are evaluated from a nonlinear mixing length model that relates turbulent stresses to quadratic products of the mean rate of strain and the mean vorticity. The definition of the mixing length, based on a three-dimensional integral measure of boundary proximity, eliminates the need for solution of additional transport equations for the turbulence quantities. Experimental data from the literature for c...
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
U. Kanoğlu, “NONLINEAR EVOLUTION OF LONG WAVES OVER A SLOPING BEACH,” 2004, vol. 10, Accessed: 00, 2020. [Online]. Available: