Initial value problem solution of nonlinear shallow water-wave equations

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 initial conditions in the physical and transform spaces is consistent. Our solution not only allows for evaluation of differences in predictions when specifying an exact initial velocity based on nonlinear theory and its linear approximation, which has been controversial in geophysical practice, but also helps clarify the differences in runup observed during the 2004 and 2005 Sumatran tsunamigenic earthquakes.


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...
Free surface flow past a circular cylinder under forced rotary oscillations
Kocabıyık, Serpıl; Bozkaya, Canan; Liverman, E. (null; 2014-07-25)
Numerical results of a viscous incompressible two-fluid model with an oscillating cylinder are analyzed. Specifically, two-dimensional flow past a circular cylinder subject to forced rotational oscillations beneath a free surface is considered. Numerical method is based on the finite volume method for solving the two-dimensional continuity and unsteady NavierStokes equations. The numerical simulations are carried out at a Reynolds number of R = 200 and a Froude number F r = 0.2, and the cylinder submergence...
Exact solution of Schrodinger equation for Pseudoharmonic potential
Sever, Ramazan; TEZCAN, CEVDET; Aktas, Metin; Yesiltas, Oezlem (2008-02-01)
Exact solution of Schrodinger equation for the pseudoharmonic potential is obtained for an arbitrary angular momentum. The energy eigenvalues and corresponding eigenfunctions are calculated by Nikiforov-Uvarov method. Wavefunctions are expressed in terms of Jacobi polynomials. The energy eigenvalues are calculated numerically for some values of l and n with n <= 5 for some diatomic molecules.
Effective-mass Klein-Gordon-Yukawa problem for bound and scattering states
Arda, Altug; Sever, Ramazan (2011-09-01)
Bound and scattering state solutions of the effective-mass Klein-Gordon equation are obtained for the Yukawa potential with any angular momentum l. Energy eigenvalues, normalized wave functions, and scattering phase shifts are calculated as well as for the constant mass case. Bound state solutions of the Coulomb potential are also studied as a limiting case. Analytical and numerical results are compared with the ones obtained before. (C) 2011 American Institute of Physics. [doi:10.1063/1.3641246]
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...
Citation Formats
U. Kanoğlu, “Initial value problem solution of nonlinear shallow water-wave equations,” PHYSICAL REVIEW LETTERS, pp. 0–0, 2006, Accessed: 00, 2020. [Online]. Available: