PROPAGATION OF FINITE STRIP SOURCES OVER A FLAT BOTTOM Utku Kânoğlu Vasily V. Titov Baran Aydın Costas E. Synolakis ITS-2009 Novosibirsk, Russia July 2009

Focusing phenomenon During the 1989 ITS meeting in Novosibirsk, Drs. Marchuk and Titov numerically verified that a plus-minus source focuses at a point where abnormal wave height is observed. Dr. Titov suggested analytical investigation of the focusing phenomenon.

Analytical Model Physical description of the problem

Analytical Model Carrier & Yeh (CMES, 2005) approach (Axisymmetric Problem) Initial conditions (FINITE-CRESTED initial waveform) (Zero initial velocity)

(Fourier-Bessel transform) Solution for Gaussian hump (Self-similar solution) Analytical Model Carrier & Yeh (CMES, 2005) approach

Extension to strip sources Analytical Model Carrier & Yeh (CMES, 2005) approach

Drawbacks of Carrier & Yeh approach Elliptic integral in the solution results in SINGULARITY Trial-error approximation for the integrand Limited application

New Analytical Model Governing partial differential equation (Linear Shallow-water Wave Equation) Initial conditions (FINITE-CRESTED initial waveform) (Zero initial velocity) η: water elevation above still water level g: gravitational acceleration d: basin depth (constant)

New Analytical Model Solution technique (Fourier integral transform over space variables) (Inverse Fourier transform)

New Analytical Model Solution in Fourier space Solution in physical space

New Analytical Model Features of the new approach No approximations involved Direct integration can be performed Different initial waveforms can be imposed

Results of Carrier&Yeh (CMES, 2005) reproduced with direct integration New Analytical Model

Solitary initial condition Steepness parameter Scaling parameter

New Analytical Model N-wave initial condition

1998 PNG Event (Figure taken from Synolakis et al. 2002) Earthquake: M = 7 Casualties: Maximum tsunami waveheight: ~ 30 m

Analytical Model Results Snapshots

Analytical Model Results Snapshots

Analytical Model Results Snapshots

Analytical Model Results Maximum wave height envelope

Analytical Model Results Maximum wave height envelope

Analytical Model Results Maximum wave height envelope

Analytical Model Results Maximum wave height envelope

Analytical Model Results Maximum wave height envelope (Figure taken from Synolakis et al. 2002)

Conclusions We presented a new analytical solution for wave propagation over a constant depth basin. Our solution Does not involve approximations Versatile in different initial waveforms New solution Can be used to explain some extreme runup observations on the field Can be used as a benchmark analytical solution for numerical models

PROPAGATION OF FINITE STRIP SOURCES OVER A FLAT BOTTOM Utku Kânoğlu Vasily V. Titov Baran Aydın Costas E. Synolakis ITS-2009 Novosibirsk, Russia July 2009