Modeling Tsunami Run-Up and Draw-Down on the Beach
Abstract
Previous literature has investigated the run-up and draw-down of tsunami waves on a one-dimensional, constant-sloped beach, but the existing solutions are complex and computationally unwieldy. Our research aims to establish a simpler model while still obtaining accurate results. We do so using a quasi-linear theory derived from the nonlinear shallow-water wave equations. These equations are considered over a linear beach, with properly imposed initial and boundary conditions. The main difficulty in solving this problem is the moving boundary associated with the shoreline motion. To eliminate this difficulty, we apply an appropriate substitution to the spatial variable, and thus replace the moving boundary of the computational domain with a stationary boundary. A key feature of our tsunami problem is the presence of the small parameter ɛ = η0/h0, where η0 is the characteristic amplitude of the wave and h0 is the characteristic depth of the ocean. Due to the presence of this small parameter, the problem can be essentially linearized using the method of perturbations and then solved analytically via an integral transformation. This explicit solution enables us to swiftly predict the behavior of the wave using an essentially linear model. We test the accuracy of our model against the numerical solution obtained using Mathematica, and find minimal discrepancy. Finally, we extend our results to a modified beach configuration that more accurately reflects real-world shoreline topography. This project is supported by the NSF award DMS - 1559788.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2016
- Bibcode:
- 2016AGUFMOS23A1978N
- Keywords:
-
- 4544 Internal and inertial waves;
- OCEANOGRAPHY: PHYSICALDE: 4546 Nearshore processes;
- OCEANOGRAPHY: PHYSICALDE: 4558 Sediment transport;
- OCEANOGRAPHY: PHYSICALDE: 4560 Surface waves and tides;
- OCEANOGRAPHY: PHYSICAL