A new method is proposed for the generation of permanent form periodic waves, in a twodimensional fully nonlinear potential flow model. In this method, a constant volume is maintained in the computational domain ("wave tank") by simultaneously generating a mean current, equal and opposite to the waves mean mass transport velocity. An absorbing beach is modeled at the far end of the tank, with : (i) an external free surface pressure, proportional to the normal particle velocity, to absorb energy from high frequency incident waves; and (ii) a piston-like condition, at the tank extremity, to absorb energy from low frequency waves. A new feedback mechanism is proposed to adaptively calibrate the beach absorption coefficient, as a function of time, for the beach to absorb the period-averaged energy of waves entering the beach. Wave generation and absorption are validated over constant depth, for tanks and beaches of various lengths, and optimal parameter values are identified for which reflection in the beach is reduced to less than a few percent. Using the new generation and absorption methods, shoaling of periodic waves is modeled over a 1:50 slope, up to very close to the breaking point. A quasi-steady state is thus reached in the tank for which (not previously calculated) characteristics of fully nonlinear shoaling waves are obtained.

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.[1] A simplified three-dimensional Navier-Stokes (3-D NS) model for two fluids, water and landslide material (mudslide) is presented and validated with standard laboratory experiments. Dubbed TSUNAMI3D (Tsunami Solution Using Navier-Stokes Algorithm with Multiple Interfaces) is applied to a 3-D full-scale landslide scenario in the Gulf of Mexico (GOM), i.e., the East-Breaks underwater landslide. The simplified 3-D NS model is conceived to be computationally efficient for tsunami calculations. The simplification is derived from the large aspect ratio of the tsunami waves (wavelength/wave-height) and the selected computational grid that has a smaller aspect ratio. This allows us to assume a horizontal fluid surface in each individual cell containing the interface (air-water, airmudslide, and water-mudslide). The tracking of fluid interfaces is based on the Volume of Fluid method and the surfaces are obtained by integrating the fluxes of each individual fluid cell along the water column. In the momentum equation, the pressure term is split into two components, hydrostatic and nonhydrostatic. The internal friction is solved in a simplified manner by adjusting the viscosity coefficient. Despite the simplification to get an efficient solution, the numerical results agree fairly well with standard landslide laboratory experiments required by the National Tsunami Hazard Mitigation Program for tsunami model validation. The numerical effect caused by using a sharp versus a diffusive watermudslide interface for a full-scale landslide-tsunami scenario is also investigated. Observations from this experiment indicated that choosing a sharp or diffusive interface seems to have no remarkable effect at early stages of the tsunami wave propagation. Last, a large scale 3-D numerical simulation is carried out for the ancient GOM's East-Breaks landslide by using the simplified model to calculate the early stages of the tsunami wave propagation.

[1] A numerical model for the global tsunami computation constructed by Kowalik et al. (2005Kowalik et al. ( , 2007a) is applied to the tsunami of November 15, 2006 in the northern Pacific with spatial resolution of one minute. Numerical results are compared to sea level data collected by Pacific DART buoys. The tide gauge at Crescent City (CC) recorded an initial tsunami wave of about 20 cm amplitude and a second larger energy packet arriving 2 hours later. The first energy input into the CC harbor was the primary (direct) wave traveling over the deep waters of the North Pacific. Interactions with submarine ridges and numerous seamounts located in the tsunami path were a larger source of tsunami energy than the direct wave. Travel time for these amplified energy fluxes is longer than for the direct wave. Prime sources for the larger fluxes at CC are interactions with Koko Guyot and Hess Rise. Tsunami waves travel next over the Mendocino Escarpment where the tsunami energy flux is concentrated owing to refraction and directed toward CC. Local tsunami amplification over the shelf break and shelf are important as well. In many locations along the North Pacific coast, the first arriving signal or forerunner has lower amplitude than the main signal, which often is delayed. Understanding this temporal distribution is important for an application to tsunami warning and prediction. As a tsunami hazard mitigation tool, we propose that along with the sea level records (which are often quite noisy), an energy flux for prediction of the delayed tsunami signals be used.

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