Mitigation through the Use of a Near-Shore Undersea Trench: A Physical and Mathematical Model

Advisor name: Michael Benson

Abstract

Purpose: Although the 2004 Indian Ocean tsunami was the most devastating in history, tsunamis are a recurring peril for all coastal communities. This experiment evaluated the possibility of using an undersea trench, offset from the shore, to physically reduce wave amplitude at the shoreline.

Procedures: A wave tank of 4.7 x 1 with a depth of 1 meter was utilized. 30 models were created using three different trench depths and widths in all combinations for each of three sea floor slopes along with a control that had no trench. Fives waves were generated for each configuration and wave amplitude was measured at the leading edge of the shoreline. Video frame analysis was used to assess waveform. A 3-way factorial analysis evaluated the effects of the three independent variables using SAS. The LaGrange's Interpolation Formula created a polynomial relating the variables to wave amplitude.

Data: Both trench depth and width independently resulted in statistically significant reductions in wave amplitude. While wave height increased with decreasing slopes, trench benefit increased. Model waveform and Froude number were quite similar to the 2004 tsunami.

Conclusion: The largest trench, with the shallowest slope, reduced wave amplitude by 53% and the estimated energy transfer to land by 77%. Given the dynamic and geometric similarities with tsunamis, this experiment suggests wave mitigation may also be seen at larger scales. Operating continuously and passively, a near-shore trench might be a valuable supplement to early warning and evacuation. Further evaluation of this concept using shallower slopes may have merit.

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