Analytical approximations for the modal acoustic impedances of simply supported, rectangular plates.

Coupling of the in vacuo modes of a fluid-loaded, vibrating structure by the resulting acoustic field, while known to be negligible for sufficiently light fluids, is still only partially understood. A particularly useful structural geometry for the study of this problem is the simply supported, rectangular flat plate, since it exhibits all the relevant physical features while still admitting an analytical description of the modes. Here the influence of the fluid can be expressed in terms of a set of doubly infinite integrals over wave number: the modal acoustic impedances. Closed-form solutions for these impedances do not exist and, while their numerical evaluation is possible, it greatly increases the computational cost of solving the coupled system of modal equations. There is thus a need for accurate analytical approximations. In this work, such approximations are sought in the limit where the modal wavelength is small in comparison with the acoustic wavelength and the plate dimensions. It is shown that contour integration techniques can be used to derive analytical formulas for this regime and that these formulas agree closely with the results of numerical evaluations. Previous approximations [Davies, J. Sound Vib. 15(1), 107-126 (1971)] are assessed in the light of the new results and are shown to give a satisfactory description of real impedance components, but (in general) erroneous expressions for imaginary parts.

Wave forecasts associated with hurricane landfalls in the vicinity of Cape Lookout, North Carolina

Hurricanes can cause extensive damage to the coastline and coastal communities due to wind-generated waves and storm surge. While extensive modeling efforts have been conducted regarding storm surge, there is far less information about the effects of waves on these communities and ecosystems as storms make landfall. This report describes a preliminary use of NCCOS’ WEMo (Wave Exposure Model; Fonseca and Malhotra 2010) to compute the wind wave exposure within an area of approximately 25 miles radius from Beaufort, North Carolina for estuarine waters encompassing Bogue Sound, Back Sound and Core Sound during three hurricane landfall scenarios. The wind wave heights and energy of a site was a computation based on wind speed, direction, fetch and local bathymetry. We used our local area (Beaufort, North Carolina) as a test bed for this product because it is frequently impacted by hurricanes and we had confidence in the bathymetry data. Our test bed conditions were based on two recent Hurricanes that strongly affected this area. First, we used hurricane Isabel which made landfall near Beaufort in September 2003. Two hurricane simulations were run first by passing hurricane Isabel along its actual path (east of Beaufort) and second by passing the same storm to the west of Beaufort to show the potential effect of the reversed wind field. We then simulated impacts by a hurricane (Ophelia) with a different landfall track, which occurred in September of 2005. The simulations produced a geographic description of wave heights revealing the changing wind and wave exposure of the region as a consequence of landfall location and storm intensity. This highly conservative simulation (water levels were that of low tide) revealed that many inhabited and developed shorelines would receive wind waves for prolonged periods of time at heights far above that found during even the top few percent of non-hurricane events. The simulations also provided a sense for how rapidly conditions could transition from moderate to highly threatening; wave heights were shown to far exceed normal conditions often long before the main body of the storm arrived and importantly, at many locations that could impede and endanger late-fleeing vessels seeking safe harbor. When joined with other factors, such as storm surge and event duration, we anticipate that the WEMo forecasting tool will have significant use by local emergency agencies and the public to anticipate the relative exposure of their property arising as a function of storm location and may also be used by resource managers to examine the effects of storms in a quantitative fashion on local living marine resources.