Boat wakes and their influence on erosion in the Atlantic Intracoastal Waterway, North Carolina

Boat wakes in the Atlantic Intracoastal Waterway (AIWW) of North Carolina occur in environments not normally subjected to (wind) wave events, making sections of AIWW potentially vulnerable to extreme wave events generated by boat wakes. The Snow’s Cut area that links the Cape Fear River to the AIWW is an area identified by the Wilmington District of the U.S. Army Corps of Engineers as having significant erosion issues; it was hypothesized that this erosion could be being exacerbated by boat wakes. We compared the boat wakes for six combinations of boat length and speed with the top 5% wind events. We also computed the benthic shear stress associated with boat wakes and whether sediment would move (erode) under those conditions. Finally, we compared the transit time across Snow’s Cut for each speed. We focused on two size classes of V-hulled boats (7 and 16m) representative of AIWW traffic and on three boat speeds (3, 10 and 20 knots). We found that at 10 knots when the boat was plowing and not yet on plane, boat wake height and potential erosion was greatest. Wakes and forecast erosion were slightly mitigated at higher, planing speeds. Vessel speeds greater than 7 knots were forecast to generate wakes and sediment movement zones greatly exceeding that arising from natural wind events. We posit that vessels larger than 7m in length transiting Snow’s Cut (and likely many other fetch-restricted areas of the AIWW) frequently generate wakes of heights that result in sediment movement over large extents of the AIWW nearshore area, substantially in exceedance of natural wind wave events. If the speed, particularly of large V-hulled vessels (here represented by the 16m length class), were reduced to pre-plowing levels (~ 7 knots down from 20), transit times for Snow’s Cut would be increased approximately 10 minutes but based on our simulations would likely substantially reduce the creation of erosion-generating boat wakes. It is likely that boat wakes significantly exceed wind wave background for much of the AIWW and similar analyses may be useful in identifying management options.

On the use of combined compact scheme for numerical solution of the two-layer oceanic shallow water equations

Many types of oceanic physical phenomena have a wide range in both space and time. In general, simplified models, such as shallow water model, are used to describe these oceanic motions. The shallow water equations are widely applied in various oceanic and atmospheric extents. By using the two-layer shallow water equations, the stratification effects can be considered too. In this research, the sixth-order combined compact method is investigated and numerically implemented as a high-order method to solve the two-layer shallow water equations. The second-order centered, fourth-order compact and sixth-order super compact finite difference methods are also used to spatial differencing of the equations. The first part of the present work is devoted to accuracy assessment of the sixth-order super compact finite difference method (SCFDM) and the sixth-order combined compact finite difference method (CCFDM) for spatial differencing of the linearized two-layer shallow water equations on the Arakawa's A-E and Randall's Z numerical grids. Two general discrete dispersion relations on different numerical grids, for inertia-gravity and Rossby waves, are derived. These general relations can be used for evaluation of the performance of any desired numerical scheme. For both inertia-gravity and Rossby waves, minimum error generally occurs on Z grid using either the sixth-order SCFDM or CCFDM methods. For the Randall's Z grid, the sixth-order CCFDM exhibits a substantial improvement , for the frequency of the barotropic and baroclinic modes of the linear inertia-gravity waves of the two layer shallow water model, over the sixth-order SCFDM. For the Rossby waves, the sixth-order SCFDM shows improvement, for the barotropic and baroclinic modes, over the sixth-order CCFDM method except on Arakawa's C grid. In the second part of the present work, the sixth-order CCFDM method is used to solve the one-layer and two-layer shallow water equations in their nonlinear form. In one-layer model with periodic boundaries, the performance of the methods for mass conservation is compared. The results show high accuracy of the sixth-order CCFDM method to simulate a complex flow field. Furthermore, to evaluate the performance of the method in a non-periodic domain the sixth-order CCFDM is applied to spatial differencing of vorticity-divergence-mass representation of one-layer shallow water equations to solve a wind-driven current problem with no-slip boundary conditions. The results show good agreement with published works. Finally, the performance of different schemes for spatial differencing of two-layer shallow water equations on Z grid with periodic boundaries is investigated. Results illustrate the high accuracy of combined compact method.