Narrow Results

A wide range of applications requires the modeling of wave propagation phenomena in media with variable physical properties in the domain of interest, while highly accurate algorithms are needed to avoid unphysical effects. Spectral element methods (SEM), based on either a Chebyshev or a Legendre polynomial basis, have excellent properties of accuracy and flexibility in describing complex models, outperforming other techniques. In the standard SEM approach the computational domain is discretized by using very coarse meshes and constant-property elements, but in some cases the accuracy and the computational efficiency may be seriously reduced. For instance, a finely heterogeneous medium requires grid resolution down to the finest scales, leading to an extremely large problem dimension. In such problems the wavelength scale of interest is much larger but cannot be exploited in order to reduce the problem size. A poly-grid Chebyshev spectral element method (PG-CSEM) can overcome this limitation. In order to accurately deal with continuous variation in the properties, or even with small scale fluctuations, temporary auxiliary grids are introduced which avoid the need of using any finer global grid, and at the macroscopic level the wave field propagation is solved maintaining the SEM accuracy and computational efficiency.

Nonlinear energy transfers due to triad interactions change the characteristics of the wave-field in the shoaling region. The degree of nonlinear coupling is examined using numerical simulations based on an accurate set of deterministic evolution equations for the propagation of fully dispersive weakly nonlinear waves. The model validation, using existing experimental measurements for wave transformation over a shoal, showed that it accurately predicts nonlinear energy transfer for irregular waves with large wave-numbers. The bound higher harmonics and nonlinear statistical measures, i.e. the wave skewness and asymmetry, are well simulated by the model in both the shoaling and deshoaling regions. Numerical simulation of steep waves in shallow water with the Ursell number O(1), showed that nonlinear dispersion and phase locking lead to triad interactions even on a horizontal bottom. Nonlinear energy transfers in monochromatic waves lead to rapid spatial recurrence of the primary wave amplitudes. This is in contrast to the case of irregular waves where the Fourier coefficients of the wave-field do not recur due to the presence of innumerable interactions, which are expected to cancel resulting in no spatial evolution of the wave spectrum.

Sabine Bank, a transgressive shoal located 30 km off the Louisiana-Texas border, USA, has been considered as one of the plausible resources for re-nourishment of the adjacent barrier islands and beaches. Little has been reported on the bottom boundary layer dynamics and sediment transport from this shallow coastal environment. A comprehensive field investigation, coupled with numerical modeling, has been implemented. Wave and bottom boundary layer interactions were strongly associated with the passage of cold fronts across the region. Strong southerly/southeasterly wind regimes also contributed to the re-suspension and transport of sediments, even during summer season. Modification in bulk wave parameters due to two mining scenarios were computed using modified bathymetries and the result shows minimum impact from the proposed mining from the shoal crest. Sediment re-suspension intensity (RI) was computed and found to be high over the inner shelf and shoal during severe storms.