The point-source method for 3D reconstructions for the Helmholtz and Maxwell equations

We use the point-source method (PSM) to reconstruct a scattered field from its associated far field pattern. The reconstruction scheme is described and numerical results are presented for three-dimensional acoustic and electromagnetic scattering problems. We give new proofs of the algorithms, based on the Green and Stratton-Chu formulae, which are more general than with the former use of the reciprocity relation. This allows us to handle the case of limited aperture data and arbitrary incident fields. Both for 3D acoustics and electromagnetics, numerical reconstructions of the field for different settings and with noisy data are shown. For shape reconstruction in acoustics, we develop an appropriate strategy to identify areas with good reconstruction quality and combine different such regions into one joint function. Then, we show how shapes of unknown sound-soft scatterers are found as level curves of the total reconstructed field.

The sediment trapping efficiency of the macro-tidal Daly Estuary, tropical Australia

Field studies were carried out on the water and sediment dynamics in the tropical, macro-tidal, Daly Estuary. The estuary is shallow, very-turbid, about 100 km long, and the entrance is funnel-shape. In the wet, high flow season, normal tidal ranges can be suppressed in the estuary, depending on inflow rates, and freshwater becomes dominant up to the mouth. At that time a fraction of the fine sediment load is exported offshore as a bottom-tagging nepheloid layer after the sediment falls out of suspension of the thin, near-surface, river plume. The remaining fraction and the riverine coarse sediment form a large sediment bar 10 km long, up to 6 m in height and extending across the whole width of the channel near the mouth. This bar, as well as shoals in the estuary, partially pond the mid- to upper-estuary. This bar builds up from the deposition of riverine sediment during a wet season with high runoff and can raise mean water level by up to 2 m in the upper estuary in the low flow season. This ponding effect takes about three successive dry years to disappear by the sediment forming the bar being redistributed all over the estuary by tidal pumping of fine and coarse sediment in the dry season, which is the low flow season. The swift reversal of the tidal currents from ebb to flood results in macro-turbulence that lasts about 20 min. Bed load transport is preferentially landward and occurs only for water currents greater than 0.6 m s(-1). This high value of the threshold velocity suggests that the sand may be cemented by the mud. The Daly Estuary thus is a leaky sediment trap with an efficiency varying both seasonally and inter-annually. (c) 2006 Elsevier Ltd. All rights reserved.

Approximations to the scattering of water waves by steep topography

A new method is developed for approximating the scattering of linear surface gravity waves on water of varying quiescent depth in two dimensions. A conformal mapping of the fluid domain onto a uniform rectangular strip transforms steep and discontinuous bed profiles into relatively slowly varying, smooth functions in the transformed free-surface condition. By analogy with the mild-slope approach used extensively in unmapped domains, an approximate solution of the transformed problem is sought in the form of a modulated propagating wave which is determined by solving a second-order ordinary differential equation. This can be achieved numerically, but an analytic solution in the form of a rapidly convergent infinite series is also derived and provides simple explicit formulae for the scattered wave amplitudes. Small-amplitude and slow variations in the bedform that are excluded from the mapping procedure are incorporated in the approximation by a straightforward extension of the theory. The error incurred in using the method is established by means of a rigorous numerical investigation and it is found that remarkably accurate estimates of the scattered wave amplitudes are given for a wide range of bedforms and frequencies.