Trapping of waves by a submerged elliptical torus

An investigation is made into the trapping of surface gravity waves by totally submerged three-dimensional obstacles and strong numerical evidence of the existence of trapped modes is presented. The specific geometry considered is a submerged elliptical torus. The depth of submergence of the torus and the aspect ratio of its cross-section are held fixed and a search for a trapped mode is made in the parameter space formed by varying the radius of the torus and the frequency. A plane wave approximation to the location of the mode in this plane is derived and an integral equation and a side condition for the exact trapped mode are obtained. Each of these conditions is satisfied on a different line in the plane and the point at which the lines cross corresponds to a trapped mode. Although it is not possible to locate this point exactly, because of numerical error, existence of the mode may be inferred with confidence as small changes in the numerical results do not alter the fact that the lines cross. If the torus makes small vertical oscillations, it is customary to try and express the fluid velocity as the gradient of the so-called heave potential, which is assumed to have the same time dependence as the body oscillations. A necessary condition for the existence of this potential at the trapped mode frequency is derived and numerical evidence is cited which shows that this condition is not satisfied for an elliptical torus. Calculations of the heave potential for such a torus are made over a range of frequencies, and it is shown that the force coefficients behave in a singular fashion in the vicinity of the trapped mode frequency. An analysis of the time domain problem for a torus which is forced to make small vertical oscillations at the trapped mode frequency shows that the potential contains a term which represents a growing oscillation

A new approximation method for scattering by long finite arrays

The scattering of water waves by a long array of evenly spaced, rigid, vertical circular cylinders is analysed under the usual assumptions of linear theory. These assumptions permit the reduction of the problem to that of solving the Helmholtz equation in two dimensions, with appropriate circular boundaries. Our primary goal is to show how solutions obtained for semi-infinite arrays can be combined to provide accurate and numerically efficient solutions to problems involving long, but finite, arrays. The particular diffraction problem considered here has been chosen both for its theoretical interest and for its applicability. The design of offshore structures supported by cylindrical columns is commonplace and understanding how the multiple interactions between the waves and the supports affect the field is clearly important. The theoretical interest comes from the fact that, for wavelengths greater than twice the geometric periodicity, the associated infinite array can support Rayleigh–Bloch surface waves that propagate along the array without attenuation. For a long finite array, we expect to see these surface waves travelling back and forth along the array and interacting with the ends. For particular sets of parameters, near-trapping has previously been observed and we provide a quantitative explanation of this phenomenon based on the excitation and reflection of surface waves by the ends of the finite array

Scattering by a semi-infinite periodic array and the excitation of surface waves

The two-dimensional problem of acoustic scattering of an incident plane wave by a semi-infinite array of either rigid or soft circular scatterers is solved. Solutions to the corresponding infinite array problems are used, together with a novel filtering approach, to enable accurate solutions to be computed efficiently. Particular attention is focussed on the determination of the amplitude of the Rayleigh–Bloch waves that can be excited along the array. In general, the far field away from the array consists of sum of a finite number of plane waves propagating in different directions (the number depending on the observation angle) and a circular wave emanating from the edge of the array. In certain resonant cases (characterised by one of the scattered plane waves propagating parallel to the array), a different far field pattern occurs, involving contributions that are neither circular waves nor plane waves. Uniform asymptotic expansions that vary continuously across all of the shadow boundaries that exist are given for both cases

Optical Scattering Artifacts Observed in the Development of Multiplexed Surface Enhanced Raman Spectroscopy Nanotag Immunoassays

Here we describe scattering based signal suppression artifacts encountered while developing multiplex lateral flow (LF) immunoassay using surface enhanced Raman spectroscopy (SERS) “nanotags” as analyte labels. Using these SERS nanotags, we have produced a quantitative test for inflammation biomarkers that is transferable to the point of care (POC). The SERS assay shows similar performance when compared with a fluorescent nanoparticle POC test. Here, using cardiac and inflammation biomarkers, we highlight the need to carefully optimize the concentration of assay components when using SERS nanotags and a single-line multiplexing approach. We show that in certain circumstances the SERS signal may be suppressed, leading to a significant underestimation of the analyte concentrations. Using electron microscopy and optical spectroscopy, we demonstrate that the error in the measurement is associated with the light scattering properties of the nanotags. These findings will be applicable to other nanoparticle labels with high light scattering coefficients. Through careful modification of the assay to reduce the impact of light scattering, it is possible to produce quantitative assays, but potentially at the expense of multiplexing capability and assay sensitivity