Dynamics of arrays of floating point-absorber wave energy converters with inter-body and bottom slack-mooring connections

If point absorbers are employed in the extensive exploitation of the offshore wave energy resource, they should be deployed in arrays, the distance between the elements in the array being possibly tens of meters. In such cases, it may be more convenient that the array is spread moored to the sea bottom through only some of its elements, located in the periphery, while the other array elements are prevented from drifting and colliding with each other by connections to adjacent elements. An array of identical floating point absorbers located at the grid points of an equilateral triangular grid is considered in the paper. A spread set of slack-mooring lines connect the peripheric floaters to the bottom. A weight is located at the centre of each triangle whose function is to pull the three floaters towards each other and keep the inter-body mooring lines under tension. The power take-off system (PTO) is a linear damper activated by the buoy heaving motion. The whole system–buoys, moorings and power take-off systems–is assumed linear, so that a frequency domain analysis may be employed. Hydrodynamic interference between the oscillating buoys in array is accounted for. Equations are presented for a set of three identical point absorbers. This is then extended to more complex equilateral triangular grid arrays. Results from numerical simulations, with regular and irregular waves, are presented for the motions and power absorption of hemispherical converters in arrays of three and seven elements and for different mooring parameters and wave incidence angles. Comparisons are given with the unmoored and independently-moored buoy situations.     

Recursive algorithms for the computation of the potential harmonic coefficients of a constant density polyhedron

The gravitational potential of a constant density general polyhedron can be expressed both in terms of a closed analytical expression and as a series expansion involving the corresponding spherical harmonic coefficients. The latter can be obtained from two independent algorithms, which differ not only in their algorithmic architecture but in their efficiency and overall performance, especially when computing the coefficients of higher degree and order. In the present paper a comparative study of all these three approaches is carried out focusing on the numerical implementation of the recursive relations appearing in the two algorithms for the computation of the polyhedral potential harmonic coefficients. The performed numerical investigations show that the linear algorithm proposed by Jamet and Thomas (Proceedings of the second international GOCE user workshop, ‘GOCE, The Geoid and Oceanography’, ESA-ESRIN, Frascati, Italy, 8–10 March 2004, ESA SP-569, 2004), but so far not implemented, achieves a reasonable accuracy at a computational expense that opens to practical applications, for instance in the field of satellite gravimetry/gradiometry interpretation. The convergence behavior of the linear recursion algorithm is studied thoroughly and a computational procedure is proposed that enables the stable computation of potential harmonic coefficients up to degree 60 when referring to an arbitrarily shaped polyhedral body.     

SELFE: A semi-implicit Eulerian–Lagrangian finite-element model for cross-scale ocean circulation

Unstructured-grid models grounded on semi-implicit, finite-volume, Eulerian–Lagrangian algorithms, such as UnTRIM and ELCIRC, have enjoyed considerable success recently in simulating 3D estuarine and coastal circulation. However, opportunities for improving the accuracy of this type of models were identified during extensive simulations of a tightly coupled estuary–plume–shelf system in the Columbia River system. Efforts to improve numerical accuracy resulted in SELFE, a new finite-element model for cross-scale ocean modeling. SELFE retains key benefits, including computational efficiency of existing semi-implicit Eulerian–Lagrangian finite-volume models, but relaxes restrictions on grids, uses higher-order shape functions for elevation, and enables superior flexibility in representing the bathymetry. Better representation of the bathymetry is enabled by a novel, “localized” vertical grid that resembles unstructured grids. At a particular horizontal location, SELFE uses either S coordinates or SZ coordinates, but the equations are consistently solved in Z space. SELFE also performs well relative to volume conservation and spurious oscillations, two problems that plague some finite-element models. This paper introduces SELFE as an open-source code available for community use and enhancement. The main focus here is on describing the formulation of the model and on showing results for a range of progressively demanding benchmark tests. While leaving details to separate publications, we also briefly illustrate the superior performance of SELFE over ELCIRC in a field application to the Columbia River estuary and plume.     

Analytical study of the swing-by maneuver in an elliptical system

The objective of the present paper is to derive a set of analytical equations that describe a swing-by maneuver realized in a system of primaries that are in elliptical orbits. The goal is to calculate the variations of energy, velocity and angular momentum as a function of the usual basic parameters that describe the swing-by maneuver, as done before for the case of circular orbits. In elliptical orbits the velocity of the secondary body is no longer constant, as in the circular case, but it varies with the position of the secondary body in its orbit. As a consequence, the variations of energy, velocity and angular momentum become functions of the magnitude and the angle between the velocity vector of the secondary body and the line connecting the primaries. The “patched-conics” approach is used to obtain these equations. The configurations that result in maximum gains and losses of energy for the spacecraft are shown next, and a comparison between the results obtained using the analytical equations and numerical simulations are made to validate the method developed here.     

Nonlinear adaptive control of an underwater towed vehicle

This paper addresses the problem of simultaneous depth tracking and attitude control of an underwater towed vehicle. The system proposed uses a two-stage towing arrangement that includes a long primary cable, a gravitic depressor, and a secondary cable. The towfish motion induced by wave driven disturbances in both the vertical and horizontal planes is described using an empirical model of the depressor motion and a spring-damper model of the secondary cable. A nonlinear, Lyapunov-based, adaptive output feedback control law is designed and shown to regulate pitch, yaw, and depth tracking errors to zero. The controller is designed to operate in the presence of plant parameter uncertainty. When subjected to bounded external disturbances, the tracking errors converge to a neighbourhood of the origin that can be made arbitrarily small. In the implementation proposed, a nonlinear observer is used to estimate the linear velocities used by the controller thus dispensing with the need for costly sensor suites. The results obtained with computer simulations show that the controlled system exhibits good performance about different operating conditions when subjected to sea-wave driven disturbances and in the presence of sensor noise. The system holds promise for application in oceanographic missions that require depth tracking or bottom-following combined with precise vehicle attitude control.     

Analysis of Physical and Chemical Parameters for Discrimination of Water Origin in a Hydroelectric Reservoir

Seventeen physical and chemical parameters were obtained from a hydroelectric reservoir located in a tropical region in the south of Brazil. Multivariate Principal Component Analysis (PCA) and Hierarchical Group Analysis (HGA) were used to identify the parameters discriminating the origin of water from the Tibagi and the Primeiro de Maio River, after it has passed the mixing region. The study was conducted during the dry and rainy seasons in July 2002 and February 2003 at three depths and three sampling sites located 0, 5, and 10 km away from the mixing region. The statistical methods showed to be appropriate for identifying the contribution of each tributary in the water mixing site of a complex water system. The most important discriminating parameter was the absorbance relation A(253 nm)/A(203 nm), followed by the concentrations of Fe(III), Mn(III), and Ni(II). An anthropogenic interference was found in the reservoir due to high Ni(II) and orthophosphate concentrations caused by a nearby town sewage discharge. The interference was more important during the dry periods due to the lower dispersion of the pollutants. Urgent initiatives should be taken from the state government to build treatment stations for the wastewater of the small cities around the Capivara hydroelectric reservoir to prevent the drinking water quality from deteriorating.     

On shallow earthquakes widely scattered in the continents

Summary Seismicity in the continents is characterized by its foci distribution. Intermediate foci are packed into small spaces with depth range of about 100–200 km. Shallow foci on the other hand, scatter quite widely. Study in the present paper is focussed to the latter feature. A suggestion is given that the wide scattering of shallow earthquakes in the continents as well as the recent remarkable uplifts of mountains are both resulted from the stress in lithosphere plate without entrance (trench) the movement of which is being impeded.