Wave driven free surface motion in the gap between a tanker and an FLNG barge

10.1016/j.apor.2015.01.011Applied Ocean Research51331-34

Reanalysis of the Spectra Observed in JONSWAP

Ocean waves are known to be both random in time and nonlinear. Surface elevation time histories measured in the Gulf of Mexico during Hurricane Camille in 1969 are reanalyzed. The average shapes of large crests and deep troughs in time are shown to be close to symmetric around the instant when the maximum (or minimum) occurs, with only slight evidence of asymmetry from wave breaking in the time histories. There is considerable vertical asymmetry with higher and sharper crests and smaller and more rounded troughs. Overall, the analysis supports the use of a focused wave group based on the scaled autocorrelation function (NewWave) as proposed by Lindgren and Boccotti, with sum harmonic corrections. There is a very small second order difference setup for both large crests and troughs, consistent with considerable directional spreading in the hurricane sea-state. This spreading is likely to be larger than that usually assumed for nontropical winter storms. The spectral tail is shown to have a decay rate proportional to -4.5 power law midway between the classical JONSWAP (Phillips) -5 form and the -4 slope proposed b

Phase manipulation and the harmonic components of ringing forces on a surface-piercing column

The Stokes-type expansion for the hydrodynamic force on a column in a regular wave can be written to 4th order as φφφφφφ 2coscos4cos3cos2coscos 44233122044433322211 afafafafafafafF ++++++= where the coefficients f represent wave to force transfer functions (including implicit phase shifts) and a is the incoming linear wave amplitude. Note the structure of the terms multiplying coefficients such as f33 where the power of the amplitude term is the same as the frequency harmonic (here both 3), and the terms multiplying terms such as f42 where the power of the amplitude is greater than that of the frequency harmonic by 2. In the notation of Stokes expansions, these correspond to sum and difference components respectively. For ringing we are mostly concerned with the sum harmonics. Whilst these individual harmonic components are easy to extract for regular wave forcing, this is much more difficult for broadbanded waves trains, either random or wave groups, where the simple Stokes terms are replaced by summations of products of linear terms and each net higher harmonic contributes across an increasingly broad range of frequencies. There are then strict limits as to what can be achieved by simple frequency filtering. Here we are concerned with the nonlinear force components generated by isolated compact wave group

Experimental observation of a near-motion trapped mode: free motion in heave with negligible radiation

A simple geometry which exhibits near-motion-trapping is tested experimentally, along with perturbed versions of the structure. The motion of the freely floating structure and the surrounding wave field is tracked and the near-motion-trapped mode is found, characterised by a slowly decaying heave motion with very small linear radiation of energy. It is found that the latter property is a better discriminator of the perturbed geometries as viscous damping masks fine differences in radiation damping as far the motion of the structure is concerned. The magnitude of this viscous damping is reasonably well predicted by a simple Stokes oscillatory boundary layer analysis

Extreme wave elevations beneath offshore platforms, second order trapping, and the near flat form of the quadratic transfer functions

Extreme free surface elevations due to wave-structure interactions are investigated to second order using Quadratic Transfer Functions (QTFs). The near-trapping phenomenon for small arrays of closely spaced columns is studied for offshore applications, and the excitation of modes by linear and second order interactions is compared. A simple method for approximating near-trapped mode shapes is shown to give good results for both linear and second order excitation. Low frequency near-trapped mode shapes are shown to be very similar whether excited linearly or to second order. Approximating surface elevation sum QTF matrices as being flat perpendicular to the leading diagonal is investigated as a method for greatly reducing lengthy QTF calculations. The effect of this approximation on second order surface elevation calculations is assessed and shown to be reasonably small with realistic geometries for semi-submersible and tension-leg platforms

Linear Wave Interaction with a Vertical Cylinder of Arbitrary Cross Section: An Asymptotic Approach

An asymptotic approach to the linear problem of regular water waves interacting with a vertical cylinder of an arbitrary cross section is presented. The incident regular wave was one-dimensional, water was of finite depth, and the rigid cylinder extended from the bottom to the water surface. The nondimensional maximum deviation of the cylinder cross section from a circular one plays the role of a small parameter of the problem. A fifth-order asymptotic solution of the problem was obtained. The problems at each order were solved by the Fourier method. It is shown that the first-order velocity potential is a linear function of the Fourier coefficients of the shape function of the cylinder, the second-order velocity potential is a quadratic function of these coefficients, and so on. The hydrodynamic forces acting on the cylinder and the water surface elevations on the cylinder are presented. The present asymptotic results show good agreement with numerical and experimental results of previous investigations. Long-wave approximation of the hydrodynamic forces was derived and used for validation of the asymptotic solutions. The obtained values of the forces are exact in the limit of zero wave numbers within the linear wave theory. An advantage of the present approach compared with the numerical solution of the problem by an integral equation method is that it provides the forces and the diffracted wave field in terms of the coefficients of the Fourier series of the deviation of the cylinder shape from the circular one. The resulting asymptotic formula can be used for optimization of the cylinder shape in terms of the wave loads and diffracted wave fields

Erratum to: Methods for evaluating medical tests and biomarkers

[This corrects the article DOI: 10.1186/s41512-016-0001-y.]

Erratum to: Methods for evaluating medical tests and biomarkers

[This corrects the article DOI: 10.1186/s41512-016-0001-y.]