The statistics of second order wave forces

A starting point in the statistical analysis of the slow drift motions of moored offshore structures is the determination of the statistical distribution of the second order exciting forces. In the past^2,6 an exponential probability density function has been used, this being the limiting case as the incident seastate becomes infinitely narrow banded. In the present note the second order force distribution is found for a general seastate and a significant deviation from an exponential distribution is found for those seastates which are likely to occur in practice. The statistical theory is based on a heuristic approximation to the second order force, which is shown to be consistent with a frequently used frequency domain approximation which has been suggested by Newman.⁸ Although Roberts² has shown that for very lightly damped systems the response statistics are independent of those of the exciting force, the present results may have a significant effect on the response statistics for higher levels of damping.     

A statistical analysis of non-linear random waves

A statistical analysis of unidirectional non-linear random waves is presented which is based on second-order random wave theory. The analysis technique is similar to a method which is available for the statistical analysis of a two-term Volterra series. It is shown that the statistical problem can be reduced to that of finding the eigenvalues and eigenvectors of two real symmetric matrices, from which the cumulants, the characteristic function, and the probability density function of the surface elevation can be found. Various numerical examples are considered, and the possibility of extending the technique to deal with spreading seas is discussed.     

Random dynamic analysis of multi-body offshore structures

A general method for the dynamic analysis of multi-body offshore structures is presented, being based on a constraint matrix approach. A method of deriving the constraint matrix for a general structure is given, and this is then used to derive the equations of motion of a whole system from those of it's component parts. The response of the system to both first and second order random wave forces is found and then used to calculate the forces and moments in the connecting mechanisms. The structure is assumed to have rigid component parts and a linearised frequency domain analysis method is used, although other methods are discussed. To illustrate it's use, the method is applied to both the SBS and Yoke-CALM design of offshore mooring terminal.     

Inventory of nonvolatile fatty acids and hydrocarbons in the oceans

A survey of the distribution of nonvolatile fatty acids and hydrocarbons in the oceans is given. The results represent more a “feel” from the literature rather than a mathematical analysis and are given in Table III. Fatty acid concentration appears to show a greater variation, presumably because they are more prone to biological influences than the hydrocarbons.     

Non-radial stellar oscillations: a perspective from potential scattering (I)

This article is the first in a series designed to gain insight into the stellar oscillation problem from a somewhat novel point of view: that of potential scattering, well-known in the quantum mechanical literature. In this paper the known theoretical foundations are developed and applied in the context of the astrophysical problem, wherein the star itself (rather than any portion of it) is the potential which scatters waves and traps them. The basis for the identification of a precisely defined scattering problem is the existence of a linear Schrödinger equation associated both globally (Section 2) and locally (Section 8) with the nonlinear eigenvalue equation for nonradial stellar pulsations. The paper is also designed to be a fairly complete account of the relevant mathematical topics that are germane to a study of this kind. This paper is dedicated to the memory of Professor Zdenèk Kopal, who was a great source of professional encouragement to me during the last fifteen years of his life.     

Rates of Deglaciation during the Last Glaciation and Holocene in the Cordillera Vilcanota-Quelccaya Ice Cap Region, Southeastern Perú

Moraine chronology is combined with digital topography to model deglacial rates of paleoglacier volumes in both the Huancané Valley on the west side of the Quelccaya Ice Cap and the Upismayo Valley on the northwest side of the Cordillera Vilcanota. The fastest rates of deglaciation (39×10⁻⁵ to 114×10⁻⁵ km³ yr⁻¹ and 112×10⁻⁵ to 247×10⁻⁵ km³ yr⁻¹ for each valley, respectively) were calculated for the most recent paleoglaciers, corresponding to the last few centuries. These results are consistent with observations in the Venezuelan Andes showing high rates of deglaciation since the Little Ice Age. These rates also fall within the range of 20th century rates of deglaciation measured on the Quelccaya Ice Cap (29×10⁻⁵ to 220×10⁻⁵ km³ yr⁻¹, Brecher and Thompson, 1993; Thompson, 2000). These results imply that rates of deglaciation may fluctuate significantly over time and that high rates of deglaciation may not be exclusive to the late 20th century. Equilibrium line altitude (ELA) depressions for the ice volumes of the last glaciation modeled here were computed as 230 m for the Quelccaya Ice Cap and 170 m for the Cordillera Vilcanota. Maximum ELA depressions are lower than previously published: <500 m for the Cordillera Vilcanota and <400 m for the Quelccaya Ice Cap. These lower values could imply a topographic control over paleoglacier extent.     

Macropores as preferential flow paths in meander bends

Macropores are subsurface connected void spaces caused by processes such as fracture of soils, micro‐erosion, and fauna burrows. They are common near streams (e.g. hyporheic and riparian zones) and may act as preferential flow paths between surface and groundwaters, affecting hydrologic and biogeochemical processes. We tested the hydrologic function of macropores by constructing an artificial macropore within the saturated zone of a meander bend (open macropore, ‘OM’) and later filling its upstream end (partially filled macropore, ‘PFM’). For each treatment, we injected saline tracer at an upgradient monitoring well within the meander and monitored downgradient hydraulics and tracer transport. Pressure transducers in monitoring wells indicated hydraulic gradients within the meander were 32% higher perpendicular to and 6% higher parallel to the macropore for the OM than for the PFM. Additionally, hydraulic conductivities measured via falling head tests were 29 to 550 times higher along the macropore than in nearby sediment. We used electrical conductivity probes in wells and electrical resistivity imaging to track solute transport. Transport velocities through the meander were on average 9 and 21% higher (per temporal moment analysis and observed tracer peak, respectively) for the OM than for the PFM. Furthermore, temporal moments of tracer breakthrough analysis indicated downgradient longitudinal dispersion and breakthrough tracer curve tailing were on average 234% and 182% higher for the OM, respectively. This suggests the OM enabled solute transport at overall shorter timescales than the matrix but also increased tailing. Our results demonstrate the importance of macropores to meander bend hydrology and solute transport. Copyright © 2012 John Wiley & Sons, Ltd.