Parametric modelling of joint probability density distributions for steepness and asymmetry in deep water waves

Traditional wave steepness s = H/L does not define steep asymmetric waves uniquely. Three additional parameters characterising single zero-downcross waves in a time series are crest front steepness, vertical asymmetry factor and horizontal asymmetry factor. Parametric models for joint probability density distributions for deep water waves are presented. The joint distributions are for crest front steepness-wave height, vertical asymmetry factor-wave height, total wave steepness-wave height and wave height-wave period. The parametric models are estimated from zero-downcross analysis of wave data obtained from measurements at sea on the Norwegian continental shelf. The results of the analysis presented here can be used in the estimation of the probabilities of occurrence of steep asymmetric waves and breaking waves in deep water. Thus the results are useful for the practical naval architect and ocean engineer who are considering unusual events in the sea, the associated accidents or responses and the probability of occurrence of such events.     

Casualties in dry bulk shipping (1963–1996)

In recent years, bulk carriers have been identified with high risks of catastrophic structural failure and foundering, and with heavy loss of human life. This study, based upon Lloyd's of London casualty records, identified four risk factors that had significant, independent effect upon the likelihood of a bulk carrier foundering. The risk of foundering increased with the age of the ship, and was related to the ship's flag of registration. Most importantly, however, increased risks were found for heavy cargoes of iron ore and scrap steel or iron, and for trading routes to the Far East and from Europe to North America. Additional safety measures, in particular regarding ship design and high-risk trades, may well be necessary to reduce the high casualty rates.     

Income distribution dynamics and cross-region convergence in Europe

This paper presents a continuous version of the model of distribution dynamics to analyse the transition dynamics and implied long-run behaviour of the EU-27 NUTS-2 regions over the period 1995–2003. It departs from previous research in two respects: first, by introducing kernel estimation and three-dimensional stacked conditional density plots as well as highest density regions plots for the visualisation of the transition function, based on Hyndman et al. (J Comput Graph Stat 5(4):315–336, 1996), and second, by combining Getis’ spatial filtering view with kernel estimation to explicitly account for the spatial dimension of the growth process. The results of the analysis indicate a very slow catching-up of the poorest regions with the richer ones, a process of shifting away of a small group of very rich regions, and highlight the importance of geography in understanding regional income distribution dynamics.

Light Requirements for Growth and Survival of Eelgrass (<Emphasis Type="Italic">Zostera marina</Emphasis> L.) in Pacific Northwest (USA) Estuaries

We developed light requirements for eelgrass in the Pacific Northwest, USA, to evaluate the effects of short- and long-term reductions in irradiance reaching eelgrass, especially related to turbidity and overwater structures. Photosynthesis-irradiance experiments and depth distribution field studies indicated that eelgrass productivity was maximum at a photosynthetic photon flux density (PPFD) of about 350–550 μmol quanta m⁻² s⁻¹. Winter plants had approximately threefold greater net apparent primary productivity rate at the same irradiance as summer plants. Growth studies using artificial shading as well as field monitoring of light and eelgrass growth indicated that long-term survival required at least 3 mol quanta m⁻² day⁻¹ on average during spring and summer (i.e., May-September), and that growth was saturated above about 7 mol quanta m⁻² day⁻¹. We conclude that non-light-limited growth of eelgrass in the Pacific Northwest requires an average of at least 7 mol quanta m⁻² day⁻¹ during spring and summer and that long-term survival requires a minimum average of 3 mol quanta m⁻² day⁻¹.     

Evolution of cool skin and direct air-sea gas transfer coefficient during daytime

Absorption of solar radiation within the thermal molecular sublayer of the ocean can modify the temperature difference across the cool skin as well as the air-sea gas transfer. Our model of renewal type is based on the assumption that the thermal and diffusive molecular sublayers below the ocean surface undergo cyclic growth and destruction, the heat and gas transfer between the successive burst events are performed by molecular diffusion. The model has been upgraded to include heating due to solar radiation. The renewal time is parameterized as a function of the surface Richardson number and the Keulegan number. A Rayleigh number criterion characterizes the convective instability of the cool skin under solar heating. Under low wind speed conditions, the solar heating can damp the convective instability, strongly increasing the renewal time and correspondingly decreasing the interfacial gas exchange. In the ocean, an additional convective instability caused by salinity flux due to evaporation becomes of importance in such cases. The new parameterization is compared with the cool skin data obtained in the western equatorial Pacific during the Tropical Ocean Global Atmosphere Coupled Ocean Atmosphere Response Experiment in February 1993. In combination with a model of the diurnal thermocline it describes main features of the field data both in nighttime and daytime. Under low wind speed conditions (< 5 m s^-1) diurnal variations of the sea surface temperature due to the formation of a diurnal thermocline were substantially larger than those across the cool skin. Under wind speeds > 5 m s^-1, diurnal variations of the surface temperature due to the variations of the thermal molecular sublayer become more important.     

About the specification of erosion flux for soft stratified cohesive sediments

The present paper deals with the specification of bed erosion flux that accounts for the effects of sediment-induced stratification in the water column. Owing to difficulties in measuring the bed shear stress _b and the erosive shear strength _s, we suggest a series of methods that combine laboratory and numerical experiments. A simplified turbulent transport model that includes these effects helps to quantify _b and _s. Focusing on soft stratified beds, the present study considers erosion rate formulas of the form =_f exp {[T_b-T_s]} where is a model constant (=1 for Gularte's (1978) formula and =1/2 for Parchure's (1984) formula). First, the bed erosive strength profile _s(Z) is adjusted by forcing the turbulent transport model with measured erosion rates. Second, three procedures are suggested to determine the erosion rate formula coefficients _f and : a global procedure and two different layer-by-layer procedures. Each procedure is applied to an erosion experiment conducted in a rotating annular flume by Villaret and Paulic (1986). The use of the layer-by-layer procedure based on a least squares fitting technique provides a closer fit than the global procedure. The present study points out the complementarity of experimental and numerical approaches and also suggests possible improvements in laboratory test procedures.     

Baroclinic instabilities in Jupiter's zonal flow

The baroclinic stability of Jupiter's zonal flow is investigated using a model consisting of two continuously stratified fluid layers. The upper layer, containing a zonal shear flow and representing the Jovian cloudy regions above p ～ 5 bars, is the same as Eady's (1949) model for the Earth. The lower layer has a relatively large but finite depth with a quiescent basic state, representing the deep Jovian fluid bulk below p ～ 5 bars. Due to the presence of the lower layer, the linearized non-dimensional growth rates are drastically reduced from the O(1) growth rates of the original Early model. Only very long wavelengths relative to the upper fluid's radius of deformation L₁ are unstable. Eddy transports of heat are also reduced relative to estimates based on scaling arguments alone. Since the hydrostatic approximation for the lower-layer perturbation breaks down at great depths, a second model is presented in which energy propagates downward in an infinitely deep lower fluid obeying the full linearized fluid equations. In this model, the growth rates are again very small, but now all wavelengths are unstable with maximum growth rates occurring for wavelengths O(1) relative to L₁. These results illustrate the importance for the upper-layer meteorology of the interface boundary condition with the lower fluid, which is radically different from the rigid lower boundary of the Earth's troposphere.     

Calculations of the effects of angular momentum on the early evolution of Jupiter

The planet Jupiter is assumed to have formed as a subcondensation in the solar nebula. The initial phase of its evolution is one of hydrostatic contraction with radiative energy transport. Calculations of evolutionary sequences through this phase are presented, including the effects of angular momentum. The calculations are carried out in two space dimensions under the assumptions of axial symmetry, constancy of angular velocity on cylindrical surfaces about the rotation axis, a pressure-density relation given by the polytrope of index 3, conservation of angular momentum, and a homogeneous composition. The results show that under certain physically reasonable initial distributions of density and angular momentum the formation of a central planet and a rotating circumplanetary envelope is possible, while under assumptions a point of instability is reached that probably results in the breakup of the condensation by fission into two or more parts. The models are discussed with reference to the present angular momenta of Jupiter and its regular satellites.