A note on significant wave height

In this note conservative bounds for significant crest height and amplitude obtained from the crossing intensity of a sea are presented. For Gaussian models of a sea level, the Rayleigh approximation for the distributions of amplitude and crest height is proved to provide conservative values for the expected significant wave characteristics. The results are illustrated by examples in which both Gaussian and non-Gaussian models for a sea are considered.     

A note on surface wind-driven flow

A simple operationally oriented model of surface wind-driven currents is presented in which Lagrangian surface drift is assumed to be composed of a linear combination of a wave-induced Stokes drift plus a wind-driven Ekman drift. Using this approach, Stokes drift accounts for as much as half the total surface current magnitude. The Lagrangian current is predicted to be about 3.5% of the 10 m wind magnitude directed in the sense of an Ekman spiral about a 20° deviation angle. For comparison to this model, a second model is proposed that accounts for the interaction of Stokes current and Coriolis force. An inference drawn from this model is that there is only weak coupling between Coriolis force and Stokes drift. Such a conclusion, if correct, leads one to focus attention on the Lagrangian model for operationally oriented current estimates. Results of the Lagrangian model agree with observations of investigators for currents at the air-sea interface and may have application in the movement f oil slicks or surface drifters at sea under fetch or duration limited sea states.     

A note on the accuracy of the mild-slope equation

The mild-slope equation is a vertically integrated refraction-diffraction equation, used to predict wave propagation in a region with uneven bottom. As its name indicates, it is based on the assumption of a mild bottom slope. The purpose of this paper is to examine the accuracy of this equation as a function of the bottom slope. To this end a number of numerical experiments is carried out comparing solutions of the three-dimensional wave equation with solutions of the mild-slope equation.For waves propagating parallel to the depth contours it turns out that the mild-slope equation produces accurate results even if the bottom slope is of order 1. For waves propagating normal to the depth contours the mild-slope equation is less accurate. The equation can be used for a bottom inclination up to 1:3.     

A note on uprighting of a ship floating upside-down

In many cases, capsized ships remain floating upside-down due to buoyancy of intact hull compartments and air cushions. Uprighting of such a ship is usually a complex salvage operation, which needs proper planning based on predictions of ship stability. This paper considers aspects affecting selection of the uprighting method, presents features of ship stability in the inverted mode and a procedure for calculating the required forces. Approximate formulae are derived for estimating the maximum lifting capacity necessary for uprighting a capsized vessel supported by buoyancy of the double bottom and double side compartments. The formulae are intended for quick estimations at the initial stage when no detail information may be available on the casualty. A practical salvage work is briefly described.     

A note on the Japan Sea Proper Water

The water under the main thermocline in the Japan Sea is a single water mass referred to as the Japan Sea Proper Water. It can be defined as having temperature below 2.0°C, salinity above 34.00%, and dissolved oxygen below 7.0 ml 1⁻¹. In the north most of the water above the potential temperature 0.1°C depth (about 800–1000 m) is a mode water, with σ_θ of 27.32 to 27.34 kg m⁻³. North of 40°N it has high oxygen (more than 6.00 ml 1⁻¹) with a distinct discontinuity (oxygen-cline) at the bottom of the mode water. The most probable region for the formation of the water is the area north of 41°N between 132° and 134°E. The deeper water probably is formed in the norther area of 43°N, and directly fills the main part of the Japan Basin north of 41°N and east of 134°E.     

A note on the hydrodynamics of a tail tube buoy

This note presents some analytical results for a tail–tube buoy configuration frequently used in wave energy conversion. The overall approach is based on Falnes and McIver's (Falnes, J., McIver, P., 1985. Surface wave interactions with systems of oscillating bodies and pressure distributions. Applied Ocean Research 7 (4), 225–234) extension to floating oscillating water columns of Evans' (Evans, D.V., 1982. Wave power absorbtion by systems of oscillating surface pressure distributions. Journal of Fluid Mechanics 114, 481–499) theory of oscillating pressure distributions. The diffraction air-flow flux through the tube and the diffraction wave force on the flotation collar are obtained using the formulation of Garrett (1970, 1971) (Garrett, C.J.R., 1970. Bottomless harbours. Journal of Fluid Mechanics 43 (3), 433–449. Garrett, C.J.R., 1971. Wave forces on a circular dock. Journal of Fluid Mechanics 46 (1), 129–139). Results can be used in sizing the tube and collar for efficient energy conversion.     

A note on the extremal properties of the morison equation

The extremal properties of the Morison equation F(t) = X′(t) + X(t)|X(t)|; for the force on a circular pile in a fluid, are derived by means of a Slepian model for the behaviour of X(t) around its local maxima. The behaviour of X′(t) near large maxima of X(t) is almost deterministic, and hence there is a simple relation between the maxima in X(t) and those in F(t).     

Technical note: A revised parameterisation of the Jonswap spectrum

Equations are derived for estimating the governing parameters of the Jonswap spectrum for a sea state specified in terms of significant waveheight and average period. Two of the equations are obtained mathematically from the Jonswap equation and are of general validity. The third is derived from empirical data published by Houmb and Overvik¹ and applies only to North Sea conditions.     

A note on eastern-boundary intensification of flow in Lake Vostok

Based on the predictions of a simple hypothetical model it is proposed that the circulation within Lake Vostok is asymmetric, with a narrow boundary layer along the eastern wall and a diffuse counter-clockwise recirculation in the interior. This differs from a recent work by Wüest and Carmack [Ocean Model. 2 (2000) 29], who predicted a symmetric, clockwise circulation in the lake. The predicted boundary-layer intensification is due to variation in the depth of the lake, which creates a dynamically important topographic β effect. The eastward intensification of the flow may have important implications for future studies of the lake's ecosystem.     

A note on the economics of Swedish Baltic Sea fisheries

The cod stocks in the Baltic Sea are important not only for fisheries but for the entire ecosystem utilized by numerous stakeholders around the coast. All such activities have economic values. In this note the economics of the Swedish Baltic Sea cod fishery is estimated in relation to the sector's interaction with other users of the Baltic Sea ecosystem. The results show a negative resource rent for the fishery, € −5 million without public expenses (subsidies and administrative costs), and € −13 million including public expenses. The interactions between the fisheries and tourism, seal population, carbon dioxide emissions, recreational fishing, and discards are discussed, and when monetary estimates are available these are related to the estimated resource rent.     

A note on wave energy dissipation over steep beaches

This paper revisits the derivation of the parametric surf zone model proposed by Baldock et al. [Baldock, T. E., Holmes, P., Bunker, S. & Van Weert, P. 1998 Cross-shore hydrodynamics within an unsaturated surf zone. Coast. Eng. 34, 173–196.]. We show that a consistent use of the proposed Rayleigh distribution for surf zone wave heights results in modification of the expressions for the bulk dissipation rate and enhanced dissipation levels on steep beaches and over-saturated surf zone conditions. As a consequence, the modification proposed herein renders the model robust even on steep beaches where it could otherwise develop a shoreline singularity.     

A note on ship-motion prediction based on wave-excitation inputestimation

In order to predict the motion of a ship effectively, a new algorithm is developed in which the wave-excitation input information is extracted from the estimated ship-motion data, and a prediction is made by extrapolating the governing equation of the ship motion. Simulations performed with the algorithm and the conventional ship-motion prediction algorithm based on the standard Kalman filter are compared     

A note on wave-induced set-up by obliquely incident waves

Water level variations due to obliquely incident, shoaling and breaking waves on a plane sloping beach were discussed recently by Hsu et al. (Coastal Engineering, 53, 865–877, 2006). An inconsistency in this work with respect to the set-down, and its implications to circulation offshore of the breakpoint, was pointed out by Shi and Kirby (Coastal Engineering, 55, 1246 – 1249, 2008). Here we extend that discussion to include the surfzone momentum balance and wave-induced set-up. We discuss some remaining inconsistencies in the approximation of the surfzone momentum balance, derive and present a consistent approximation, and validate the new approximation through numerical comparison to a more exact model.