Wave enhancement due to blockage in semi-submersible and TLP structures

An exact analytical method is described to solve the diffraction problem of a group of truncated vertical cylinders. In order to account for the interaction between the cylinders, Kagemoto and Yue's exact algebraic method is utilised (Kagemoto, H., Yue, D.K.P., 1986. Interactions among multiple three-dimensional bodies in water waves: an exact algebraic method. J Fluid Mech, 46, 129–139). The isolated cylinder diffraction potential is obtained using Garret's solution and evanescent mode solutions are derived in a similar manner (Garret, C.J.R., 1971. Wave forces on a circular dock. J Fluid Mech, 46, 129–139).Free surface elevations are calculated for an array of four cylinders and compared with experiments. Comparisons show good agreement.     

Two sets of higher-order Boussinesq-type equations for water waves

Based on the classical Boussinesq model by Peregrine [Peregrine, D.H., 1967. Long waves on a beach. J. Fluid Mech. 27 (4), 815–827], two parameters are introduced to improve dispersion and linear shoaling characteristics. The higher order non-linear terms are added to the modified Boussinesq equations. The non-linearity of the Boussinesq model is analyzed. A parameter related to h/L₀ is used to improve the quadratic transfer function in relatively deep water. Since the dispersion characteristic of the modified Boussinesq equations with two parameters is only equal to the second-order Padé expansion of the linear dispersion relation, further improvement is done by introducing a new velocity vector to replace the depth-averaged one in the modified Boussinesq equations. The dispersion characteristic of the further modified Boussinesq equations is accurate to the fourth-order Padé approximation of the linear dispersion relation. Compared to the modified Boussinesq equations, the accuracy of quadratic transfer functions is improved and the shoaling characteristic of the equations has higher accuracy from shallow water to deep water.     

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.     

Extended mild-slope equation for random waves

A time-dependent extended mild-slope equation is derived from the elliptic equation of Chamberlain and Porter [J. Fluid Mech. 291 (1995) 393] using the Taylor series technique. Numerical tests are made on a horizontally one-dimensional case for regular waves over sloping beds and for both regular and irregular waves over a ripple patch. Numerical results prove that the proposed model gives accurate results for both regular and irregular waves over rapidly varying topography.     

Effects of hull–ice friction coefficient on predictions of pack ice forces for moored offshore vessels

Designers and offshore operators frequently predict pack ice loading on offshore vessels by conducting scale model tests. One factor that can affect pack ice loading is the hull–ice friction coefficient. This research investigates the effect of hull–ice friction coefficients for a moored offshore vessel model and includes ice floe size and ice concentration as additional variables. A method of non-dimensional analysis is modified in order to deal with the multivariate nature of the new data. The resulting non-dimensional equation provides insight on relationships between the predicted pack ice force and the variables under investigation. The relationship between pack ice force and hull–ice friction coefficient is shown to be approximately a fourth root function, while the relationship for ice floe size, non-dimensionalised by the vessel beam, is approximately linear. The relationship between predicted pack ice force and ice concentration exists in a band bounded by cubic and sixth power curves. Applying the modified equation to the previous data sets shows the current analysis slightly improves the normalization of pack ice forces.     

An iterative procedure for the diffraction of water waves by multiple cylinders

Diffraction of water waves by an array of vertical cylinders of circular cross section is studied. In order to account for first order interaction among the cylinders, the body boundary condition is satisfied for each cylinder considering the scattered wave field from other cylinders in an iterative way. After each iteration, coefficients in the partial wave decomposition of the wave potential are modified. Convergence is fast for the whole range of frequencies and for a large number of bodies, compared with exact algebraic methods of Linton and Evans [J. Fluid Mech. 46 (1990) 549] and Kagemoto and Yue [J. Fluid Mech. 166 (1) (1986) 189].     

On the role of shoreline boundary conditions in wave overtopping modelling with non-linear shallow water equations

The note extends and completes the analysis carried out by Briganti and Dodd [Briganti, R., Dodd, N., 2009. Shoreline motion in nonlinear shallow water coastal models. Coastal Eng. 56(5–6) (doi:101016/j.coastaleng.2008.10.008), 495–505.] on the performance of a state of the art Non-Linear Shallow Water Equations solver in common coastal engineering applications. The case of bore-generated overtopping of a truncated plane beach is considered and the performance of the model is assessed by comparing with the Peregrine and Williams [Peregrine, D., Williams, S.M., 2001. Swash overtopping a truncated beach. J. Fluid Mech. 440, 391–399.] analytical solution. In particular the influence of shoreline boundary conditions is investigated by considering the two best performing approaches discussed in Briganti and Dodd [Briganti, R., Dodd, N., 2009. Shoreline motion in nonlinear shallow water coastal models. Coastal Eng. 56(5–6) (doi:101016/j.coastaleng.2008.10.008), 495–505.]. Different distances of the edge of the beach from the bore collapse point are tested. For larger distances, the accuracy of the overtopping modelling decreases, as a consequence of the error in modelling the tip of the swash lens and, consequently, the run-up. A sensitivity analysis using the numerical resolution is carried out. This reveals that the approach in which cells shallower than a prescribed threshold are drained and wave propagation speeds for wet/dry Riemann problem are used at the interface between a wet and a dry cell (referred as Option 2ea in [Briganti, R., Dodd, N., 2009. Shoreline motion in nonlinear shallow water coastal models. Coastal Eng. 56(5–6) (doi:101016/j.coastaleng.2008.10.008), 495–505.]) performs consistently better than the other.     

Statistical distribution of wave-surface elevation for second-order random directional ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a statistical distribution of the wave-surface elevation is derived by using the characteristic function expansion method. It is found that the distribution, after normalization of the wave-surface elevation, depends only on two parameters. One parameter describes the small mean bias of the surface produced by the second-order wave-wave interactions. Another one is approximately proportional to the skewness of the distribution. Both of these two parameters can be determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, we consider a fully developed wind-generated sea and the parameters are calculated for various wind speeds and water depths by using Donelan and Pierson spectrum. It is also found that, for deep water, the dimensionless distribution reduces to the third-order Gram–Charlier series obtained by Longuet-Higgins [J. Fluid Mech. 17 (1963) 459]. The newly proposed distribution is compared with the data of Bitner [Appl. Ocean Res. 2 (1980) 63], Gaussian distribution and the fourth-order Gram–Charlier series, and found our distribution gives a more reasonable fit to the data.     

An analytical approach for the calculation of random wave forces on submerged tunnels

This paper deals with the random forces produced by high ocean waves on submerged horizontal circular cylinders. Arena [Arena F, Interaction between long-crested random waves and a submerged horizontal cylinder. Phys Fluids 2006;18(7):1–9 (paper 076602)] obtained the analytical solution of the random wave field for two dimensional waves by extending the classical Ogilvie solution [Ogilvie TF, First- and second-order forces on a cylinder submerged under a free surface. J Fluid Mech 1963;16:451–472; Arena F, Note on a paper by Ogilvie: The interaction between waves and a submerged horizontal cylinder. J Fluid Mech 1999;394:355–356] to the case of random waves. In this paper, the wave force acting on the cylinder is investigated and the Froude Krylov force [Sarpkaya T, Isaacson M, Mechanics of wave forces on offshore structures, Van Nostrand Reinhold Co.; 1981], on the ideal water cylinder, is calculated from the random incident wave field. Both forces represent a Gaussian random process of time. The diffraction coefficient of the wave force is obtained as quotient between the standard deviations of the force on the solid cylinder and of the Froude Krylov force. It is found that the diffraction coefficient of the horizontal force C_do is equal to the C_dv of the vertical force. Finally, it is shown that, since a very large wave force occurs on the cylinder, it may be calculated, in time domain, starting from the Froude Krylov force. It is then shown that this result is due to the fact that the frequency spectrum of the force acting on the cylinder is nearly identical to that of the Froude–Krylov force.     

A coupled-mode technique for the transformation of ship-generated waves over variable bathymetry regions

In the present work, a coupled-mode technique is applied to the transformation of ship's waves over variable bathymetry regions, characterised by parallel depth-contours, without any mild-slope assumption. This method can be used, in conjunction with ship's near-field wave data in deep water or in constant-depth, as obtained by the application of modern (linearised or non-linear) ship computational fluid dynamic (CFD) codes, or experimental measurements, to support the study of wave wash generated by fast ships and its effects on the nearshore/coastal environment.

Under the assumption that the ship's track is straight and parallel to the depth-contours, and relatively far from the bottom irregularity, the problem of propagation–refraction–diffraction of ship-generated waves in a coastal environment is efficiently treated in the frequency domain, by applying the consistent coupled-mode model developed by Athanassoulis and Belibassakis [J. Fluid Mech. 1999;389] to the calculation of the transfer function enabling the pointwise transformation of ship-wave spectra over the variable bathymetry region.

Numerical results are presented for simplified ship-wave systems, obtained by the superposition of source–sink Havelock singularities simulating the basic features of the ship's wave pattern. The spatial evolution of the ship-wave system is examined over a smooth but steep shoal, resembling coastal environments, both in the subcritical and in the supercritical case. Since any ship free-wave system, either in deep water or in finite depth, can be adequately modelled by wavecut analysis and suitable distribution of Havelock singularities e.g. as presented by Scrags [21st Int. Conf. Offshore Mech. Arctic Eng., OMAE2002, Oslo, Norway, June 2002], the present method, in conjunction with ship CFD codes, supports the prediction of ship wash and its impact on coastal areas, including the effects of steep sloping-bed parts.     

Some parameters in arctic sea ice dynamics from an expedition in the summer of 2003

1Introduction Seaiceoccupiesthemainpartofthesurfaceof theArcticOcean.ThefocusoftheSecondChineseNa- tionalArcticResearchExpedition(CHINAE-2003) wastounderstandthevariationsofarcticmarineenvi- ronmentsandtheseaiceeffectsontheclimatechanges ofglobalextent,inmiddleandlowerlatitudesareas, especiallyinChina.Therefore,thejointsea-ice-airob- servationforseaicestudieswasoneofthekeypro- jectsinCHINARE-2003.Theinvestigatedareacov- ered3000kmfromsouthtonorthand900kmfrom westtoeast.Seventemporali…     

Fixed-frequency Stokes wave expansion

The study describes a new fixed-frequency Stokes wave theory that differs from previous Stokes wave theories that fix the wave number. The present wave expansion analytically reveals that the wavelength increases with wave height and exceeds than the wavelength obtained by linear wave theory. A method proposed to comparably transform the wave celerity of Fenton's [Fenton, J.D., 1985. A fifth-order Stokes theory for steady waves. Journal of Waterway, Port, Coastal and Ocean Engineering 111, 216–234.] wave theory to the present one. A direct calculation of the wavelength is introduced for practical solutions, avoiding the need to solve a nonlinear equation using an iterative numerical method.     

Comparison of Dirichlet–Neumann operator expansions for nonlinear surface gravity waves

The Dirichlet–Neumann operator for the water-wave problem was introduced and expanded by Craig and Sulem [Craig, W., Sulem, C., 1993. [CS] Numerical simulation of gravity waves. J. Comput. Phys. 108, 73–83] and in a slightly different form and for 3D waves by Bateman, Swan and Taylor [Bateman, W.J.D., Swan, C., Taylor, P.H., 2001. [BST] On the efficient numerical simulation of directionally spread surface water waves. J. Comput. Phys. 174, 277–305]. This approach is supposedly superior to techniques derived earlier by West et al. [West, B.J., Brueckner, K.A., Janda, R.S., Milder, D.M., Milton, R.L., 1987. [WW] A new numerical method for surface hydrodynamics. J. Geophys. Res. 92 (C11), 11803–11824] and Dommermuth and Yue [Dommermuth, D.G., Yue, D.K.P., 1987. [DY] A high-order spectral method for the study of nonlinear gravity waves. J. Fluid Mech. 184, 267–288] under seemingly more restrictive assumptions. This paper extracts the Dirichlet–Neumann operator expansions from West et al. and Dommermuth and Yue. Concerning the operator expansions alone it is found that Bateman et al. is identical to West et al. and Dommermuth and Yue while Craig and Sulem is slightly different due to minor differences in the operator definition. For application to the free-surface boundary conditions West et al. devised a consistent truncation at nonlinear order. This alters the equivalence of the different approaches when it comes to the evaluation of the temporal derivative of the free surface elevation, which is decisive for wave evolution. In this regard Craig and Sulem is found to be identical to West et al. while Bateman et al. is identical to Dommermuth and Yue. Pseudo code is provided for alternative computational schemes in Fourier-space and physical space, respectively, along with a discussion of efficiency and potential flexibility.     

An application of Boussinesq equations to Bragg reflection of irregular waves

A numerical model based on the second-order fully nonlinear Boussinesq equations of Wei et al. [1995. Journal of Waterway, Port, Coastal and Ocean Engineering 121 (5), 251-263] is developed to simulate the Bragg reflection of both regular and irregular surface waves scattered by submerged bars. Particularly for incident regular waves, the computed results are observed to agree very well with the existing experimental data as presented by Davies and Heathershaw [1984. Journal of Fluid Mechanics 144, 419-446] and Kirby and Anton [1990. Proceedings of the 22nd International Conference on Coastal Engineering, ASCE, New York, pp. 757–768). In the case of incident irregular waves, the simulated results reveal that the distribution of Bragg reflection from irregular waves becomes more flat than that of regular waves. Due to lack of experimental data, the numerical results for incident irregular waves are compared with those of the evolution equation of the mild-slope equation [Hsu et al., 2002 Proceedings of the 24th Ocean Engineering Conference in Taiwan, pp. 70–77 (in Chinese)]. In addition, several parameters such as the number of bars, the relative height of bars and the spacing of bars affecting Bragg reflection are also discussed.     

Estimation of Sea Ice Freeboard from SARAL/AltiKa Data

An attempt has been made to derive sea ice freeboard from Ka-band Altimeter (SARAL/AltiKa) over Arctic region for 15 March–15 April 2013 (spring) and 15 September–15 October 2013 (autumn). A waveform template matching technique is employed for classification of leads and floe pixels. The estimated sea ice freeboards were found in close agreement with “Operation IceBridge quick look” freeboards (RMSD = 0.30 m). The differences between the two freeboards were largely due to snow layer over sea ice (R = 0.8). The estimated freeboards were of the order of 0.08–0.15 m during the two seasons.     

北极巴伦支海和拉普捷夫海海冰中细菌和微藻的垂直分布

通过计算机图像测定系统测定、计算获得海冰细菌的大小、面积和碳含量,研究了北极巴伦支海和拉普捷夫海的浮冰中细菌大小、丰度和生物量的垂直分布及其与海冰微藻生物量的关系.细菌在冰心中是非均匀分布的,至少有两种不同分布类型:第一类有单一的丰度峰值,在冰心底部或在冰心中部;第二类有两个丰度峰值.海冰中细菌的丰度为0.4×105～36.7×105个/cm3.不同类型海冰中的细菌大小变化极大,在多年冰中,最大的细菌与叶绿素a最大值出现在同一层,而在一年冰中,细菌大小几乎没有垂直变化.整柱冰心的细菌生物量变化为19.2～79.2mg/cm2,细菌与海冰微藻生物量之比为0.43～10.00.对固定冰比较和研究的结果发现,海冰冰心中细菌大小、丰度和生物量的垂直分布差别极大.据此,分析了对目前海冰研究采样方法的局限性,并提出了规范采样方法的设想.     

Wave forces on a large, horizontal submerged cylinder

A numerical boundary integral equation method combined with a non-linear time stepping procedure is used for the calculation of wave forces on a large, submerged, horizontal circular cylinder. As the method is based on potential theory, all computations are performed in the inertia dominated domain, that is, for small Keulegan-Carpenter numbers. Computations are carried out for the Eulerian mean current under wave trough level equal to zero. When the cylinder is moved towards the sea bed the computations show that the inertia coefficients increase significantly, which is associated with a blockage effect. Furthermore, the effect of the wave steepness is reduced when the submergence of the cylinder is increased. In the vicinity of the free water surface the vertical inertia coefficient is highly dependent upon the wave steepness, which tends to reduce it, whereas the horizontal inertia coefficient is only slightly dependent on the wave steepness. Computations are also carried out for cylinder diameters comparable with the wave length. Finally, inertia coefficients computed by the present method are compared with some analytical results by Ogilvie [(1963), First and second order forces on a cylinder submerged under a free surface. J. Fluid Mech. 16, 451–472]. As long as the assumptions leading to Ogilvie's theory are fulfilled (cylinder radius small compared to the wave length), the results are quite similar.     

On the heave radiation of a rectangular structure

In this paper, an analytic solution to the heave radiation problem of a rectangular structure is presented. To solve the problem analytically, the nonhomogeneous boundary value problem is linearly decomposed into homogeneous ones, which can be readily solved. To provide further comparisons to the present analytic solution, a boundary element method is also presented to solve the problem. The present analytic solution is compared with the result by Black et al. [(1971)] Radiation and scattering of water waves by rigid bodies. J. Fluid Mech. 46, 151–164], and the boundary element solution, and the comparisons show very good agreements. Upon examination of the present analytic solution, it is shown that the solution satisfies the nonhomogeneous boundary condition in a sense of series convergence. Using the present analytic solution, the generated waves, the added mass and the radiation damping coefficients, as well as the hydrodynamic effects of the submergence and the width of the structure, are investigated.     

Combined tidal ice drift and ice-induced changes in the dynamics and energy of the combined tide on the Siberian continental shelf

The results of a simulation of the combined tidal ice drift corresponding to a linear superposition of the M ₂, S ₂, K ₁, and O ₁ harmonics of the tidal generating force are discussed. Also, ice-induced maximal (during the tropical month, i.e., over 27.322 mean solar days) values of the dynamic and energy characteristics of combined motions are estimated in the marginal seas of the Siberian continental shelf. Special attention was paid to the revealing of zones of compression-rarefaction and zones of ice floe ridging.     

A Gibbs–Pitzer function for high-salinity seawater thermodynamics

A high-salinity Gibbs function for seawater is derived from Pitzer equations of the sea salt components, in conjunction with the 2003 Gibbs function of seawater for low salinities. Various properties, computed from both formulations by thermodynamic rules, are compared with each other, and with high-salinity measurements. The new Gibbs–Pitzer function presented in this paper is valid in the range 0–110 g kg⁻¹ in absolute salinity, −7 to +25 °C in temperature, and 0–100 MPa in applied pressure. The formulation is expressed in the International Temperature Scale 1990 (ITS-90), and is consistent with the International Standard for Fluid Water (IAPWS-95), and with the 2005/2006 equations of state of ice Ih.