Design of a prototype ocean current turbine—Part I: mathematical modeling and dynamics simulation

The “C-Plane” is a submerged variable depth ocean current turbine that is tethered to the sea floor and uses sustained ocean currents to produce electricity. As part of the development of a $\frac{1}{30}$th scale physical model of the C-Plane, a mathematical model and dynamics simulation of the prototype was developed and is presented in this paper. This three-dimensional mathematical model represents the C-Plane as a rigid body with moveable control surfaces that is moored with three linear elastic cable elements. Gravitational, buoyancy, hydrodynamic, cable, gyroscopic, and inertial forces are included and a PC-based dynamics simulation is created. The simulation demonstrates that the C-Plane is stable and capable of changing depth in all expected operating conditions. The C-Plane prototype can fly level from a height of 3 to 6 m using the configuration suggested in this paper. The maximum ascent rates of the C-Plane with a water speed of 0.3 m/s are 0.015 m/s when the pitch is fixed at 0° and 0.030 m/s when the pitch is fixed at 4°. The maximum descent rates of the C-Plane are 0.018 m/s when the pitch is held at 0° and 0.031 m/s if the pitch is held at −4°.     

Ice-ocean acoustic energy transfer:: ambient noise in the ice-edge region

The ambient noise produced by large areas of ice floes, such as the Odden and the marginal ice zone, was recorded and analysed. A model based on the collision, compression and shearing of floes driven by ocean swell was constructed. This model allows the level and variance of the ambient noise to be predicted provided the conditions of the ice and the sea state are known. The frequency spectrum of the ambient noise in the range 100 Hz to 100 kHz is explained in terms of acoustic propagation and absorption by sea water. The probability distribution of ambient noise intensity, obtained from a statistical analysis of collision frequencies, is a form of K distribution and agrees with observations.     

Constrained near-optimal control of a wave energy converter in three oscillation modes

This paper investigates the performance of a small axisymmetric buoy under wave-by-wave near optimal control in surge, heave, and pitch modes in long-crested irregular waves. Wave prediction is obtained using a deterministic propagation model. The paper describes the overall formulation leading up to the derivation of the feedforward control forces in surge and heave, and the control moment in pitch. The radiation coupling between surge and pitch modes is accounted for in the model. Actuation is relative to deeply submerged reaction masses. Heave oscillations are constrained by the swept-volume limit. Oscillation constraints are also applied on the surge and pitch oscillations. The paper discusses time-domain simulations for an irregular wave input with and without the present control. Also discussed are results obtained over a range of irregular wave conditions derived for energy periods from 7 s to 17 s, and a significant wave height of 1 m. It is found that, while the gains in power capture enabled by the present control are significant, the actuation forces are also very large, given the small size of the buoy. Further, due to the small size, heave is found to be the dominant contributor to power capture, with relatively modest contributions from surge and pitch.     

Modeling wave-mud interaction on the central chenier-plain coast,western Louisiana Shelf,USA

The strong coupling between hydrodynamics and seafloors on shallow muddy shelves, and resulting bed reworking, have been extensively documented. On these shelves, spectral wave transformation is driven by a complex combination of forcing mechanisms that include nonlinear wave interactions and wave energy dissipation induced by fluid-mud at a range of frequencies. Wave-mud interaction is investigated herein by using a previously validated nonlinear spectral wave model and observations of waves and near-bed conditions on a mildly-sloping seafloor off the muddy central chenier-plain coast, western Louisiana Shelf, United States. Measurements were made along a cross-shelf transect spanning 1 km between 4 and 3 m water depths. The high-resolution observations of waves and near-bed conditions suggest presence of a fluid mud layer with thickness sometimes exceeding 10 cm under strong long wave action (1 meter wave height with 7 s peak period at 4 meter depth). Spectral wave transformation is modeled using the stochastic formulation of the nonlinear Mild Slope Equation, modified to account for wave-breaking and mud-induced dissipation. The model is used in an inverse manner in order to estimate the viscosity of the fluid mud layer, which is a key parameter controlling mud-induced wave dissipation but complicated to measure in the field during major wave events. Estimated kinematic viscosities vary between 10⁻⁴-10⁻³ m²/s. Combining these results of the wave model simulations with in-depth analysis of near-bed conditions and boundary layer modeling allows for a detailed investigation of the interaction of nonlinear wave propagation and mud characteristics. The results indicate that mud-induced dissipation is most efficient when the wave-induced resuspensions of concentrations  > 10 g/L settle due to relatively small bottom stresses to form a fluid mud layer that is not as thin and viscous as a consolidated seafloor in absence of wave action but also not as thick and soft as a near-bed high concentration layer that forms during strong wave action.     

Seasonal changes in the vertical distribution and community structure of Antarctic macrozooplankton and micronekton

The macrozooplankton and micronekton community of the Lazarev Sea (Southern Ocean) was investigated at 3 depth layers during austral summer, autumn and winter: (1) the surface layer (0–2 m); (2) the epipelagic layer (0–200 m); and (3) the deep layer (0–3000 m). Altogether, 132 species were identified. Species composition changed with depth from a euphausiid-dominated community in the surface layer, via a siphonophore-dominated community in the epipelagic layer, to a chaetognath-dominated community in the deep layer. The surface layer community predominantly changed along gradients of surface water temperature and sea ice parameters, whereas the epipelagic community mainly changed along hydrographical gradients. Although representing only 1% of the depth range of the epipelagic layer, mean per-area macrofauna densities in the surface layer ranged at 8% of corresponding epipelagic densities in summer, 6% in autumn, and 24% in winter. Seasonal shifts of these proportional densities in abundant species indicated different strategies in the use of the surface layer, including both hibernal downward and hibernal upward shift in the vertical distribution, as well as year-round surface layer use by Antarctic krill. These findings imply that the surface layer, especially when it is ice-covered, is an important functional node of the pelagic ecosystem that has been underestimated by conventional depth-integrated sampling in the past. The exposure of this key habitat to climate-driven forces most likely adds to the known susceptibility of Antarctic pelagic ecosystems to temperature rise and changing sea ice conditions.     

Dimethylsulphide and dimethylsulphoniopropionate in Antarctic sea ice and their release during sea ice melting

This study presents concentrations of dimethylsulphide (DMS) and its precursor compound dimethylsulphoniopropionate (DMSP) in a variety of sea ice and seawater habitats in the Antarctic Sea Ice Zone (ASIZ) during spring and summer. Sixty-two sea ice cores of pack and fast ice were collected from twenty-seven sites across an area of the eastern ASIZ (64°E to 110°E; and the Antarctic coastline north to 62°S). Concentrations of DMS in 81 sections of sea ice ranged from < 0.3 to 75 nM, with an average of 12 nM. DMSP in 60 whole sea ice cores ranged from 25 to 796 nM and showed a negative relationship with ice thickness (y = 125x^− 0.8). Extremely high DMSP concentrations were found in 2 cores of rafted sea ice (2910 and 1110 nM). The relationship of DMSP with ice thickness (excluding rafted ice) suggests that the release of large amounts of DMSP during sea ice melting may occur in discrete areas defined by ice thickness distribution, and may produce ‘hot spots’ of elevated seawater DMS concentration of the order of 100 nM. During early summer across a 500 km transect through melting pack ice, elevated DMS concentrations (range 21–37 nM, mean 31 nM, n = 15) were found in surface seawater. This band of elevated DMS concentration appeared to have been associated with the release of sea ice DMS and DMSP rather than in situ production by an ice edge algal bloom, as chlorophyll a concentrations were relatively low (0.09–0.42 μg l^− 1). During fast ice melting in the area of Davis station, Prydz Bay, sea ice DMSP was released mostly as extracellular DMSP, since intracellular DMSP was negligible in both hyposaline brine (5 ppt) and in a melt water lens (4–5 ppt), while extracellular DMSP concentrations were as high as 149 and 54 nM, respectively in these habitats. DMS in a melt water lens was relatively high at 11 nM. During the ice-free summer in the coastal Davis area, DMS concentrations in surface seawater were highest immediately following breakout of the fast ice cover in late December (range 5–14 nM), and then remained at relatively low concentrations through to late February (< 0.3–6 nM). These measurements support the view that the melting of Antarctic sea ice produces elevated seawater DMS due to release of sea ice DMS and DMSP.     

Sea-ice-thickness variability in the Chukchi Sea,spring and summer 2002–2004

Measurements of sea-ice thickness were obtained from drill holes, an ice-based electromagnetic induction instrument (IEM), and a ship-borne electromagnetic induction instrument (SEM) during the early-melt season in the southern Chukchi Sea in 2002 and 2004, and in late summer 2003 at the time of minimum ice extent in the northern Chukchi Sea. An ice roughness criterion was applied to distinguish between level and rough or ridged ice. Ice-thickness modes in the probability density functions (PDFs) derived from drill-hole and IEM measurements agreed well, with modes at 1.5–1.6 and 1.8–1.9 m for all data from level ice. The PDFs derived from SEM measurements show that the primary modes are at 0.1 and 1.1 m in 2003 and 0.7 m in 2004. In 2002 and 2004, significant fractions (between one-third and one-half) of level ice were found to consist of rafted ice segments. Snow depth varied significantly between years, with 2004 data showing more than half the snow cover on level ice to be at or below 0.05 m depth in late spring. Ice growth simulations and examination of ice drift and deformation history indicate that impacts of atmospheric and oceanic warming on level-ice thickness in the region over the past few decades are masked to a large extent by variability in snow depth and the contribution of deformation processes. In comparison with submarine sonar ice-thickness data from previous decades, a reduction in ice thickness by about 0.5–1 m is in part explained by the replacement of multi-year with first-year ice over the Chukchi and Beaufort shelves.     

Focused wave evolution using linear and second order wavemaker theory

In this paper, the evolution of focused waves using different paddle displacements (piston type) under laboratory conditions is presented. It is well known that in intermediate water depths, linear paddle displacements will generate spurious, free, sub and super harmonics. Thus, a second order correction to suppress these spurious free sub and super harmonics was used to generate the focused waves. The focused waves were generated in the laboratory using a linear superimposition principle, in which the wave paddle displacement is derived based on the sum of a number of sinusoidal components at discrete frequencies, whose phases are accordingly set to focus at a particular location. For this method of generation, the second order wave maker theory proposed by Schäffer [24] can be easily adopted and was used in the present study. Two different centre frequencies (f_c = 0.68 Hz and 1.08 Hz) with three different bandwidth ratios (Δf/f_c = 0.5, 0.75 and 1.0) were tested in a constant water depth, to consider both narrow and broadband spectra. These test cases correspond to wave focusing packets propagating in intermediate and deep water regions. Further, for each wave packet, two different amplitudes were considered in order to analyze non-breaking and breaking cases. Thus, by systematically generating the wave packets using the linear and second order paddle displacements, the analysis was carried out for the spectral and temporal evolution of selected long waves. The temporal evolution of the selected harmonics was analyzed using the Inverse Fast Fourier Transform (IFFT), to show the propagation of the spurious, free, long waves. Further, the variations in energy for the lower, higher and primary frequency ranges are reported for different wave paddle displacements. The analysis revealed that for the broadband spectrum the differences are more pronounced when using linear paddle displacements. We have also noticed a shift in focusing/breaking location and time (i.e. premature) due to the increase in crest height using linear displacements. The experiment data used in this paper has been provided as a supplementary, which can be used to validate the numerical models.     

Solitary wave generation dynamics at Luzon Strait

A high resolution modeling study is undertaken, with a 2.5-dimensional nonhydrostatic model, of the generation of internal waves induced by tidal motion over the ridges in Luzon Strait. The model is forced by the barotropic tidal components K1, M2, and O1. These tidal components, along with the initial density field, were extracted from data and models. As the barotropic tide moves over the Luzon Strait sills, there is a conversion of barotropic tidal energy into baroclinic tidal energy. Depressions are generated that propagate towards the Asian Seas International Acoustics Experiment (ASIAEX) test site on the Chinese continental shelf. Nonlinear effects steepen the depressions, frequency and amplitude dispersion set in, and disintegration into large amplitude solitary waves occurs. The effects of varying the initial density field, tidal component magnitudes, as well as adding a steady background current to represent the occasional excursions of the Kuroshio Current into the strait, are considered.Depressions are generated at each of the two sills in Luzon Strait which radiate away, steepening and evolving into internal solitary wave trains. Baroclinic fluxes of available potential energy, kinetic energy and linear are calculated for various parameter combinations. The solitary wave trains produced in the simulations generally consist of large amplitude wave trains alternating with small amplitude wave trains. During strong tidal flow, Kelvin–Helmholtz type instabilities can develop over the taller double-humped sill. The solitary waves propagating towards the ASIAEX test site have been observed to reach amplitudes of 120–250 m, depending on the tidal strength. ASIAEX observations indicate amplitudes up to 150 m and the Windy Island Experiment (WISE) measurements contain magnitudes over 200 m. The model results yield solitary wave amplitudes of 70–300 m and half widths of 0.60–3.25 km, depending on parameter values. These are in the range of observations. Measurements by Klymak et al. (2006), in the South China Sea, exhibit amplitudes of 170 m, half widths of 3 km and phase speeds of 2.9 m s^?1. Model predictions indicate that the solitary waves making up the wave packet each experience different background currents with strong near surface shear.The energy in the leading soliton of the large amplitude wave trains ranges between 1.8 and 9.0 GJ m^?1. The smaller value, produced using barotropic tidal currents based on the Oregon State University data base, is the same as the energy estimated to be in a solitary wave observed by Klymak et al. (2006). Estimates of the conversion of barotropic tidal energy into radiating internal wave energy yield conversion rates ranging between 3.6% and 8.3%.     

Sea-ice algae: Major contributors to primary production and algal biomass in the Chukchi and Beaufort Seas during May/June 2002

Sea-ice and water samples were collected at 14 stations on the shelves and slope regions of the Chukchi and Beaufort Seas during the spring 2002 expedition as part of the Shelf–Basin Interaction Studies. Algal pigment content, particulate organic carbon and nitrogen, and primary productivity were estimated for both habitats based on ice cores, brine collection and water samples from 5-m depth. The pigment content (0.2–304.3 mg pigments m⁻²) and primary productivity (0.1–23.0 mg C m⁻³ h⁻¹) of the sea-ice algae significantly exceeded water-column parameters (0.2 and 1.0 mg pigments m⁻³; <0.1–0.4 mg C m⁻³ h⁻¹), making sea ice the habitat with the highest food availability for herbivores in early spring in the Chukchi and Beaufort Seas. Stable isotope signatures for ice and water samples did not differ significantly for δ¹⁵N, but for δ¹³C (ice: −25.1‰ to −14.2‰; water: −26.1‰ to −22.4‰). The analysis of nutrient concentrations and the pulse-amplitude-modulated fluorescence signal of ice algae and phytoplankton indicate that nutrients were the prime limiting factor for sea-ice algal productivity. The estimated spring primary production of about 1–2 g C m⁻² of sea-ice algae on the shelves requires the use of substantial nutrient reservoirs from the water column.     

Numerical simulations of wave–current flow in an ocean basin

Wave–current flow is a phenomenon that is present in many practical engineering situations. Over the past several decades, this type of flow has been increasingly investigated under controlled laboratory conditions. This paper presents a numerical study of wave–current flow in the ocean basin of the LabOceano (COPPE/UFRJ). A homogeneous multiphase model based on the RANS equations and the k–ɛ turbulence model implemented in ANSYS-CFX code were used. A cross section of the ocean basin was represented. A regular wave with a height of 0.08 m and a period of 1.80 s (i.e., a wave steepness of H/L = 0.016), propagating on favourable currents, was simulated. The behaviour of the free surface elevation over time and the streamlines along the basin for wave and wave–current flows were presented. The numerical results were compared to the non-viscous theory given by the Rayleigh equation applied to the problem of wave–current interaction. Good agreement was found between the wave length estimated by the numerical results and the analytical solutions, with a deviation of less than 2%.     

Wave forces and moments on an intake well

A sea water intake well of size 20 m diameter and 15.5 m height in a water depth of 9.8 m is proposed north of the Visakhapatnam Port for a project to extract magnesia from sea water. A 1:25 scale model of the intake well was tested in the wave basin of the Ocean Engineering Centre, Indian Institute of Technology, Madras to measure the wave forces and moments on the intake well and the variation of water levels inside and outside the well. Accordingly, an intake well model of 0.8 m diameter and 0.62 m height was fabricated and fixed over a false bottom in a wave basin. The well model was subjected to the action of both regular waves for two test conditions, intake well inlet closed during installation and intake well inlet open. The experimental results on wave forces and moments were compared with the results of the Linear Diffraction Theory. The water level inside the well was measured to determine the submergence of suction pipes of pumps and location of the inlet opening of the intake well. The wave crest elevation in front of the well was also measured in order to fix the deck level of the well so as to avoid water overspill onto the deck. The salient results of the present study are presented and discussed in this paper.     

Abundance,biomass and composition of the sea ice biota of the Greenland Sea pack ice

During two cruises to the Greenland Sea, we studied the abundance and biomass of the sea ice biota in summer and late autumn. The mean calculated biomass of the sympagic community was 0.2 g C m⁻² ice. Algae contributed on average 43% to total biomass, followed by bacteria (31%), heterotrophic flagellates (20%), and meiofauna (4%). Diatoms were the main primary producers (60% of total algal biomass), but flagellated cells contributed significantly to the algal biomass. Among the meiofauna, ciliates, nematodes, acoel turbellarians and crustaceans were dominant. Calculated potential ingestion rates of meiofauna (0.6 g C m⁻² (120 d)⁻¹) are on the same order of magnitude as annual primary production estimates for Arctic multi-year sea ice. We therefore assume that grazing can control biomass accumulation of primary producers inside the sea ice.     

The near surface hydrography beneath the Odden ice tongue

As part of the European Subpolar Ocean Programme (ESOP), the German research icebreaker Polarstern worked in the Greenland Sea in the late winter of 1993. Whilst on passage, the ship encountered a severe winter storm with winds consistently above 20 m s⁻¹ coupled to air temperatures of below −10°C. The underway sensors revealed heat fluxes of greater than 700 W m⁻² across most of the Nordic Basin, peaking at greater than 1200 W m⁻² when the ship crossed the cold, fresh water of the Jan Mayen Current. This large heat flux coupled to the unique hydrographic conditions present in the Jan Mayen Current allowed sea-ice generation in the form of frazil ice at a rate of 28 cm d⁻¹. This frazil ice then developed into pancake ice. Measurements also were made in the late winter beneath this pancake ice in two remnants of the Odden. In the Jan Mayen Current, hydrographic conditions are such that the ice can exist for a long period of time before eventually decaying due to short-wave radiation at the surface. Towards the centre of the Greenland Sea, hydrographic measurements reveal that the ice is more transient and decays four times more rapidly than ice in the Jan Mayen Current. We discuss the development of the Odden ice tongue in light of these results and add evidence to the argument that the eventual fate of the water stored in the ice is important and could be a relevant factor in the formation of Greenland Sea Deep Water.     

Offshore wind farm impacts on surface waves and circulation in Eastern Lake Ontario

A coupled wave and hydrodynamic model was applied to the Kingston Basin of eastern Lake Ontario, a region with bathymetric variability due to channels and shoals, to assess the potential impacts on surface waves and wind-driven circulation of an offshore wind farm. The model was used to simulate a series of storm events with time-varying wind forcing and validated against wave, current and water level observations. The wind farm was simulated by adding semi-permeable structures in the surface wave model to represent the turbine monopiles, and by adding an energy loss term to the fluid momentum equations in the hydrodynamic model to represent the added drag of the monopiles on the flow. The results suggest that the wind farm would have a small influence on waves and circulation throughout the wind farm area, with spatial variability due to focussing of wave energy and re-direction of the flow. Overall, the results indicate that the wave height in coastal areas will be minimally affected with changes in significant wave height predicted to be < 3%. Larger changes to the strength of circulation occur inside the wind farm region with localized changes in current magnitude of up to 8 cm s^− 1. The results of this study may help to understand the impacts of future offshore wind farms and other offshore structures in the Great Lakes.     

Scale of temperature variability in the maritime Antarctic intertidal zone

The Antarctic Peninsula is currently considered as one of the fastest changing regions on Earth yet temperature variability in some of its environments and habitats is not well-documented. Given the increased glacier retreat, summer melts, sea level rise and ozone losses the intertidal zone is likely to be one of the most rapidly altering of environments but also one of the least investigated in polar waters. This study aims to quantify summer temperature variability in some habitats of the intertidal zone at King George Island. Three transects were selected across tidal flat. Four temperature loggers were deployed at each of them from extreme low water spring tide level to extreme high water spring tide level between 07.12.2010 and 18.03.2011. All the loggers were deployed at the rocky substratum. The temperature range across the study tidal flat was between − 2.26 °C and + 21.18 °C. The average (summer) temperature obtained from 12 loggers varied from + 1.89 to + 3.26 °C. In all the three transects average temperature increased with tidal height. Much higher temperature variability was recorded at higher than at lower tide locations. Differences in temperature between the three study transects existed. Results obtained from the studied tidal flat show that several factors combined altogether, including: water movement by tidal forces, wave action, air temperature, sun light intensity, shore lithology and the presence of ice and snow in the area, seem to influence its temperature.     

Wave–current interaction in a river and wave dominant estuary: A seasonal contrast

The dynamic feature of the Modaomen Estuary (ME) in the Pearl River Delta in southern China has been the subject of extensive research. In previous studies, wave–current interaction (WCI) was often neglected due to its complexity. This study uses a coupled hydrodynamic module TELEMAC-2D and wave propagation module TOMAWAC in the TELEMAC-Mascaret modeling system to quantify the effects of WCI on the hydrodynamics in the ME. The coupled wave and current modeling system was well validated against the field measurements at selected locations. The model results show that WCI varies with the seasonal change in runoff in the ME. The effect of waves on the currents is insignificant during the wet season with a current change of no more than 0.07 m/s; but, in contrast, the currents have a noticeable effect on waves. However, during the dry season, the interactions of waves and currents on each other are found to be equally significant. When wave model and current model are coupled, the velocity could increase up to a maximum of 0.30 m/s and decrease up to a maximum of 0.17 m/s. WCI is greatly affected by the propagation directions of wave and current in both seasons. Generally, wave height decreases and current increases for a following wave and current; wave height increases and current decreases for an opposing wave and current. The effects of waves on currents change with the tide. Changes are larger during neap tide than during spring tide, and stronger during ebb tide than during flood tide.