On the distortion of turbulence by a progressive surface wave

A rapid-distortion model is developed to investigate the interaction of weak turbulence with a monochromatic irrotational surface water wave. The model is applicable when the orbital velocity of the wave is larger than the turbulence intensity, and when the slope of the wave is sufficiently high that the straining of the turbulence by the wave dominates over the straining of the turbulence by itself. The turbulence suffers two distortions. Firstly, vorticity in the turbulence is modulated by the wave orbital motions, which leads to the streamwise Reynolds stress attaining maxima at the wave crests and minima at the wave troughs; the Reynolds stress normal to the free surface develops minima at the wave crests and maxima at the troughs. Secondly, over several wave cycles the Stokes drift associated with the wave tilts vertical vorticity into the horizontal direction, subsequently stretching it into elongated streamwise vortices, which come to dominate the flow. These results are shown to be strikingly different from turbulence distorted by a mean shear flow, when `streaky structures' of high and low streamwise velocity fluctuations develop. It is shown that, in the case of distortion by a mean shear flow, the tendency for the mean shear to produce streamwise vortices by distortion of the turbulent vorticity is largely cancelled by a distortion of the mean vorticity by the turbulent fluctuations. This latter process is absent in distortion by Stokes drift, since there is then no mean vorticity. The components of the Reynolds stress and the integral length scales computed from turbulence distorted by Stokes drift show the same behaviour as in the simulations of Langmuir turbulence reported by McWilliams, Sullivan & Moeng (1997). Hence we suggest that turbulent vorticity in the upper ocean, such as produced by breaking waves, may help to provide the initial seeds for Langmuir circulations, thereby complementing the shear-flow instability mechanism developed by Craik & Leibovich (1976). The tilting of the vertical vorticity into the horizontal by the Stokes drift tends also to produce a shear stress that does work against the mean straining associated with the wave orbital motions. The turbulent kinetic energy then increases at the expense of energy in the wave. Hence the wave decays. An expression for the wave attenuation rate is obtained by scaling the equation for the wave energy, and is found to be broadly consistent with available laboratory data.

Self-consistent wave-particle interactions in dispersive scale long-period field-line-resonances

Using 1D Vlasov drift-kinetic computer simulations, it is shown that electron trapping in long period standing shear Alfven waves (SAWs) provides an efficient energy sink for wave energy that is much more effective than Landau damping. It is also suggested that the plasma environment of low altitude auroral-zone geomagnetic field lines is more suited to electron acceleration by inertial or kinetic scale Alfven waves. This is due to the self-consistent response of the electron distribution function to SAWs, which must accommodate the low altitude large-scale current system in standing waves. We characterize these effects in terms of the relative magnitude of the wave phase and electron thermal velocities. While particle trapping is shown to be significant across a wide range of plasma temperatures and wave frequencies, we find that electron beam formation in long period waves is more effective in relatively cold plasma.

Optimising power take-off of an oscillating wave surge converter using high fidelity numerical simulations

Oscillating wave surge converters are a promising technology to harvest ocean wave energy in the near shore region. Although research has been going on for many years, the characteristics of the wave action on the structure and especially the phase relation between the driving force and wave quantities like velocity or surface elevation have not been investigated in detail. The main reason for this is the lack of suitable methods. Experimental investigations using tank tests do not give direct access to overall hydrodynamic loads, only damping torque of a power take off system can be measured directly. Non-linear computational fluid dynamics methods have only recently been applied in the research of this type of devices. This paper presents a new metric named wave torque, which is the total hydrodynamic torque minus the still water pitch stiffness at any given angle of rotation. Changes in characteristics of that metric over a wave cycle and for different power take off settings are investigated using computational fluid dynamics methods. Firstly, it is shown that linearised methods cannot predict optimum damping in typical operating states of OWSCs. We then present phase relationships between main kinetic parameters for different damping levels. Although the flap seems to operate close to resonance, as predicted by linear theory, no obvious condition defining optimum damping is found.

Penetration of hydromagnetic energy deep into the magnetosphere

Magnetometer data, acquired on spacecraft and simultaneously at high and low latitudes on the ground, are compared in order to study the propagation characteristics of hydromagnetic energy deep into the magnetosphere. Single events provide evidence that wave energy at L ∼ 3 can at times be only one order of magnitude lower than at L ∼ 13. In addition, statistical analyses of the H-component groundbased data obtained during local daytime hours of 17 July-3 August 1985 show that wave amplitudes at L ∼ 3 are generally 10-30 times lower than at L ∼ 13. The L-dependence of near-equator magnetic field fluctuations measured on ISEE-2 show a sharp drop in energy near the magnetopause and a more gradual fall-off of energy deeper inside the magnetosphere. Such high levels of wave power deep in the magnetosphere have not been quantitatively understood previously. Our initial attempt is to calculate the decay length of an evanescent wave generated at a thick magnetopause boundary. Numerical calculations show that fast magnetosonic modes (called magnetopause and inner mode) can be generated under very restrictive conditions for the field and plasma parameters. These fast compressional modes may have their energy reduced by only one order of magnitude over a penetration depth of about 8RE. More realistic numerical simulations need to be carried out to see whether better agreement with the data can be attained.

Coupled electro-mechanical response of an electroactive polymer cantilever structure and its application in energy harvesting

Ionic polymer-metal composites (IPMC), piezoelectric polymer composites and nematic elastomer composites are materials, which exhibit characteristics of both sensors and actuators. Large deformation and curvature are observed in these systems when electric potential is applied. Effects of geometric non-linearity due to the chargeinduced motion in these materials are poorly understood. In this paper, a coupled model for understanding the behavior of an ionic polymer beam undergoing large deformation and large curvature is presented. Maxwell's equations and charge transport equations are considered which couple the distribution of the ion concentration and the pressure gradient along length of a cantilever beam with interdigital electrodes. A nonlinear constitutive model is derived accounting for the visco-elasto-plastic behavior of these polymers and based on the hypothesis that the presence of electrical charge stretches/contracts bonds, which give rise to electrical field dependent softening/hardening. Polymer chain orientation in statistical sense plays a role on such softening or hardening. Elementary beam kinematics with large curvature is considered. A model for understanding the deformation due to electrostatic repulsion between asymmetrical charge distributions across the cross-sections is presented. Experimental evidence that Silver(Ag) nanoparticle coated IPMCs can be used for energy harvesting is reported. An IPMC strip is vibrated in different environments and the electric power against a resistive load is measured. The electrical power generated was observed to vary with the environment with maximum power being generated when the strip is in wet state. IPMC based energy harvesting systems have potential applications in tidal wave energy harvesting, residual environmental energy harvesting to power MEMS and NEMS devices.

WEMo (Wave Exposure Model): Formulation, Procedures and Validation

This report describes the working of National Centers for Coastal Ocean Service (NCCOS) Wave Exposure Model (WEMo) capable of predicting the exposure of a site in estuarine and closed water to local wind generated waves. WEMo works in two different modes: the Representative Wave Energy (RWE) mode calculates the exposure using physical parameters like wave energy and wave height, while the Relative Exposure Index (REI) empirically calculates exposure as a unitless index. Detailed working of the model in both modes and their procedures are described along with a few sample runs. WEMo model output in RWE mode (wave height and wave energy) is compared against data collected from wave sensors near Harkers Island, North Carolina for validation purposes. Computed results agreed well with the wave sensors data indicating that WEMo can be an effective tool in predicting local wave energy in closed estuarine environments. (PDF contains 31 pages)

Wave Sensor Technologies, St Petersburg, Florida, March 7-9, 2007: workshop proceedings

The Alliance for Coastal Technologies (ACT) convened a workshop on "Wave Sensor Technologies" in St. Petersburg, Florida on March 7-9, 2007, hosted by the University of South Florida (USF) College of Marine Science, an ACT partner institution. The primary objectives of this workshop were to: 1) define the present state of wave measurement technologies, 2) identify the major impediments to their advancement, and 3) make strategic recommendations for future development and on the necessary steps to integrate wave measurement sensors into operational coastal ocean observing systems. The participants were from various sectors, including research scientists, technology developers and industry providers, and technology users, such as operational coastal managers and coastal decision makers. Waves consistently are ranked as a critical variable for numerous coastal issues, from maritime transportation to beach erosion to habitat restoration. For the purposes of this workshop, the participants focused on measuring "wind waves" (i.e., waves on the water surface, generated by the wind, restored by gravity and existing between approximately 3 and 30-second periods), although it was recognized that a wide range of both forced and free waves exist on and in the oceans. Also, whereas the workshop put emphasis on the nearshore coastal component of wave measurements, the participants also stressed the importance of open ocean surface waves measurement. Wave sensor technologies that are presently available for both environments include bottom-mounted pressure gauges, surface following buoys, wave staffs, acoustic Doppler current profilers, and shore-based remote sensing radar instruments. One of the recurring themes of workshop discussions was the dichotomous nature of wave data users. The two separate groups, open ocean wave data users and the nearshore/coastal wave data users, have different requirements. Generally, the user requirements increase both in spatial/temporal resolution and precision as one moves closer to shore. Most ocean going mariners are adequately satisfied with measurements of wave period and height and a wave general direction. However, most coastal and nearshore users require at least the first five Fourier parameters ("First 5"): wave energy and the first four directional Fourier coefficients. Furthermore, wave research scientists would like sensors capable of providing measurements beyond the first four Fourier coefficients. It was debated whether or not high precision wave observations in one location can take the place of a less precise measurement at a different location. This could be accomplished by advancing wave models and using wave models to extend data to nearby areas. However, the consensus was that models are no substitution for in situ wave data.[PDF contains 26 pages]

Wave induced oscillations in harbors of arbitrary shape

Theoretical and experimental studies were conducted to investigate the wave induced oscillations in an arbitrary shaped harbor with constant depth which is connected to the open-sea.

A theory termed the “arbitrary shaped harbor” theory is developed. The solution of the Helmholtz equation, ∇²f + k²f = 0, is formulated as an integral equation; an approximate method is employed to solve the integral equation by converting it to a matrix equation. The final solution is obtained by equating, at the harbor entrance, the wave amplitude and its normal derivative obtained from the solutions for the regions outside and inside the harbor.

Two special theories called the circular harbor theory and the rectangular harbor theory are also developed. The coordinates inside a circular and a rectangular harbor are separable; therefore, the solution for the region inside these harbors is obtained by the method of separation of variables. For the solution in the open-sea region, the same method is used as that employed for the arbitrary shaped harbor theory. The final solution is also obtained by a matching procedure similar to that used for the arbitrary shaped harbor theory. These two special theories provide a useful analytical check on the arbitrary shaped harbor theory.

Experiments were conducted to verify the theories in a wave basin 15 ft wide by 31 ft long with an effective system of wave energy dissipators mounted along the boundary to simulate the open-sea condition.

Four harbors were investigated theoretically and experimentally: circular harbors with a 10° opening and a 60° opening, a rectangular harbor, and a model of the East and West Basins of Long Beach Harbor located in Long Beach, California.

Theoretical solutions for these four harbors using the arbitrary shaped harbor theory were obtained. In addition, the theoretical solutions for the circular harbors and the rectangular harbor using the two special theories were also obtained. In each case, the theories have proven to agree well with the experimental data.

It is found that: (1) the resonant frequencies for a specific harbor are predicted correctly by the theory, although the amplification factors at resonance are somewhat larger than those found experimentally,(2) for the circular harbors, as the width of the harbor entrance increases, the amplification at resonance decreases, but the wave number bandwidth at resonance increases, (3) each peak in the curve of entrance velocity vs incident wave period corresponds to a distinct mode of resonant oscillation inside the harbor, thus the velocity at the harbor entrance appears to be a good indicator for resonance in harbors of complicated shape, (4) the results show that the present theory can be applied with confidence to prototype harbors with relatively uniform depth and reflective interior boundaries.

DEVELOPMENT OF THE WAVE CONTOURING RAFT.

The wave contouring raft system is the outcome of ideas initiated and developed by Sir Christopher Cockerell from 1972 onwards. His objective was to develop a wave energy device which is within the bounds of current technology. It should consist of simple, relatively small units, amenable to quantity production, which would enable a power generating system to be built up and commissioned in stages according to needs and production capability. This thinking led to the investigation of chains of pontoons, hinged together so that the passage of a wave down the chain causes the pontoons to oscillate relative to one another. Energy is extracted from the sea by applying a torque about the hinges to damp the motion. The work has involved extensive model testing in wave tanks and the building and testing of a 3-unit 1/10 scale power generating installation in the Solent, as well as design studies for a full size installation for Atlantic conditions.

Design and commissioning of a 30kw direct drive wave generator

The Trident Energy TE5 is a prototype wave energy converter operating on the principle of having direct-drive linear generators mounted above the water surface, coupled to floats moving under the rig deck. This paper describes aspects of the TE5 design, including its generators, power electronic systems and the conception of its marine structure.

Applications of improved 2-D numerical wave tanks in wave breaking

Song and Banner (2002, henceforth referred to as SB02) used a numerical wave tank (developed by Drimer and Agnon, and further refined by Segre, henceforth referred to as DAS) to study the wave breaking in the deep water, and proposed a dimensionless breaking threshold that based on the behaviour of the wave energy modulation and focusing during the evolution of the wave group. In this paper, two modified DAS models are used to further test the SB02's results, the first one (referred to MDAS1) corrected many integral calculation errors appeared in the DAS code, and the second one (referred to MDAS2) replaced the linear boundary element approximation of DAS into the cubic element on the free surface. Researches show that the results of MDAS1 are the same with those of DAS for the simulations of deep water wave breaking, but, the different values of the wavemaker amplitude, the breaking time and the maximum local average energy growth rate delta(max) for the marginal breaking cases are founded by MDAS2 and MDAS1. However, MDAS2 still satisfies the SB02' s breaking threshold. Furthermore, MDAS1 is utilized to study the marginal breaking case in the intermediate water depth when wave passes over a submerged slope, where the slope is given by 1 : 500, 1 : 300, 1 : 150 or 1 : 100. It is found that the maximum local energy density U increases significantly if the slope becomes steeper, and the delta(max) decreases weakly and increases intensively for the marginal recurrence case and marginal breaking case respectively. SB02's breaking threshold is still valid for the wave passing over a submerged slope gentler than 1 : 100 in the intermediate water depth.

Electrical machine characterisation and analysis for renewable energy applications

There has been an increased use of the Doubly-Fed Induction Machine (DFIM) in ac drive applications in recent times, particularly in the field of renewable energy systems and other high power variable-speed drives. The DFIM is widely regarded as the optimal generation system for both onshore and offshore wind turbines and has also been considered in wave power applications. Wind power generation is the most mature renewable technology. However, wave energy has attracted a large interest recently as the potential for power extraction is very significant. Various wave energy converter (WEC) technologies currently exist with the oscillating water column (OWC) type converter being one of the most advanced. There are fundemental differences in the power profile of the pneumatic power supplied by the OWC WEC and that of a wind turbine and this causes significant challenges in the selection and rating of electrical generators for the OWC devises. The thesis initially aims to provide an accurate per-phase equivalent circuit model of the DFIM by investigating various characterisation testing procedures. Novel testing methodologies based on the series-coupling tests is employed and is found to provide a more accurate representation of the DFIM than the standard IEEE testing methods because the series-coupling tests provide a direct method of determining the equivalent-circuit resistances and inductances of the machine. A second novel method known as the extended short-circuit test is also presented and investigated as an alternative characterisation method. Experimental results on a 1.1 kW DFIM and a 30 kW DFIM utilising the various characterisation procedures are presented in the thesis. The various test methods are analysed and validated through comparison of model predictions and torque-versus-speed curves for each induction machine. Sensitivity analysis is also used as a means of quantifying the effect of experimental error on the results taken from each of the testing procedures and is used to determine the suitability of the test procedures for characterising each of the devices. The series-coupling differential test is demonstrated to be the optimum test. The research then focuses on the OWC WEC and the modelling of this device. A software model is implemented based on data obtained from a scaled prototype device situated at the Irish test site. Test data from the electrical system of the device is analysed and this data is used to develop a performance curve for the air turbine utilised in the WEC. This performance curve was applied in a software model to represent the turbine in the electro-mechanical system and the software results are validated by the measured electrical output data from the prototype test device. Finally, once both the DFIM and OWC WEC power take-off system have been modeled succesfully, an investigation of the application of the DFIM to the OWC WEC model is carried out to determine the electrical machine rating required for the pulsating power derived from OWC WEC device. Thermal analysis of a 30 kW induction machine is carried out using a first-order thermal model. The simulations quantify the limits of operation of the machine and enable thedevelopment of rating requirements for the electrical generation system of the OWC WEC. The thesis can be considered to have three sections. The first section of the thesis contains Chapters 2 and 3 and focuses on the accurate characterisation of the doubly-fed induction machine using various testing procedures. The second section, containing Chapter 4, concentrates on the modelling of the OWC WEC power-takeoff with particular focus on the Wells turbine. Validation of this model is carried out through comparision of simulations and experimental measurements. The third section of the thesis utilises the OWC WEC model from Chapter 4 with a 30 kW induction machine model to determine the optimum device rating for the specified machine. Simulations are carried out to perform thermal analysis of the machine to give a general insight into electrical machine rating for an OWC WEC device.

Energy recovery in individuals with knee osteoarthritis.

OBJECTIVE: Pathological gaits have been shown to limit transfer between potential (PE) and kinetic (KE) energy during walking, which can increase locomotor costs. The purpose of this study was to examine whether energy exchange would be limited in people with knee osteoarthritis (OA). METHODS: Ground reaction forces during walking were collected from 93 subjects with symptomatic knee OA (self-selected and fast speeds) and 13 healthy controls (self-selected speed) and used to calculate their center of mass (COM) movements, PE and KE relationships, and energy recovery during a stride. Correlations and linear regressions examined the impact of energy fluctuation phase and amplitude, walking velocity, body mass, self-reported pain, and radiographic severity on recovery. Paired t-tests were run to compare energy recovery between cohorts. RESULTS: Symptomatic knee OA subjects displayed lower energetic recovery during self-selected walking speeds than healthy controls (P = 0.0018). PE and KE phase relationships explained the majority (66%) of variance in recovery. Recovery had a complex relationship with velocity and its change across speeds was significantly influenced by the self-selected walking speed of each subject. Neither radiographic OA scores nor subject self-reported measures demonstrated any relationship with energy recovery. CONCLUSIONS: Knee OA reduces effective exchange of PE and KE, potentially increasing the muscular work required to control movements of the COM. Gait retraining may return subjects to more normal patterns of energy exchange and allow them to reduce fatigue.

The island-scale internal wave climate of Moorea, French Polynesia

Analysis of five-year records of temperatures and currents collected at Moorea reveal strong internal wave activity at predominantly semi-diurnal frequencies impacting reef slopes at depths 30m around the entire island. Temperature changes of 1.5C to 3C are accompanied by surges of upward and onshore flow and vertical shear in onshore currents. Superimposed on annual temperature changes of approximately 3C, internal wave activity is high from Oct-May and markedly lower from Jun-Sep. The offshore pycnocline is broadly distributed with continuous stratification to at least 500m depth, and a subsurface fluorescence maximum above the strong nutricline at approximately 200m. Minimum buoyancy periods range from 4.8 to 6min, with the maximum density gradient occurring at 50 to 60m depth in summer and deepening to approximately 150 to 200m in winter. The bottom slope angle around all of Moorea is super-critical relative to the vertical stratification angle suggesting that energy propagating into shallow water is only a portion of total incident internal wave energy. Vertical gradient Richardson numbers indicate dominance by density stability relative to current shear with relatively limited diapycnal mixing. Coherence and lagged cross-correlation of semi-diurnal temperature variation indicate complex patterns of inter-site arrival of internal waves and no clear coherence or lagged correlation relationships among island sides. Semi-diurnal and high frequency internal wave packets likely arrive on Moorea from a combination of local and distant sources and may have important impacts for nutrient and particle fluxes in deep reef environments. © 2012 American Geophysical Union. All Rights Reserved.