scholarly journals Wave energy attenuation in fields of colliding ice floes – Part 1: Discrete-element modelling of dissipation due to ice–water drag

2019 ◽  
Vol 13 (11) ◽  
pp. 2887-2900 ◽  
Author(s):  
Agnieszka Herman ◽  
Sukun Cheng ◽  
Hayley H. Shen
Keyword(s):  
Dispersion Relation ◽  
Wave Energy ◽  
High Frequency ◽  
Water Waves ◽  
Discrete Element ◽  
Unit Surface Area ◽  
Energy Propagation ◽  
Quadratic Drag ◽  
Ice Floes ◽  
Ice Water

Abstract. The energy of water waves propagating through sea ice is attenuated due to non-dissipative (scattering) and dissipative processes. The nature of those processes and their contribution to attenuation depends on wave characteristics and ice properties and is usually difficult (or impossible) to determine from limited observations available. Therefore, many aspects of relevant dissipation mechanisms remain poorly understood. In this work, a discrete-element model (DEM) is used to study one of those mechanisms: dissipation due to ice–water drag. The model consists of two coupled parts, a DEM simulating the surge motion and collisions of ice floes driven by waves and a wave module solving the wave energy transport equation with source terms computed based on phase-averaged DEM results. The wave energy attenuation is analysed analytically for a limiting case of a compact, horizontally confined ice cover. It is shown that the usage of a quadratic drag law leads to non-exponential attenuation of wave amplitude a with distance x, of the form a(x)=1/(αx+1/a0), with the attenuation rate α linearly proportional to the drag coefficient. The dependence of α on wave frequency ω varies with the dispersion relation used. For the open-water (OW) dispersion relation, α∼ω4. For the mass loading dispersion relation, suitable for ice covers composed of small floes, the increase in α with ω is much faster than in the OW case, leading to very fast elimination of high-frequency components from the wave energy spectrum. For elastic-plate dispersion relation, suitable for large floes or continuous ice, α∼ωm within the high-frequency tail, with m close to 2.0–2.5; i.e. dissipation is much slower than in the OW case. The coupled DEM–wave model predicts the existence of two zones: a relatively narrow area of very strong attenuation close to the ice edge, with energetic floe collisions and therefore high instantaneous ice–water velocities, and an inner zone where ice floes are in permanent or semi-permanent contact with each other, with attenuation rates close to those analysed theoretically. Dissipation in the collisional zone increases with an increasing restitution coefficient of the ice and with decreasing floe size. In effect, two factors contribute to strong attenuation in fields of small ice floes: lower wave energy propagation speeds and higher relative ice–water velocities due to larger accelerations of floes with smaller mass and more collisions per unit surface area.

scholarly journals Wave energy attenuation in fields of colliding ice floes. Part A: Discrete-element modelling of dissipation due to ice–water drag

2019 ◽  
Author(s):  
Agnieszka Herman ◽  
Sukun Cheng ◽  
Hayley H. Shen
Keyword(s):  
Dispersion Relation ◽  
Wave Energy ◽  
High Frequency ◽  
Water Waves ◽  
Discrete Element ◽  
Unit Surface Area ◽  
Energy Propagation ◽  
Quadratic Drag ◽  
Ice Floes ◽  
Ice Water

Abstract. The energy of water waves propagating through sea ice is attenuated due to nondissipative (scattering) and dissipative processes. The nature of those processes and their contribution to attenuation depends on wave characteristics and ice properties, and is usually difficult (or impossible) to determine from limited observations available. Therefore, many aspects of relevant dissipation mechanisms remain poorly understood. In this work, a discrete-element model (DEM) is used to study one of those mechanisms: dissipation due to ice-water drag. The model consists of two coupled parts, a DEM simulating the surge motion and collisions of ice floes driven by waves, and a wave module solving the wave energy transport equation with source terms computed based on phase-averaged DEM results. The wave energy attenuation is analyzed analytically for a limiting case of a compact, horizontally confined ice cover. It is shown that the usage of a quadratic drag law leads to nonexponential attenuation of wave amplitude a with distance x, of a form a(x)=1/(α x+1/a0), with the attenuation rate α linearly proportional to the drag coefficient. The dependence of α on wave frequency ω varies with the dispersion relation used: for the open-water (ow) dispersion relation, α~ω4; for mass-loading dispersion relation, suitable for ice covers composed of small floes, the increase of α with ω is much faster than in the ow case, leading to very fast elimination of high-frequency components from the wave energy spectrum; for elastic-plate dispersion relation, suitable for large floes or continuous ice, α~ωm within the high-frequency tail, with m close to 2.0–2.5, i.e., dissipation is much slower than in the ow case. The coupled DEM-wave model predicts the existence of two zones: a relatively narrow area of very strong attenuation close to the ice edge, with energetic floe collisions and therefore high instantaneous ice-water velocities; and an inner zone where ice floes are in (semi)permanent contact with each other, with attenuation rates close to those analyzed theoretically. Dissipation in the collisional zone increases with increasing restitution coefficient of the ice and with decreasing floe size. In effect, two factors contribute to strong attenuation in fields of small ice floes: lower wave energy propagation speeds and higher relative ice--water velocities due to larger accelerations of floes with smaller mass and more collisions per unit surface area.

Ion-cyclotron modes in weakly relativistic plasmas

1994 ◽  
Vol 51 (3) ◽  
pp. 371-379 ◽  
Author(s):  
Chandu Venugopal ◽  
P. J. Kurian ◽  
G. Renuka
Keyword(s):  
Dispersion Relation ◽  
High Frequency ◽  
Low Frequency ◽  
Dispersion Relations ◽  
The Other ◽  
Larmor Radius ◽  
Relativistic Plasmas ◽  
Ion Plasma ◽  
Maxwellian Plasma ◽  
Relativistic Dispersion

We derive a dispersion relation for the perpendicular propagation of ioncyclotron waves around the ion gyrofrequency ω+ in a weaklu relaticistic anisotropic Maxwellian plasma. These waves, with wavelength greater than the ion Larmor radius rL+ (k⊥ rL+ < 1), propagate in a plasma characterized by large ion plasma frequencies (). Using an ordering parameter ε, we separated out two dispersion relations, one of which is independent of the relativistic terms, while the other depends sensitively on them. The solutions of the former dispersion relation yield two modes: a low-frequency (LF) mode with a frequency ω < ω+ and a high-frequency (HF) mode with ω > ω+. The plasma is stable to the propagation of these modes. The latter dispersion relation yields a new LF mode in addition to the modes supported by the non-relativistic dispersion relation. The two LF modes can coalesce to make the plasma unstable. These results are also verified numerically using a standard root solver.

Spatial distribution of high-frequency energy radiation on the fault of the 1995 Hyogo-Ken Nanbu, Japan, earthquake (MW 6.9) on the basis of the seismogram envelope inversion

1999 ◽  
Vol 89 (1) ◽  
pp. 22-35 ◽  
Author(s):  
Hisashi Nakahara ◽  
Haruo Sato ◽  
Masakazu Ohtake ◽  
Takeshi Nishimura
Keyword(s):  
Spatial Distribution ◽  
Wave Energy ◽  
High Frequency ◽  
Fault Plane ◽  
Time Window ◽  
Source Region ◽  
Inversion Method ◽  
S Wave ◽  
Energy Radiation ◽  
Initial Rupture

Abstract We studied the generation and propagation of high-frequency (above 1 Hz) S-wave energy from the 1995 Hyogo-Ken Nanbu (Kobe), Japan, earthquake (MW 6.9) by analyzing seismogram envelopes of the mainshock and aftershocks. We first investigated the propagation characteristics of high-frequency S-wave energy in the heterogeneous lithosphere around the source region. By applying the multiple lapse time window analysis method to aftershock records, we estimated two parameters that quantitatively characterize the heterogeneity of the medium: the total scattering coefficient and the intrinsic absorption of the medium for S waves. Observed envelopes of aftershocks were well reproduced by the envelope Green functions synthesized based on the radiative transfer theory with the obtained parameters. Next, we applied the envelope inversion method to 13 strong-motion records of the mainshock. We divided the mainshock fault plane of 49 × 21 km into 21 subfaults of 7 × 7 km square and estimated the spatial distribution of the high-frequency energy radiation on that plane. The average constant rupture velocity and the duration of energy radiation for each subfault were determined by grid searching to be 3.0 km/sec and 5.0 sec, respectively. Energy radiated from the whole fault plane was estimated as 4.9 × 1014 J for 1 to 2 Hz, 3.3 × 1014 J for 2 to 4 Hz, 1.5 × 1014 J for 4 to 8 Hz, 8.9 × 1012 J for 8 to 16 Hz, and 9.8 × 1014 J in all four frequency bands. We found that strong energy was mainly radiated from three regions on the mainshock fault plane: around the initial rupture point, near the surface at Awaji Island, and a shallow portion beneath Kobe. We interpret that energetic portions were associated with rupture acceleration, a fault surface break, and rupture termination, respectively.

scholarly journals Optimization of HF waves energy source for thermal treatment of building materials

2018 ◽  
Vol 251 ◽  
pp. 04010
Author(s):  
Irina Vorotyntseva
Keyword(s):  
Energy Source ◽  
Wave Energy ◽  
High Frequency ◽  
Energy Exchange ◽  
Building Materials ◽  
Functional Dependencies ◽  
Strength Change ◽  
Wave Heating ◽  
Characteristic Features ◽  
Hf Wave

Building materials processing with the help of HF waves demonstrates a great number of perspective advantages as compared to traditional heating methods. In order to upgrade the technology of HF wave heating there exist a need to optimize the HF waves sources that enable us to consider some characteristic features of the process to a greater extend. To solve the task of optimizing a HF wave energy source we use the methods of the optimal control theory. The optimization has been carried out based on the gradient method. As a result we have found some optimal functional dependencies that describe the laws strength change of an electrostatic and a high-frequency field. Established managements help considerably enhance the efficiency of the energy exchange. The calculations we have carried out show that the chosen method enables an efficient optimization of a HF wave energy source with different restrictions of the governing function.

Stochastic Analysis of a Nonlinear Energy Harvester Model

2014 ◽  
Author(s):  
P. D. Spanos ◽  
A. Richichi ◽  
F. Arena
Keyword(s):  
Dynamic Analysis ◽  
Wave Energy ◽  
Water Waves ◽  
Nonlinear Dynamic Analysis ◽  
Nonlinear Effects ◽  
Wave Energy Converter ◽  
Statistical Linearization ◽  
Energy Converter ◽  
Domain Integration ◽  
Stiffness And Damping

Floating oscillating-bodies are a kind of wave energy converter developed for harvesting the great amount of energy related to water waves (see Falcão [1] for a review). Although the assumptions of small-wave and linear behavior of oscillating system are reasonable for most of the time during which a floating point harvester is in operation, nonlinear effects may be significant in extreme sea states situations. In this paper a nonlinear dynamic analysis of a point harvester wave energy converter is conducted. The model involves a tightly moored single-body floating device; it captures motion in the horizontal and vertical directions. The stiffness and damping forces, being functions of the displacement and velocity components, make the system nonlinear and coupled. For the input forces, the erratic nature of the waves is modeled by a stochastic process. Specifically, wind-generated waves are modeled by means of the JONSWAP spectrum. The method of statistical linearization [2] is used to determine iteratively the effective linear stiffness and damping matrices and response statistics of the system and to proceed to conducting a dynamic analysis of the harvester model. The reliability of the linearization based approach is demonstrated by comparison with time domain integration, Monte Carlo simulation, data. This approach offers the appealing feature of conducting efficiently a variety of parameter studies which can expedite preliminary evaluations, inter alia, of competing design scenarios for the energy converter in a stochastic environmental setting.

Dispersion relation of high-frequency plasma oscillations in Hall thrusters

2008 ◽  
Vol 15 (3) ◽  
pp. 034502 ◽  
Author(s):  
A. Lazurenko ◽  
G. Coduti ◽  
S. Mazouffre ◽  
G. Bonhomme
Keyword(s):  
Dispersion Relation ◽  
High Frequency ◽  
Hall Thrusters ◽  
Plasma Oscillations ◽  
High Frequency Plasma ◽  
Frequency Plasma

High-Frequency Seismic Wave Propagation in Northeastern North America

1990 ◽  
Vol 61 (3-4) ◽  
pp. 193-208 ◽  
Author(s):  
S. E. Hough ◽  
K. H. Jacob ◽  
L. Seeber
Keyword(s):  
North America ◽  
High Frequency ◽  
Characteristic Length ◽  
Body Waves ◽  
Eastern North America ◽  
Western North America ◽  
Energy Propagation ◽  
Length Scales ◽  
Near Surface ◽  
High Frequencies

Abstract A key element in the assessment of seismic hazard is the estimation of how energy propagation from a given earthquake is affected by crustal structure near the receiver and along the more distant propagation path. In this paper, we present data from a variety of sources in eastern North America recorded at epicentral distances of a few to 800 km, and characterize and interpret systematic features. Site effects have been classically considered in terms of amplification either within a sediment-filled valley or from a single topographic feature (Geli et al., 1988). We present evidence of high frequency (5–30 Hz) resonances observed in hard-rock recordings of both body waves and Lg waves, and suggest that site effect should be expanded regionally to include structural and topographic information over sufficiently large areas to include several wavelengths of any features that may interact with seismic waves in the frequency range of interest. A growing body of evidence suggests that ground motions at high frequencies recorded at large epicentral distances in eastern North America are controlled by resonance effects. We hypothesize that a fundamental difference between eastern and western North America spectra stems from a combination of differences in the character of topography and near-surface structure. Active tectonics of western North America gives rise to a complex crust that scatters seismic energy in a random manner and results in very effective attenuation of high frequencies. The older eastern North American crust contains scatterers that are more ordered, with characteristic length scales that give rise to resonance phenomena in the frequency band critical for earthquake hazard. We present preliminary analysis of topographic data from the Adirondack Mountains in New York that demonstrates the existence of characteristic length scales on the order of up to 1–3 kilometers. Features with these length scales will effectively scatter energy at frequencies in the 1 to 10 Hz range.

scholarly journals Pancake sea ice kinematics and dynamics using shipboard stereo video

2019 ◽  
Vol 61 (82) ◽  
pp. 1-11 ◽  
Author(s):  
Madison Smith ◽  
Jim Thomson
Keyword(s):  
Sea Ice ◽  
Energy Loss ◽  
Wave Energy ◽  
Wave Attenuation ◽  
Bulk Wave ◽  
Ocean Turbulence ◽  
Stereo Video ◽  
Ice Floes ◽  
Turbulence Generation

AbstractIn the marginal ice zone, surface waves drive motion of sea ice floes. The motion of floes relative to each other can cause periodic collisions, and drives the formation of pancake sea ice. Additionally, the motion of floes relative to the water results in turbulence generation at the interface between the ice and ocean below. These are important processes for the formation and growth of pancakes, and likely contribute to wave energy loss. Models and laboratory studies have been used to describe these motions, but there have been no in situ observations of relative ice velocities in a natural wave field. Here, we use shipboard stereo video to measure wave motion and relative motion of pancake floes simultaneously. The relative velocities of pancake floes are typically small compared to wave orbital motion (i.e. floes mostly follow the wave orbits). We find that relative velocities are well-captured by existing phase-resolved models, and are only somewhat over-estimated by using bulk wave parameters. Under the conditions observed, estimates of wave energy loss from ice–ocean turbulence are much larger than from pancake collisions. Increased relative pancake floe velocities in steeper wave fields may then result in more wave attenuation by increasing ice–ocean shear.

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