Damping of Regular Waves in Model Ice

2020 ◽  
Author(s):  
Moritz C. N. Hartmann ◽  
R. U. Franz von Bock und Polach ◽  
Marco Klein
Keyword(s):  
Dispersion Relation ◽  
Water Waves ◽  
Wave Amplitude ◽  
Wave Length ◽  
Open Water ◽  
Angular Frequency ◽  
Wave Number ◽  
Regular Waves ◽  
Incident Waves ◽  
The Waves

Abstract Wave characteristics change significantly when the waves propagate in a solid ice field. The damping of the incident waves due to the presence of the ice sheet has a significant impact on the modification of wave propagation and dispersion. In this study the interaction of waves with solid ice are investigated by means of model tests. The objective of the study is to measure wave and ice characteristics and analyze the data regarding wave damping and the change of wave parameters in model ice. The experiments were performed in the ice tank of the Hamburg ship model basin (HSVA) with a set of regular waves with varying wave number and steepness. The surface elevation of the waves is recorded by acoustic and motion capturing measurement devices. By comparing the measurements of the incident open water waves with the waves in ice, the change in terms of wave amplitude and dispersion due to the presence of ice is analyzed. It is shown that once the waves travels through the ice the angular frequency remains unchanged while the wave amplitude exponentially decays, with an increasing decay coefficient at smaller wave length. Furthermore, the dispersion relation in ice, represented by the measured angular frequency and wave number, is consistent with the theoretical dispersion relation.

Magnetic Excitations in Locally Non-Equilibrium Media

2012 ◽  
Vol 190 ◽  
pp. 19-22
Author(s):  
A. Kabychenkov
Keyword(s):  
Dispersion Relation ◽  
Vector Potential ◽  
Energy Gap ◽  
Wave Number ◽  
Magnetic Vector Potential ◽  
Magnetic Vector ◽  
Equilibrium Fluctuations ◽  
The Waves ◽  
Number Relation ◽  
Non Equilibrium

The motion equation for magnetization in locally non-equilibrium media is derived. It is shown that in non-ordered media locally non-equilibrium excitations have peculiarities. There exist coupled waves of the magnetization and magnetic vector potential. Dispersion relation of the waves have frequencies corresponding to undamped waves or constant-phase damped waves and frequencies corresponding to change of real and imaginary parts of the wave number relation. Spectrum of the non-equilibrium fluctuations exhibits some pair of spin-electromagnetic modes without energy gap and electromagnetic-spin modes with energy gap branches.

Short-life mode of electrostatic electroncyclotron harmonic waves

1972 ◽  
Vol 8 (2) ◽  
pp. 183-196 ◽  
Author(s):  
Hiroshi Oya
Keyword(s):  
Angular Frequency ◽  
Wave Number ◽  
Harmonic Waves ◽  
Magnetic Field Direction ◽  
Short Life ◽  
Oblique Propagation ◽  
Dipole Excitation ◽  
Short Dipole ◽  
Life Mode ◽  
The Waves

Dispersion curves of electrostatic electron cyclotron harmonic waves with a phase exp {i(k. r – ωt)}, where ω and k are the angular frequency and wave vector, respectively, are calculated numerically for a case of real ω and complex k that is pertinent for a case of pulsed short dipole excitation of plasma waves. Oblique propagation with respect to the ambient magnetic field direction is considered. There are positive κi and negative κi modes, where k is the imaginary part of the wave number κ = ∣κ∣ in the solutions. The energy propagates in opposite directions in the two modes, and the waves are always subjected to thermal damping. The positive κi mode usually indicates a large κi value (i.e. a large attentuation rate); and it is here called the ‘short-life’ mode.

scholarly journals SUBHARMONIC GENERATION OF TRANSVERSE OSCILLATIONS INDUCED BY INCIDENT REGULAR WAVES

2012 ◽  
Vol 1 (33) ◽  
pp. 11 ◽  
Author(s):  
Gang Wang ◽  
Jin-Hai Zheng
Keyword(s):  
Numerical Investigation ◽  
Incident Wave ◽  
Growth Rates ◽  
Wave Amplitude ◽  
Threshold Value ◽  
Steep Slope ◽  
Regular Waves ◽  
Constant Slope ◽  
Incident Waves ◽  
Transverse Oscillations

It is generally accepted that there are transverse oscillation, which are concentrated and confined to the backwall and decay asymptotically offshore, existed in the harbor of constant slope, however, whether these oscillations can be induced by the normally incident waves is not clear. This numerical investigation aims at providing the subharmonic generations of transverse oscillations within the harbor of a plane slope by waves normally impacting on. For the harbor of perfectly plane slopes, the subharmonic transverse oscillations are small on the mild and moderate slopes but evident on the steep slope. This instability can take place only if the incident wave amplitude exceeds a threshold value, and transverse oscillations can even grow up to a larger value than that of longitudinal oscillations. The magnitudes of transverse oscillations are approximately the same, only their growth rates are affected by the incident wave amplitude.

ON THE PROPAGATION OF RAYLEIGH WAVES ON THE SURFACE OF A VISCO‐ELASTIC SOLID

Geophysics ◽  
1953 ◽  
Vol 18 (1) ◽  
pp. 70-74 ◽  
Author(s):  
C. W. Horton
Keyword(s):  
Rayleigh Waves ◽  
Dimensionless Parameter ◽  
Attenuation Factor ◽  
Wave Length ◽  
Elastic Solid ◽  
Angular Frequency ◽  
Elastic Parameters ◽  
Lissajous Figure ◽  
The Waves ◽  
Horizontal Displacements

The propagation of Rayleigh waves over the surface of a visco‐elastic solid is examined. It is shown that for a Poisson solid (λ=μ), the behavior of the waves can be characterized by a dimensionless parameter δ=ωη/μ which is less than 0.1 for the frequencies and elastic parameters of interest in geophysics. In this expression ω=angular frequency, μ=shear modulus, η=viscosity. For small values of δ it is possible to modify the usual analysis of Rayleigh waves and obtain the new characteristics without much difficulty. It is shown that the motion of a particle on the earth’s surface is changed from an ellipse to a Lissajous’ figure and that the phase angle between the vertical and horizontal displacements is changed from [Formula: see text] to [Formula: see text] radians. The surface wave has an attenuation factor of [Formula: see text] where [Formula: see text] is the wave length of the Rayleigh wave in the absence of internal friction.

scholarly journals WATER-WAVES SCATTERING BY PERMEABLE BOTTOM IN TWO-LAYER FLUID IN THE PRESENCE OF SURFACE TENSION

2017 ◽  
Vol 22 (6) ◽  
pp. 827-851 ◽  
Author(s):  
Srikumar Panda ◽  
Subash C. Martha
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Reflection And Transmission Coefficients ◽  
Wave Number ◽  
Physical Parameters ◽  
Fluid System ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Linearized Theory ◽  
Incident Waves

In the present paper, reflection and transmission phenomena of water waves due to undulating permeable bottom in a two-layer fluid system are investigated using two-dimensional linearized theory. The effect of surface tension on the free surface is included in this work. In two-layer fluid system, there exist waves with two different wave numbers (modes). When a wave of a particular wave number encounters the undulating bottom, reflection and transmission phenomena occur in both the layers. The reflection and transmission coefficients in both layers due to incident waves of both modes are analyzed with the aid of perturbation analysis along with Fourier transform technique. It is found that these coefficients are obtained in terms of integrals which depend on the shape function of the undulating bottom. Two different kinds of undulating bottoms are considered to determine these coefficients. For a particular undulating bottom, namely sinusoidal bottom undulation the effect of various physical parameters such as number of ripples, surface tension and porous effect parameters are demonstrated graphically. The study further elaborates the energy balance relations associated with the reflection and transmission coefficients to ascertain the correctness of all the computed results.

scholarly journals TRANSMISSION OF REGULAR WAVES PAST FLOATING PLATES

1974 ◽  
Vol 1 (14) ◽  
pp. 112
Author(s):  
Uygur Sendil ◽  
W.H. Graf
Keyword(s):  
Water Depth ◽  
Wave Length ◽  
Wave Theory ◽  
Finite Amplitude ◽  
Linear Wave ◽  
Regular Waves ◽  
Transmission Coefficients ◽  
Wave Flume ◽  
Wave Heights ◽  
Incident Waves

Theoretical solutions for the transmission beyond and reflection of waves from fixed and floating plates are based upon linear wave theory, as put forth by John (1949), and Stoker (1957), according to which the flow is irrotational, the fluid is incompressible and frictionless, and the waves are of small amplitude. The resulting theoretical relations are rather complicated, and furthermore, it is assumed that the water depth is very small in comparison to the wave length. Wave transmissions beyond floating horizontal plates are studied in a laboratory wave flume. Regular (harmonic) waves of different heights and periods are generated. The experiments are carried out over a range of wave heights from 0.21 to 8.17 cm (0.007 to 0.268 ft), and wave periods from 0.60 to 4.00 seconds in water depth of 15.2, 30.5, and 45.7 cm (0.5, 1.0 and 1.5 ft). Floating plates of 61, 91 and 122 cm (2, 3 and 4 ft) long were used. From the analyses of regular waves it was found that: (1) the transmission coefficients, H /H , obtained from the experiments are usually less than those obtained from the theory. This is due to the energy dissipation by the plate, which is not considered in the theory. (2) John's (1949) theory predicts the transmission coefficients, H /H , reasonably well for a floating plywood plate, moored to the bottom and under the action of non-breaking incident waves of finite amplitude. (3) a floating plate is less effective in damping the incident waves than a fixed plate of the same length.

scholarly journals Porosity Effects on the Dispersion Relation of Water Waves through Dense Array of Vertical Cylinders

2020 ◽  
Vol 8 (12) ◽  
pp. 960
Author(s):  
Joffrey Jamain ◽  
Julien Touboul ◽  
Vincent Rey ◽  
Kostas Belibassakis
Keyword(s):  
Dispersion Relation ◽  
Water Waves ◽  
Environmental Flows ◽  
Numerical Study ◽  
Wave Number ◽  
Coastal Vegetation ◽  
The Finite Element Method ◽  
Dense Array ◽  
Wide Range ◽  
Vertical Cylinders

There is growing interest for water-wave flows through arrangements of cylinders with application to the performance of porous marine structures and environmental flows in coastal vegetation. For specific few cases experimental data are available in the literature concerning the modification of the dispersion equation for waves through a dense array of vertical cylinders. This paper presents a numerical study of the porosity effects on the dispersion relation of water waves through such configurations. To this aim, the sloshing problem in a tank full of vertical cylinders intersecting the free surface is studied using the finite element method, and the influence of the porosity on the wave number is quantified. On the basis of numerical results, a new modification of a dispersion relation for porous medium is suggested based on a wide range of collected data. Moreover, the domain of validity of this new dispersion relation is examined considering the number of cylinders and the extrapolation to the infinite medium.

Analysis of Hydrodynamic Resonant Effects in Side-by-Side Configuration

2014 ◽  
Author(s):  
Pasquale Dinoi ◽  
Rafael A. Watai ◽  
Hugo Ramos-Castro ◽  
Jesus Gómez-Goñi ◽  
Felipe Ruggeri ◽  
...  
Keyword(s):  
Time Domain ◽  
Wave Amplitude ◽  
Numerical Models ◽  
Vertical Plane ◽  
Damping Factor ◽  
Regular Waves ◽  
Resonant Behavior ◽  
Response Amplitude Operators ◽  
The Time Domain ◽  
The Waves

Seakeeping behavior of a multibody system in side-by-side configuration in head sea condition is discussed in this paper. The system, which can be assimilated to a FLNG and LNG carrier during an offloading operation is composed of a barge and a prismatic geosim with two gap values. Seakeeping tests in regular waves have been performed in the model basin of CEHINAV-Technical University of Madrid (UPM). The movements for the geosim were restricted to the surge, heave and pitch motions (on the vertical plane), whereas the barge was kept fixed. In this way the gap remained constant during the tests. Numerical modeling has been undertaken using WAMIT and an in-house time-domain Rankine Panel Method (TDRPM). Response amplitude operators in terms of movements and wave amplitude in the gap obtained from seakeeping test and numerical models are documented in the paper, illustrating the limitation of the numerical codes regarding the modeling of this hydrodynamic problem. Numerical results indicate a resonant behavior of the waves in the gap for a range of frequencies, with amplitudes much higher than those observed during the tests. Due to the small distances considered in the experiments, these resonant waves are related to longitudinal wave modes in the gap. In order to overcome this problem, a procedure for introducing an external damping factor that attenuates the wave amplitude along the gap in the time-domain RPM is evaluated based on the experimental data.

The effect of surface tension on the waves produced by a heaving circular cylinder

1968 ◽  
Vol 64 (3) ◽  
pp. 833-847 ◽  
Author(s):  
D. V. Evans
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Circular Cylinder ◽  
Water Waves ◽  
Wave Amplitude ◽  
Velocity Potential ◽  
Linearized Theory ◽  
The Waves ◽  
Energy Argument ◽  
Effect Of Surface

AbstractIn this paper the effect of surface tension on water waves is considered. The usual assumptions of the linearized theory are made. A uniqueness theorem is derived for the waves at infinity for a general class of bounded two-dimensional obstacles in a free surface by means of an energy argument. It is shown how the wave amplitude at infinity depends on the prescribed angle at which the free surface meets the normal to the obstacle. The particular case of a heaving half-immersed circular cylinder is considered in detail, and an expression obtained for the velocity potential in terms of a convergent infinite series, the coefficients of which may be computed.

scholarly journals WIND-GENERATED CURRENT AND PHASE SPEED OF WIND WAVES

1972 ◽  
Vol 1 (13) ◽  
pp. 26
Author(s):  
Omar H. Shemdin
Keyword(s):  
Wind Waves ◽  
Wave Length ◽  
Phase Speed ◽  
Shear Velocity ◽  
Wave Number ◽  
Coherent Signals ◽  
Number Range ◽  
Wave Number Range ◽  
The Waves ◽  
Measured Phase

Measurements of drift were made in a wind and wave facility at different elevations below the mean water level. The drift profiles were obtained for reference wind speeds, Ur = 3.1, 5.7 and 9.6 m/sec. The measurement technique involved tracing the movement of small paper discs which were soaked in water to become neutrally buoyant at the elevation of release. A logarithmic drift profile is proposed. The water shear velocity, U*w, predicts a surface stress, TS = pw U*S, in agreement with that obtained from the wind shear velocity, Ts = Pa U*li where pa and pw refer to air and water densities, respectively. The influence of wind on phase speeds of waves was investigated by solving the first order perturbation problem of the coupled shear flows in air and water. The air velocity profile was described by a logarithmic distribution and the drift profile was described by the proposed drift profile. Adequate agreement is found between the calculated and measured phase speed using Doppler radar in the wave number range 1.9 - 10 cm-1. In the wave number range 0.05 - 0.5 cm-1, measurements of phase speeds were obtained by using two wave gages. The waves were mechanically generated without wind and the wave gages were spaced to obtain coherent signals. The wind was then allowed to blow over the waves and the distance between wave gages was increased to maintain coherence. The wave length and frequency were obtained from the distance between the gages and from the generator frequency, respectively. The measured phase speeds were found to increase with wind speed consistent with theoretical computations.

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