Wave Spectral Density Research Articles

Analysis and Prediction of Ocean Swell Using Instrumented Buoys

During the period 20-23 September 1990, the remnants of Supertyphoon Flo moved into the central North Pacific Ocean with sustained wind speeds of 28 m/s. The strong wind and large fetch area associated with this storm generated long-period swell that propagated to the west coast of North America. National Data Buoy Center moored-buoy stations, located in a network that ranged from the Gulf of Alaska to the California Bight, provided wave spectral estimates of the swell from this storm. The greatest dominant wave periods measured were approximately 20-25 s, and significant wave heights measured ranged from 3 to 8 m. Wave spectra from an array of three nondirectional buoys are used to find the source of the long-period swell. Directional wave spectra from a heave-pitch-roll buoy are also used to make an independent estimate of the source of the swell. The ridge-line method, using time-frequency contour plots of wave spectral energy density, is used to determine the time of swell generation, which is used with the appropriate surface pressure analysis to infer the swell generation area. The diagnosed sources of the swell are also compared with nowcasts from the Global Spectral Ocean Wave Model of the Fleet Numerical Oceanography Center. A simple method of predicting the propagation of ocean swell, by applying a simple kinematic model of wave propagation to the estimated point and time source, is demonstrated.

A model of beam–plasma discharge in a nonuniform plasma

This paper presents a model of beam–plasma discharge resulting from the quasilinear heating of plasma electrons by Langmuir waves which are excited by beam–plasma interactions. The heating is made possible by the spectral transformation of waves propagating radially from the central beam-occupied region toward the region of lower plasma density. In this paper equations describing the wave spectral density, the distribution function of a high-energy electron tail, and its stationary density profile are obtained and numerically solved; to do so a balanced diffusion and ionization is assumed. The possibility of significant plasma density enhancement in beam–plasma discharge is demonstrated.

Experimentation with various difference schemes for numerical solution of the equation for wind wave spectral density transport

Some test problems are presented designed for qualitative evaluation of the accuracy of the numerical solution for the transport equation. The tests are conducted for three types of difference schemes. The accuracy of numerical solutions for specific evolution cases is evaluated and recommendations are given on the application of the schemes.

Low‐frequency oscillations associated with a polar cap auroral arc: Local spectral density estimation

Enhanced low‐frequency electrostatic oscillations measured from a rocket in the high‐latitude upper F region during the crossing of a polar cap auroral arc are analyzed using local spectral analysis techniques. The turbulent spectra were reduced from measurements made by Langmuir probes whose orientation remained approximately perpendicular to B throughout the flight. The increased low‐frequency turbulence appears at an altitude of 400 km, coincident with electrostatic analyzer indications of increased energetic particle flux. Langmuir probe measurements simultaneously show an increasing temperature and generally decreasing, although irregular, electron density profiles. Electrostatic wave data are analyzed using cross‐correlation analysis to determine phase shift; local wave number approximations provide an estimate of the plasma wave spectral density, S(k, ω). Theoretical expectations for threshold excitation and growth rates of possible instabilities in a two‐component high‐latitude F region ionosphere are investigated. The most likely source for the measured oscillations appears to be excitation of a collisionless electrostatic ion cyclotron mode.

Average electric wave spectra across the plasma sheet and their relation to ion bulk speed

Using 4 months of tail data obtained by the ELF/MF spectrum analyzer of the wave experiment and the three‐dimensional plasma instrument on board the AMPTE/IRM satellite, we have done a statistical survey on the electric wave spectral density in the Earth's plasma sheet. More than 50,000 10‐s‐averaged electric wave spectra were analyzed with respect to differences between their values in the inner and outer central plasma sheet and the plasma sheet boundary layer as well as their dependence on radial distance and ion bulk speed. High‐speed flows are dominated by broadband electrostatic noise with highest spectral densities in the plasma sheet boundary layer, where broadband electrostatic noise also exists during periods of low‐speed flows. The broadband electrostatic noise has a typical spectral index of about −2. During low‐speed flows the spectra in the central plasma sheet show distinct emissions at the electron cyclotron odd half‐harmonic and and upper hybrid frequency. On average, such waves do not appear as distinct emissions in the plasma sheet boundary layer, where they are either absent or masked by the intense broadband electrostatic noise always observed there. Finally, wave intensities during episodes of fast perpendicular flows are higher than those associated with fast parallel flows.

A nonstationary signal simulation model for continuous wave and pulsed Doppler ultrasound

A computer simulation model of the nonstationary Doppler ultrasound signals arising from pulsatile blood flow is presented. The model uses sinusoidal components that are modulated by a power spectral density function that varies over the cardiac cycle. An empirical model consisting of two exponential functions is used to represent both the continuous wave and pulsed Doppler power spectral density for normal carotid arteries. It is shown that the spectrogram speckle patterns of the synthesized Doppler signals compare very well with those clinically recorded.

Closed-loop discrete-time control of a hinged wavemaker

The waves produced by a flap-type wavemaker are modelled using first-order linear wavemaker theory. A simplified closed-loop, discrete-time control system is proposed. This includes with the wavemaker, a proportional plus integral plus derivative (PID) controller comparing the actual wave spectral density with the desired wave spectral density at a single frequency. Discrete-time control theory is used with the time step being sufficiently long that the process reaches steady state response between changes in waveboard motion spectral content. System stability is analyzed for control gain combinations by using two different methods. One method is an extension of the Routh criterion to discrete-time and the other is a state-space eigenvalue approach. The computer simulation and stability analysis provide a means for selecting possible controller gains for use at a specific frequency in an actual wave tank experiment. It is found that integral control is essential in order to achieve a desired response for this long duration timestep application. The variation in discrete timestep duration and in desired spectral density (an indirect indication of frequency variation) provides variation in the constraints on controller gain selection. The controller gain combinations yielding the fastest stable response at a single frequency are for large proportional gain and small integral and derivative gains.

A model of day-time ELF emissions

A quasilinear model of hiss type emissions developed by Sazhin [(1984) Planet. Space Sci. 32, 1263] is extended in order to include deformation of the dayside magnetosphere. Explicit analytical expressions for wave spectral density are obtained and applied for interpretation of some properties of polar chorus emission spectra.

Numerical model for nonstationary shallow water wave spectral transformations

A nonstationary wave transformation model is developed, based upon a finite difference scheme. This model computes spatial and temporal distributions of wave spectral density in shallow water areas with irregular bottom topography. Current knowledge of the dynamic and kinematic processes is incorporated into the model, which include the usual wave refraction and shoaling effects as well as nonlinear dissipative processes (breaking, bottom friction, and a constraint on total energy growth in a depth‐limited situation), and local wind wave generation processes (a combined Phillips‐Miles model). Another important feature of the model is the inclusion of current effects; spatial and temporal current distributions can be introduced as input conditions. Based upon this model, a number of sample computations are given to examine the characteristics of nonstationary wave transformation processes. Finally, one set of wave data collected in the North Sea during the MARSEN Project is used to compare with numerical model computations.

Coordinated measurements of slot region electron precipitation by plasmaspheric wave bands

It has been hypothesized by Lyons et al. that electrons in the slot region are precipitated by cyclotron resonance interactions with the plasmaspheric whistler mode wave bands. The energy spectra and the variations with L shell of the energy bands of the precipitating electrons have been found by Imhof et al. (1974) to be consistent with cyclotron resonance by waves in the few hundred Hz to few kHz range. Now, for the first time, simultaneous measurements have been made of the precipitating electron spectra, the wave frequency distributions, and the plasma density profiles. The electron measurements were performed from the P78‐1 low‐altitude satellite, whereas the wave and plasma density observations were made with the plasma wave experiment on the ISEE 1 spacecraft. Broad bands are often observed in the electron energy spectra with a well‐defined low‐energy cutoff that decreases in energy with increasing L value in a manner consistent with that calculated for first‐order cyclotron resonance with waves at the high‐frequency cutoff of the band. On the basis of the electron spectra from P78‐1 and the plasma densities obtained from the upper hybrid resonance frequencies measured on ISEE 1, the hiss cutoff frequencies are calculated for an assumed first‐order cyclotron resonance interaction and compared with the wave spectral density profiles measured on ISEE. Overall, the plasma wave and the electron measurements are consistent with each other, supporting the earlier hypothesis for the precipitation mechanisms.

Wave induced vibrations of gravity platforms: a stochastic theory

This paper presents a consistent stochastic method to evaluate wave induced vibrations of offshore platforms with special emphasis on gravity type structures. The wavy sea surface is idealized as a stationary and homogeneous stochastic Gaussian (or semi-Gaussian) field. The wave loading processes are treated by applying the concepts of probabilistic potential theory and the stochastic linearization method. The structure is modelled according to the finite element method using boundary spring-dashpot elements to idealize the soil-foundation system. The linearized equations of motion are solved by the frequency response method accounting properly for the temporal and spatial structure of waves as well as for time dependent system function. Numerical results for a 170m high concrete platform are presented including a parametric study of effects due to the shape of the wave spectral density.

Performance Prediction of Floating Drilling Vessels for Various Operating Areas

This paper describes a computer program, composed of weather and drilling models, that was developed to help select floating drilling vessels for specific operating areas and start-up times. With these models, expected performance of different vessels can be simulated and their costs performance of different vessels can be simulated and their costs compared. Introduction Weather conditions vary considerably from area to area and even during the course of a year in a single area. Consequently, drilling vessels that have been used successfully in one region or at one time might not be suitable for different circumstances. Since the day rate for different vessels also may vary, selection of a proper vessel involves both engineering and economic factors. If expected adverse weather or sea ice place time restraints on operations, reaching a desired place time restraints on operations, reaching a desired well depth by a certain date becomes an important consideration in vessel selection. Criteria necessary to establish estimated performance of a floating drilling vessel are moron characteristics, operating limits with respect to sea conditions or vessel motion, well design and expected drillability of the formation with no vessel motion, and weather data for the geographical area. This information is incorporated in drilling and weather models that then are combined to calculate predicted performance of the vessel. Vessel-Motion Characteristics Heave, roll, and pitch data for a specific vessel are determined from model tests in wave basins or from theoretical calculations. These data usually occur as response-amplitude operators (RAO) for regular waves (Figs. 1 through 3). Since sea conditions are not regular, vessel-motion characteristics in irregular seas must be determined. As described by Michel and Minkenberg and Gie, vessel motion in irregular seas (heave, pitch, and roll spectra) can be determined by multiplying wave spectral density by the square of the vessel response for a range of frequencies. The wave spectral density, Sw(w), for a frequency w is given by the Bretschneider spectrum: 4,200 H 2 - 1,050s Ts 4 w 4 Sw(w) = -------------- e, ..............(1)T 4 w5s where Sw(w) = wave spectral density, sq ft-sec forfrequency wHs = significant wave height, ftTs = significant wave period, secondsw = wave frequency, sec-1. With this definition, the area under the spectral curve equals the square of the significant wave height. Fig. 4 illustrates this spectrum for a significant wave height of 17 ft and a significant wave period of 10 seconds. The heave spectrum in Fig. 5 was obtained by multiplying the wave spectral density by the square of the RAO for the corresponding frequency. Z(w) = Sw(w) . RAO 2 (w),...................(2) where Z (w)= heave-spectral density, sq ft-sec forfrequency w. Significant heave, Zs, is obtained by Zs (Hs, Ts) = Z(w) dw,...................(3) JPT P. 1688

The mechanism of the development of wind-wave spectra

The mechanism of the development of wind-waves will be proposed on the basis of the observed wave spectra in the wind tunnels and at Lake Biwa (Imasato, 1976). It consists of two aspects: One is that the air flow over the wind-waves transfers momentum concentratively to the steepest component waves and the other is that the upper limit of the growth of a wave spectral density is given by the ultimate value in the slope spectral density. The first aspect means that the wave field has the “momentum transfer filter” on receiving the momentum from the air flow. Wind-waves in the stage of “sea-waves” receive the necessary amount of momentum by the form drag,e.g. according to the Miles' (1960) inviscid mechanism, through a very narrow frequency region around a dominant spectral peak. On the other hand, wind-waves in the stage of “initial-wavelets” receive it according to the Miles' (1962a) viscous model through a fairly broad frequency region around the peak. The upper limit ofSmax developing according to viscous mechanism is given bySmax=6.40×10−4kmax−2cm2s andSmax=2.03C(fmax)−2cm2s(Smax is the power density of the wave spectral peak with the frequencyfmax,kmax is the wave number corresponding to the frequencyfmax andC is the phase velocity).

Spectral density of ion acoustic plasma turbulence

Plasma wave spectral density has been measured as a function of wavenumber and frequency by a two-step technique: an analog analyzer measures the cross-power spectral density, and then a digital computer performs the spatial Fourier transform.

Replenishment of electrons lost in the south atlantic anomaly by gyroresonant pitch-angle diffusion

Experimental data describing the effect of the South Atlantic anomaly on E⩾ 280 keV electron flux at L = 2 and high B values, are compared to the numerical solution of a pitch-angle diffusion equation with a varying loss cone. The diffusion coefficient needed to explain replenishment of the electrons lost over the anomaly is found to be 3.2 × 10 −2 sec −1 Calculation of the diffusion coefficient due to cyclotron resonant interaction with VLF electro-magnetic waves leads to the conclusion that the observed wave spectral density can yield the needed diffusion coefficient.

Measurement of plasma wave spectral density from the cross-power density spectrum

Determination of the spectral density of plasma waves from the cross-power density spectrum is shown to be simpler than the alternative determination from the cross-correlation function. A device for measuring the cross-power spectral density is described in detail. A model with a bandwidth of 30 MHz has been constructed using integrated circuits, and applied to the study of ion acoustic wave propagation on a plasma positive column. Since it is an analog device, it should be possible to extend the bandwidth for operation into the gigahertz range. Only a fixed delay is required to measure the quadrature component of the cross-power spectral density. These features are in contrast to other correlators and cross-power spectrum analyzers described to date, which are either limited to the low megahertz range, or require a variable delay line.

Excitation of mantle Love waves and definition of mantle wave magnitude

abstract A study is made of the excitation of mantle Love waves of 100 seconds period as a function of magnitude. 153 measurements of Love wave spectral density for earthquakes since 1930 ranging in magnitude from 6.0 to 8.9 are used to determine an excitation curve. The observations were first corrected to a standard distance of 90°. The excitation curve supports earlier results for mantle Rayleigh waves and, for strike-slip motion, an earlier curve for seismic moment versus mantle-wave magnitude. For dip-slip motion, the moments should be multiplied by a factor of about 212. A definition of mantle wave magnitude MM, is set up, and the largest earthquake since 1930 found on this scale is the Alaskan earthquake of March 28, 1964 where MM = 8.9. Other comparably large earthquakes, MM = 8.8, were the Kamchatka earthquake of November 4, 1952 and the Chilean earthquake of May 22, 1960. It is suggested that mantle-wave magnitudes be used as a diagnostic aid in estimating the Tsunami potential of earthquakes.

Some peculiarities of Vavilov-Čerenkov radiation in biaxial crystals

The spectral density of the Vavilov-Cherenkov radiation emitted by charged particles moving in the direction of the biradial of biaxial crystal is calculated. The particles are assumed to move with a velocity ( BETA ) near the critical velocity for Cherenkov radiation ( BETA /sub c/). The dependence of the spectral density on BETA has a sharp edge at BETA = BETA /sub c/. The wave vectors of the Cherenkov radiation at BETA = BETA /sub c/ form a cone that is identical with the cone of conical refraction. As BETA becomes larger than BETA /sub c/, however, this initial cone decomposes into two cones. These properties of the Cherenkov wave vectors and spectral density are concluded to be peculiar to biaxial crystals. (T.F.H.)