摘要:

Semi‐implicit time integration schemes have been combined with finite element space discretization in developing a numerical scheme for the solution of the classical shallow water equations. The principal advantages of this approach are twofold: first, a highly variable gridding capability that allows selective regions of high resolution to be constructed within the computing domain, and second, the use of large time steps chosen on the basis of accuracy rather than by a Courant‐type restriction on their magnitude. The method will be useful in computing the low‐frequency–long wave motions driven by tides and wind on continental shelves and in marginal seas where higher grid resolution is necessary to describe adequately the nearshore dynamics. Application of the methodology is demonstrated by the calculation of the currents and sea surface heights in a hypothetical shelf domain that is driven by a single consituent deep oce

ISSN:0148-0227    

DOI:10.1029/JC086iC05p04029

年代:1981

数据来源: WILEY

摘要:

Five ground‐based VHF receivers were used to trace paths followed by flashes of lightning. Every lightning flash radiates a succession of radio noise pulses, and three Cartesian coordinates of the positions of pulse sources were determined by measuring the times at which the noise pulses arrived at each of the spaced receivers. Lightning channels were mapped in space and time by locating a large number of radio noise sources for each flash, whose shape and position then became apparent despite the presence of intervening hydrometeors. A center frequency of 253 MHz was chosen for the receivers and their bandwidths were wide enough for time differences to be measured with rms errors of 140 ns. Hence two of the three spatial coordinates of a particular source could be determined to an accuracy of 25 m rms and the vertical coordinate could be found to an accuracy which was typically 140 m rms, but the actual height accuracy depended on source position. Some factors that affect the design of the receivers are discussed and case studies of five cloud flashes are presented. Cloud flashes could be classified into two types according to the rates at which they emitted pulses in the VHF part of the radio spectrum. One class radiated pulses at rates that approximated 103pulses per second when received in bandwidths of 10 MHz. These pulses were often nearly rectangular in form, lasted approximately 1 ms on average, and occurred in synchronism with pulses received at HF and at UHF. The second class emitted much shorter pulses (median durations of 0.2 to 0.4 ms were measured) at higher rates typically 105pulses per second, and pulses were generally not in synchronism with those received at other radio frequencies. Diameters of the channels occupied by radio sources varied from 100 m to several hundred meters, and were enlarged by the extents of the sources themselves. It was possible to measure the principal extents of many individual sources active during low‐pulse‐frequency cloud flashes. Average sizes near 300 m were measured for low‐pulse‐frequency flashes, and sizes near 60 m were estimated for sources active during high‐pulse‐frequency flashes. It was found that pulses originated in regions near streamer tips, and that pulses were associated with initial ionization. First streamers progressed at speeds that ranged from 0.9 × 105m/s to 2.1 × 105m/s except for one extensive, positive flash that moved at 5 × 105m/s for the first few kilometers. We define a positive flash as being one which conducts excess positive charge in the same direction as that in which the streamer progresses. Subsequent discharges along paths that had been ionized previously seldom radiated much noise but noise was radiated by channels that were several tens of milliseconds old, and then we measured streamer speeds that were at least an order of magnitude higher than first streamer speeds. Relatively few cloud flashes were found to have been oriented vertically. Most were horizontal and often consisted of several streamers that extended from a common origin. Measurements of electric field change were used to estimate quantities of charge involved. These estimates were made by adopting various models for the distribution of charge along the known paths, and the quantities were not greatly dependent on the form of the distribution. Most estimates yielded line densities near 10−3C m−1. Only one of the cloud discharges had been a positive flash. Trains of band‐limited noise which lasted for times that ranged approximately from 10 μs to about 1.5 ms were also emitted by lightning flashes of all kinds, but in cloud flashes this type of noise, which was distinctly different from the pulsed emission, occurred more frequently and with longer durations during theJ‐type portions or final stages of cloud flashes. It accompanied streamers which progressed at speeds near 107m/s, often accompaniedKchanges, which were usually delayed after the start of this noise by tens of microseconds, and the streamers that caused the noise were positive streamers, with the single exception of one train which was found to have been due to a negative streamer that formed near the origin of an extensive, positive cloud flash. There was evidence that events that produced this noise sometimes triggered dart leaders and recoil streamers and most sources of this band‐limited noise were located near the origins of the flashes, and streamers which caused the noise served also to discharge the origins but not usually by way of the paths formed by first streamers. The principal results of this work are lis

ISSN:0148-0227    

DOI:10.1029/JC086iC05p04041

年代:1981

数据来源: WILEY

摘要:

The results of a hemispheric experiment to investigate gravity waves with intrinsic periods between 0.5 and 3 hours are presented. Over 200 wave observations were made by using the vertical oscillations of drifting constant‐volume balloons gathered with a pressure sensor, a temperature sensor, and an altimeter. Since these wave observations are 38% of the total sample, the results indicate that these waves are ubiquitous. All observations are made at nearly the same level in the atmosphere (140–170 mbar); at low latitudes the observations are in the tropical upper troposphere and at mid‐ and high latitudes they are in the lower stratosphere. The observed intrinsic frequency, the average amplitudes of the atmospheric pressure perturbation and vertical velocity, the vertical fluxes of wave energy and horizontal momentum, the total wave energy density, the vertical group velocity of the wave, and the wave action density are shown. The distributions of the average amplitudes show a few very large values for both regions. The distributions of vertical energy flux and vertical group velocity indicate that the dominant wave in the lower stratosphere of the mid‐ and high latitude is an evanescent or trapped wave, while in the upper tropical troposphere upward propagating, untrapped internal waves dominate. The distributions of wave action density are very similar for the two regions, while the distributions of intrinsic frequency, total wave energy density, and vertical flux of horizontal momentum are different for the two regions. The balloonborne observing system proved to be extremely good; however, the experimental system could be improved by making in situ measurements of the lapse rate and horizontal wind shear and by including a horizontal accelerometer. Such a completely instrumented system could prove to be very useful in determining how these waves influence the mean flow on a globa

ISSN:0148-0227    

DOI:10.1029/JC086iC05p04072

年代:1981

数据来源: WILEY

摘要:

Acoustic scattering cross sections for medium fluctuations are derived from the funadmental wave equation. Analysis of the effect of a finite scattering volume is made. Fluid velocity fluctuations are shown to produce no backscatter at scattering angle θ = 180° independent of the statistical form of the velocity field and valid for both atomspheric and oceanic cases. Scattering cross sections for the atmospheric and oceanic cases are compared. Temperature fluctuations for the atmospheric case result in a scattering cross section proportional to a cos2θ factor whereas for the oceanic case no such factor arises. Using a cylindrically symmetric form about the vertical direction for temperature fluctuations, explicit expressions for the angular dependence of the scattering cross sections are obtained. These results depend strongly on the parameter α, the ratio of the vertical length scale of the temperature variability to the horizontal length scale. For a typical echo sounder operating at 20 kHz, scattering strengths based on observed one dimensional spectra of temperature microstructure are of order −120 dB if isotropy is assumed (α = 1). For the layered case, where the horizontal scale of the variability is larger than the horizontal dimension of the scattering volume, the same values of variability yield, scattering strengths are of order −70 dB. These results can be applied at other frequencies provided the medium variability spectrum

ISSN:0148-0227    

DOI:10.1029/JC086iC05p04083

年代:1981

数据来源: WILEY

摘要:

Sea‐echo data from three separate narrow‐beam HF radar experiments on the Pacific Ocean are analyzed here by techniques presented in Lipa and Barrick (1980). Only those wave spectral components whose periods exceeded 10 s were included. Close agreement of radar‐deduced wave field parameters with surface observations confirms the validity of the second‐order theoretical solution for the echo Doppler spectrum, upon which this analysis is based. Depending on the particular experiment, a variety of wave parameters are extracted, including rms wave height, mean wave direction, dominant period, angular spread of the wave field, the nondirectional wave height spectrum, and higher Fourier angular coefficients versus wave frequency. The radar‐deduced wave parameters fall within the combined error bounds estimated for the radar and buoy wave observations; consequently, we contend that the primary source of error for radar data is finite sample size. Typical accuracies for specific parameters resulting from observations averaged over a 2‐hour period are ±5% for wave height, ±0.5 s for wave period, and ±7° for wave direction. Hence the utility of HF radars for long‐wave measurements h

ISSN:0148-0227    

DOI:10.1029/JC086iC05p04089

年代:1981

数据来源: WILEY

摘要:

The general characteristics of the energy spectrum for internal gravity waves in the ocean are well known from the large body of recent experimental observations. The theoretical understanding has not developed at the same rate, perhaps due to the limitation of linear or quasi‐linear theories, which can cope only with weak interaction processes and are inadequate for representing the more violent and sporadic wave breaking processes present in nature. A detailed study of energy transfer among two‐dimensional internal gravity modes in a fully nonlinear regime was performed. Wave‐wave interactions and overturning were included in the solutions of a two‐dimensional numerical model, and the results are presented here. A background spectrum of finite amplitude, random internal gravity wave field was generated by a long time integration of a two‐dimensional model with random body forcing. Over this background field, two sets of experiments were performed: spike‐random, where energy at low, medium, and high wave numbers were introduced and integrated in time, and band‐random, where energy was introduced over a band of wave numbers instead of introducing only discrete modes. The results can be summarized as follows. Multiple triad interactions will result in a filling of the energy spectrum when energy is introduced in a particular band of wave numbers. For bands where the energy level is high enough to result in nonlinear time scales of only a few intrinsic periods, wave‐wave interactions (resonant and nonresonant) provide the mechanism for filling the spectrum. The energy transfer becomes more and more rapid with increasing energy, and no universal spectrum appears to result from these processes. As the energy input increases, energy will accumulate in high wave numbers until localized instabilities (over‐turning) occur. From that point on, these high wave numbers will remain at a saturation such that any additional energy input at the saturated band, either directly or via wave‐wave interactions, will result in localized mixing. On the other hand, additional energy input at bands other than the saturated band will result in an increase of low and medium wave band energy (via wave‐wave interactions) until an equilibrium level is achieved. The equilibrium level of any particular band will depend on the high wave number bands being saturated. For instance, any energy above the equilibrium at low wave numbers will produce localized mixing in physical space almost instantaneously. This does not mean that the low wave numbers are saturated, as their energy levels can be much lower than a saturation level. What takes place at or near an equilibrium level is that the contributions from high and low wave numbers result in localized regions in physical space where the criterion for instability is almost met. In fact, this superposition effect means that low and medium wave numbers are far from meeting any breaking criterion when taken individually, yet cannot tolerate any additional input energy when in the presence of a saturated band of high wave numbers. It was found also that the dissipation is approximately constant over the wave numbers and small compared with the large transfer of energy between neighboring waves. However, if bands of waves are considered, very little energy is transferred between neighboring bands above the equilibrium level. Rather, a direct cascade of energy from low to high wave numbers occurs due to localized instabilities which result in overturning, and it is this amount of energy flux which is dissipated by

ISSN:0148-0227    

DOI:10.1029/JC086iC05p04103

年代:1981

数据来源: WILEY

摘要:

There is increasing evidence from field observations that beach cusps are often formed by subharmonic edge waves, edge waves which are generated by an instability in the incoming wind waves. A theoretical analysis suggests that the changing beach topography as the cusps grow provides a negative feedback to the excitation of the subharmonic edge waves. As the cusps grow, the edge waves subside. A maximum cusp amplitude is calculated, based on the assumption that some edge wave activity must persist to maintain the cusps. The theoretical prediction that cusp amplitude will increase with increasing beach slope and increasing incident wave period is in agreement with the trends suggested by some of the more detailed field observations of beach cusps.

ISSN:0148-0227    

DOI:10.1029/JC086iC05p04125

年代:1981

数据来源: WILEY

摘要:

Wave set‐up, the superelevation of mean water level owing to the presence of breaking incident waves, was measured at the shoreline of a natural beach. Offshore pressure sensors monitored incident wave conditions. The set‐up of the shoreline was found to be about 0.17Hs,∞, whereHs∞is the significant wave height in dee

ISSN:0148-0227    

DOI:10.1029/JC086iC05p04133

年代:1981

数据来源: WILEY

摘要:

A general expression is derived for the horizontal particle velocities in long waves. The derivation is based on a polynomial expansion in the vertical coordinatezwhich results in an expression foruin terms of the surface elevation η and its derivatives. The result is valid for high waves but is in the preliminary form not directly applicable. It is shown, however, that for waves of relatively small amplitude to depth ratio the result corresponds to the well‐known cnoidal wave theory. The horizontal velocities predicted by that theory are then critically examined, and it is shown that there are conflicting properties, which imply that no cnoidal theory can be satisfactory for waves higher than 30–40% of the depth of water. Instead, a simple formula based on a parabolic truncation of the above‐mentioned polynomial inzis derived for the velocity under the crest of arbitrary high waves. The results are compared both with experiments and with stream function theory, and, particularly, the latter gives remarkably good agreement even for the highest

ISSN:0148-0227    

DOI:10.1029/JC086iC05p04138

年代:1981

数据来源: WILEY

摘要:

Measurements of wave elevation and orbital velocity in the shoaling, breaking, and bore regime of single‐frequency laboratory waves show that third‐order Stokes theory, when energy flux is conserved, predicts the wave height change and harmonic growth in the regime where the Ursell numberUr= (H/h)/(kh)2is0(1) or less. Shoreward of the Stokes region and up to the breakpoint, harmonic amplitudes are well described by the cnoidal theory. It is shown theoretically that a smooth transition regime exists between Stokes and cnoidal regions for waves which eventually break by plunging. The wave profile asymmetry about the vertical plane observed in near‐breaking waves and bores is due to slow changes of phase of the harmonics relative to the primary wave as the wave train shoals. By contrast, only asymmetry about the horizontal plane is possible in the Stokes and cnoidal wave theories, since these classical solutions allow no relative phase shifts between harmonics. Velocity measurements made with hot‐film anemometers show that ‘unorganized’ fluctuations at the bottom under breaking waves are of the order of half the rms amplitude of the wave‐induced ‘organized’ flow. The correlation between surface elevation and bottom velocity under breakers and bores suggests that turbulence contributes more strongly to the unorganized flow at the bottom under plunging than und

ISSN:0148-0227    

DOI:10.1029/JC086iC05p04149

年代:1981

数据来源: WILEY