Shear Flow Dispersion Under Wave and Current

The longitudinal dispersion of solute in open channel flow with short period progressive waves is investigated. The waves induce second order drift velocity in the direction of propagation and enhance the mixing process in concurrent direction. The 1-D wave-period-averaged dispersion equation is derived and an expression for the wave-current induced longitudinal dispersion coefficient (WCLDC) is proposed based on Fischer's expression (1979) for dispersion in unidirectional flow. The result shows that the effect of waves on dispersion is mainly due to the cross-sectional variation of the drift velocity. Furthermore, to obtain a more practical expression of the WCLDC, the longitudinal dispersion coefficient due to Seo and Cheong (1998) is modified to incluee the effect of drift velocity. Laboratory experiments have been conducted to verify the proposed expression. The experimental results, together with dimensional analysis, show that the wave effect can be reflected by the ratio between the wave amplitude and wave period. A comparative study between the cases with and without waves demonstrates that the magnitude of the longitudinal dispersion coefficient is increased under the presence of waves.     

Studying possibilities for the classification of infrasonic signals from different sources

Atmospheric infrasonic signals were classified on the basis of data obtained in the United States (University of Alaska, Fairbanks) and in the Antarctic region (Windless Bight) from 1980 to 1983. The data archive included five classes of signals from different sources: explosions, mountain associated waves, microbaroms, volcanic infrasound, and auroral infrasonic waves. This classification was based on the theory of testing statistical hypotheses. The possibilities of separating these classes were studied. It was shown that the signals (from the archive used) that are characteristic of explosions and volcanic activity can be rather easily separated from those characteristic of mountain associated waves, microbaroms, and auroral infrasonic waves.     

Using the acoustic-pulse conservation law in estimating the energy of surface acoustic sources by remote sounding

The atmospheric effect on the characteristics of infrasonic signals from explosions has been studied. New methods have been proposed to remotely estimate the energy of explosions using the data of infrasonic wave registration. One method is based on the law of conservation of acoustic pulse I, which is equal to the product of the wave profile area S/2 of the studied infrasonic signal and the distance to the source E_I [kt] = 1.38 × 10^–10 (I [kg/s])^1.482. The second method is based on the relationship between the explosion energy and the dominant period T of the recorded signal, EТ [kt] =1.02 × (Т [s]²/σ)^3/2, where σ is a dimensionless distance used for determining the degree of manifestation of nonlinear effects in the propagation of sound along ray trajectories. When compared to the conventional E_W (Whitaker’s) relation, the advantage of the EI relation is that it can be used for pulsed sources located at an arbitrary height over the land surface and having an arbitrary form of the initial-pulse profile and for any type of infrasonic arrivals. A distinctive feature of the expression for E_Т is that the atmospheric effect on the characteristics of recorded infrasonic signals is explicitly taken into account. These methods have been tested using infrasonic data recorded at a distance of 322 km from the sources (30 explosions caused by a fire that occurred at the Pugachevo armory in Udmurtia on June 2, 2011). For the same explosion, empirical relations have been found between energy values obtained by different methods: E_I = 1.107 × E _W , E _Т = 2.201 × E _I .     

Study on dynamics of shear waves——Ⅰ. Scale analysis and dispersion relation

- Starting from satellite remote sensing data, the dynamical processes of shear waves occurring at the boundary between the western boundary current and the shelf slope water are studied and dynamically analyzed in this study. The average wavelength is 75 km, and the average amplitude (from crest to trough )17 km. the average phase speed 100 cms-1 for the shear waves along the north wall of the Gulf Stream to the east of Cape Hatteras measured from NOAA satellite IR (infrared ) images. The average wavelength of shear waves along the north wall of the Kuroshio Current is 57 km, and the average amplitude 17 km. For the shear waves occurring along the west wall of the Gulf Stream to the south of Cape Hatteras, the average wavelength is 131 km, and the average amplitude 33 km measured from Seasat SAR (synthetic aperture radar )images. The time for one cycle of shear wave event is about one week.In order to explore the dynamical mechanisms of shear waves, we solved the vorticity equation for a stratified flu     

Generating–absorbing sponge layers for phase-resolving wave models

The accurate generation and absorption of water waves in phase-resolving models are critical issues in representing nearshore processes. Here, we present a source function method for combined wave generation and absorption using modified sponge layers. This technique can be easily adapted to a wide variety of systems, and does not require the solution of Green's functions but rather the simpler knowledge of solutions for free waves. These solutions may be linear or nonlinear, regular or irregular, and generated waves can be made arbitrarily accurate through simple selection of sponge layer coefficients. Generating–absorbing sponge layer systems are shown to have a close correspondence to relaxation zones for wave generation if relaxation coefficients are chosen appropriately.     

随机波浪下泰勒离散系数的时域解

利用Wolk提出的粒子追踪方程,通过等分频率法划分不规则波谱,利用MATLAB做粒子运动模拟计算,得到无因次化泰勒离散系数K/D随时间t变化的曲线;通过与Huang等得到的P-M谱的泰勒离散系数K/D计算结果比较证明了本计算方法的可靠性。采用该方法研究了不规则波条件下,波序列(同一谱型不同波面序列)和谱型(谱峰周期、有效波高、谱峰升高因子)对波浪离散系数的影响;计算结果表明:同一谱型不同波序列对泰勒纵向离散系数稳定值和稳定时间无影响;不规则波谱峰周期越大,纵向离散系数K/D越小,稳定时间越短;有效波高越大,纵向离散系数K/D越大,稳定时间越长;谱峰升高因子越大,泰勒离散系数K/D越大,稳定时间越长;与规则波相比,不规则波的泰勒离散系数K/D的值略小10%~30%。     

Waves and diffusion on the sea surface

The frequency spectrum of surface elevations in the presence of wind waves is well known. On this basis, one can estimate the frequency spectrum of vertical velocities in sea-surface waves. Owing to liquid incompressibility, the spectrum of horizontal velocities should have the same frequency dependence. The use of the dispersion equation for waves on the surface of a heavy liquid allows one to obtain to the spatial spectrum of velocities. Therefore, one can estimate the spatial structure function of the velocity field. For short waves and large depths, the structure function increases as r ^1/2, where r is the distance between the points of observations. For long waves and shallow depths h, this increase is proportional to r. The coefficient of turbulent mixing K(r) of pollution spots of size r on the sea surface is now estimated as the product of the spot size and the rms difference of velocities. As a result, depending on r and h, the exponent in the r ⁿ dependence of K(r) may vary between 1.25 and 1.5. This outcome provides an explanation for a scatter in the values of the exponent n, a phenomenon that has been observed by many experimentalists.     

Longitudinal dispersion in wave-current-vegetation flow

The flow, turbulence, and longitudinal dispersion in wave-current flow through submerged vegetation are experimentally examined. Laboratory experiments are carried out by superimposing progressive waves on a steady flow through simulated submerged vegetation. The resultant wave-current-vegetation interaction shows strong interface shear with increase in the velocity due to the wave-induced drift. The increase in turbulence in the region of vegetation is found to be about twice higher than in the no-wave case due to the additional mixing by wave motions. Solute experiments are conducted to quantify the wave-current-vegetation longitudinal dispersion coefficient (WCVLDC) by the routing method and by defining length and velocity scales for the wave-current-vegetation flow. An empirical expression for the WCVLDC is proposed. Although the increase in vertical diffusivity is observed as compared with bare-bed channels, the shear effect is stronger, which increases the value of the WCVLDC. The study can be a guideline to understand the combined hydrodynamics of waves, current, and vegetation and quantify the longitudinal dispersion therein. Published in Morskoi Gidrofizicheskii Zhurnal, No. 1, pp. 50–67, January–February, 2009.     

A dispersion equation and dispersion coefficient for material transport in Inland Seas

To analyse material transport in inland seas, a horizontal two-dimensional dispersion equation is derived, and the dispersion coefficient due to the combined effect of vertical turbulent mixing and vertical shear of both a steady current and a tidal current is studied. In the present study, the assumption that velocity is uniform in horizontal planes is not necessary, and velocity has a free vertical profile; thus the dispersion coefficient formulated is general, and is represented by a tensor of the second order. The properties of the dispersion coefficient in the horizontal two-dimensional dispersion model are also investigated, and it is shown that the time-averaged dispersion coefficient due to the tidal current over a tidal period is approximately half that due to the steady current, if the velocity amplitude and the vertical profile of the tidal current are the same as those of the steady current (a similar result was presented byBowden (1965) for horizontal one-dimensional models). Finally, the dispersion coefficient in Hiuchi-Nada (Hiuchi Sound) in the central part of the Seto Inland Sea is evaluated by using the model. The values of the dispersion coefficient in that region range from 10³ cm² s^–1 to 10⁵ cm² s^–1 when vertical turbulent diffusivity is taken to be 50 cm² s^–1.     

Spectral characteristics of Rossby waves in the Northwestern Pacific based on satellite altimetry

Using satellite altimetry measurement data for 1993–2013, we study the spectral characteristics of Rossby waves in the Northwestern Pacific (25°–50° N, 140°–180° E). For each latitude degree, we draw integral plots of spectral power density calculated with a two-dimensional Fourier transform (2D-FFT). We compare the dispersion equations of Rossby waves calculated from the WKB-approximation and an approximation of a two-layer ocean model with the empirical velocities determined by the slope of isopleths by the Radon method; also, we compare the dispersion equations with the spectral distributions of level variations. It is shown that the main energy of Rossby waves in the Northwestern Pacific corresponds to the first baroclinic mode. At almost all latitudes, there is good agreement between the empirical phase velocities calculated by isopleths by the Radon method and the theoretical values; also, the spectral peaks correspond to graphs of the dispersion equations for the first baroclinic mode Rossby waves, except for the Kuroshio region, where some peaks correspond to the second mode.     

Improved explicit approximation of linear dispersion relationship for gravity waves

For water waves the transcendental dispersion relationship is solved by iterative methods when wave period and water depth are given and wavelength or wave number is required. A highly accurate explicit approximation to linear dispersion relationship is proposed based on Eckart's explicit relationship. While Eckart's expression is accurate to within 5%, the improved relationship has a maximum relative error of less than 0.05%. A simpler form of the relationship with 0.2% accuracy is also given.     

Simulating the Propagation of Infrasonic Waves and Estimating the Energy of the Chelyabinsk Meteoroid Explosion Observed on February 15, 2013

Results obtained from simulating the propagation of infrasonic waves from the Chelyabinsk meteoroid explosion observed on February 15, 2013, are given. The pseudodifferential parabolic equation (PDPE) method has been used for calculations. Data on infrasonic waves recorded at the IS31 station (Aktyubinsk, Kazakhstan), located 542.7 km from the likely location of the explosion, have been analyzed. Six infrasonic arrivals (isolated clearly defined pulse signals) were recorded. It is shown that the first “fast” arrival (F) corresponds to the propagation of infrasound in a surface acoustic waveguide. The rest of the arrivals (T1–T5) are thermospheric. The agreement between the results of calculations based on the PDPE method and experimental data is satisfactory. The energy E of the explosion has been estimated using two methods. One of these methods is based on the law of conservation of the acoustic pulse I, which is a product of the wave profile area S/2 of the signal under analysis and the distance to its source E _I [kt] = 1.38 × 10^–10 (I [kg/s])^1.482. The other method is based on the relation between the energy of explosion and the dominant period T of recorded signal E _T [kt] = 1.02 × (T [s]²/σ)^3/2, where σ is the dimensionless distance determining the degree of nonlinear effects during the propagation of sound along ray trajectories. According to the data, the explosion energy E _I,T ranges from 1.87 to 32 kt TNT.     

Collisions Between Lumps/Rogue Waves and Solitons for A (3+1)-Dimensional Generalized Variable-Coefficient Shallow Water Wave Equation

In this paper, we investigate a (3+1)-dimensional generalized variable-coefficient shallow water wave equation, which can be used to describe the flow below a pressure surface in oceanography and atmospheric science. Employing the Kadomtsev-Petviashvili hierarchy reduction, we obtain the semi-rational solutions which describe the lumps and rogue waves interacting with the kink solitons. We find that the lump appears from one kink soliton and fuses into the other on the x−y and x−t planes. However, on the x−z plane, the localized waves in the middle of the parallel kink solitons are in two forms: lumps and line rogue waves. The effects of the variable coefficients on the two forms are discussed. The dispersion coefficient influences the speed of solitons, while the background coefficient influences the background’s height.

     

A study of SAR remote sensing of internal solitary waves in the north of the South China Sea: Ⅰ. Simulation of internal tide transformation

For settlement of the well-known problem of contemporary radar imaging models, i. e. , the problem of a general underestimation of radar signatures of hydrodynamic features over oceanic internal waves and underwater bottom topography in tidal waters at high radar frequency bands （ X-band and C-band）, the impact of the ocean surface mixed layer turbulence and the significance of strat- ified oceanic model on SAR remote sensing of internal solitary waves are proposed. In the north of the South China Sea by utilizing some observed data of background field the nonlinearity coefficient, the dispersion coefficient, the horizontal variability coefficient and the phase speed in the generalized K-dV equation are determined approximately. Through simulations of internal tide transfor- mation the temporal evolution and spatial distribution of the vertical displacement and horizontal velocity of internal wave field are obtained. The simulation results indicate that the maximum amplitudes of internal solitary waves occur at depth 35 m, but the maximum current speeds take place at depth 20 m in this area of the sea （about 20°30＇N, 114°E） in August. It was noticed that considering the effects of flood current and ebb current respectively is appropriate to investigate influence of the background shear flow on coefficients of the K-dV equation. The obtained results provide the possibility for the simulation of SAR signatures of internal solitary waves under considering the impact of ocean surface mixed layer turbulence in the companion paper.     

Estimation of contingency of parameters of human EEG and background infrasonic vibrations of pressure revealed in monitoring studies

The contingency of variations in parameters of the background infrasonic waves and changes in parameters of human EEG during different time intervals has been revealed with the use of synchronized monitoring. The results suggest that the variations of the background infrasound could be considered an external pacemaker (synchronizing factor). It has been established that there is a significant contingency of changes in a sufficiently wide range of infra- and ultradian periodicities; for different ranges the positive and negative correlations alternate.     

Wave damping over artificial Posidonia oceanica meadow: A large-scale experimental study

An experimental study, conducted in the large wave flume of CIEM in Barcelona, is presented to evaluate the effects of Posidonia oceanica meadows on the wave height damping and on the wave induced velocities. The experiments were performed for irregular waves from intermediate to shallow waters with the dispersion parameter h/λ ranging from 0.09 to 0.29. Various configurations of the artificial P. oceanica meadow were tested for two stem density patterns (360 and 180 stems/m²) and for plant's height ranging from 1/3 to 1/2 of the water depth.The results for wave height attenuation are in good agreement with the analytical expressions found in literature, based on the assumption that the energy loss over the vegetated field is due to the drag forces. Based on this hypothesis, an empirical relationship for the drag coefficient related to the Reynolds number, Re, is proposed. The Reynolds number, calculated using the artificial P. oceanica leaf width as the length scale and the maximum orbital velocity over the meadow edge as the characteristic velocity scale, ranges from 1000 to 3500 and the drag coefficient C_d ranges from 0.75 to 2.0.The calculated wave heights, using the analytical expression from literature and the proposed relationship for the estimation of C_d, are in satisfactory agreement with those measured. Wave orbital velocities are shown to be significantly attenuated inside the meadow and just above the flume bed as indicated by the calculation of an attenuation parameter. Near the meadow edge, energy transfer is found in spectral wave velocities from the longer to the shorter wave period components. From the analysis it is shown that the submerged vegetation attenuates mostly longer waves.     

Validation and Improvement of Satellite-Derived Surface Solar Radiation over the Northwestern Pacific Ocean

The purpose of this study is to validate and improve satellite-derived downward surface shortwave radiation (DSSR) over the northwestern Pacific Ocean using abundant in situ data. The DSSR derivation model used here assumes that the reduction of solar radiation by clouds is proportional to the product of satellite-measured albedo and a cloud attenuation coefficient. DSSR is calculated from Geostationary Meteorological Satellite-5/Visible Infrared Spin-Scan Radiometer data in 0.05° × 0.05° grids. The authors first compare the satellite DSSR derived with a cloud attenuation coefficient table determined in past research with in situ values. Although the hourly satellite DSSR agrees well with land in situ values in Japan, it has a bias of +13∼+34 W/m² over the ocean and the bias is especially large in the low latitudes. The authors then improve the coefficient table using the ocean in situ data. Usage of the new table successfully reduces the bias of the satellite DSSR over the ocean. The cloud attenuation coefficient for low-albedo cases over the ocean needs to be larger in the low latitudes than past research has indicated. Daily and hourly DSSR can be evaluated from the satellite data with RMS errors of 11–14% and 30–33%, respectively, over a wide region of the ocean by this model. It is also shown that the cloud attenuation coefficient over land needs to be smaller than over the ocean because the effect of the radiation reflected by the land surface cannot be ignored.     

A study of SAR remote sensing of internal solitary waves in the north of the South China Sea:I.Simulation of internal tide transformation

For settlement of the well-known problem of contemporary radar imaging models,i.e.,the pmblem of a general underestimation of radar signatures of hydrodynamic features over oceanic internal waves and underwater bottom topography in tidal watels at at high radar frequency bands(X-band and C-band),the impact of the ocean surface mixed layer turbulence and the significance of strat-ified oceanic model on SAR remote sensing of internal solitary waves are proposed.In the north of the South China Sea by utilizing seme observed data of background field the nonlinearity coefficient,the dispersion coefficient,the horizontal variability coefficient and the phase speed in the generalized K-dV equation are determined approximately.Through simulations of internal tide transfor-mation the temporal evolution and spatial distribution of the vertical displacement and horizontal velocity of intereal wave field are obtained.The simulation results indicate that the maximum amplitudes of internal solitary waves occur at depth 35 m,but the maximum current speeds take place at depth 20 m in this area of the sea(about 20°30'N,114°E)in August.It was noticed that considering the effects of flood current and ebb current respectively is appropriate to investigate influence of the background shear flow on coefficients of the K-dV equation.The obtained results provide the possibility for the simulation of SAR signatures of inter-nal solitary waves under considering the impact of ocean surface mixed layer turbulence in the companion paper.     

Experimental determination of wavelengths in the presence of a mean current

This paper describes a simple method for determining the wavelength of small amplitude waves under laboratory conditions where reflected wave components are present both with and without a mean current flow superimposed. It assumes a locally horizontal bed but requires no a priori assumption concerning the form of the dispersion relation with a coexisting current. Synchronous measurements of the water surface recorded along any straight line are analysed to yield Fourier coefficients at each location. It is then shown that for all practical conditions excluding a perfect standing wave, the average rate of change of wave phase in the chosen direction can be related directly to the component of incident wave number in that direction, irrespective of reflection coefficient or relative current strength. The technique has been applied to regular and bichromatic waves in a flume with an absorbing wave generator, and can also be applied in 3-D wave basins where waves and currents intersect at arbitrary angles. In combined wave–current experiments, by assuming the linear dispersion relation, it is also possible to estimate the effective current velocity.     

Accuracy of asymptotic series for the kinematics of high solitary waves

The accuracy of several asymptotic series expansions for wave speed and particle velocity under the crest of a solitary wave (on a fluid at rest) up to maximum height is investigated. The very accurate numerical results of Williams (1985) are the measure for our comparisons. The results are based on a scaling of calculated properties of long periodic waves to the case of solitary waves.For wave speeds the classical Boussinesq–Rayleigh expression gives good agreement up to a relative wave height of, say, 0.3. An asymptotic fourth-order expression based on Fenton (1990) can be used up to a relative wave height of 0.7, whereas the corresponding fifth-order expression is slightly less accurate.The Eulerian particle velocity profile under the wave crest is examined using a cnoidal wave expression from Fenton (1990) in the limit of the solitary wave. For low waves a `consistent' (i.e. properly truncated) fifth-order expression and an `inconsistent' ditto both coincide with Williams' results. Beginning at medium high waves, the consistent expression surprisingly exhibits oscillations in the velocity profile, and the oscillations become stronger as the wave gets higher. The inconsistent expression, however, yields the same shape as Williams' profile, but is displaced parallel to this, resulting in slightly larger velocities. For high waves also the inconsistent expression begins to differ in shape from Williams' profile, and asymptotic theory fails. Only for low waves `lowest order theory' gives acceptable results. We show analytically that for the highest wave the particle velocity profile has a horizontal tangent at the water surface; this is corroborated by Williams' numerical results.We also study the particle velocity at the wave crest as a function of wave height. It is shown that the variation has a vertical tangent for the highest wave. Two fifth-order asymptotic series for this velocity, based on the wave speed through the Bernoulli equation, show very good agreement with Williams up to a relative wave height of about 0.6.It is finally shown that it is possible to produce very accurate rational-function approximations to Williams' results for the wave speed as well as for the particle velocity at the wave crest.