Root Mean Square Wave Research Articles

Estimation of air-bubble-induced wave height and set-up using representative wave approach

ABSTRACT This study aimed to investigate the possibility of modeling the wave height and set-up by using the representative wave method caused by air bubbles in irregular waves in the surf zone. Two regular wave-breaking models with air bubble effects were directly employed in the irregular waves and modified to obtain new irregular wave-breaking models. These models can be used to compute the root mean square (RMS) wave height and wave set-up based on the conservation laws of energy flux and momentum. Model I was solved analytically for a beach with a plane slope and numerically for a beach with an irregular slope for spilling and plunging breakers, separately. Additionally, model II was solved numerically for both slope types and breaking conditions. The modified models were calibrated and validated using a large amount of experimental data and a broad range of trial situations. These conditions included large-scale, small-scale, and field experiments. Finally, it was discovered that the modified models had excellent accuracy in computing the wave heights and set-ups. In terms of accuracy, Model I outperformed Model II for the computation of the RMS wave height and set-up of wave breakers in irregular waves.

Energy dissipation model for irregular breaking waves owing to air bubbles

Based on the air bubbles effect, an irregular energy dissipation model for plunging and spilling breaking waves has been developed theoretically. To develop the model, the probability of fraction of breaking wave phenomenon has been applied. The developed model has been numerically solved for irregular beaches and analytically solved for plane sloping beaches. The energy balance and the momentum balance equations are used to calculate the root mean square (RMS) wave height and the wave set-up, respectively. To validate the new model, a large number and a variety of test circumstances, involving small-scale, large-scale, and experimental field data, have been employed. Finally, the intended models execute a smaller amount of normalized RMS error (NRMSE) in calculating RMS wave height as well as wave set-up compared with the different categories of experimental data.

Research on a Simulation Model of a Skywave Over-the-Horizon Radar Sea Echo Spectrum

The capability of a skywave over-the-horizon radar (SWR) to achieve the continuous observation of a wide range of ocean dynamics parameters via a single ionospheric reflection has been demonstrated by many scholars. In order to expand the method of SWR detection of ocean dynamics parameters, a simulation model of an SWR sea echo spectrum based on the Barrick sea surface scattering cross-section model (Barrick model) and 3D ray-tracing method, suitable for a narrow-beam, frequency-modulated continuous-wave radar system (FMCW), was established. Based on this model, we simulated ideal and contaminated SWR sea echo spectra, respectively with the 3D electron density data output by the International Reference Ionosphere (IRI) model. Then, we further analyzed the effects of the grazing incidence angle, scattering angle, scattering azimuth angle and fetch length on the sea surface scattering cross-sections, the retrieval precision of the sea surface wind direction, and the root-mean-square (RMS) wave height, using the simulation data calculated by the Barrick model. The results show that these angles and fetch length cause a small expansion and contraction of the scattering cross-section, and have no influence on the retrieval precision of the sea surface wind direction, but will affect the retrieval precision of the RMS wave height; the influence of the grazing incidence angle and scattering angle is ~2.5 times that of the scattering azimuth angle. The ideal SWR sea echo spectrum has small broadening, but the ionosphere phase contamination will cause serious broadening and shifting of the SWR sea echo spectrum, and the higher order nonlinear term has greater contamination.

Photon-Counting Lidar: An Adaptive Signal Detection Method for Different Land Cover Types in Coastal Areas

Airborne or space-borne photon-counting lidar can provide successive photon clouds of the Earth’s surface. The distribution and density of signal photons are very different because different land cover types have different surface profiles and reflectance, especially in coastal areas where the land cover types are various and complex. A new adaptive signal photon detection method is proposed to extract the signal photons for different land cover types from the raw photons captured by the MABEL (Multiple Altimeter Beam Experimental Lidar) photon-counting lidar in coastal areas. First, the surface types with 30 m resolution are obtained via matching the geographic coordinates of the MABEL trajectory with the NLCD (National Land Cover Database) datasets. Second, in each along-track segment with a specific land cover type, an improved DBSCAN (Density-Based Spatial Clustering of Applications with Noise) algorithm with adaptive thresholds and a JONSWAP (Joint North Sea Wave Project) wave algorithm is proposed and integrated to detect signal photons on different surface types. The result in Pamlico Sound indicates that this new method can effectively detect signal photons and successfully eliminate noise photons below the water level, whereas the MABEL result failed to extract the signal photons in vegetation segments and failed to discard the after-pulsing noise photons. In the Atlantic Ocean and Pamlico Sound, the errors of the RMS (Root Mean Square) wave height between our result and in-situ result are −0.06 m and 0.00 m, respectively. However, between the MABEL and in-situ result, the errors are −0.44 m and −0.37 m, respectively. The mean vegetation height between the East Lake and Pamlico Sound was also calculated as 15.17 m using the detecting signal photons from our method, which agrees well with the results (15.56 m) from the GFCH (Global Forest Canopy Height) dataset. Overall, for different land cover types in coastal areas, our study indicates that the proposed method can significantly improve the performance of the signal photon detection for photon-counting lidar data, and the detected signal photons can further obtain the water levels and vegetation heights. The proposed approach can also be extended for ICESat-2 (Ice, Cloud, and land Elevation Satellite-2) datasets in the future.

Turbulent boundary layers under irregular waves and currents: Experiments and the equivalent‐wave concept

AbstractA full‐scale experimental study of turbulent boundary layer flows under irregular waves and currents is conducted with the primary objective to investigate the equivalent‐wave concept by Madsen (1994). Irregular oscillatory flows following the bottom‐velocity spectrum under realistic surface irregular waves are produced over two fixed rough bottoms in an oscillatory water tunnel, and flow velocities are measured using a Particle Image Velocimetry. The root‐mean‐square (RMS) value and representative phase lead of wave velocities have vertical variations very similar to those of the first‐harmonic velocity of periodic wave boundary layers, e.g., the RMS wave velocity follows a logarithmic distribution controlled by the physical bottom roughness in the very near‐bottom region. The RMS wave bottom shear stress and the associated representative phase lead can be accurately predicted using the equivalent‐wave approach. The spectra of wave bottom shear stress and boundary layer velocity are found to be proportional to the spectrum of free‐stream velocity. Currents in the presence of irregular waves exhibit the classic two‐log‐profile structure with the lower log‐profile controlled by the physical bottom roughness and the upper log‐profile controlled by a much larger apparent roughness. Replacing the irregular waves by their equivalent sinusoidal waves virtually makes no difference for the coexisting currents. These observations, together with the excellent agreement between measurements and model predictions, suggest that the equivalent‐wave representation adequately characterizes the basic wave‐current interaction under irregular waves.

半透膜阵列平板波导式头戴显示器光学系统设计

In order to reduce the weight and volume of the head-mounted display (HMD), a planar waveguide HMD is designed based on semi-transparent film array. Two orthogonally placed semi-transparent film arrays are used to expand the eyepiece's exit pupil, as well as to make the HMD compact and light in weight. By analyzing the structure of planar optical waveguide, an optical system model is established. Then, imaging quality and irradiance distribution of the system is discussed. This system has a gross weight of about 36 g, a field of view (FOV) of 1520 and an exit pupil of 7 mm12 mm. The distortion is less than 0.13%. The root mean square (RMS) spot diameter is less than 3.75 m. The RMS wave aberration is less than 0.045. The modulation transfer function (MTF) is higher than 0.58 at the spatial frequency of 40 lp/mm across the entire FOV. The results indicate that planar waveguide of semi-transparent film array can enlarge eyepiece's exit pupil effectively. This system satisfies the requirements of the HMD optical system.

An evaluation of wave propagation simulations over a barred beach with a Boussinesq-type model

The FUNWAVE model is used for simulating simulation of monochromatic and irregular wave propagation in a channel with a bar-trough profile. FUNWAVE is based upon the extended Boussinesq equations. The study aims to analyze the model's performance when simulating shoaling, wave breaking and nonlinear interactions that are present in nearshore wave propagation. For that, high-order time domain statistics (root mean-square wave height, skewness, asymmetry and the kurtosis) of the model simulations and of the observations were compared along the whole channel. Also, a frequency domain analysis including standard spectral analysis and the bispectrum was carried out in selected points of the flume. The evaluation included the role of the wave breaking internal model parameters. The main conclusion is that, in general, the one-dimensional version of FUNWAVE simulates quite well the nonlinear transformation of a wave over a bottom with a bar-tough profile, for both regular and irregular wave conditions. The model reproduces the transformation of the wave shape, specially the increasing sharper wave crests and flatter troughs and also the lack of vertical symmetry with crests pitching forward, as it propagates along the domain. However, some differences persist after wave breaking, mainly due to the nature of the wave-breaking module. In this module, the energy dissipation is induced by the increase of viscosity, a rather simple mechanism, without the modification of the wave shape. Also, the energy dissipation develops in a smooth way which is appropriated for spilling breaking waves, but not for plunging breaking waves where the dissipation starts more abruptly.

The effect of Nd:YAG laser posterior capsulotomy on ocular wave front aberrations

Objective: To assess the effect of Nd:YAG laser posterior capsulotomy on ocular wave front aberrations. Study Design: Retrospective comparative study. Participants: Twenty-four eyes of 24 consecutive pseudophakic patients with symptomatic PCO, who presented for Nd:YAG laser posterior capsulotomy at our clinic, were included in this study. Methods: The wave front aberrations of the entire optical path of 24 pseudophakic eyes of 24 patients before, and 1 month after, Nd:YAG laser posterior capsulotomy were measured using the Nidek Optical Path Difference (OPD) scan aberrometer. Total, tilt, and high-order aberrations, and total coma, total trefoil, total tetrafoil, total spherical, and total high astigmatism aberrations were analyzed statistically. Secondary measures included changes in visual acuity and refraction, and repeatability of wave front measurements in the fellow eye. Results: Before Nd:YAG laser posterior capsulotomy, the total higher-order aberrations root mean-square (RMS) wave front aberration was 2.08 (SD 2.20) μm, with total trefoil being a major contributor at 1.19 (SD 1.15) μm. One month after the procedure, significant decreases in total, tilt, and high-order aberrations, and total trefoil, total tetrafoil, total spherical, and total high astigmatism aberrations were noted ( p < 0.05). No significant changes in total coma aberrations were found ( p > 0.05). Additionally, significant improvement in visual acuity without significant change in refraction was observed. No statistically significant differences were detected in any of the RMS values of wave front measurements taken 1 month later in the fellow eye. Conclusions: Nd:YAG laser posterior capsulotomy causes significant decrease in ocular wave front aberrations measured using the Nidek-OPD scan aberrometer, which can account for a better optical quality after the procedure. Further research to examine the impact of wave front aberrations in visual function after Nd:YAG laser posterior capsulotomy is needed.

Allometry and scaling of wave aberration of eyes

The scaling of root mean square (RMS) wave aberration in an isometrically growing eye is investigated, along with changes due to measurements made at different relative pupil sizes. It is found that, relative to an initial state, if an eye expands in all directions by the factor k, and the wave aberration is then measured at a relative pupil size which has changed over the pupil size used for the original measurement by a factor b, the new wave aberration will be increased or decreased by a factor kb n , where n is the exponent relating RMS wave aberration, to pupil radius, r, in the equation: RMS = qr n in the initial eye. This implies that, if wave aberration is measured in a growing eye with a constant measurement pupil size, the measured RMS will decrease by the factor 1/ k n−1 .

Errors in bathymetric retrievals using linear dispersion in 3-D FFT analysis of marine radar ocean wave imagery

The phenomenon of ocean wave-shoaling, and the associated reduction of ocean wave phase speed with decreased water depth, provides useful information for inferring water depth D (bathymetry) in coastal environments. One strategy for relating D to phase speed C and wave-vector K of long wavelength ocean waves involves using the one-dimensional (1-D) linear (gravity wave) dispersion relationship C/sup 2/=g*tanh(KD)/K. In principle, this approach has limitations because the approach is based on a WKB approximation, so it cannot be applied when D varies appreciably over the wavelength of a shoaling wave. Also, the approach is restricted to waves that have small wave height. The author uses a set of marine radar image sequences and applies this linear approximation, using a 3-D FFT analysis of 88 sets of image sequences spaced half an hour apart. The author inverts the dispersion relation to solve for D. Depths between 3.6 and 5.8 m were tested, for root mean square (RMS) wave heights offshore between 8 and 3 m. The author shows that for low to moderate wave heights, the approach does generally retrieve the correct depth in water depths of 5 m and greater for moderate wave RMS heights. However, an increase in the RMS wave height from 1 m to 3.5 m produced a much poorer depth estimate, proving the need for an application of a nonlinear wave model to the problem. The errors also increase with shallower depths as expected, as the error dependence on depth and wave height is determined.

Statistical study of the spectral broadening of skywave signals backscattered by the sea surface: application to RMS wave height measurement with a skywave radar

HF skywave signals backscattered by the sea surface are studied on a large set of data (more than 30 h of 64 independent signals) to identify the sources of the broadening of the first-order spectral line. Using high-quality signals reflected by sporadic E ionospheric layers, the natural broadening due to sea-scattering effects has been scaled to about 3/100 Hz. When the signals propagate via F layer, the total broadening due to ionospheric effects is similar in magnitude and can be attributed to two causes. The first, due to frequency modulation effects, which can be identified and corrected, scales on average to 1/100 Hz. The second, called unresolved ionospheric effects, scales on average to 2/100 Hz and is probably due to the spatial variation of the ionospheric Doppler within the ionospheric control volume. Since they are greatly variable with time and space, the influence of these unresolved ionospheric effects can be reduced by sorting spectra, according to the value of the equivalent spectral width, before averaging. Using such sorting and correcting the signals for the ionospheric frequency modulation, 70% of the considered set of data are usable to measure the root mean square (RMS) wave height.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>