Derivation of Water Particle Kinematics in the Near Surface Zone by the Effective Water Depth Procedure

Author(s):  
N. I. Mohd Zaki ◽  
G. Najafian

Linear Random Wave Theory (LRWT) is frequently used to simulate water particle kinematics at different nodes of an offshore structure from a reference surface elevation record. However, it is well known that LRWT leads to water particle kinematics with exaggerated high-frequency components in the vicinity of mean water level (MWL). To avoid this problem, empirical techniques (such as Wheeler & vertical stretching methods) are frequently used to provide a more realistic representation of the wave kinematics in the near surface zone. In this paper, a modified version of LRWT, based on the derivation of an effective water depth, is introduced. The proposed technique leads to predicted kinematics (in the near surface zone) which lie between corresponding values from the Wheeler and the vertical stretching methods. Furthermore, it does not suffer from exaggerated high-frequency components in the near surface zone.

Author(s):  
G. Najafian ◽  
N. I. Mohd Zaki ◽  
G. Aqel

Linear Random Wave Theory (LRWT) is frequently used to simulate water particle kinematics at different nodes of an offshore structure from a reference surface elevation record. It is, however, well known that wave kinematics calculated from LRWT suffer from unrealistically large high-frequency components in the vicinity of mean water level. To overcome this deficiency, a common industry practice consists of using linear wave theory in conjunction with empirical techniques, such as the Wheeler or the vertical stretching methods, to provide a more realistic representation of the near-surface water particle kinematics. In this paper, a modified version of LRWT is introduced, which, unlike the standard LRWT, does not lead to unrealistically large high-frequency components in the vicinity of mean water level. The proposed method leads to predicted kinematics in the near surface zone which lie between corresponding values from the Wheeler and the vertical stretching methods, respectively.


2013 ◽  
Vol 7 (1) ◽  
pp. 273-281 ◽  
Author(s):  
N.I. Mohd Zaki ◽  
M.K. Abu Husain ◽  
G. Najafian

Linear random wave theory (LRWT) has successfully explained most properties of real sea waves with the ex-ception of some nonlinear effects for surface elevation and water particle kinematics. Due to its simplicity, it is frequently used to simulate water particle kinematics at different nodes of an offshore structure from a reference surface elevation record; however, predicted water particle kinematics from LRWT suffer from unrealistically large high-frequency compo-nents in the vicinity of mean water level (MWL). To overcome this deficiency, a common industry practice for evaluation of wave kinematics in the free surface zone consists of using linear random wave theory in conjunction with empirical techniques (such as Wheeler and vertical stretching methods) to provide a more realistic representation of near-surface wave kinematics. It is well known that the predicted kinematics from these methods are different; however, no systematic study has been conducted to investigate the effect of this on the magnitude of extreme responses of an offshore structure. In this paper, probability distributions of extreme responses of an offshore structure from Wheeler and vertical stretching methods are compared. It is shown that the difference is significant; consequently, further research is required to deter-mine which method is more reliable.


Author(s):  
N. I. Mohd Zaki ◽  
M. K. Abu Husain ◽  
N. Abdullah Shuhaimy ◽  
G. Najafian

Linear random wave theory (LRWT) is frequently used to simulate water particle kinematics at different nodes of an offshore structure from a reference surface elevation record. However, it is well known that LRWT leads to water particle kinematics with exaggerated high-frequency components in the vicinity of mean water level (MWL). A number of empirical techniques have been suggested to provide a more realistic representation of near surface wave kinematics. The empirical techniques popular in the offshore industry include Wheeler stretching, linear extrapolation, delta stretching, and vertical stretching. Each of these methods is intended to calculate sensible kinematics above the MWL, yet they have been found to differ from one another in the results yielded. In this paper, two new methods of simulating water particle kinematics are introduced. In this study, the values of 100-year responses derived from different methods of simulating wave kinematics are compared.


Author(s):  
N. I. Mohd Zaki ◽  
M. K. Abu Husain ◽  
G. Najafian

Linear random wave theory (LRWT) is frequently used to simulate water particle kinematics at different nodes of an offshore structure from a reference surface elevation record. However, it is well known that LRWT leads to water particle kinematics with exaggerated high-frequency components in the vicinity of mean water level (MWL). To avoid this problem, empirical techniques such as Wheeler and vertical stretching methods are frequently used to provide a more realistic representation of the wave kinematics in the near surface zone. In this paper, the Monte Carlo time simulation technique is used to investigate the effect of these two different methods of simulating water particle kinematics on the probability distribution of extreme responses. It is shown that the difference could be significant leading to uncertainty as to which method should be used.


2012 ◽  
Vol 9 (10) ◽  
pp. 3917-3930 ◽  
Author(s):  
C. A. Frieder ◽  
S. H. Nam ◽  
T. R. Martz ◽  
L. A. Levin

Abstract. Predicting consequences of ocean deoxygenation and ocean acidification for nearshore marine ecosystems requires baseline dissolved oxygen (DO) and carbonate chemistry data that are both high-frequency and high-quality. Such data allow accurate assessment of environmental variability and present-day organism exposure regimes. In this study, scales of DO and pH variability were characterized over one year in a nearshore kelp forest ecosystem in the Southern California Bight. DO and pH were strongly, positively correlated, revealing that organisms on this upwelling shelf are not only exposed to low pH but also to low DO. The dominant scale of temporal DO and pH variability occurred on semidiurnal, diurnal and event (days–weeks) time scales. Daily ranges in DO and pH at 7 m water depth (13 mab) could be as large as 220 μmol kg−1 and 0.36 units, respectively. Sources of pH and DO variation include photosynthesis within the kelp forest ecosystem, which can elevate DO and pH by up to 60 μmol kg−1 and 0.1 units over one week following the intrusion of high-density, nutrient-rich water. Accordingly, highly productive macrophyte-based ecosystems could serve as deoxygenation and acidification refugia by acting to elevate DO and pH relative to surrounding waters. DO and pH exhibited greater spatial variation over a 10 m increase in water depth (from 7 to 17 m) than along a 5 km stretch of shelf in a cross-shore or alongshore direction. Over a three-month time period, mean DO and pH at 17 m water depth were 168 μmol kg−1 and 7.87, respectively. These values represent a 35% decrease in mean DO and 37% increase in [H+] relative to near-surface waters. High-frequency variation was also reduced at depth. The mean daily range in DO and pH was 39% and 37% less, respectively, at 17 m water depth relative to 7 m. As a consequence, the exposure history of an organism is largely a function of its depth of occurrence within the kelp forest. With knowledge of local alkalinity conditions and high-frequency temperature, salinity, and pH data, we estimated pCO2 and calcium carbonate saturation states with respect to calcite and aragonite (Ωcalc and Ωarag) for the La Jolla kelp forest at 7 m and 17 m water depth. pCO2 ranged from 246 to 1016 μatm, Ωcalc was always supersaturated, and Ωarag was undersaturated at the beginning of March for five days when pH was less than 7.75 and DO was less than 115 μmol kg−1. These findings raise the possibility that the benthic communities along eastern boundary current systems are currently acclimatized and adapted to natural, variable, and low DO and pH. Still, future exposure of coastal California populations to even lower DO and pH may increase as upwelling intensifies and hypoxic boundaries shoal, compressing habitats and challenging the physiological capacity of intolerant species.


1991 ◽  
Vol 113 (1) ◽  
pp. 14-22 ◽  
Author(s):  
M. Isaacson ◽  
K. Subbiah

The present paper describes the numerical simulation of random wave forces acting on a section of fixed slender vertical cylinder near the free surface, taking account of the intermittency of submergence. Time histories of water particle kinematics corresponding to a specified wave spectrum are generated using linear numerical transforms and corresponding force time histories at different sections are computed using the Morison equation. Analytical predictions of various statistical properties of water particle kinematics and forces for the intermittent flow are compared with results of the numerical simulations. These include the probability density of particle kinematics, the spectral density of the force, the probability density of force maxima, and the mean and standard deviation of the force maxima. In general, the agreement is found to be quite satisfactory. The effects of simulation time and random phases on the mean and standard deviation of intermittent force maxima are also investigated.


Author(s):  
Vasiliki Katsardi ◽  
Chris Swan

This paper concerns the description of large waves in intermediate and shallow water depths. In deep water it is well known that the evolution of the largest waves is governed by linear dispersion. In contrast, as the water depth reduces the effects of wave dispersion are weakened and the relative significance of wave modulation shown to be increasingly important. This leads to very different extreme wave groups, the properties of which are critically dependent upon the directionality of the wave field. The paper also concerns the water particle kinematics arising beneath these nonlinear wave groups and contrasts fully non-linear predictions based on a state-of-the-art wave model with the results of the commonly applied design wave solutions. To explore these effects, and to provide a physical explanation for their occurrence, two wave models are employed. The first, proposed by Bateman, Swan & Taylor [1, 2], allows fully-nonlinear descriptions of the evolution of large waves in realistic seas, involving a significant spread of wave energy in both frequency and direction. The second is a wave evolution equation based upon the early work of Zakharov [3] and written in Hamiltonian form by Kasitskii [4]. This model is only valid to a fourth-order of wave steepness, but has the over-riding advantage that it gives physical insight into the evolution process.


2019 ◽  
Vol 867 ◽  
pp. 348-373 ◽  
Author(s):  
Z. Liu ◽  
D. Xie

Finite-amplitude wave groups with multiple near-resonances are investigated to extend the existing results due to Liu et al. (J. Fluid Mech., vol. 835, 2018, pp. 624–653) from steady-state wave groups in deep water to steady-state wave groups in finite water depth. The slow convergence rate of the series solution in the homotopy analysis method and extra unpredictable high-frequency components in finite water depth make it hard to obtain finite-amplitude wave groups accurately. To overcome these difficulties, a solution procedure that combines the homotopy analysis method-based analytical approach and Galerkin method-based numerical approaches has been used. For weakly nonlinear wave groups, the continuum of steady-state resonance from deep water to finite water depth is established. As nonlinearity increases, the frequency bands broaden and more steady-state wave groups are obtained. Finite-amplitude wave groups with steepness no less than $0.20$ are obtained and the resonant sets configuration of steady-state wave groups are analysed in different water depths. For waves in deep water, the majority of non-trivial components appear around the primary ones due to four-wave, six-wave, eight-wave or even ten-wave resonant interactions. The dominant role of four-wave resonant interactions for steady-state wave groups in deep water is demonstrated. For waves in finite water depth, additional non-trivial high-frequency components appear in the spectra due to three-wave, four-wave, five-wave or even six-wave resonant interactions with the components around the primary ones. The amplitude of these high-frequency components increases further as the water depth decreases. Resonances composed by components only around the primary ones are suppressed while resonances composed by components around the primary ones and from the high-frequency domain are enhanced. The spectrum of steady-state resonant wave groups changes with the water depth and the significant role of three-wave resonant interactions in finite water depth is demonstrated.


Author(s):  
Srinivasan Chandrasekaran ◽  
Madhavi Natarajan ◽  
Natarajan Chithambara Thanu

Presence of the perforated outer cover on the existing column members of offshore platforms reduces the direct wave impact on these members. Such applications are common in the coastal structures where perforated covers are provided on the seaside to dissipate the wave energy and to reduce the pressure on the members. Detailed studies on the variations of the hydrodynamic characteristics on the inner cylinder, encompassed by a perforated outer cover are scarce in the literature. Present study is focused the development of numerical model to investigate the variations in the water particle kinematics on the inner cylinder encompassed by perforated outer cover. Hydrodynamic characteristics are examined along the water depth through computation fluid dynamics (CFD) for perforation ratios (p%) varying in the range of 10 to 15%. Velocity profiles for different wave steepness are developed along with the design charts for the chosen perforation ratios. These design charts can be readily used for estimating the water particle kinematics for perforated members along the water depth.


Author(s):  
G. Y. Fan ◽  
J. M. Cowley

It is well known that the structure information on the specimen is not always faithfully transferred through the electron microscope. Firstly, the spatial frequency spectrum is modulated by the transfer function (TF) at the focal plane. Secondly, the spectrum suffers high frequency cut-off by the aperture (or effectively damping terms such as chromatic aberration). While these do not have essential effect on imaging crystal periodicity as long as the low order Bragg spots are inside the aperture, although the contrast may be reversed, they may change the appearance of images of amorphous materials completely. Because the spectrum of amorphous materials is continuous, modulation of it emphasizes some components while weakening others. Especially the cut-off of high frequency components, which contribute to amorphous image just as strongly as low frequency components can have a fundamental effect. This can be illustrated through computer simulation. Imaging of a whitenoise object with an electron microscope without TF limitation gives Fig. 1a, which is obtained by Fourier transformation of a constant amplitude combined with random phases generated by computer.


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