Characteristics Of Shallow Water Waves Research Articles

Uncertainties in regularized long-wave equation and its modified form: A triangular fuzzy-based approach

This article explores the solution of the regularized long-wave equation (RLWE) and modified RLWE (MRLWE) using a semi-analytical approach known as the homotopy perturbation transform method (HPTM), revealing the characteristics of shallow water waves and ion-acoustic plasma waves. The effectiveness and accuracy of the technique are demonstrated by solving scenarios involving a single solitary wave (SSW) and two solitary waves (TSW) presented and compared with the exact solution of the RLWE. Furthermore, we introduced a fuzzy model for both RLWE and MRLWE, considering uncertainties in the coefficients related to the wave amplitude, and to understand the behavior of both fuzzy RLWE (FRLWE) and fuzzy MRLWE (FMRLWE) in the SSW by examining various numerical results using MATLAB.

Full-scale unsteady RANS simulations of vertical ship motions in shallow water

The seakeeping behaviour of a vessel in shallow water differs significantly from its behaviour in deep water. In shallow water, a vessel's motion responses to incident waves will be affected by hydrodynamic effects caused by the presence of a finite depth. Given that a vessel will sail in shallow water at various times during its service life, such as when entering harbours, it is important to have an understanding of the influence of shallow water on ship motions. In this study, using a commercial unsteady Reynolds–Averaged Navier–Stokes solver, a numerical study of ship motions in shallow water was carried out. Firstly, the characteristics of shallow water waves were investigated by conducting a series of simulations. Then, a full-scale large tanker model was used as a case study to predict its heave and pitch responses to head waves at various water depths, covering a range of wave frequencies at zero speed. The motion results obtained were validated against related experimental studies available in the literature, and were also compared to those from 3-D potential theory. The results were found to be in good agreement with the experimental data. Finally, it was shown that vertical motions were significantly affected by shallow water.

Directional characteristics of shallow water waves along southwestern Bay of Bengal

The aim of the present research is to investigate the directional characteristics of waves along the southwestern Bay of Bengal based on the measured data during 2010 at 14m water depth. Diurnal, monthly and annual variation of reflected waves is studied for waves within a frequency range of 0.03–0.125Hz to eliminate the influence of local wave growth processes. High values of directional width during the annual cycle over the southwestern Bay of Bengal is associated with the swell reflection from the coast during southwest monsoon season (June–September) and intrusion of moderate easterly winds propagating from Gulf of Thailand over the narrow land mass of Thailand and Myanmar. The reflected wave energy is maximum (14%) during the southwest monsoon due to the presence of long period and intermediate period waves and minimum (9%) during the northeast monsoon season (October–January). During fair-weather period (February–May), 10% of the total energy is propagated towards offshore. We also analyzed the relationship between directional and non-directional wave parameters using continuous wavelet transform and wavelet coherence analysis (WCA). WCA shown that reflection coefficient and total energy is directly/inversely proportional to the swells, when signal of period approximately less/greater than one day is observed.

Characteristics of shallow water waves off the central west coast of India before, during and after the onset of the Indian summer monsoon

We studied the wave characteristics before, during and after the onset of the Indian summer monsoon based on data measured using the buoy moored at 3 locations off the central west coast of India. The study reveals the dramatic changes that occur in wave field due to the monsoon. Mean significant wave height before the onset of the monsoon was 0.7–0.9m and it increased to 2.4–2.6m during the onset of monsoon at the locations studied. Before the monsoon, due to the sea breeze, the wave height increased and reached its peak at ~1100 UTC. Variation of wave height in one day was up to 2m with the high values (>1m) occurring during the monsoon. In contrast, the range of the peak wave period in one day varied up to 15s before the monsoon due to the influence of the land breeze-sea breeze system. Also, before the monsoon, the spectral energy was in a wide range of frequencies due to the co-existence of swells and wind-seas, and 26% of the total spectral energy was in frequencies >0.25Hz. Conversely, during the monsoon, only 7.1% of the total energy was in frequencies >0.25Hz.

Directionality and spread of shallow water waves along the eastern Arabian Sea

Abstract. The directional characteristics of shallow water waves are described based on measured data during 2011 at two locations spaced at 350 km along the eastern Arabian Sea. Study shows that, for high swells (significant wave height > 1 m) approaching almost parallel to the coast, the difference between mean and principal wave direction at spectral peak is negligible. The directional spreading of wind-sea-dominated wave spectrum is less than that of the swell-dominated spectrum. Average value of the ratio of the directional width at twice the peak frequency and that at the peak frequency is 1.9 indicating that the directional width increased at higher frequency. Even though both locations studied are along the eastern Arabian Sea, there are more northwest waves due to shamal events and local winds found at the northern location (27%) than at the southern location (7%).

Shallow water wave spectral characteristics along the eastern Arabian Sea

The spectral characteristics of shallow water waves were studied at two locations along the eastern Arabian Sea during 2011. Wave spectra were single-peaked from June to October and predominantly double-peaked during the rest of the year. Even though both locations were subjected to open sea conditions, the percentage of single-peaked spectra was large (63 %) in the southern location compared to a location 350 km north (46 %), because of variation in local winds. Throughout the year, the double-peaked spectra were mostly swell dominated in the southern location. In the northern location, the double-peaked spectra during January to May and December were sea dominated due to the strong local winds blowing from north-west. For the double-peaked wave spectra, the average difference between the spectral peaks was 0.11 Hz, and the average ratio of the spectral energy density at the two peaks was 0.5. Significant wave heights up to 4.2 m and a maximum wave height of 7 m were observed during the south-west monsoon period. Fifty per cent of the waves recorded had spectral peak wave periods between 6 and 12 s. The narrowest directional spectra were found for waves with 10–12-s peak wave periods. Inverse wave age values were biased towards lower values with peaks in the range of 0.2–0.6, indicating a swell-driven wave regime along the eastern Arabian Sea.

Study on Wave Spectra in South Coastal Waters of Jiangsu

The paper examined the spectral characteristics of shallow water waves, which was based on the wave data collected along the south coast of Jiangsu. It proposes a tentative spectra model which can work better than Joint North Sea Wave Project (JONSWAP)spectra. Both of the value of tentative spectral parameters (α and γ) increase with significant wave height and spectral peak frequency. According to a regression analysis, empirical equations are achieved, which is related to the parameters with significant wave height and spectral peak frequency. The study shows that the measured wave spectra can be represented by tentative spectra, and the fitting results in high-frequency tail of tentative spectra are better than that of JONSWAP spectrum with modified parameters.

Spectral characteristics of high shallow water waves

The spectral characteristics of shallow water waves with significant wave height more than 2 m based on the data collected along the Indian coast is examined. It was found that the value of Joint North Sea Wave Project (JONSWAP) parameters ( α and γ) increases with significant wave height and mean wave period and decreases with spectral peak period. The estimated average value (0.0027 and 1.63) of the JONSWAP parameters, α and γ were less than the generally recommended values of 0.0081 and 3.3, respectively. By carrying out a multi-regression analysis, an empirical equation is arrived relating the JONSWAP parameters with significant wave height, peak wave period and mean wave period. It was found that the Scott spectra underestimate the maximum spectral energy of high waves. The study shows that the measured wave spectra can be represented by JONSWAP spectra with the JONSWAP parameters estimated based on the equation proposed in this paper.

EXPERIMENTAL AND NUMERICAL STUDIES ON THE TSUNAMI WAVE CHARACTERISTICS

ABSTRACT The devastating effects of the great Indian ocean tsunami has forced researchers in focusing their attention more vigorously on understanding the behaviour during its propagation and its effects on structures. This can obviously be accomplished through numerical and physical model studies or combination of both. The characteristics of a tsunami wave can approximately be same as that of a solitary wave which is basically a shallow water wave. Hence, the studies on the characteristics of shallow water waves have become an emerging topic of interest. An important aspect of a mitigation effort is to predict the tsunami wave kinematics. A combination of experimental and numerical simulation of tsunami represented by the solitary wave was studied and their comparison is discussed in this paper. The details of the numerical approach, methodology, instrumentation and measurement adopted for the present study are reported. The disagreement of the experimental simulation of solitary wave elevations with that of numerical simulation has been addressed and the possible discrepancies are overcome, the procedure of which are briefly discussed. The dynamics of the tsunami wave propagation over an uneven topography is studied using the developed numerical model.

4P-1180 Prognostic impact of aortic calcification index in patients under hemodialysis

The seakeeping behaviour of a vessel in shallow water differs significantly from its behaviour in deep water. In shallow water, a vessel's motion responses to incident waves will be affected by hydrodynamic effects caused by the presence of a finite depth. Given that a vessel will sail in shallow water at various times during its service life, such as when entering harbours, it is important to have an understanding of the influence of shallow water on ship motions. In this study, using a commercial unsteady Reynolds–Averaged Navier–Stokes solver, a numerical study of ship motions in shallow water was carried out. Firstly, the characteristics of shallow water waves were investigated by conducting a series of simulations. Then, a full-scale large tanker model was used as a case study to predict its heave and pitch responses to head waves at various water depths, covering a range of wave frequencies at zero speed. The motion results obtained were validated against related experimental studies available in the literature, and were also compared to those from 3-D potential theory. The results were found to be in good agreement with the experimental data. Finally, it was shown that vertical motions were significantly affected by shallow water.

Over-reflection and shear instability in a shallow-water model

The characteristics of shallow-water waves in a linear shear flow are studied, and the relationship between waves and unstable modes is examined. Numerical integration of the linear shallow-water equations shows that over-reflection occurs when a wave packet is incident at the turning surface. This phenomenon can be explained by the conservation of momentum as discussed by Acheson (1976). The unstable modes of linear shear flow in a shallow water found by Satomura (1981) are described in terms of the properties of wave propagation as proposed by Lindzen and others. Ripas's (1983) theorem, which is the sufficient condition for stability of flows in shallow water, is also related to the wave geometry. The Orr mechanism, which is proposed by Lindzen (1988) as the primary mechanism of wave amplification, cannot explain the over-reflection of shallow-water waves. The amplification of these waves occurs in the opposite sense to that of Orr's solution.

Simulating the characteristics of shallow water waves

An efficient algorithm, called ZEROIN, which uses the techniques of bisection, inverse quadratic interpolation, and the secant process, is presented to calculate the modulus k of cnoidal waves when k < 0.99, and for solitary waves when k > 0.99. To simulate random deepwater waves which are transformed as they propagate shorewards a subprogram is used to simulate autocorrelated Rayleigh distributed variates for wave periods and deepwater wave heights.

On spectral and statistical characteristics of shallow water waves

Spectral, zero up-crossing and Tucker's methods of analysis are examined for shallow water wave records. Among the wave height parameters H s and H _- are most reliable and consistent irrespective of the analysis technique. Tucker analysis, though simple, seems versatile for estimating these wave height parameters. The standard period parameters are less consistent. For practical purposes every period that might reasonably occur has to be considered along with their corresponding height estimate. Joint distribution of heights and periods is in agreement with the function proposed by CNEXO.

Two-Dimensional Characteristics of Shallow Water Waves

The shallow water channel is often applied to the investigation of the high speed air flow. But the behavior of the shallow water wave is not exactly the same as that of the shock wave in air. This is due to the essential difference of both properties and boundary conditions between the air and the water. This paper presents the information on the two-dimensional characteristics of shallow water waves. Assuming that the disturbance is small, the expression for wave-pattern is analyzed and the effects of the scale, the water-depth, the surface-tension and the velocity are explained. They are compared with the findings of the experiments.