Kadomtsev–Petviashvili type equation for entire range of relative water depths

2018 ◽  
Vol 60 (1) ◽  
pp. 60-68
Author(s):  
Serdar Beji
Author(s):  
T J Jemi Jeya ◽  
V Sriram ◽  
V Sundar

This paper presents the results from a comprehensive experimental study on the Quadrant Face Pile Supported Breakwater (QPSB) in two different water depths exposed to three different oblique wave attacks. The results are compared with that for a Vertical face Pile Supported Breakwater (VPSB) for identical test conditions. The paper compares the reflection coefficient, transmission coefficient, energy loss coefficient, non-dimensional pressure, and non-dimensional run-up as a function of the relative water depth and scattering parameter. The results obtained for QPSB are validated with existing results. The salient observations show that QPSB experiences better hydrodynamic performance characteristics than the VPSB under oblique waves.


Author(s):  
Serdar Beji

A Korteweg & de Vries type equation with improved dispersion characteristics for uneven water depths is presented. The new KdV type equation contains mixed dispersion and shoaling terms, which extend its applicable range of relative depths to virtually deep waters. The wave equation also satisfies an important consistency condition that there is an exact agreement between the shoaling rate of the equation itself and the rate obtained from the constancy of energy flux. A finite-difference scheme is devised for simulating several linear and nonlinear cases over varying bathymetry. The performance the new KdV type equation is observed to be quite satisfactory.


Author(s):  
Peter McCallum ◽  
Vengatesan Venugopal ◽  
David Forehand ◽  
Rebecca Sykes

A frequency domain hydrodynamic assessment was carried out using WAMIT on buoy type wave energy converters (WECs), constrained to move in heave only. Control of the power take-off (PTO) system has been established through real control (damping resistance only) for an isolated WEC. This fixed value has then been applied to all WECs in an array of ten devices, set out in two rows. The array has been tested in six water depths, represented by the relative water depth d/λ0, ranging from 0.25 to infinite depth, where λ0 is the resonant wavelength of an isolated WEC in infinitely deep water. Incremental reductions in water depth, result in an drop in peak q̄-factor, which was also marked with a small shift in ka. It was deemed appropriate here to re-tune the PTO settings for the different water depths. The various interactions within the array were examined in more detail by considering the radiation forces between WECs. Results are presented, highlighting the most significant device interactions due to the variations in water depth. The growth and shift in ka of the peak forces are also evident in shallower water. Depth modified JONSWAP and Pierson-Moskowitz spectra have also been applied in order to calculate mean power production estimates for the various water depths. For the particular array and conditions considered, there was a clear downward trend in power captured when moving into progressively shallower water. This was in part due to the reduction in total energy available in the shallower spectra, but also because the frequency of peak performance of the array has shifted significantly.


1991 ◽  
Vol 155 (1) ◽  
pp. 219-226 ◽  
Author(s):  
PAUL W. WEBB ◽  
DOMINIQUE SIMS ◽  
WILLIAM W. SCHULTZ

Fast-start performance of rainbow trout (mass 0.187±0.022kg; mean±2S.E., N= 10) was measured in water of various depths. Relative water depth was defined as z/B, where z is the water depth measured from the air/water surface to the longitudinal midline of the body and B is the span of the caudal fin, 0.062±0.004m. Relative water depths (at absolute depths) tested were; 0.31 (at 0.05m), 1.11 (at 0.1m), 1.92 (at 0.15m), 2.73 (at 0.2m) and 7.56 (at 0.5m). Performance was defined in terms of the motion of the centre of mass as measured by the turning radius and the cumulative distance travelled in a given elapsed time. Turning radius was not affected by water depth and averaged 0.018±0.003m. Distance travelled was a positive function of water depth, although paired t-tests showed no significant effect of depth at 0.15 and 0.2 m after about 70 ms. Energy dispersion due to the formation of surface waves increased with decreasing relative water depth. The largest energy dispersion in wave formation at a relative water depth of 0.31 averaged about 70% of the useful mechanical work performed in deep water. Energy dispersion in wave generation was negligible for relative water depths larger than approximately 3. Energy dispersion is similar to that for rigid streamlined bodies moving at constant speed


Author(s):  
Lokesha ◽  
SA Sannasiraj ◽  
Vallam Sundar

Submerged structures serve as wave attenuators and are widely adopted for protecting the coast against erosion or to reduce forces on structures situated on its leeward side. Conventional submerged breakwaters are composed of rubble stones, and the sources for quarrying such stones have depleted drastically over a period of time. The artificial reefs are a replacement for submerged breakwaters formed by natural rocks due to its minimum impact on the marine environment, flexibility in molding to any desired shape and size. It is also believed to serve as a habitable environment to marine flora and fauna. In this study, a comprehensive experimental investigation is carried out in order to examine the effect of perforations on a submerged artificial reef exposed to regular and random waves. The tests with models of crest width ( B) of 0.2 m and crest height ( h) of 0.4 m are conducted for three different degrees of submergence ( d/ h) of 1.5, 1.38 and 1.25 in three different water depths, d. The article emphasizes the influence of relative water depth, relative crest width and the nature of the surface of the structure (impermeable or permeable) on its hydrodynamic performance characteristics.


Author(s):  
Kai Yan ◽  
Zhili Zou ◽  
Yalong Zhou

A laboratory experiment on the instability of Stokes wave trains with large steepness in finite water depths in a wave basin is performed. Two class instabilities of Stokes wave, quartet interaction and quintet interaction, were observed, and it is found that the evolution of crescent wave pattern is affected by the development of quintet interaction. The dependence of this effect on relative water depth was analyzed. The wave steepness for the occurrence of the competition is examined by applying linear instability analysis of Stokes wave.


2019 ◽  
Vol 153 ◽  
pp. 103542 ◽  
Author(s):  
Byeong Wook Lee ◽  
Changhoon Lee
Keyword(s):  

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