Twenty-Second Symposium on Naval Hydrodynamics (1999) / Chapter Skim
Currently Skimming:
9 Shallow Water Hydrodynamics
9 Shallow Water Hydrodynamics
Pages 601-621
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 601... ...
ABSTRACT The shallow-water wave equations of Boussinesq type are used to simulate the ship waves at subcritical, transcritical, and supercritical speeds. An implicit difference method based on the CrankNicholson scheme is applied for the time and space discretization.
|
From page 602... ...
A slender-body theory along with the technique of asymptotic expansions is applied to approximate the flow generated by the hull. Both calculated integral quantities, such as wave resistance, sinkage and trim, as well as field quantities, such as wave profiles in the tank, are compared with those from recent measurements in the Duisburg Shallow Water Tank.
|
From page 603... ...
The application of the above shallow-water wave equations to ship waves is some what restricted by the assumption of small ratio it. Since all possible wave lengths are present in a ship wave pattern this assumption is not satisfied for wave components of small wave length, i.e., it violates the dispersion law of waves of small wave length.
|
From page 605... ...
is the local draft of the ship, the wave resistance can be obtained by a single-integral formulation L 2 RW =-Pg I (o~x,t)
|
From page 606... ...
at the transcritical speed range, and finally by a slow drop in the supercritical range. Representative wave patterns in these three speed ranges are visualized as density plots in Fig.
|
From page 607... ...
CONCLUSIONS An implicit difference method based on the CrankNicholson scheme was implemented to approximate the shallow-water wave equations of Boussinesq type. To simulate the wave generation by a slender ship in a shallow-water channel the technique of matched asymptotic expansions was applied.
|
From page 608... ...
Choi, H.S. and Mei, C.C., " Wave Resistance and Squat of a Slender Ship Moving Near the Critical Speed in Restricted Water," Proceedings of the 5th International Conference on Numerical Ship Hydrodynamics, 1989, pp.
|
From page 609... ...
1 1 1 1 1 i 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Fnh Fig. 3 Calculated wave resistance of a Series 60 hull moving along the centerline of a shallow-water channel at water-depth ho = 2.0 and channel-width ~ = 2.09 (a)
|
From page 610... ...
', , '(a) Specific total resistance + measured mean values, , , O calculated mean values - - - viscous component .
|
From page 611... ...
and measured (plus symbols) wave records from wave gauges fixed in the tank but observed from the Series 60 model passing by at the critical speed 611
|
From page 612... ...
and modified (dashed line) slender-body theory in the near field at the critical speed 0.20 0.15 0.100.050.00-0.05-0.10-0.15 0.200.150.100.050.00-0.05-0.10-0.15 1 ~ -- - ,,,,, - A , ~....
|
From page 613... ...
In finite depth water or shallow water, the mechanisms that influence the sea surface, including its homogeneity or inhomogeneity, become more complex than the associated deep water mechanisms. In the former case, water depth becomes important, and is not only functionally related to spatial gradients, per se, but water depth is also functionally related to temporal changes, which are dictated by appropriate formulations for the nonlinear source function and wave breaking dissipation.
|
From page 614... ...
Recently, [17] developed a shallow water wave model, which is based on Wave interactions, the so called 'quasi-resonant interactions'.
|
From page 615... ...
Finally, when the 4-wave interactions become coupled with wave interactions and when the waves are very steep and the angular propagation spread is very narrow, the three-dimensional wave-wave interactions may dominate even in deep water [31,193. In conclusion, shallow water Sn' is far more complicated than deep water Sn`.
|
From page 616... ...
1 is the only observed data for this hurricane event available to us. A detailed modeling of this storm must involve high-quality "ridded wind fields for the northwest Atlantic, time-series of observed wave spectra for the entire storm, from sites in shallow water as well as deep water, and implementation of the wave model for a reasonably fine-mesh grid (20km or better, for a mesoscale event such as this hurricane)
|
From page 617... ...
, Wave interactions decrease with decreasing water depth. Therefore, the wavelength of these shallow water waves, in case 2, should be shorter than that of the hurricane case, in case 1.
|
From page 618... ...
1 from the hurricane storm are not generated locally in the shallow water of the duck site. These swell waves propagate from deep water in the Orson ocean far from Duck, where they are generated during the active hurricane growth and evolution stages.
|
From page 619... ...
In any case, the alternate theory, which suggests that 4 wave interactions increase rapidly with decreasing water depth, cannot tune to both cases. 4 Conclusions Our new coastal wave model was shown to agree well with the observed data for both the hurricane storm and the winter storm cases of this study, with respect to peak frequency and wave height.
|
From page 620... ...
Su, M Y., 1982a: Three dimensional dee~water waves part I, Experimental measurement of skew and symmetric wave patterns, J
|
From page 621... ...
and N Huang, 1996: The Goddard Coastal Wave Model.
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.