Fifth Order Stokes Wave Profiles

This study established the conditions in which mooring load is minimized in a fish cage that includes a damping buoy in specific wave conditions. To derive these conditions, numerical simulations of various mooring contexts were conducted on a fish cage (1/15 scale) using a simplified mass-spring model and fifth-order Stokes wave theory. The simulation conditions were as follows: (1) bridle-line length of 0.8–3.2 m; (2) buoyancy of 2.894–20.513 N for the damping buoy; and (3) mooring-rope thickness of 0.002–0.004 m. The wave conditions were 0.333 m in height and 1.291–2.324 s of arrival period. Consequently, the mooring tensions tended to decrease with decreasing mooring line thickness and increasing bridle-line length and buoyancy of the buoy. Accordingly, it was assumed to be advantageous to minimize the mooring tension by designing a thin mooring line and long bridle line and for the buoyancy of the buoy to be as large as possible. This approach shows a valuable technique because it can contribute to the improvement of the mooring stability of the fish cage by establishing a method that can be used to minimize the load on the mooring line.

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Full-Scale CFD Analysis of Double-M Craft Seakeeping Performance in Regular Head Waves

Journal of Marine Science and Engineering ◽

10.3390/jmse9050504 ◽

2021 ◽

Vol 9 (5) ◽

pp. 504

Author(s):

Deniz Ozturk ◽

Cihad Delen ◽

Simone Mancini ◽

Mehmet Ozan Serifoglu ◽

Turgay Hizarci

Keyword(s):

Full Scale ◽

Stokes Wave ◽

Added Resistance ◽

Motion Responses ◽

Seakeeping Performance ◽

Head Waves ◽

Calm Water ◽

Maximum Improvement ◽

Fifth Order ◽

Regular Head Waves

This study presents the full-scale resistance and seakeeping performance of an awarded Double-M craft designed as a 15 m next-generation Emergency Response and Rescue Vessel (ERRV). For this purpose, the Double-M craft is designed by comprising the benchmark Delft 372 catamaran with an additional center and two side hulls. First, the resistance and seakeeping analyses of Delft 372 catamaran are simulated on the model scale to verify and compare the numerical setup for Fr = 0.7. Second, the seakeeping performance of the full-scale Double-M craft is examined at Fr = 0.7 in regular head waves (λ/L = 1 to 2.5) for added resistance and 2-DOF motion responses. The turbulent flow is simulated by the unsteady RANS method with the Realizable Two-Layer k-ε scheme. The calm water is represented by the flat VOF (Volume of Fluid) wave, while the incident long waves are represented by the fifth-order Stokes wave. The residual resistance of the Double-M craft is improved by 2.45% compared to that of the Delft 372 catamaran. In the case of maximum improvement (at λ/L = 1.50), the relative added resistance of the Double-M craft is 10.34% lower than the Delft 372 catamaran; moreover, the heave and pitch motion responses were 72.5% and 35.5% less, respectively.

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A high-order cnoidal wave theory

Journal of Fluid Mechanics ◽

10.1017/s0022112079000975 ◽

1979 ◽

Vol 94 (1) ◽

pp. 129-161 ◽

Cited By ~ 64

Author(s):

J. D. Fenton

Keyword(s):

Shallow Water ◽

Wave Height ◽

Water Depth ◽

Wave Theory ◽

High Order ◽

Stokes Wave ◽

Cnoidal Wave ◽

Expansion Parameter ◽

Wave Solutions ◽

Fifth Order

A method is outlined by which high-order solutions are obtained for steadily progressing shallow water waves. It is shown that a suitable expansion parameter for these cnoidal wave solutions is the dimensionless wave height divided by the parameter m of the cn functions: this explicitly shows the limitation of the theory to waves in relatively shallow water. The corresponding deep water limitation for Stokes waves is analysed and a modified expansion parameter suggested.Cnoidal wave solutions to fifth order are given so that a steady wave problem with known water depth, wave height and wave period or length may be solved to give expressions for the wave profile and fluid velocities, as well as integral quantities such as wave power and radiation stress. These series solutions seem to exhibit asymptotic behaviour such that there is no gain in including terms beyond fifth order. Results from the present theory are compared with exact numerical results and with experiment. It is concluded that the fifth-order cnoidal theory should be used in preference to fifth-order Stokes wave theory for wavelengths greater than eight times the water depth, when it gives quite accurate results.

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On the realization of nonlinear wave profiles using the Banach fixed-point theorem: Stokes wave in a finite depth

Journal of Marine Science and Technology ◽

10.1007/s00773-005-0200-7 ◽

2005 ◽

Vol 10 (4) ◽

pp. 181-187 ◽

Cited By ~ 4

Author(s):

Taek S. Jang ◽

S.H. Kwon ◽

Takeshi Kinoshita

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Nonlinear Wave ◽

Point Theorem ◽

Finite Depth ◽

Stokes Wave ◽

Banach Fixed Point Theorem ◽

Wave Profiles

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Physics of Traveling Waves in Shallow Water Environment

Water ◽

10.3390/w13212990 ◽

2021 ◽

Vol 13 (21) ◽

pp. 2990

Author(s):

Igor Shugan ◽

Sergey Kuznetsov ◽

Yana Saprykina ◽

Yang-Yih Chen

Keyword(s):

Traveling Waves ◽

Water Environment ◽

Stokes Wave ◽

Type Model ◽

Intermediate Water ◽

Boussinesq Model ◽

Weakly Nonlinear ◽

Shallow Water Environment ◽

Fifth Order ◽

Wave Properties

We present a study of the physical characteristics of traveling waves at shallow and intermediate water depths. The main subject of study is to the influence of nonlinearity on the dispersion properties of waves, their limiting heights and steepness, the shape of solitary waves, etc. A fully nonlinear Serre–Green–Naghdi-type model, a classical weakly nonlinear Boussinesq model and fifth-order Stokes wave solutions were chosen as models for comparison. The analysis showed significant, if not critical, differences in the effect of nonlinearity on the properties of traveling waves for these models. A comparison with experiments was carried out on the basis of the results of a joint Russian–Taiwanese experiment, which was carried out in 2015 at the Tainan Hydraulic Laboratory, and on available experimental data. A comparison with the experimental results confirms the applicability of a completely nonlinear model for calculating traveling waves over the entire range of applicability of the model in contrast to the Boussinesq model, which shows contradictory and unrealistic wave properties for moderate wavelengths.

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