scholarly journals Sinusoidal Water Wave Dispersion Equation Formulated Using the Total Velocity Potential Equation

2021 ◽  
Vol 8 (8) ◽  
pp. 367-373
Author(s):  
Syawaluddin Hutahaean
Keyword(s):  
Dispersion Equation ◽  
Water Wave ◽  
Velocity Potential ◽  
Wave Dispersion ◽  
Potential Equation ◽  
Total Velocity

scholarly journals New Weighted Total Acceleration on Momentum Euler Equation for Formulating Water Wave Dispersion Equation

2021 ◽  
Vol 8 (4) ◽  
pp. 209-216
Author(s):  
Syawaluddin Hutahaean
Keyword(s):  
Euler Equation ◽  
Dispersion Equation ◽  
Water Wave ◽  
Wave Dispersion ◽  
Weighting Coefficient ◽  
Surface Boundary ◽  
Maximum Wave Height ◽  
Free Surface Boundary Condition ◽  
Surface Boundary Condition ◽  
Total Acceleration

In this present study, weighted total acceleration for Kinematic Free Surface Boundary Condition (KFSBC) and in momentum Euler equation was formulated. Furthermore, by using both aforementioned equations, the nonlinear water wave dispersion equation was then formulated. The wavelength obtained from dispersion equation is determined by weighting coefficient. The weighting coefficient value was determined by using the maximum wave height and critical wave steepness criteria which have been obtained from the previous studies.

Comments on Jacobs and Tsakonas: “Propeller Loading-Induced Velocity Field by Means of Unsteady Lifting Surface Theory”

1982 ◽  
Vol 26 (04) ◽  
pp. 266-268
Author(s):  
Theodore R. Goodman
Keyword(s):  
Velocity Field ◽  
Velocity Potential ◽  
Fourier Component ◽  
Surface Theory ◽  
Lifting Surface ◽  
Induced Velocity ◽  
Total Velocity

In the cited paper (2) a formula is given for the lth Fourier component of the velocity potential of an N-bladed propeller [equations (9) and (10) of the paper], (2). The total velocity potential is then, of course, given by the sum of all the components.

Analysis of water wave interaction with a submerged quarter-circular breakwater using multipole method

2020 ◽  
Vol 234 (4) ◽  
pp. 846-860
Author(s):  
Ai-jun Li ◽  
Yong Liu ◽  
Zuo-rui Lyu
Keyword(s):  
Water Wave ◽  
Series Solution ◽  
Velocity Potential ◽  
Separation Of Variables ◽  
Wave Interaction ◽  
Wave Forces ◽  
Submerged Breakwater ◽  
Circular Arc ◽  
Internal Fluid ◽  
Multipole Expansion Method

This article studies water wave interaction with a submerged quarter-circular breakwater based on potential theory and multipole expansion method. The obliquely and normally incident waves are independently considered. The series solution of velocity potential in the external fluid domain is expressed through the multipole expansions, while the series solution of velocity potential in the quarter-circular internal fluid domain is obtained through the separation of variables. Then, the unknown coefficients in the series solutions are determined by matching the boundary conditions between external and internal fluid domains. The calculation methods for the reflection and transmission coefficients of the submerged quarter-circular breakwater as well as the horizontal and vertical wave forces on the breakwater are presented. The wave forces acting on the submerged breakwater with a seaside quarter-circular-arc and that with a leeside quarter-circular-arc are compared. The hydrodynamic quantities of the submerged quarter-circular breakwater are also compared with those of the submerged semi-circular breakwater. In addition, the effects of breakwater radius, incident frequency, and incident angle on the hydrodynamic quantities of the quarter-circular breakwater are clarified. Valuable results for practical engineering application are drawn.

scholarly journals Horizontal circulation and jumps in Hamiltonian wave models

2013 ◽  
Vol 20 (4) ◽  
pp. 483-500 ◽  
Author(s):  
E. Gagarina ◽  
J. van der Vegt ◽  
O. Bokhove
Keyword(s):  
Velocity Field ◽  
Water Wave ◽  
Hamiltonian Dynamics ◽  
Hamiltonian Formulation ◽  
Three Dimensional ◽  
Wave Model ◽  
Wave Dispersion ◽  
Flow Profile ◽  
New Model ◽  
Wave Models

Abstract. We are interested in the modelling of wave-current interactions around surf zones at beaches. Any model that aims to predict the onset of wave breaking at the breaker line needs to capture both the nonlinearity of the wave and its dispersion. We have therefore formulated the Hamiltonian dynamics of a new water wave model, incorporating both the shallow water and pure potential flow water wave models as limiting systems. It is based on a Hamiltonian reformulation of the variational principle derived by Cotter and Bokhove (2010) by using more convenient variables. Our new model has a three-dimensional velocity field consisting of the full three-dimensional potential velocity field plus extra horizontal velocity components. This implies that only the vertical vorticity component is nonzero. Variational Boussinesq models and Green–Naghdi equations, and extensions thereof, follow directly from the new Hamiltonian formulation after using simplifications of the vertical flow profile. Since the full water wave dispersion is retained in the new model, waves can break. We therefore explore a variational approach to derive jump conditions for the new model and its Boussinesq simplifications.

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