Capillary gravity waves caused by a moving disturbance: Wave resistance

1996 ◽  
Vol 53 (4) ◽  
pp. 3448-3455 ◽  
Author(s):  
E. Raphaël ◽  
P.-G. de Gennes
Keyword(s):  
Gravity Waves ◽  
Wave Resistance ◽  
Disturbance Wave

A Dissipative Green's Function Approach to Modeling Gravity Waves Behind Submerged Bodies

2020 ◽  
pp. 1-14
Author(s):  
Mirjam Fürth ◽  
Mingyi Tan ◽  
Zhi-Min Chen ◽  
Makoto Arai
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Gravity Waves ◽  
Potential Flow ◽  
Wave Resistance ◽  
Damping Term ◽  
Early Design ◽  
Resistance Components ◽  
Rayleigh Damping ◽  
Early Design Stages

Potential flow-based methods are common in early design stages because of their associated speed and relative simplicity. By separating the resistance components of a ship into viscous and wave resistance, an inviscid method such as potential flow can be used for wave resistance determination. However, gravity waves are affected by viscosity and decay with time and distance. It has, therefore, long been assumed that the inclusion of a damping parameter in potential flow would better model the wave resistance. This article presents a Kelvin–Neumann dissipative potential flow model. A Rayleigh damping term is inserted into the Navier–Stokes equations to capture the decay of waves. A new 3D Green's function based on the Havelock–Lunde formulation is derived by the use of a Fourier transform. An upper limit for the Rayleigh damping term is found by comparison with experiments and a possible improvement on conventional potential flow models for the wave making resistance prediction of a submerged ellipsoid is proposed. 1. Introduction To accurately determine the resistance is of great importance when designing a ship. Therefore, steady ship motion in calm water is a classical problem in ship hydrodynamics. Potential flow modeling is a common method to predict the wave resistance of ships. One benefit of potential flow is its computational speed. Speedy determination of the wave resistance is of great importance in early design stages. Because all ship properties are intertwined, it is not beneficial to dwell too much on one parameter. Potential flow-based models are, therefore, used for a wide range of industry applications during early phases of ship design (Wilson et al. 2010). A potential model using image sources to fulfill the free-surface condition and an exact body condition is known as a Kelvin–Neumann model. The Kelvin– Neumann problem is well known and well described, but it continues to be a topic of interest (Kuznetsov et al. 2002). Developments of Green's functions for resistance predictions is continuing to be of interest long after Michell (1898) developed his theory on the wave resistance of a ship. Recent Green's function applications include wave resistance determination (Taravella & Vorus 2012) and the calculations of forces acting on a submerged ellipsoid (Chatjigeorgiou & Miloh 2013). Doctors (2012) used a linearized potential flow method to determine the resistance components of a marine cushion vehicle.

scholarly journals Wave resistance for capillary gravity waves: Finite-size effects

2011 ◽  
Vol 96 (3) ◽  
pp. 34003 ◽  
Author(s):  
M. Benzaquen ◽  
F. Chevy ◽  
E. Raphaël
Keyword(s):  
Gravity Waves ◽  
Size Effects ◽  
Finite Size ◽  
Wave Resistance ◽  
Finite Size Effects

Wave resistance to vertical motion in a stratified fluid

1960 ◽  
Vol 7 (2) ◽  
pp. 209-229 ◽  
Author(s):  
F. W. G. Warren
Keyword(s):  
Gravity Waves ◽  
Equations Of Motion ◽  
Vertical Motion ◽  
Approximate Solutions ◽  
Stratified Fluid ◽  
Wave Resistance ◽  
Constant Density ◽  
Shaped Body ◽  
Set Up ◽  
Surrounding Fluid

When a body moves through a stratified fluid, i.e. one whose density decreases upwards, gravity waves are set up and this causes a resistance to motion. An axisymmetric case is considered in which a body moves steadily and vertically through a fluid whose density decreases exponentially upwards. The fluid is supposed perfect, incompressible, and unbounded in all directions. The equations of motion are linearized, and with a fairly general initial motion of the surrounding fluid, the limit of the solution as t → ∞ is evaluated. Transform methods are used to solve the equation of motion, and the methods of steepest descents and stationary phase are used to obtain approximate solutions.Streamlines and the distortion of the constant density levels for a spindle-shaped body are shown. The curves of resistance against a function of the velocity for the circular cylinder, the sphere, and a spindle-shaped body are also given. A criterion is given for when the maximum wave resistance for a sphere may be expected, and an estimate of this maximum resistance is made.

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