It is convenient to combine the first-order terms first and then to compute its contribution to the total slowly varying second-order potential. Here attention is paid to the interaction between passing ships in restricted water. The additional terms in the Laplace equation are small and may be neglected. If no subscript is used the operator acting on S or a0 is two-dimensional in the horizontal plane. Here we derive a coupled algebraic set of equations for the expansion coefficients of the potential in the fluid region and the deflection.
However, we do not ignore the small term to determine its effect on the second-order force. In the three-dimensional case one also may derive such an expression. The latter term is the interaction effect of the incident and reflected waves. In order to solve the eikonal equation 5. Wave-drift forces and moments -- 4.
If the double body potential around the ship is known one can use an asymptotic short wave theory. For small values of F , for instance for very large vessels, it overestimates the wave resistance greatly, while for blunt ships it is not valid at all. First of all the forces described in 4. Later we take other effects into account as well. The finite draft problem -- 6.
Here S ω as defined by 7. The easiest way is to follow the derivation, presented in Sect. However we considered objects with zero draft only. Hermans در ۹ فصل به نگارش در آمده است. Generally these effects are hardly taken into account in numerical codes. For the wave resistance the theory results in the classical Michell integral as published in 1898 for the first time. We make use of this fact later.
One must keep in mind that the latter is quadratic with respect to the wave height and may become dominant in high sea states. Here again σ and γ are the unknown densities as in 8. To describe this phenomenon we first derive the second-order waves in the case that we have a simple spectrum of waves consisting of two monochromatic plane waves with frequencies close to each other. Roseau, Asymptotic Wave Theory North-Holland, Amsterdam, 1976 17. The first one uses the Fourier transforms; the other one is by means of a distribution of sources on the centre-plane.
Yeung, Application of slender body theory of ships moving in restricted shallow water, in Proc. Based on small amplitude waves, linearised problems for the velocity potential function and for the free surface elevation are formulated. In the deep water case it is similar to the disturbance of the moving pressure point. One may conclude that a proper description of the velocity field near the stagnation point influences the wave pattern near the bow greatly and that the added resistance increases significantly for increasing values of the velocity. If the function η x belongs to L2 , i. The solutions of these equations 5.
The latter integral follows from 2. In the next section it will be shown that, if the wall is free to move, the corresponding reaction potential also plays a role in the free surface condition 4. Cover design: eStudio Calamar S. In the downstream region a wavy disturbance may be present. The velocity potential can be derived from 8. To eliminate τ from 2.
The fluid velocity normal to the surface has to be equal to the normal component of the velocity of the surface itself. The characteristic equations of the first-order partial differential equation 2. Scattering of free surface waves -- 3. In principle, their method can be extended to the flexible platform case. At first the equations and linearized boundary conditions are derived describing the non-viscous free surface water waves, with special attention to the combination of steady and non-steady flow fields. The method of stationary phase -- B. No proofs of validity are given.
The second term is the modification due to small values of the forward velocity. . The waves are created at the free surface, which is characterised by the condition that along this surface the pressure is a constant. Therefore the contour passes the negative real pole above and the positive real pole below. This case is chosen because it is possible to determine most of the essential parts of the first- and second-order effects explicitly.