Added resistance using Salvesen–Tuck–Faltinsen strip theory and the Kochin function

Mostafa Amini-Afshar*, Harry B. Bingham

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


It is now more than half a century since the development of the renowned and well-established strip theory of Salvesen–Tuck–Faltinsen (STF), Salvesen et al.(1970). One of the existing, and widely used, methods for calculating the wave drift force (zero-speed case), or added resistance (forward-speed case), within this strip theory, is a near-field formulation which was developed by Salvesen himself in Salvesen (1974), Salvesen (1978). This method invokes a weak-scattererassumption to drop one term, and also approximates the exponential terms as constant in the integrals over each two-dimensional ship section. These approximations are essentially a long-wave assumption Salvesen (1974). The main objective of this paper, which has been entirely inspired by the method of Kashiwagi et al. (2010), is to apply a far-fieldformulation, in the context of STF strip theory, without the above-mentioned assumptions. This far-field method is implemented following Maruo (1960b), Maruo (1963) and employs the Kochin function Kochin (1936) to express the wave kinematics in the far field. The necessary ingredients for this method are obtained by an implementation of STF theory using a low-order Boundary Element Method (BEM) and the two-dimensional free-surface Green function. No weak-scatterer assumption is required as the Kochin function explicitly includes the interaction of the disturbance potentials. Sectional integrals of the Kochin function are calculated analytically, assuming piecewise-constant variation of the potentials. Within this far-field framework all three integrals from Maruo's relation are treated, and the line integral along the vessel's length is calculated exactly assuming either a linear or a Fourier-mode decomposition of the non-exponential terms. The outcome is a far-field calculation procedure inside STF theory which compares very well with experimental measurements and relevant reference solutions. This is verified by the calculation of wave drift force and added resistance for six different ship hulls. One notable advantage of the presented framework, in comparison to Salvesen's method (and also to that of Gerritsma and Beukelman (1972)), is its ability to accurately predict the zero-speed wave drift force. In addition, the long-wave approximate form of the Kochin function method is also discussed. Similar to Salvesen's method, the wave drift force using this approximation, is expressed in terms of the body motion, the hydrodynamic coefficients and the sectional geometric constants. The approximate form performs well at zero-speed, but deteriorates quickly as the speed increases.
Original languageEnglish
Article number102481
JournalApplied Ocean Research
Number of pages22
Publication statusPublished - 2021


  • Wave drift force
  • Added resistance
  • Strip theory
  • The Kochin function
  • Far-field method


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