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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line A DESIGN TOOL FOR HIGH SPEED FERRIES WASHES 957 A Design Tool for High Speed Ferries Washes D.Aelbrecht1 J.-C.Dern2,3 Y.Doutreleau4 (1EDF—Laboratoire National d'Hydraulique et Environnement, 2Consultant, 3Océanide BGO/FIRST, 4DGA-Bassin d'Essais des Carènes, France) ABSTRACT The high waves generated by fast ferries may have detrimental effects when approaching the coast. The aim of this study is to determine the characteristics of ship wash or groups of high-speed ship waves in coastal and shallow water regions. The purpose of the method developed herein is to provide a tool for authorities as regards speed limits and routes for fast ferries approaching the coasts. The waves generated by high-speed ships are represented by their free wave spectrum. This spectrum is determined digitally using a wave resistance program (POTFLO) based on the Neumann Kelvin model. It is assumed that the free waves propagate in the same manner as a short crested sea, defined by a directional energy spectrum. This energy spectrum is expressed explicitly in terms of the free wave spectrum. Spatial wave propagation is then modeled over time using a third-generation spectral wave model named TOMAWAC, based on a finite element technique. Evolution over time is depicted at certain critical positions along the shore. Results are given in terms of significant wave heights and mean wave periods for different ship routes and speeds. INTRODUCTION In recent years, numerous papers have been published on fast ship wash (Danish M.A. 1997, Henrik Kofoed et al 1996, Kirkegaard et al 1998, Stumbo et al 1999). The term “ship wash” (or “wake wash”) refers to the arrival on the coast of waves created by fast ships travelling offshore. If the ship is travelling at high speed, the amplitude of the waves arriving on the coast may be high. These high waves are potentially dangerous in that they provoke unacceptable motions and reduced stability for small vessels and ships in coastal waters, plus unacceptable wave agitation and risks for swimmers and other users along the coast and on beaches. This paper describes a simulation method developed as a tool for maritime safety authorities and shipyards involved in the design and building of high-speed ships. Recent simulation results are presented for the case of a standard high-speed ferry referred to as “Nrt” (navire rapide type), approaching the Port of Nice from Corsica. The characteristics of the Nrt are as follows: - length at waterline LPP=87 mètres - displaced volume ∇=1200 m3 - length/width ratio equal to 5.7 - length/draft ratio equal to 36 - max. speed u0=37 noeuds i.e. a Froude number corresponding to a hydrodynamically fast ship - the Froude number based on the displaced volume is equal to 1.865, hence categorizing this ship as a fast ship according to IMO regulations (safety code—chapter 10 of SOLAS). According to this rule, adopted by Bureau Veritas in the framework of its regulations concerning high-speed ships, a ship is considered to be fast if F∇≥1.181. SHIP WAVE FIELD AND AMPLITUDE SPECTRUM Ships travelling at a constant speed in calm waters generate a complex wave system (referred to as “ship wave field”) moving at the same speed as the ship itself and therefore appearing as immobile to observers on board the ship. Using a fixed point, the wash can be modeled in the form of superimposed plane waves (Newman 1977): the authoritative version for attribution. (1) within a Cartesian coordinate system ΩXYZ whereby: - Z=0 signifies undisturbed water, - ΩZ is directed upwards,

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line A DESIGN TOOL FOR HIGH SPEED FERRIES WASHES 959 This determination can be carried out in two manners: - Numerically, with the aid of a calculation code based on the Neumann-Kelvin model: density σ (x, y, z) results directly from this calculation. - Experimentally, by measuring the ship wave field using a towing tank (longitudinal cuts) and pinpointing the singularity distribution which is most representative of the measured field. - The Kochin function H (k, θ) is then calculated using formula (8). - The free wave amplitude spectrum is then calculated using formula (14). - The ship wave field is then deduced ζ (x, y) using formula (13). - The ship waves are significant in the following sector (16) (17) is the Kelvin angle. - formula (13) is relative to an Oxy point related to the ship; O being the bow, Ox being in the symmetrical plane and directed to the fore and Oy being in the transverse plane directed to portside. - the scope of the wave field is x=0 to x=−∞ Particular case of ultra high-speed ships Ultra high-speed ships sail at higher speeds than the standard high-speed ships currently in service. Ultra high-speed ships can briefly be described as ships travelling at a higher speed than that corresponding to the last bump on the wave resistance curve. Associated with these high speeds, the ship wave far-field is composed mainly of divergent waves, providing the hull is streamlined (Ogilvie 1977). As regards wave resistance, transverse waves remain important as demonstrated by the following formula valid to infinite depths (Newman 1977): (18) whereby the factor cos3 θ implies that the portion of wave resistance is more strongly-associated with transverse waves (θ≈0) than with divergent waves The amplitude spectrum of ultra high-speed ships is given for the first approximation order by a very simple formula (demonstrated in Kostyukov 1968): (19) K(θ)=k0.sec2θ. whereby zc<0 is the hull center immersion, W is the hull volume and If the formula is written as follows: (20) the amplitude spectrum tends towards zero when the Froude number based on hull center immersion rises indefinitely. In this limit case, the wave system is reduced to a single wave enveloping the ship, whose amplitude, which is independent of speed, drops very rapidly as we head away from the ship: (21) This wave is a local disturbance; all free waves having disappeared. Formula (19) gives the amplitude of energy-radiating free waves creating coastal wash. This formula is applicable to high Froude numbers, before reaching the degenerated case represented by formula (21). An ultra-fast ship may therefore create less wash than a high-speed ship. We therefore obtain the classic result illustrated by (Sharma 1968), in which the decrease in the amplitude spectrum with a Froude number between 0.5 and 0.7 was demonstrated for a particular case. the authoritative version for attribution.

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line A DESIGN TOOL FOR HIGH SPEED FERRIES WASHES 960 Numerical computation of the wave amplitude spectrum We first find the singularity distribution [for instance a source distribution σ(x, y, z)] equivalent to the hull using a Neumann-Kelvin code (Brard 1972). Solving the Neumann-Kelvin system of equations is a rather difficult task, for which a completely satisfactory answer can't be given for the moment: however, some numerical code have been implemented, that can give interesting results. POTFLO implements the method of source distribution of singularity, which allows to solve the Neumann-Kelvin problem by solving an integral equation over the hull. As soon as the source distribution σ is known, we can compute: • The wave amplitude A(θ), throught the computation of Kochin function H (θ) (formula (8) and (15)). This is the direct method. • The free surface elevation η along longitudinal cuts. Then, using a kind of Fourier analysis (a code called ACVCL) of it, we can obtain the wave amplitude spectrum. This is the indirect method. This second method is useful to check the computations done by the first method. Results Neumann-Kelvin theory assumes that the ship is slender and that the speed is not too high. As the case of a high speed ship is perhaps out of the scope of this theory, we have tried to have the most confident result as we can. To achieve this, we did a sensitivity study of the results with respect to the refinement of the mesh of the hull. The case called Nrt1 contains 320 elements, whereas Nrt2 has 477 and Nrt3 580. Longitudinal cuts Fig 1 shows 1 longitudinal cuts computed by POTFLO for the 3 meshes at a transverse distance of 50 meters for a speed of 35 knots. The origin of the axis is located at the bow of the ship. We see a fairly good convergence of these curves with the refinement of the hull mesh: The two last meshes (nrt2 et nrt3) give closer results than the first one (nrt1). However, the wave elevation at 35 knots seem to be a bit exaggerated: this is undoubtedly due to the limitation of Neumann-Kelvin theory at high speed. Wave amplitude spectrum The wave amplitude spectrum A(θ) is expressed from Kochin function H(θ) using formula (14). Figure 2 shows the modulus of the Kochin function with respect to θ at 35 knots using the two method of computation (direct use of POTFLO or indirect use of POTFLO through ACVL). We find a relative good agreement between the results of the two methods. However a maximum appears around 75 degrees: we can be doubtful about the real existence of it, and it corresponds, according to the dispersion equation (12) to high frequencies. Also, these waves should not propagate very far. Generally speaking, big angles (above 70°) are problematic: indeed, the Kochin function should vanish when θ tends to 90°. But, computations are hardier, as this area corresponds to frequency going to infinity. The direct consequence is that the values of the Kochin function are not very accurate in this area, and the division by cos3θ to obtain A(θ) makes it worse. It is necessary to truncate the wave amplitude spectrum in the vicinity of 90°. Conclusion Although some limitations of the code, the wave amplitude spectra computed are representative. So they can be used as inputs of a wave propagation code. The spectra have been computed at 3 speeds, 15, 25 and 35 knots with the mesh Nrt3. For the sake ok clarity, their amplitudes has been multiplied by cos3θ. We note f(θ)+ig(θ)=cos3θA(θ). Fig 3 shows real part f and imaginary part g at 35 knots. COASTAL WAVE PROPAGATION MODELLING Once the ship wave field has been computed, one has to determine the wave characteristics in the nearshore zone. It is then necessary to describe the wave field in a fixed geographical frame. In this fixed frame Ω'X'Y' Z', the Z' axis is directed vertically upward, X'Y' defining the horizontal plan coincident with the still water level. The ship route is oriented with an angle β such that it is possible to express quantities from the frame Oxyz to the frame Ω'X'Y'Z' through following formulae: (22) the authoritative version for attribution. In the following text, the prime (′) symbol will be omitted in order to simplify the notations. Then, the wave field described by equation (13) is expressed in the ΩXYZ frame by:

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line A DESIGN TOOL FOR HIGH SPEED FERRIES WASHES 961 (23) where ω is the pulsation given by relation (2) with th kh=1, when the ship evolves in deep water. To each propagation angle θ, we can associate a frequency f in the fixed frame such that: (24) Coupling between amplitude spectrum and variance (or energy) spectrum The third-generation spectral wave model TOMAWAC is used here for modelling the wave propagtion towards the shore. It computes the directional wave variance (or energy) spectrum. As for all spectral models, it assumes that the phases related to each wave component (i.e. each frequency) are distributed in a random way. A lot of details on this model can be found in the following references (Aelbrecht et al 1998, Benoit 1995, Benoit et al 1997). When comparing the expressions for the sea level variations through the amplitude spectrum approach in one hand, and through the wave variance spectrum approach in the other hand, we can propose a relation between the amplitude spectrum and the directional variance spectrum F(f, θ): (25) where ∆θ and ∆f are the directional and frequencial discretizations used by the model respectively. This is a purely numerical relation, which has no real significance in termes of mathematical equivalence. The values of F related to depends on the discretizations used in the wave propagation model. Practically speaking, for each angle θ, one computes a frequency f following equation (24), and one computes values of F(f, θ) following equation (25), once ∆f and ∆θ are fixed. The instabilities that have been found by the Bassin d'Essais des Carènes in the numerical results related to the amplitude spectrum for θ angles greater than 70°, suggest to adopt a truncature of the wave amplitude spectrum and to forget the wave amplitude spedctrum information for such high angles. Highlighting simulations Wave propagation simulations have been performed on a maritime domain concerned by the ferries routes coming from Corsica (towns of Bastia and Ajaccio) and reaching the harbour of Nice along the French Riviera (Figure 4). Bathymetry and map SHOM n° 5176 of the French Navy. A minimum water depth of 5 m is imposed in the model: the TOMAWAC model used here is no more valid for regions of shallower water depths. We investigated few routes and ship speeds along computational domain is coincident with the ship route. We report here only few of the numerous simulations which have been performed. Simulation 2: Route A-B-Harbour. Speed of 35 knots on A-B, 15 knots on B-Harbour The computational domain is illustrated on Figure 5. Point B is located 1 nautic mile southward from the East light of the Nice harbour. Point A is roughly located 1 nautic mile along the direction 313°N from B, and corresponds to the initial position of the ship in our simulations. We assume that the ship wave field that has been generated before its position in A has no influence on the coastal area of interest. Simulation 4: Route A′-B′-Harbour. Speed of 35 knots on A′-B′, 15 knots on B′-Harbour In addition to simulation 4 above, it has been decided to look at the case of a ship approaching very near the coastline and keeping its cruise speed of 35 knots on this A′-B′-Harbour route. This lead to: Simulation 4bis: Route A′-B′-Harbour. Speed of 35 knots on A′-B′, 35 knots on B′-Harbour The computational domain for these two simulations is given on Figure 6. Point B′ is located 1 nautic mile in the 159°N cape from the east light of the Nice harbour. Point A′ is roughly located at 0.6 nautic mile (1000 m) along the 309° N direction from point B′, and as before corresponds to the initial position of the ship. Again, we assume that the ship wave field that has been generated before its position in A′ has no influence on the coastal area of interest. Simulation 6: Route A″-B-Harbour. Speed of 35 knots on A″-B, 15 knots on B-Harbour The computational domain for this simulation is given on Figure 7. Point B is the same as for simulation 2 (see texte before). Point A″ is roughly located at 1 nautic mile along the 332° direction from point B, and as before corresponds to the initial position of the ship in this simulation. Again, we the authoritative version for attribution.

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line A DESIGN TOOL FOR HIGH SPEED FERRIES WASHES 962 assume that the ship wave field that has been generated before its position in A″ has no influence on the coastal area of interest. Simulations parameters Simulations are performed in a unsteady mode, in order to reproduce the time-varying development of the wave field generated by the high-speed ferry. At each time step, one determines the ship position and assigns the wave variance spectrum deduced from the ship speed at each node along the boundary of the domain, that coincides with the ship position. This is a realistic procedure which enables to reproduce the wave energy quantity that is transferred by the ferry to the oceanic domain. With the help of finite element technique, mesh size for all simulations varies from 80 m offshore to less than 15 m near the shore. Time step is fixed at 1 s. In addition to the usual processes that affect the wave propagation (geometric refraction and shoaling mainly), the model also accounts for the dissipative process through depth-induced wave breaking. The wave variance spectrum is discretized using 25 frequencies fj distributed with respect to a geometric serie (fj=0.05. (1.12)j), and 24 directions regularly spaced with ∆θ=15°. For information, one simulation, which roughly corresponds to 6 minutes duration in real time (time necessary for the ship to reach the harbour from the initial position A or A′ or A″), requires 10 hours of computational time on a HP B132 work station. This relatively high CPU time is due to a very small time step and a fine discretization in frequency and direction of the wave variance (or energy) spectrum. Simulations results For each simulation, we provide, for 4 “strategic” points along the shore (Pt1, Pt2, Pt3, Pt4), the time-evolution of the significant wave height Hs computed by the model from the directional variance spectrum. Water depths at these 4 locations are: Point Pt1: water depth: 6 m Point Pt2: water depth: 9 m Point Pt3: water depth: 10 m Point Pt4: water depth: 20 m This information particularly enables to determine, for each simulation, (1) the maximum significant wave height Hsmax reached at these 4 positions (NB: Hsmax is different from the maximum wave height Hmax of a wave train), and (2) the time Tmax corresponding to this maximum value. Results for the 4 simulations presented here are given on figures 8 to 11. Nota: Results of nearshore wave propagation modelling are given in terms of a spectral significant wave height computed at each node of the computational domain. The spectral significant wave height is a characteristic quantity of the wave energy spectrum. For standard sea states, this value is equivalent to the statistic significant wave height, i.e. the arithmetic mean of the 1/3 upper percentile of the wave heights serie of a wave train. The time varying evolution of the significant wave height is particularly useful to determine the maximum value reached during the simulation at all locations, i.e. Hsmax, which corresponds to the peak of wave energy observed at these points. For all simulations, except simulation 4bis which corresponds to an exceptional case, values of Hsmax do not exceed 0.20 m near the coast. Corresponding maximum wave heights Hmax could be 0.30 m. Two other informations can also be deduced from the simulations: - First information deals with the time-lag between the time when the ferry reaches the latitude of one coastal location and the one when maximum waves reach the same coastal location. This time-lag could reach about 2 minutes - Second is the suddenness of the ship-wash development when arriving at the coast, which could be measured by a time τmax necessary for the waves to go from a zero value to their maximum value Hsmax at one location. This time τmax depends on the ship route and speed, and on the coastal location of interest. For simulation 4bis, value of τmax at point 2 is about 20 s. This clearly illustrates the rapidity of the ship-wash phenomena at the coast. the authoritative version for attribution.

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line A DESIGN TOOL FOR HIGH SPEED FERRIES WASHES 963 FUTURE WORK AND CONCLUSIONS Ships approaching ports at relatively high speeds generate waves which propagate naturally towards the coast and die down on the shore in the form of so-called “wash”. The initial aim of this study was to assess whether the height of these wash waves is significant or not. The study was conducted using available tools, which we were able to use in a complementary manner thanks to an original methodology drawn up for the study. The main advantage of this methodology is that it enables a non-stationary calculation of wave propagation over time. The ship's trajectory with regards to the coast is therefore unimportant. The feasibility and validity of the proposed methodology have been demonstrated on a standard high-speed ship. The study enabled the pinpointing of coastal areas most exposed to the wash phenomenon. As regards the example of the Port of Nice, wash wave height in the most exposed coastal areas is 10 cm to 50 cm on average (in water depths of 5 meters), at speeds compliant with the legal limit laid down on June 3, 1998 (decree 23/98). At maximum values, the wash waves could reach a height of 65 cm. If no speed limit is imposed, average wash wave height is 70 cm on average with a maximum theoretical value of 90 cm. The shipping authorities and shipyards now have access to a range of calculation codes enabling the prior quantitative evaluation of high-speed ship wash, using coastal zone relief and bathymetry maps for the areas crossed by the ship. Operators will therefore, in the future, be able to equip themselves with new high-speed car ferries satisfying the safety standards laid down by shipping authorities. The aim of current research is to optimize calculation rules, in particular as regards hull discretization (number of sources), bathymetry, the amplitude and energy spectrum (angle and frequency) and the length of the Kelvin sector to be taken into account. Other parameters should also be considered, such as the effect of the ship's sinkage and trim. In the longer term, studies could be undertaken on the influence of the ship's non-stationary character on wash and in particular the effect of speed reduction and heading change during port approach. This type of non-stationary situation is well represented by the TOMAWAK software but not by the POTFLO pre-processor. ACKNOWLEDGMENTS: The development of this method for computing ship wash was requested by the “Bureau des Enquêtes Techniques et Administratives après Accidents en Mer (BEA-MFR)” (Maritime Technical & Administrative Board of Inquiry) and backed by the French Ministry of Transport, (Department of Research and Scientific & Technical Affairs). The authors would like to thank the “Institut Français de Navigation” (French Shipping Institute) and the experts from BEA-MER who enabled the authors to draw up this practical tool thanks to their advice, expertise and in-depth knowledge of the site. REFERENCES Aelbrecht D., Benoit M., Marcos F., Goasguen G. 1998—Prediction of Offshore and Nearshore Storm Waves Using a Third Generation Spectral Wave Model. Proc. of ISOPE'98 conference, Vol. III, 71–76, Montréal, Canada, May 1998. Benoit M. 1995—Logiciel Tomawac de simulation des états de mer en éléments finis. Note théorique de la version 1.0—Rapport EDF-DER HE-42/95/047/A Benoit M., Marcos F., Becq F.. 1997. Development of a third generation shallow water wave model with unstructured spatial meshing. Proc. of ICCE'96 conference, Orlando, USA, September 1996. Brard, R. 1972—The representation of a given ship from by singularity distributions when the boundary condition on the free surface is linearized— Journal of Ship Research, Vol 16, number 1, March. Danish Maritime Authority, January 1997—Report on the Impact of High Speed Ferries on the External Environment. Eggers, K.W.H, Sharma, S.D., Ward, L.W. 1967—An assessment of some experimental methods for determining the wave making characteristics of a ship form, Transactions Sname 75, 112–144. Henrik Kofoed—Hansen, October 1996—Technical Investigation of Wake Wash from Fast Ferries—DHI/Danish Maritime Authorities Kirkegaard J., Højtved N., Holmegaard krsitensen H.O., 1998—Fast Ferry Operation in the authoritative version for attribution.

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line A DESIGN TOOL FOR HIGH SPEED FERRIES WASHES 964 Danish Waters—XXIX session de l'association internationale des congrés de navigation, La Have. Kostyukov, A.R—Theory of Ship Waves and Wave resistance—ECI, Towa City, Iawa, 1968. Newman, J.N. 1977—Marine Hydrodynamics—MIT Press, Massachusetts. Ogilvie, T.F. 1977—Singular perturbation problems in ship hydrodynamics, Adv. Appl. Rech. 17, Academic Press. Sharma, S.D., 1969—Some Results Concerning the Wavemaking of a Thin Ship, Journal of Ship Research, 13, 72–81. Stumbo, S., Fox, K., Dvorak, F. Elliot, L. The Prediction, Measurement and Analysis of Wake Wash from Marine Vessels—Marine Technology, vol 36, n° 4, Winter 1999, pp 248–260. Figure 1: longitudinal cuts Figure 2: Kochin function Figure 3: Wave amplitude spectrum at 35 knots the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. coming from Bastia—Corsica) coming from Bastia very near the coastline) A DESIGN TOOL FOR HIGH SPEED FERRIES WASHES on the A'-B'-Harbour route (Exceptional case of ferries Figure 5—Configurations for simulations 1, 2 and 2 bis Figure 6—Configurations for simulations 3, 4 and 4bis on the A-B-Harbour route (normal route for ferries from Ajaccio—Corsica) A”-B-Harbour route (normal route for ferries coming Figure 7—Configurations for simulations 5 and 6 on the 965

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. A DESIGN TOOL FOR HIGH SPEED FERRIES WASHES 966

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line A DESIGN TOOL FOR HIGH SPEED FERRIES WASHES 967 DISCUSSION L.Doctors The University of New South Wales, Australia Could the authors kindly confirm that the first part of their calculation employs a deep-water quasi-steady-state calculation for the estimation of the wave spectrum. Presumably the second part of the calculation is truly unsteady as the procedure follows the waves as they enter the shallow water and refract. Would there be a large error for those cases where the vessel is, in fact, accelerating or deccelerating? I would like to thank the authors for an interesting and practical paper on an important topic. AUTHOR'S REPLY Referring to Dr Doctor's question, we confirm that in the first part of the calculation we use a deep-water quasi- steady-state calculation for the estimation of the wave spectrum. That is, we neglect the phase during which the vessel pass from a constant speed to a smaller one as it arrives near the harbour. In fact the effect of an accelerating motion on the wave making of a vessel is a very complicated problem for which solutions exist only in some cases. We make for instance reference to the work by Doctors L.J. and Sharma S.D. on the wave resistance of an air-cushion vehicle in steady and accelerated motion (J. of Ship Res. 16, 1972). For the general case of a ship, to our knowledge, there is no validated programme computing the wave resistance in accelerated motion. Our application to high speed ferries washes corresponds to the more difficult case of wave resistance in decelerated motion for which no validated solution seems to exist. Let us add that the assumption of deep water for the calculation of the ship wave spectrum is correct for the case of the approach of the harbour of Nice. Indeed, the water depth is very large along the coast except very near the harbour entrance. We confirm also that our calculation is truly unsteady in the second part when the waves propagate into shallow water. DISCUSSION D.Hendrix Naval Surface Warfare Center, Carderock Division, USA This paper presents a very interesting application of potential flow to a current design problem. Since, as the authors observe, “Solving the Neumann-Kelvin system of equations is a rather difficult task.” I would like to suggest that the authors consider using the slender ship theory to determine the wave amplitude function. As we reported earlier this week, (in Practical CFD application to design of Wave Cancellation Multihull Ship) the use of slender ship theory allows the computation of many more conditions than other competing methods while correctly capturing trends due to geometry. The use of this wave amplitude function should allow design of high speed ferries to consider the effect of wake wash. AUTHOR'S REPLY Referring to Dr. Hendrix's comment, we consider favourably its suggestion to use another ship wave theory to determine the wave spectrum. One candidate is the slender ship theory which has been successfully used for the design of wave cancellation multihull ship as mentioned by Dr. Hendrix. We have been very much impressed by the results obtained by him and his co-authors. In fact, one of our project was to use the high speed slender theory of Tuck E.O. presented in 1988 at the Third International Workshop on Water Waves and Floating Bodies (a strip theory for wave resistance). But it seems that this theory is valid only for very large Froude numbers. Probably the slender theory used in Dr Hendrix's paper is more efficient the authoritative version for attribution.