Beck and Tuck 
DISCUSSION 
Valter Kostilainen 
Shtp Hydrodynamics Laboratory 
Untverstty of Technology, Helstnkt, Finland 
We all know that we cannot use the results obtained in study- 
ing ship motions in deep water to compute ship motion in shallow 
water. For instance, most of the ships sailing in Finnish fair-ways 
should, according to this shallow-water theory, touch the bottom 
quite frequently. We do have some groundings now and then but not 
quite so often. The importance of research on ship motion in shal- 
low water has been recognised and the present paper is an important 
step forward in the study of this topic. In our laboratory we try to 
approach the problem experimentally and one of the most important 
things from our point of view is the effect of viscosity. If the shipis 
moving in shallow water the thickness of the boundary layer is of the 
same order as the clearance between the bottom of the ship and the 
bottom of the sea. This introduces some scaling problems in model 
testing and I should like to ask the authors, first, if they have taken 
account of viscous effects in their computation in zero speed and, 
secondly, wether they are, as I hope, planning any further investi- 
gation for non-zero speed and how they are then going to take account 
of viscous effect. 
REPLY TO DISCUSSION 
Robert F. Beck 
Untverstty of Michtgan 
Ann Arbor, Michigan, U.S.A. 
This theory was derived for zero forward speed and an ideal 
fluid. Thus, no account was taken of viscous effects. At this time I 
do not know if we will include forward speed in the theory or not. At 
zero forward speed, I am not sure what the effect of viscosity will be. 
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