Tuak and Taylor 



tugs or bow thrusters. 



From the theoretical point of view, this mode is interesting 

 in that it provides a transition between the case of a fully -grounded 

 ship where the clearance is zero and the whole flow must pass around 

 the ends of the ship, and the case when the depth is sufficiently large 

 compared with the draft of the ship to allow nearly all the flow to pass 

 beneath the keel. At draft/depth ratios intermediate between zero 

 and unity (but close to unity) the ship acts like a porous wall, some 

 fluid particles passing "through" (i.e. under) it, while others are 

 diverted toward the bow or the stern. 



Just as the steady problem has an aerodynamic analogy, so 

 the unsteady problem is shown in Section 5 to be analogous to an 

 acoustic scattering problem, with the ship playing the role of a partly 

 permeable acoustic barrier of negligible thickness (assuming the ship 

 is thin). Some results may be obtained directly from the acoustic 

 literature for such ribbon-like barriers, but new computations are 

 needed for the general porous case. 



In Section 6 we describe techniques for obtaining the effective 

 acoustic porosity of the ship, i.e. the extent to which each section of 

 the ship blocks (or rather, fails to block) the flow of fluid particles 

 beneath it. This porosity is then used in Section 7 to obtain sway 

 exciting forces on a Series 60 ship at zero speed. 



II. ONE DIMENSIONAL THEORIES OF SQUAT IN SHALLOW, 

 NARROW CANALS 



Perhaps the most easily treated shallow-water problem in- 

 volving ships is that for ships moving in a waterway so restricted 

 in both width and depth that the problem may be treated as if one- 

 dimensional. The effect of the ship is then little more than that of 

 an obstruction in an (open) pipe. 



This approach clearly has very important applications to 

 canals and river traffic, and it is not surprising that a number of 

 similar analyses have been made in response to actual squat prob- 

 lems arising in the use of such restricted waterways. For instance 

 Garthune et al, [ 1948] and Moody [ 1964] , following the method of 

 LemmermarTX 1942] , derive a squat formula for use in the Panama 

 canal, Constantine [ 1961] , following Kreitner [ 1934] , was concerned 

 with the Manchester ship canal, Sjostrom [ 1965] with the Suez canal, 

 Tothill [ 1967] with the St. Lawrence seaway and Sharpe and Fenton 

 [ 1968] with the Yarra river, Australia. No doubt every important 

 shallow and narrow waterway has had its independent squat investi- 

 gation. 



The theoretical development is in the main quite elementary, 

 once we accept the one- dimensional hypothesis, which can itself be 



630 



