pressure, and F is force. The primed variables represent dimensional 

 quantities; the nonprimed variables, nondimensional quantities. 



The fluid region is described in terms of a fixed (x,y)-coordinate system 

 chosen so that the y-axis points vertically upward and the undisturbed free 

 surface is at y = (Fig. 1). A fluid region of infinite depth and infinite 

 lateral extent is modeled by a rectangular tank so deep that the effect of the 

 bottom boundary is insignificant and so wide that no waves reflect from the 

 side boundaries during the time for which the fluid motion is modeled. The 

 rectangular tank is bounded by the lines y = -h, x = w, and x = -w. The 

 contour of the body moving in the free surface is given as a function of time 

 t and a parameter, a, by the equations 



X = Bx(a,t) = A (cos (a) - 0.1 cos (3 a)) (la) 



y = By(a,t) = A (sin (a) + 0.1 sin (3 a)) - hg cos (t) (lb) 



where A is a measure of the size of the body, a is the angle measured 

 counterclockwise from the direction of the positive x-axis (Fig. 2), and hg is 

 the amplitude of the heave motion. The position of the free surface is given 

 in terms of a parameter e and the time t by x = xp(e,t) and y = yp(e,t). The 

 functions xjr(e,t) and yp(e,t) are to be calculated. 



Since the flows considered in this paper are symmetric about the y-axis, 

 only the half of the fluid region where x > is considered (Fig. 3). The 

 region is bounded by five curves. Across the boundaries AE (x = 0) , 

 CD (x = w), and ED (y = -h) there is no flow. The curved line AB, given by 

 Equations (la,b), is the contour of the moving body. EC is the free surface, 

 whose location must be computed. 



